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Accumulation of mischief. Mathematical processing of results in equal-precision values of the same quantity

analytical chemistry

UDC 543.08 + 543.422.7

PREDICTION OF CHECK BY PHOTOMETRY WITH VIKORISTANIA TO THE LAW OF ACCUMULATED PREPARATIONS I BY THE MONTE CARLO METHOD

V.I. Golovanov, EM Danilina

In the numerical experiment, under the law of the broadening of pardons and the Monte Carlo method, it was reported that there were errors in the preparation of solutions, the errors of the idle admission and the errors in the transmission on the metrological analysis of the photometric characteristics. It is known that the results of predicting errors by analytical and statistical methods of mutual use. It is shown that the Monte Carlo method is especially capable of predicting the law of inconsistencies in photometry. On the basis of the scenario of routine analysis, a flow of heteroscedasticity of the graded graph for the quality of the analysis is shown.

Key words: photometric analysis, law of pardon accumulation, grading graphs, metrological characteristics, Monte Carlo method, stochastic model.

Entry

Prediction of incidents of photometric analysis will mainly be based on the law of accumulation of pardons (ZNO). To match the line form to the law of light absorption:

8A _ 8C _ 0.434-10 ^

A '8T-

At the same standard vimіryuvannya vimіryuvannya step transmission is transferred permanently to the entire dynamic range of the photometer. At the same time, as it means in, in addition to hardware errors, the accuracy of the analysis is infused with the error of an idle message, the error between the scale of the adjuster, a test case, a chemical factor, the error of setting an analytical basis. The officials use the main reasons for the analysis of the result. By contributing to the accumulated error in accuracy, you can make the most of the gradients.

Zvidsi bachimo, well, ryvnyannya (1) does not have a sutta prognostic power, but a few drops of an infusion of only one factor. In addition, it is equal to (1), which is closely related to the distribution of the glazed clay law in the Taylor series. Zvidsi vinikє of food about this accuracy, poured over by angry members of the first order. The mathematical analysis of the surplus of dressings distribution with numerical difficulties and in practical chemical analysis does not get stuck.

By the method of the given robotics, the possibility of saving the Monte Carlo method (the method of statistical testing) in the capacity of an independent method for the development and forecasting of the accumulated losses of the photometric analysis, which will add to the deadlocked potential.

Theoretical part

We will respect the robotics, but the adjustment of the calibration function was not only amped up by the instrumental adjustments to the optical power, but the adjustments of the scale will be adjusted to 0 and 100% of the transmission (the adjustment is

Lost dosvidu), as well as the habits of preparing city breaks. The Іnshim, called vishche, dzherels, are unhealthy. Todi can be rewritten as a rule for the Bouguer-Lambert-Beer law in a manual form for further encouragement:

Ai = ks "+ A

At the same level, C51 - the concentration of the head standard size of the flavored speech, the aliquoti (Va) which is added in flasks with a nominal volume of Oud for rejecting the gradation series of flasks, and the maximum Oscillations during photometry, the optical power of the test results is reduced to a blank value, i.e. s "low sense of the concentration of the working solution, which is in units of the concentration of the head standard. Coefficients before the called extinction to the standard, fragments of Ag1 = e1c81 at s" = 1.

Zastosuєmo before turning (2) the operator to the law of accumulation of grades, vvazhayuchi Va, Ud and a and vypadkovyh values. otrimuєmo:

The same square size, which is poured into the outlet, the value of A, є steps of passage, oskilki

A = -1§T, (4)

In addition, before the dispersion in the Lviv part of the household (3) is given one more addition:

52a = (0.434-10a) H + 8Іbі +

The residual record of the law of accumulation of pardons is always absolute standard T, ai and Ud, and for Va permanent, a standard deduction is evident.

When prompting the stochastic model of the gradation function based on the Monte Carlo method, it is very important that x * values of T, ai Va and Oud are possible, the distribution is based on the normal law. Based on the Monte Carlo principle, we can use the method zvorotnoy function :

X; = M (x1) + p-1 (z]) - bX |, (6)

de M (x) - mathematical clarification (meaningless) change, ¥ (g ^) - Laplace-Gauss function, c - can be equal to the interval (0,1) vipadkovo magnitude I, i.e., Vypadkovy numbers, zx - the standard indication of vidpovidnіy vіdpovіdnіy \ = 1 ... t - ordinal number of an independent vypadkovoi value. For setting viraz (6) in іvnyannya (4) and (2) maєmo:

A "= -18Xi = -1810-a + P-1 (r]) 8t,

de A "=" up- + x2

The calculation for the equivalents (7) turns around the implementation of the calibration function, so that the status of A is "from the mathematical evaluation of M (s") (the nominal value of z "). numbers in the skin point of gradation. Vibirkova is based on the methods of mathematical statistics based on the estimation of general parameters of gradation and reconciliation of hypotheses about the power of the general population.

Obviously, we are looking at two approaches to the problem of predicting metrological characteristics in photometry - on the basis of ZNO, from one side, and on the basis of the Monte Carlo method, and from the other, one is guilty of adding one to one. Zokrema, from the level (5), it is possible to correct the result in case of a small amount, in the case of a small amount (7), the calculation, as well as the ranking

to determine the size of the value for the significance of their contributions to the result of the hijacking. The ranking is allowed to be seen as a result of the experiment in the case of statistical tests and aprilings from the view of insignificant changes. Equivalent (5) is awkward to analyze mathematically in order to judge the nature of the contributions of factors to the initial variance. The private contributions of the factors can be made to the independent form A, as well as growing from the increase in optical proficiency. To this, the function A is to blame for the monotonous growth of fallow lands, relieved by the minimum. When approximating experimental tributes to the family (5), the private contribution of the same character will be changed, for example, a young woman's feebleness can be changed from a feeble single person's consent. On the other hand, with statistical tests of the model using the Monte Carlo method, it is possible to determine such important power of the graded graph as the law (laws) to raise errors, as well as to assess the efficiency of vibrating assessments to general assessments. On the basis of malignant neoplasm, such an analysis of the ill-feeling.

Description of the numerical experiment

When prompting an imitational model of gradation, the calibration series of rosters is prepared in peace flasks with a nominal mixture of 50 ml and a borderline limit of +0.05 ml. In a series of flasks, add from 1 to 17 ml of the head standard size with a flexibility of> 1%. Possibilities of vimіryuvannya obsyagіv assessed for the presenter. Aliquot should be added with 1 ml of equal croc. In total, there are 17 solutions in the series, the optical range of which is hunted at an interval of 0.1 to 1.7 od. Todi in іvnyannі (2) kofіtsієnt up to = 5. optical grade. The risk of changing the passage step, it’s worthwhile, is to lie only from the class and to be in the interval from 0.1 to 0.5% T.

For a greater connection of the minds of a numerical experiment to a laboratory experiment, the data on the production of optical strengths of K2Cr207 in the presence of 0.05 M H2S04 on the spectrophotometer SF-26. Author approximate the experimental data on the interval A = 0.1 ... 1.5 times the parabola:

sBOCn * 103 = 7.9-3.53A + 10.3A2. (eight)

We were given the opportunity to learn from the theoretical level (5) to the level according to the empirical level (8) from the newton's optimized method. You knew that I would describe the experiment thoroughly with s (T) = 0.12%, s (Abi) = 0.007 and s r (Va) = 1.1%.

Pointing in the front paragraph of the independent assessments of the need to be well-used with the knowledge at the time. For the calculation of the level (7), a program has been installed in the form of a sheet of MS Excel spreadsheets. Naybіlsh sutta especialty of our Excel-programs є vikorystannya virazu NORMSSTOBR (SLChIS ()) for the generation of normally incurred errors, see Rivnyannya (6). In the special literature for statistical razrakhunki in Excel, the report describes the utility "Generation of Vipadkovy Numbers", as in bagatokh vipadks it is important to substitute for the function of the NORMSTOBR (SLCHIS ()) type. Such a change is especially useful when opening the power programs for modeling by the Monte Carlo method.

The results of this discussion

First step down to statistical viprobauvan, estimate the contribution of donations to the last part of the country (5) to the backward dispersion of optical scholarship. For a wide range of dermal supplements, the dispersion should be normalized. Rozrakhunki viconani at s (T) = 0.12%, s (Aw) = 0.007, Sr (Va) = l, l% і s (Vfi) = 0.05. The calculation results are shown in Fig. 1. Bachimo, the contributions to the outward dispersion of the vimiryuvannya Vfl can be made unhealthy.

Todi yak contributions іnshy, pouring in on the mistakes of preparing decisions, size Va

dominate in the range of optical power 0.8__1.2. However, the visnovok is not a magical one.

character, splinters with vimir on the photometer s s (T) = 0.5% of the loss of the hail, at the same time with the rozrahunk, are the head rank, rozkid a and і rozkid T. In Fig. 2 Determine the differences in optical performance predicted on the basis of ZNO (scientific line) and the Monte Carlo method (icons). With statistical tests, the curve

grants were taken into account for 100 realizations of the graduated deposition (1700 values of the optical density). Bachimo! The points are grouped up to the theoretical curve. However, to navigate with this, to achieve meaningful, statistical material, there is no need to be discouraged. In every case, the rosary does not allow the nature of the malignant neoplasm to emerge, see Introduction.

0 0.4 0.8 1.2 1.6

Small. 1. Vahovi contributions of the previous period (5) to the variance A: 1 - for ai; 2 - for Ya; 3 - for T; 4 - for

Small. 2. Curve of adjustments of the graded graph

From the theory of mathematical statistics, it seems that in the case of an interval assessment of the mathematical evaluation of the size of the value, the hope of estimating the value of the value should be determined as the law of growth for the whole value. In addition, in the time of the normal distribution of the assessment, it is the most effective. To this admission to the law, the incidents of the graduated graph are raised to important employees. With such a message, it’s for everything, to reconsider the hypothesis of normal distribution of optical power in the surrounding points of the graph.

In a simple way to reconcile the main hypotheses є calculating the asymmetry rates (a) and the efficiency rates (e) of the empirical conditions, as well as the calculation of the critical values. The need for statistical data to move forward with the improvement of vibrating tributes. In fig. 3 indications of last values for 17 recalibration functions. Coefficiencies calculated for the results of 100 viprobes in skin points. Critical value of performance for our butt rivn | and | = 0.72 i | e | = 0.23.

3 fig. 3 it is possible to create a visnovka about those, where the value in the points of the graph is, in general, not

To supervise the hypotheses of normality, some of the results of the performance may not be as straightforward as possible. Koefіtsієnti in the same rank is localized close to the zero line (shown by a dotted line). For a normal rise, as in the case of mathematical calculations, the asymmetry coefficient and the efficiency coefficient are zero. Judging from the fact that with all the changes in the efficiency of the asymmetry, it is possible to talk about the symmetry of the rise in errors of gradation. Mozhlvo, scho rozpodilu pohibok may be slightly fierce in a normal crooked rozpodilu. The chain of visnovok viplyaє is shown in Fig. 3 small

Small. 3. Performance (1) and asymmetry performance (2) at the points of the graded graph

zhizhennya substitution of the central line of development of efficiency. Thus, from the advancement of the model of the normal calibration function of the photometric analysis by the Monte Carlo method (2), it is possible to create a picture about a close to normal rate of error. In addition, the calculation of the basic intervals for the results of the photometric analysis of the student's performance can be varied in a number of ways.

With the determination of the stochastic model of the bull, the frequency of the changeability of the vibrating curves of failures was estimated (div. Fig. 2) to the mathematical comparison of the curve. For a mathematical ochіkuvannya crooked othibok, it is acceptable to be insured from the ZNO curve. The closeness of the results in statistical tests with a small number of implementations of gradation and up to a theoretically crooked estimate by the factor of non-value 1 - L2. Tsei kofіtsієnt characterizes a part of variation in vibration, as it was not described theoretically. We have established that the accumulation of the factor of non-value in the number of realizations of the calibration function can be described by the empirical equivalents I - K2 = -2.3n-1 + 1.6n ~ / a -0.1. Rivnyannya is recognizable, but at n = 213, a practically complete increase in theoretical and empirical curves of misbehavior was achieved. In such a rank, I can assess the errors of photometric analysis, it is possible to correct only for the delivery of great statistical material.

The possibilities of the method of statistical tests for predicting the results of the regression analysis of the graduated graph and the recording of the graph for the prediction of the concentration of photometric measurements are clear. For the whole, in the context of the scenario, we are able to simulate the situation of routine analysis. Prompt the graphic to come back with one-time optical measurements of a series of standard solutions. Concentration of the difference, which can be analyzed from the graph according to 3-4 results of parallel measurements. When choosing a regression model, take to respect those that the optical power distribution at the different points of the graduated graph is not similar, see Equivalent (8). In case of a heteroedastic rozkid, it is recommended to use a vicorist scheme for the method of least squares (VMNK). However, in the literature, no clear cues were made for the reasons, behind which the MNC scheme is classical, one of the minds of conscientiousness, which is vimogo-stricto, rozkidu, mensh krascha. The reason can be established when processing one and the same statistical material, discarded by the Monte Carlo method for the scenario of routine analysis, two variants of the MNC - the classic one.

As a result of the regression analysis of only one implementation of the calibration function, the offset of the onset of the MNC-estimate: k = 4.979 at Bq = 0.023. When assessing the quiet characteristics of the HMNC, it is acceptable to k = 5,000 at Bq = 0.016. The regressions were adopted by 17 standard ratios. The concentration in the calibration series grew in arithmetic progress, and the optical density was changed from 0.1 to 1.7 od. In the case of VMS, the statistical variables of the points of the graded graph were determined from the results of the analysis for the equal (5) variances.

The variance of the estimates to the quiet and by the method is statistically unviable according to Fisher's criterion at 1% equal significance. However, at the same time, the value of the MNC-estimate before being displayed is from the MNC-estimate by 1; -criteria. The OLS-estimation of the performance of the graded graph is substituted for the performance value M (k) = 5,000, judging from the 1> test at 5% equal value. Today, the MNC gives an estimate, as not to take revenge on systematic misbehavior.

Now, the rank of the anger of the heteroscedastic can be seen as a chemical analysis. At the table, the results of an imitational experiment with the analysis of 17 control samples of a refined speech with a reduced concentration are shown. Moreover, the skin analitic seria included chotiri roschin, tobto for skin probes viconano by chotiri parallel viznennya. To process the results, we took two different gradations of fallowness: we forgive the MNC, and the other - for the replacement. Vazhaєmo, scho control solutions were prepared for analysis in the same way as gradation.

From the table, there is no reason for the value of the concentration of control deviations in the case of VMNC, so if the MNC does not go beyond between the most important intervals, i.e. The results of the analysis do not take the place of significant systematic faults. Boundary deviations of this and this method are not statistically discernible, in other words, and the same assessment

Adjustment of the results in the value of the concentration of volodya by the same efficiency. від-

control differences by two methods, here you can create patterns against those that are

Routine analysis of the simple scheme of a non-engraved MNC is completely correct. The stagnation of the VMNK is more beautiful, as well as to the pre-admission to the past є only to the value of the molar extinction. On the other hand, the mother on uvaz, but the broken ones by us, may be statistical in nature. Generally, with an increase in the number of parallel values, the hypothesis about the lack of MNC-assessments of concentrations is not known to be confirmed, to find a systematic error from a practical point of view.

We found it necessary to achieve a high quality of analysis on the basis of a simple scheme of a classical MNC to be built especially unsupported, if we take to respect those that, at the interval of optical power of 0.1 h-1.7, are able to make it possible to achieve a strong Goethe-rostedness. The degree of heterogeneity of these can be judged by their function, which can be approximated by the polynomial w = 0.057A2 - 0.193A + 0.173. Z ts'go rіvnyannya viplyaє, scho in extreme points The gradation of statistical wages is increased by more than 20 times. However, I have a lot of respect for those whose gradation functions were monitored by 17 points of the graph, while only 4 parallel values were displayed during the analysis. To this, we have seen a significant insight into the MNC and MNC of gradation functions and insignificant divergence of the results in the analysis of the vicarious functions of these functions.

visnovok

1. The new idea is projected to the stochastic model in the photometric analysis based on the Monte Carlo method and the law of accumulation of pardons from the results of the Excel spreadsheet processor.

2. Based on 100 realizations of calibration deposits, it is shown that predicting errors by an analytical and statistical method of interconnection is shown.

3. Vivcheno efficiency of asymmetry and ekssesu uzdovzh graduated graph. It is known that the variation of attempts to graduate is to abide by the law of growth, which is close to normal.

4. The flow of heteroscedasticity to the optical range for the hour of gradation for the quality of the analysis has been shown. It has been revealed that during routine analyzes, the analysis of the idle scheme of a non-invasive OLS does not lead to a decrease in the accuracy of the analysis results.

literature

1. Bernstein, I. Ya. Spectrophotometric analysis in organic chemistry/ I Ya. Bernshtein, Yu.L. Kaminskiy. - L.: Khimiya, 1986 .-- 200 p.

2. Bulatov, M.I. Practical handbook of photometric methods of analysis / M.I. Bulatov, I.P. Kalinkin. - L.: Khimiya, 1986 .-- 432 p.

3. Gmurman, V.Є. Theory of imovings and mathematical statistics / V.Є. Gmurman. - M .: Vischa school, 1977 .-- 470 p.

No. z ", z", it is known (P = 95%)

n / i is given by OLS VMS

1 0.020 0.021 ± 0.002 0.021 ± 0.002

2 0.040 0.041 ± 0.001 0.041 ± 0.001

3 0.060 0.061 ± 0.003 0.061 ± 0.003

4 0.080 0.080 ± 0.004 0.080 ± 0.004

5 0.100 0.098 ± 0.004 0.098 ± 0.004

6 0.120 0.122 ± 0.006 0.121 ± 0.006

7 0.140 0.140 ± 0.006 0.139 ± 0.006

8 0.160 0.163 ± 0.003 0.162 ± 0.003

9 0.180 0.181 ± 0.006 0.180 ± 0.006

10 0.200 0.201 ± 0.002 0.200 ± 0.002

11 0.220 0.219 ± 0.008 0.218 ± 0.008

12 0.240 0.242 ± 0.002 0.241 ± 0.002

13 0.260 0.262 ± 0.008 0.261 ± 0.008

14 0.280 0.281 ± 0.010 0.280 ± 0.010

15 0.300 0.307 ± 0.015 0.306 ± 0.015

16 0.320 0.325 ± 0.013 0.323 ± 0.013

17 0.340 0.340 ± 0.026 0.339 ± 0.026

4. Pravdin, P.V. Pravdin. - M .: Khimiya, 1988.-336 p.

5. Makarova, N.V. Statistics in Excel / N.V. Makarova, V. Ya. Trofimets. - M .: Finance and statistics, 2002 .-- 368 p.

PREDICTION OF ERRORS IN PHOTOMETRY WITH THE USE OF ACCUMULATION OF ERRORS LAW AND MONTE CARLO METHOD

During computing experiment, in combination of the accumulation of errors law and Monte Carlo method, the influence of solution-making errors, blank experiment errors and optical transmission measurement errors upon metrological performance of photometrical analysis has been studied. It has been shown that the results of prediction by analytical and statistical methods are interconsistent. The unique feature of Monte Carlo method has been found to enable prediction of the accumulation of errors law in photometry. For the version of routine analysis the influence of heteroscedasticity of dispersion along calibration curve upon analysis quality has been studied.

Keywords: photometric analysis, accumulation of errors law, calibration curve, metrological performance, Monte Carlo method, stochastic modeling.

Golovanov Vladimir Ivanovich - Dr. Sc. (Chemistry), Professor, Head of the Analytical Chemistry Subdepartment, South Ural State University.

Volodymyr Ivanovich Golovanov - Doctor of Chemistry, Professor, Head of the Department of Analytical Chemistry, Pivdenno-Ural State University.

Email: [Email protected]

Danilina Elena Ivanovna - PhD (Chemistry), Associate Professor, Analytical Chemistry Subdepartment, South Ural State University.

Danilina Olena Ivanivna - Candidate of Chemistry, Associate Professor, Department of Analytical Chemistry, Pivdenno-U Ralsky State University.

the scheme of the sound analysis of the field in the offensive. Calculated by the direct method

The value of the direct method is to assess for the most beautiful april assessment, which can be given for the norms of a matrix and a vector. Such "nice" and stars. based on the matrix and the vector of equivalent drilling for the method M.

If the estimates are for і, then theoretically, the grasp of the approximate solution can be assessed by the uncertainty

Here is the number of matrices of the matrix A, and the matrix norm in (3) is transferred to the ordered vector norm

As a matter of fact, an estimate for a little bit of a house, and a basic sense (2) of the field in the flexibility of adapting the quality of other methods. Below, the view of some typical evaluations for the matrix is shown for methods with orthogonal transformations and arithmetic with a floating coma (in the system (1) Ai b are considered valid)

At tsіy otsіntsі - the accuracy of arithmetic. operations in EOM, - Euclidean matrix norm, f (n) - function of the form, de n-order of the system. The exact values of the constant Ci of the indicator k are determined by such details of the calculation process, such as the way of rounding, registering the operation of accumulating scalar creations and T. D. Nybilsh often k = 1 or 3/2.

For methods of the Gauss type, in the right part of the assessment (4), there is a multiplier that shows the possibility of growing elements in the matrix An intermediate crochet method in the context of the cob (also) growing in the orthogonal method. To change the meaning, to change the way to select the appropriate element, to change the growth of the elements in the matrix.

for square root method, to-riy to get stuck in a positively singing matrix A, otrimana is very strong

Finding direct methods (Zhordan, oblyamivka, with the resulting gradients), for those who took a bezposeredn zastosuvannya schemes of verbal analysis not to produce effective estimates. In cich vipadkah with pre-sluggish N. p.

Lit.: Givens W., "TJ S. Atomic Energy Commiss. Repts. Ser. OR NL", 1954, No. 1574; Wilkinson J. H., Rounding errors in algebraic processes, L., 1963; Wilkinson J.

X.D. Ikramov.

N. p. Rounding off, for the mistakes of the method of vicinities in the case of the revision of the works, de ration є the result of a great number of the last viconuable arithmetic. operations.

A significant part of such projects is tied to the solutions of algebra. tasks, linear or non-linear (div. vishche). Have your own middle of algebra. tasks are the most extended of the plant, which are found in the approximation of differential equations. Tsim zavdannyam vlastivі nek-ryє specific. specialties.

N. n. The method of solving tasks is to follow them, or according to more forgiven laws, such as N. n. N., p. To the method to be heard when evaluating the method of solving problems.

When there is a pre-accumulation of calculating errors, two steps are taken. In the first place, it is important to consider that the numbered deceit on the skin is introduced by the unfriendly rank and the majority estimate of the deceit. Another vvazhayut vypadku, tsі mischief vypadkovі with the singing law of rozpodіlu.

The nature of the N. p. To lay aside the problem, the method of approach and a number of other factors, at first glance you can build up unimportant; Here the form of writing numbers in EOM (from a fixed coma or from a floating coma) is introduced, the order of arithmetic is entered. operation and etc. For example, in the established calculation of the sum N

іstotny order vikonannya operatsіy. Let the calculation be carried out on a machine with a floating ball with two discharges and all the numbers lie in the boundaries ... In case of non-averaged calculation of the additional recursive formula of the majority of the estimate of the misbehavior, there is an order 2 -t N. You can vchiniti inakshe (div.). When calculating pairwise sums (yaksho N = 2l + 1 unpaired) vvazayut ... Dal are counted in pairs of sums and t. D. When writing steps to review paired sums for the formulas

to obtain the majority of the evaluation of the order

For typical tasks, the values and t to be calculated according to the formulas, the spring is recurrent, or to come up lastly into the operational memory of the EOM; in the cich vipadkah of storing the described priyom to make the memory of the EOM more secure. However, it is possible to organize the end of the calculation so that the operational memory will not be overturned - log 2 N sequentially.

With a numerical solution of the differential level, there may be a fall. When the crochet of the mesh h is reduced to zero, the increase in growth yak de ... Such methods are brought up to the class of unstable ones. Їх stasosuvannya maє epizodich. character.

For steadfast methods, it is characteristic of the growth of the abduction of such methods. There will be a rіvnyannya soodo drilling, which will be brought in either rounded, or by the method, and then the solution will be achieved

In the majority of foldable types, the method of equivalents is stagnant (div.,), Of accusations, it is obvious that the accumulation of numerical errors in the case of viral differential races (div. ,,). Calculated according to the deyakoi rozrahunkovaya scheme with rounded curves, it is possible to calculate without rounding, but for a rivnyannya with drilled kofitsinty. Determination of the solution of the wicked sieve ryvnyannya with the solutions of the match with the drilled specialists

Appreciate the value of respect for the vibration method according to the possibility of lower values of Q and A (h) . With a fixed method of solving the problems of developing the formulas, let the formulas go back to being redone to the eye, de (div.,). It is especially true in the form of very different differential races, the number of crocs in the vicinity of the fall appears even great.

The value of (h) can grow strongly with an increase in the interval of integration. This will be rewarded with methods according to the possibility of lower values of A (h) . At the time of the head of the cat, the pomegranate is rounded on the skin specific stage according to the date before the onset of crocs, you can see the pomade in the cob. That is, the lower boundary (h) is based on the characteristics of the difference between the close solutions of the differential equation, which should start in the versatility.

At a single numerical solution of a specific differential equation rivnyannya in options maє viglyad

and in addition, with the vikonannya zavdannya vіdrizka ( x 0, X) It is not possible to deduce the constant A (h) in the dominance of the estimate of the numerical suppression of the sutta, nizh

To that, with the revision of the best practices, one-step methods of the Runge-Kutta type, or the method of the Adams type (div.,), De N. p.

For a number of methods, the head member of the method is to accumulate for a similar law, in that hour it is necessary to accumulate a lot more meaningfully (div.). Practical area However, such methods will appear more or less the same.

The accumulation of the calculation of the gratitude of the sutta can be laid down in a method that is accumulated for the revision of the gratitude of the frequent development. For example, in the case of the viralization of the network of regional estates, of the type of differential differentials, by the methods of shooting and the run of N. p. Maє character A (h) h -q, de q is the same and the same. The value of A (h) in these methods can be changed, but in the current situation one of the methods becomes unauthorized. When using the method of adjustment of gratuitous edge problems for Laplace N. p. Maє character s 1 / h, s> 1, and in the case of the sweep method Ah -q. With an imovinous approach to the preliminaries of N. n. In some cases, it is aptly allowed for the law of abduction (div.),

With an increase in the accuracy of the solution of the tasks of the majority and the imovirnіsnі go to the estimation of the accumulated numerical error, you will give obviously the same results: for in both types of N. p.

Lit.: Voevodin V.V., Numerical bases of linear algebra, M., 1977; Shura-Bura M.R., "Prikl. Mat. I mechan.", 1952, vol. 16, no. 5, p. 575-88; Bakhvalov N. S, Chiselnі methods, 2nd type., M., 1975; Wilkinson J. X., The Algebraic Problem of Power Values, Prov. s English., M .. 1970; Bakhvalov N. S, in the book: Computational methods and programs, V. 1, M., 1962, S. 69-79; Godunov S.K., Ryabenkiy V.S., Riznitsev's schemes, 2nd type., M., 1977; Bakhvalov N. S, “Dokl. AN SRSR ", 1955, v. 104, no. 5, pp. 683-86; yogo zh," J. virahuє, mat. і mat. fiziki ", 1964; v. 4, no. 3, pp. 399-404; Lapshin E. A., ibid., 1971, v. 11, no. 6, pp. 1425-36.

- the recognition of the results of the true value of the true value. Systematic ...
- visualization of metrology. authorities or the parameters of the vimiryuvan from the memorials, which pour into the abductions of the results of the vimiryuvan ...
Natural science. encyclopedic vocabulary
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Encyclopedic Dictionary of Metallurgy
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- “...
Official terminology
- "... Post-misbehavior - misbehavior, as it is a trivial hour to save your meaning, for example, it takes an hour to see all the time.
Official terminology
- "... Progressive misbehavior - uninterruptedly growing or declining misbehavior ...
Official terminology
- see pardons with caution ...
Encyclopedic Dictionary of Brockhaus and Euphron
- pardons for vimiryuvan, indicating the results of vimiryuvan on the basis of true values of vimiryuvan values. Razrіznyayut systematic, vypadkovі and rude P. i. ...
- the identification of metrological authorities, or the parameters in the amount of the nominal ones, which inject into the mistakes the results of the time, won for the help of the cich ...
Velyka Radianska Encyclopedia
- the difference between the results in the name of the true and true values of the value. It is an admirable deceit to be called an absolutely deceitful deception to its true meaning ...
happy encyclopedia
- the assessment of the results in vimiryuvan from the true values of the vimiryuvan value ...
Great encyclopedic vocabulary
- dod., Number of synonyms: 3 correcting inaccuracies after inserting pardons ...
Glossary of synonyms
- dod., Number of synonyms: 4 corrections are used
Glossary of synonyms

"ACCUMULATED KHIBKI" in books

Technical troubles

3 books of Zirka and Trokhi nervovo the author

Technical troubles

3 books of Marní of thoroughness and іnshі vіntki the author Zhovkivsky Oleksandr Kostyantinovich

Technical grievances about the success of the prototypical forces are not so implausible as they are overwhelmingly. Go ahead and call on the passiveness of the victim, and that will not think over the next step, and I will not show the counterattack. Dad told me about one such

Grishki and infidels

3 books Yak NASA showed American Misyats author Rene Ralph

Sins and Deceit Unimportant for the whole activity of its space navigation, NASA wanted to be sly accurate in everything, it would not be embarrassing. Nine times asleep, the Apollo capsules were ideally kicked into a thousandth orbit, without requiring a serious course correction. Monthly module,

First accumulated capital. The rapist is the landlessness of the villagers. Accumulation of riches.

the author

First accumulated capital. The rapist is the landlessness of the villagers. Accumulation of riches. Capitalistic transmission of two basic minds: 1) the appearance of a lot of unkempt people, especially vilny and in the same hour

Socialistic accumulation. Accumulation and living in the socialist suspension.

3 books Political Economy the author Ostrov'yani Kostyantin Vasilovich

Socialistic accumulation. Accumulation and living in the socialist suspension. Dzherelom expanded socialist education є socialist accumulation. Social accumulation є victorious part of the net income of the suspension,

abductions vimiryuvan

Vіkіpedіya

Hijacking with the help of vimiruval technology

3 books by Velyka Radianska Encyclopedia (PO) of the author Vіkіpedіya

uzd tweaks

3 books Renovation of the thyroid gland Kerivnistvo for patients the author Ushakov Andriy Valeriyovich

UZD Koli from St. Petersburg before me came to the consultation of the patient, I beat three protocols of ultrasonic treatment at once. All the stinks are crushed by young fakhivtsy. In a simple description. At the same date, one of the same may be seen

Dodatok 13 Movements

The Book of Mastery to Get Your Own the author Stepanov Sergiy Sergiyovich

Dodatok 13 Movnі abductions Navіtіdlivі for the first glance, phrases can often become a serious bar'er in the service. Vidomiy American Fakhivets Marketing John R. Graham has compiled a list of viraziv

movnі chibi

From the book Skilka you stand [Technology of successful kar'єri] the author Stepanov Sergiy Sergiyovich

Most of the time, it’s not shy to look at the phrases that can often become a serious bar in the service. Vidomiy American Fakhivets in Marketing John R. Graham has compiled a list of virazs, implantation of those who, behind him, amused by zmogi

mouthful

3 books Black Lebid the author Taleb Nassim Nikolas

Tooth abductions Abductions also have a pernicious power: what the stink is more important, the more the mask the impact. chim

Abductions in the event of an accident

3 books ABC of tourism the author Bardin Kirilo Vasilovich

Habits at the opening Otzhe, zvychane zavdannya for the trip, how to be brought to the tourist, if you need to come from one point to the other, use only a compass and a map. Unknowingly mischievous, and until then it is closed, i.e.

Hobbies: Philosophy

3 books of the author

Abductions: Philosophy At the intuitive level of reason, our knowledge of bagatokh is not accurate. You can safely let it go, but to be exact, our knowledge can only be used with a discrete scale. It is possible for sure nobility, slipping a bag into a bear, but it is not possible - a kind of ehny vaga,

Hobbies: models

3 books of the author

Hints: Models If we are in a state of mind, I’ll frankly present at the time of the ear of information (both learned and unaware) to present them by hand in the view of the models of the object or the phenomenon. The “zero level” model is the whole model of the magnitude of the magnitude. Mi virimo in those who won є -

Hobbies: scho i yak control

3 books of the author

Deviations: how to control the vibration of controlled parameters, circuits of control, the method and control of control to work with the changes in the external parameters of the virobi, its design and technology, and the need, which is stagnant and controlled. I know,

with a numerical solution of algebra - a summarized infusion of rounding, crumbling on the edges of the crocs of the calculating process, to the accuracy of the rejected solution of linear algebra. systems. We will broaden the method of an apiorny assessment of the total amount of rounding in the numerical methods of linear algebra. In the zasosuvanny to the date of the system of linear algebra. Rivnyan diagram of the annoying analysis of the polyaga in the offensive. Calculated by the direct method The solution is not happy (1), but it can also be presented as a more accurate solution of the drilling system. Such "nice" and stars. based on the matrix and the vector of equivalent drilling for the method of M. and the main sense (2) of the field in the flexibility of varying the quality of the other methods. Below, the view of some typical evaluations for the matrix is shown. For methods with orthogonal transformations and arithmetic with a floating coma (in the system (1) Ai are considered valid). operations in EOM, is the Euclidean matrix norm, f (n) is a function of the form, de n-order of the system. The exact values of the constant Ci of the indicator k are determined by such details of the calculation process, such as the way of rounding, registering the operation of accumulating scalar creations and T. D. Nybilsh often k = 1 or 3/2. For methods of the Gauss type, in the right part of the assessment (4), there is a multiplier that shows the possibility of growing elements in the matrix An intermediate crochet method in the context of the cob (also) growing in the orthogonal method. To change the meaning, to change the way to select the appropriate element, to change the growth of the elements in the matrix. For the square root, the method, which stagnates in the times of the positively singing matrix A. In cich vipadkah with pre-sluggish N. p. Lit .: Givens W., "TJ. S. Atomic Energy Commiss. Repts. Ser. OR NL", 1954, No. 1574; Wilkinson J. H., Rounding errors in algebraic processes, L. , 1963; Wilkinson J.
For steadfast methods, it is characteristic of the growth of the abduction of such methods. There will be a rіvnyannya soodo drilling, which will be brought in either rounded, or by the method, and then the solution will be achieved In the majority of foldable types, the method of equivalents is stagnant (div.,), Of accusations, it is obvious that the accumulation of numerical errors in the case of viral differential races (div. ,,). Calculated according to the deyakoi rozrahunkovaya scheme with rounded curves, it is possible to calculate without rounding, but for a rivnyannya with drilled kofitsinty. Determination of the solution of the wicked sieve ryvnyannya with the solutions of the match with the drilled specialists Appreciate the value of respect for the vibration method according to the possibility of lower values of Q and A (h). With a fixed method of solving the problems of developing the formulas, let the formulas go back to being redone to the eye, de (div.,). It is especially true in the form of very different differential races, the number of crocs in the vicinity of the fall appears even great. The value of (h) can grow strongly with an increase in the interval of integration. To this, you will be able to use the methods according to the possibility of lower values of A (h). At the time of the head of the cat, the pomegranate is rounded on the skin specific stage according to the date before the onset of crocs, you can see the pomade in the cob. That is, the lower boundary (h) is based on the characteristics of the difference between the close solutions of the differential equation, which should start in the versatility. At razі chiselnogo rіshennya zvichaynogo diferentsіalnogo rіvnyannya rіvnyannya in varіatsіyah Got viglyad i that when vikonannі zavdannya on vіdrіzku (x 0, X) mozhna rozrahovuvati a constant A (h) in mazhorantnostі otsіntsі obchislyuvalnoї pohibki suttєvo maintained upstream, nіzh Tom at virіshennі tsogo zavdannya naybіlsh spozhivanі odnoschagovie methods of the Runge-Kutta type or methods of the Adams type (div.,), de N. p. in the main form of rіvnyannya solutions in options. For a number of methods, the head member of the method is to accumulate for a similar law, in that hour it is necessary to accumulate a lot more meaningfully (div.). Practical area However, such methods will appear more or less the same. The accumulation of the calculation of the gratitude of the sutta can be laid down in a method that is accumulated for the revision of the gratitude of the frequent development. For example, in the case of the virus network regional buildings, of the kind of differential equations, by shooting methods and by running the N. p., The character is A (h) h-q, but the same is the same. The value of A (h) in these methods can be changed, but in the current situation one of the methods becomes unauthorized. When using the method of adjusting the gratuitous edge problem for Laplace N. p. Maє character z 1 / h, z> 1, and in the case of the sweep method Ah-q. With an imovinous approach to the preliminaries of N. n. In some cases, it is aptly allowed for the law of abduction (div.), With an increase in the accuracy of the solution of the tasks of the majority and the imovirnіsnі go to the estimation of the accumulated numerical error, you will give obviously the same results: for in both types of N. p. Lit.: VV Voevodin, Computational bases of linear algebra, M., 1977; Shura-Bura M.R., "Prikl. Mat. I mechan.", 1952, vol. 16, no. 5, p. 575-88; Bakhvalov N. S, Chiselnі methods, 2nd type., M., 1975; Wilkinson J. X., The Algebraic Problem of Power Values, Prov. s English., M .. 1970; Bakhvalov N. S, in the book: Computational methods and programs, V. 1, M., 1962, S. 69-79; Godunov S.K., Ryabenkiy V.S., Riznitsev's schemes, 2nd type., M., 1977; Bakhvalov N. S, “Dokl. AN SRSR ", 1955, v. 104, no. 5, pp. 683-86; yogo zh," J. virahuє, mat. і mat. fiziki ", 1964; v. 4, no. 3, pp. 399-404; Lapshin E. A., ibid., 1971, v. 11, no. 6, pp. 1425-36. N. S. Bakhvalov.

marvel at the meaning accumulation of Pohibka in the last dictionaries

accumulation- accumulated, then. (Book.). 1.Tilki od. Diya by verb. accumulate-nagromadzhuvati and accumulate-accumulate. drive. First accumulated capital (entry point ........
Ushakov's Tlumachny vocabulary

Accumulation of Por.- 1. Process of diy by value. verb .: accumulate, accumulate. 2. Stan by value. verb .: accumulate, accumulate. 3. Those scho accumulated.
Tlumachny vocabulary of Єfremovo

accumulation- -I am; since.
1. to accumulate - accumulate. N. Bagatstv. N. znan. Dzherela accumulated.
2. only plural: accumulation. Those that have been accumulated; sparing. Zbіlshiti razmіri accumulate ........
Tlumachny vocabulary of Kuznetsov

accumulation- - 1. increase of special capitals, stocks, lane; 2.
part of the national
income, as a vicarist, to replenish virobnic and non-viral funds in ........
economical vocabulary

Accumulation - Accumulation- Situation, when you see
Growth of trade positions established earlier. Call the price for
rakhunok adding new critical positions to the already existing ones .........
economical vocabulary

accumulation of Valove- add items that are vibrated in a sound
Periodi, don't wait.
exponent
rakhunki
Operations with the capital of the system of national rakhunks, including ........
economical vocabulary

accumulation of dividends- In insurance of life: a way to regulate, how to take revenge in the minds of the policy for insurance of life, so we have the opportunity to surrender to the deposit insurance fund ........
economical vocabulary

Accumulation by the investor of less than 5% of the Shares of the Company, by means of re-purchase- Yak tilka get 5% of the shares,
the buyer is guilty of submitting information to the Commission for
paper that
birzh, on the basis of the merchant and the company, ........
economical vocabulary

Accumulation of the Main Capital of Valove- the investment of funds in the main capital of the main (fund) for the establishment of new income in the future.
economical vocabulary

Main Capital Accumulation, Valove- - the contribution of the
Main
capital (
basic funds) for the establishment of a new
income in the future. V.N.O.K. stock up on the next elements: a)
binge ........
economical vocabulary

accumulated Strakhove- ENDOWMENT INSURANCE
INSURANCE and obovyazkov
accumulation. It’s going to be seen from the life insurance of the team, when it’s the end of the singing ........
economical vocabulary

Accumulation, Akumulyuvannya- Finance of corporations: arrival, yak do not pay yak dividendy, but reach the main capital of the company. Div. Also accumulated profits tax. Investments: ........
economical vocabulary

Zaluchennya, Accumulation, Osvita Capital; Priority to Main Capital- Adequate or expanded by a way of accumulating capital for a capital or using a producer goods - a budget, a set-up, a mechanism - necessary for a number of virobnits ........
economical vocabulary

accumulation- - the re-creation of a part of the arrival in capital, an increase in stocks of materials, a lane, pennies, an increase in capital, the main gains by the state, enterprises, ........
legal vocabulary

accumulation- Subscription of a part of income for the expansion of production and improvement on the basis of the release of products and services. Growth of accumulation and rate of growth to lie down for a long time ........

First Capital Accumulation- the process of recreating the main mass of small commodities (the chief rank of the villagers) in the recruiting work by means of updating and recreating ........
Great encyclopedic vocabulary

abductions vimiryuvan- (pardons vimiryuvan) - an indication of the results of measurements from the true values of the vimiryuvan value. Systematic errors in the name of the head rank ........
Great encyclopedic vocabulary

Khoibki Koshtyv vimiryuvan- the determination of the metrological authorities and parameters by adding them to the nominal ones, which will infuse into the errors of the results of the measurements (set by T.
Great encyclopedic vocabulary

first accumulation- - the process of redevelopment of the main mass of other commodities, mainly villagers, in hired robots. The activities are saved up for the organization ........
historical vocabulary

first accumulation- the accumulation of capital, ahead of the capital. the way of virobration, how to rob the whole way of virobration, historically, we can and become one of the right, out-of-the-box ........
Radianska Historical Encyclopedia

Valove Heap of the Main Capital- investments by resident units of households in the main capital for the establishment of new income in the maybutny way of the Victory Day. Valove piled up the main capital ........
sociological vocabulary

Vimіryuvannya Orієntovaniye on the Possible Indicator- - eng. measurement, indicator error, -oriented; new. Fehlermessung. For V. Thorgerson - vimir, direct to the appearance in the reaction of the information about the indicator or the promiscuity, ........
sociological vocabulary

capital Accumulation- - eng. capital accumulation; new. Akkumulation. Reincarnation of the pre-existing part in the capital, so that it can be seen in the process of expanded revision.
sociological vocabulary

Capital Accumulation First- - eng. capital accumulation, primitive; new. Akkumulation, urprungliche. In front of the capital, the way of virobniting the process of visualization of non-priori virobniks (Ch. Arr. Selyan) ........
sociological vocabulary

capital Accumulation- (capital accumulation) - capital accumulation div.
sociological vocabulary

Accumulation (about the Rozshiene Vidvorennya) Capital- (accumulation (or expanded or extended reproduction) of capital) (Marxism) - the process, in the course of which capitalism develops for the help of recruiting work force for the development of additional ........
sociological vocabulary

first accumulation- (primitive accumulation) (Marxism) - is a historical process, behind the addition of what kind of accumulation has been capitalized, there is no capitalism. In "Das Kapital" Marx ask about food, ........
sociological vocabulary

Timchasov Accumulation of Visits to the Prom-Maidanchik- - the selection of entries on the territory of the enterprise in special areas for the whole family of missions until the moment of the week in the second technological cycle, or for updates ........
Ecological vocabulary

STORAGE- ACCUMULATED, -I, then. 1. see Zbirate, -sya. 2. pl. Amount of money has been accumulated. Great heap. || dod. accumulative, -a, -e (special). Accumulated visibility.
Tlumachny vocabulary of Ozhegov

Biological storage- Biological accumulation of concentrated (accumulation) a number of cheery speeches(Pesticides, important metals, radionuclides and in.) In trophic ........
Ecological vocabulary

For a feeble vimіryuvannya, we will be reasonable about all the pardons of vimіryuvannya.

You can classify vimiriv on the following types:

Absolute and general,

Positive and negative,

Permanently and proportionally,

Vipadkovі and systematic,

absolute pardon A y) The difference between the offensive values begins:

A y = y i - yіst.  y i - y,

de: y i - a single result of a vim_ryuvannya; yіst. - the true result of the registration;  y- the arithmetic mean of the result of the value (distance of the mean).

post_noї to be called an absolute pardon, as you do not lie in any value of a vimiryuvan value ( y y).

Graveyard proportional , which is the name of the fallowness of isnu. The nature of the pardon vimiryuvannya (post-or proportional) is determined by the conduct of special education.

good gratitude which is the same as the result ( V y) Rosrakhovuєtsya yak vіdnoshennya offensive values:

Because of the formula of viplivay, the value of an acceptable pardon is not only due to the magnitude of the absolute pardon, but rather to the value of the vimiryuvanny magnitude. With the invariability of the value ( y( A y). When an absolute pardon has become, for a change in a certain pardon, a pardon can be made more important.

The sign of a pardon (positive or negative) is meant to start with a difference between a single and a rejection (mean arithmetic) result of the following:

y i - y> 0 (pardon is positive );

y i - y< 0 (grave is negative ).

Seriozna grave vimir (miss) vinnikє in case of damaged methods of vimiruvannya. The result of the change is to take revenge on a rude pardon, and to signify for the value of all the results. The occurrence of gross pardons in the name of n> 2). By methods of revealing gross pardons, learn independently.

Before vipadkovyh pardons to make pardons, as not to conceal the permanent magnitude and sign. Such pardons are recognized for the next offensive factors: vidomich, ale irregular; constantly change.

Vypadkovі pomki can be assessed only after the conduct of the period.

A large estimate of the modulus of the magnitude of the vypadkovoj pomuvannya vimiryuvannya can be the following parameters: vibration variance of single values \ u200b \ u200b mean value; vibration absolute standard display of single values and average values; vibration standard indications of single values and average values; the general variance of single values), apparently, і ін.

Vypadkovі pomki vimіru is uncomfortable to win, їх it is possible only to change. One of the main ways of reducing the value of the n). It will be clarified that the value of the grades of grapes is expressed in proportion to the value n, For example:

systematic pardons - the price of pardon with unchanged values and a sign to change the law. Tsі gratis viklikayuyutsya post-everyday factors. Systematic pardons can only be assessed, changed and driven.

Systematic grants are classified as grants I, IIіIIItypes.

Before systematic pardonsItype to give pardons at home, as they can be done before the assessment is carried out by the way of the rosary. It is possible to change the number of pardons by introducing them into the result of the change in the view of the amendments. Butt of this type of grating is a grating at titrometric values of the volume concentration, as the titrant of the preparation at the same temperature, and the vimir of the concentration was carried out at the same temperature. Knowing the abundance of titrant titrant in terms of temperature, it is possible, before carrying out an increase in titrant concentration, due to the cold temperature, and due to the increase in temperature in view of the corrections in the result.

systematicpardonsIItype- the process of pardoning every home trip, as it is possible to evaluate only in the course of the experiment, or as a result of conducting special training sessions. To the whole type of pardons, there are instrumental (priladov), reactive, etalon and ін. Pombs. Make yourself aware of the peculiarities of such pardons by yourself.

Be an adjunct when you are stuck in the procedures to add your own pardons to the result. At the same time, the part of the cich grasses is vipadkov, and the іnsha part is systematic. Vypadkovy grants were attached, not to be judged, but appreciated in a foreign country with the help of those vypadkovy vymyryuvannya.

I will add my own personal, systematic pardon to the skin copy. In order to assess the pardon, it is necessary to carry out special information.

Naybіlsh nadіyny way of assessing the ladder systematic pardon of the II type - the trick of robots setting the standards. For washing dishes (pipette, burette, cylindrical and in.) Carry out a special procedure - calibrating.

In practice, most often it is not necessary to evaluate, but to change or make a systematic pardon of the II type. By the most popular methods of reducing systematic grants є methods of relativization and randomization.Learn about these self-help methods.

Before pardonIIItype to give pardons to the unwanted prokazhennya. It is possible to see a lot of gratitude only when we see all the systematic mistakes of the IIIIItypes.

Before іnshim pomops every day, all those who see pardons, do not see them (it is allowed, there may be border pardons, etc.).

The understanding of the junior border pardons is stagnant at the vikorystannya vimiryuvannya and transferring as much as possible for the size of the instrumentally mercy pardon (in reality, the value of the pardon can be less than the size of the junior boundary pardon).

With victorian zasob_vim_ryuvannya, it is possible to develop an absolute limit (
) Anyway (
) pick up vim_ryuvannya. So, for example, it is possible that there is an absolute limitation in the presence of such a sum of vertebrate boundary species (
) I do not include systematic (
) Pomonek:

=
+

When vibrating a small obsyagu ( n20) of the inconvenience of general sufficiency, but to abide by the normal law of growth, in which there are some border grants in the world can be judged by the following rank:

= =
,

de: - prevіrchy interval for general information R;

-Quant_l student's tester for ymov_rnost_ R and vibrating volume n for with the number of steps of freedom f = n – 1.

Absolutely, the borderline cancellation is absolutely possible in any case, if it will be available:

=
+
.

If the results of the tests do not conform to the normal law of growth, then the evaluation of the errors is carried out according to the same formulas.

value of value
to lay aside the appearance of a certain class of accuracy. If the accuracy class is not good, then per value
you can take the minimum price for the scale(Abo її half) take in vimіryuvannya. To add the accuracy to the class of accuracy for the value
can be absolutely tolerated systematic pardon for vimіryuvannya (
):


.

magnitude
rozrakhovuєtsya vyhodyachi from the formulas, hovering in the table. 2.

For a bagatty, you can use the accuracy class to match the number viewer a10 n, de a door 1; 1.5; 2; 2.5; 4; 5; 6 i n door 1; 0; -1; -2, etc., which show the value of the possible boundary permissible systematic pardon (E y , add.) І special signs, which indicate about її types (specific, given, post_yna, proportional).

If we look at the warehouses of an absolutely systematic pardon of the average arithmetic result (for example, priladova pardon, pardon for the method і іn.)

de: m- the number of warehouses is systematically pardoned for the average result;

k- kofіtsієnt, which visas start ymovіrnіstyu R and number m;

absolutely systematic grating near the warehouse.

Outside warehouse hassle can be avoided in the presence of a large number of minds.

Table 2

Apply the specified classes of accuracy using the time

class accuracy		Formula for rozrahunku and the value of the boundary permissible systematic pardon	Characteristics of a systematic pardon
in the documentation	on zasobi vimiryuvannya		Characteristics of a systematic pardon
			It is admitted to allow a systematic pardon in several hundredths of the nominal value of the vimiryuvannya value, as it is based on the type of scale for the vimiryuvannya
			A systematic grading was introduced as a percentage of the scale of the victorian scale on the basis of a vimiryuvannya (A) in the case of rejection of single values
			Permanently admitted systematic pardon as a percentage of the rejected single value of the given value
		c = 0,02; d = 0,01	Proportionally, a systematic pardon is allowed in parts of the discarded single value of the vimiryuvannya magnitude, as it grows with an increase in the value range of vimiruvannya given by means of vimiryuvannya ( y k) anyway, a change in the single value of a vimiruvana value ( y i)

Systematic pardons can be unhealthy, as if you were unhappy

0.8.

In general vipadyuyut


 
.

With vipadkovy pardons, you can win

8.

For tsoi vipadku

.

As a result, the rejection of the change began only with systematic pardons, increasing the number of repeated checks. It is minimally necessary for the whole number of repeated tests ( n min) it is possible to develop only when the general value of the general sufficiency of single results is based on the formula

Estimation of the reasons for getting lost is not only of the minds of the mind, but of the type of vimiryuvannya (direct and indirect).

Rozpodil vimiryuvan in the direct and indirect є to make things clearer. Nadal pid direct vimirs We will be reasonable to measure the value of which to take without a priori from the preliminary data, for example, read from the scale of the adjunct (widely view the butt of direct vimir - vimir temperature with a thermometer). Before indirect wimir We will be aware that the result of which will be recognized at the presentation of the fallowness and the size of the shukanoy value and the values that are in the result of straightforwardness. With tsom result indirect vimіryuvannya take a rosary trail what is the meaning of the function  , arguments such as є results and direct vimiryuvan ( x 1 ,x 2 , …,x j,. ..., x k).

It is necessary for the nobility, that the pardons of the indirect vimiryuvan are more important, the lower the pardons of the direct vimiryuvan.

Indirect priests vimiryuvan assess the applicable laws for the accumulation of pardons (if k2).

The Law of Accumulation of Vypadkovy Pardons indirect vimіryuvan viglyadaє by the offensive rank:

The law of accumulation of possible boundary absolute systematic pardons Indirect Vimiryuvan appear as offensive fallows:

;
.

The law of accumulation of possible border exemplary systematic pardons indirect vimіryuvan maє nasty viglyad:

;

In vipadkah, if the shukan has a value ( y) The function of the results in the decilkokh independent straightforward in the mind
, The law of accumulation of borderline systematic pardons of indirect vimiryuvan accept more simple viglyad:

;
.

Punishments and mistakes are made in order to ensure the accuracy, accuracy and correctness.

accuracy Tim vische, less than the amount of the wimіryuvannya.

visibility The results in the month of June will be increased with the change in the number of grants in the country.

correctness As a result, there will be an increase in the amount of changes in the surplus systematic pardons of vimiriv.

You can learn more about the theory of mercy in the history of the world and its special features independently. I wrap up your respect for those who are fortunate in the form of presenting the results of the end of the year. With a lot of mistakes and pardons, we are guilty of being guilty numbers, how to take revenge no more two significant digits .

JOIN

Be-like vimiryuvannya, as they didn’t vikonuvali, supervised by misbehavior (pardons), that is. It’s worth explaining that, in the process of imіryuvan, you must constantly change your mind: the camp of the worldly middle, the worldly attachment and objectivism, and also respect the viconavtsya. Therefore, when the magnitude is varied, it will be necessary to find the approximate value, the accuracy of which is required to be assessed. Vinikak and іnshe zavdannya: vibrate the adjuster, think and method, schob viconati vimіryuvannya with a given accuracy. The process of developing additional assistance to the theory of pardons, how to vivch the laws and regulations of failures, establishing the criteria for assessing and tolerances to the accuracy of the values, the methods of determining the accuracy of the values, the rules for calculating the exact values.

12.1. Vimiru and їkh KLASIFIKATSIYA

Vimir refers to the process of changing the size of the size from the one taken as the unit of the size of the house.
All the quantities that I can tell you rightly can be summed up and calculated. vimirya I call it the size of the closest meaning, you know, go by the way of the one-sided odinitsa. So, lastly, laying down the land line along a given straight line and the number of layouts, it will be close to the value of the delay.
enumerated We call it the value of the meaning, because of the value of the variable values, we will functionally tie it with it. For example, the area of the rectangular shape є tvir and vimiryah dozhini і width.
For detecting misses (gross pardons) and adjusting the accuracy of the results in one and the same value, increase the number of times. For the exactness, such vimіryuvannya is attributed to equal accuracy and unequal accuracy. equal accuracy - one-sided bagatorazovy results of changing the same and the same magnitude, viconious by one and the same adjuster (or different adjusters of one and the same class of accuracy), in the same way and by the number of primes, in identical minds. unequal - vimіryuvannya, vikonanі at nedotrimanіnі minds of equal precision.
In case of mathematical analysis of the results, there is a large number of values. For example, trim the size of the tricot skin cut, complete two of them - tse i bude necessary number of quantities. In a zealous vipad, for the solution of any topographic and geodesic task, it is necessary to change the minimum number of values that will preserve the solution of the set manager. Їх name number of required quantities abo vimiryuvan. Ale schob judge about the quality of the tricycle, check the correctness and adjust the accuracy of the result, change the third cut of the tricycle - superfluous . The number of superfluous quantities (k ) Call the difference between the number of all variable values ( NS ) І number of required quantities ( t ):

k = n - t

In topographic and geodesic practice, the oversize is varied in magnitude. The stench allows the appearance of pardons (abductions) in values and numbers and to improve the accuracy of values.

Behind the physical vikonannya Vimiryuvannya can be direct, indirect and remote.
straight vimiryuvannya є the simplest and in the historical plan the first types of vimiryuvan, for example, vimir dovzhin line zemlemirnaya line or roulette.
indirect to be primed on the basis of mathematic deposits between shukany and non-average values. For example, the area of the rectangle on the m_scevosti viznakayut, vimіryavshi dozhini th side.
distance It can be primed on a number of physical processes and events, which, as a rule, are connected to the statistics of other technical problems: light range finders, electronic tachometers, photo theodolite, etc.

Vimiryuvalny attachments, vikoristovuvani in topographic and geodesic virobnistvі, can be distributed on three main classes :

high-current (precision);
exact;
technical.

12.2. MEASUREMENT BUCKETS

With bagatorazovy vimiri of the same and the same size of the skin, once the troche is removed, the results are obtained, as in absolute value So, according to the signs, which are not biased by the visitor, and by the high-current butts that are not victorious.
Possibilities to develop: rude, systematic and vipadkov.
belly rude tweak ( miss ) It is tied with serious pardons with virobnistvі vimіryuvalnyh robіt. Quite a few pills are easily discovered and absorbed as a result of the control of vimiryuvan.
systematic abductions to enter the skin result in accordance with the strict law. The stench was overwhelmed by the infused design of the vimiruvalny attachments, the tweaks of the gradation of the scales, wear, etc. instrumental hijacking) They emerge through the nerauvannya of the minds in the name of the laws of their changes, the closeness of the actions of the formulas and in. ( methodical misbehavior). Systematic mistakes are made for post_yn_ (Indispensable by the sign і great rank) і change (Change your value from one vimir to one according to the singing law).
Such mistakes are made early on in the agreement and may be made up to the minimum necessary to introduce new amendments.
by the way, Lately, it can be secured by the inflow of the curvature of the Earth to the accuracy of the value of the vertical walls, the inflow of the temperature to the atmospheric vice if you use a light range finder or an electronic total station, you can use the refraction of the atmosphere in advance, etc.
If you do not allow gross pardons and systematic use, then as soon as you start, only with bad humiliations. Cs do not need repairs, however, they behave in accordance with the laws of great numbers. It can be analyzed, controlled and produced to the required minimum.
In order to change the flow of inappropriate errors on the results, you can go up to bagatorazny vimirs, until the minds of robots are polished, you need to use more thorough methods to find out how to do it.
There are a number of vipadkovnyh mischiefs of equal vimiryuvan, it is possible to emerge, as the stench may cause the onset of power:
a) for a given type and minds, a certain amount of mischief cannot be overtaken by the absolute value of the singular boundary;
b) little for the absolute value of the deceit is a part of the great;
c) positive abuses occur as often as they are in terms of the absolute value of negative;
d) the arithmetic mean of the errors of the same and the same value of the pragne to zero with an unbounded increase in the number of vimiryuvan.
The distribution of pardons, depending on the authorities, is called normal (Fig. 12.1).

Small. 12.1. The curve of the normal growth of the gauss deviations

Riznitsya mіzh result of vimіryuvannya deyakoi magnitude ( l) і її true values ( X) name absolutely (true) .

Δ = l - X

True (absolutely accurate) value of a vimiryuvan magnitude is not harsh, it’s hard to find a vicious one, but it’s very accurate and found a method of vimiryuvan. Liche, in some cases, can be of a theoretical value. Accumulation of errors should be brought up to the approval of the differences between the results of the increase and the performance of the values.
Riznitsa sumi practically vimiryanyh (or calculated) values and theoretical meaning are called non-viscous. For example, the theoretical sum of kutiv in a flat tricycle road is 180º, and the sum of vimiry kutiv is 180º02 "; the sum of the kutіv in a warehouse is + 0º02". Qia pohibka bude kutoviy non-viscous tricycle.
Absolute misbehavior is not є, another indicator of the accuracy of the viconious robots. For example, if deyaka linea, actually dovzhina how to become 1000 m, Vimiryana zemlemіrnoї stіchkoyu with pardon 0.5 m, А відрізок zavdovzhki 200 m- with mercy 0.2 m That, unaffected by those who absolutely abdicate the first vimir more than the other, all the first vimir bulo vikonano with a precision twice. To introduce the understanding admissible tweaks:

The imposition of the absolute abduction of the great magnitudeΔ up to the sizelname admirable.

Every time a mistake is made, it turns out to be a fraction with a number, equal odinits (aliquotna drib). So, at the pointed eye, the first wimira can easily become

and the other

12.3 MATHEMATICAL REDUCTION OF THE RESULTS IN EQUAL ACCURATE MEASUREMENTS OF ONE VALUE

Let the deyaka value with true values X vimiryana equal n once and for all the results: l 1 , l 2 , l 3 , … li (i = 1, 2, 3, … n), Yaki is often called next to Vimiryuvan. It is necessary to know the best value of the current magnitude, as I call imovirno , and assess the accuracy of the result.
The theory of infringements has the greatest imoviry values for a number of equal-precision results in vimiryuvan accept arithmetic mean , i.e.

(12.1)

When there are systematic errors, the arithmetic mean in the world of the unbounded increase in the number of vimiryuvan pragne to the true meaning of vimiryuvana magnitude.
To make it possible to infuse more errors on the result of the accuracy assessment in a number of ways, nasty (UPC). If the value is not true, but the systematic deceit is even small, then the mean quadratic deduction ( m ) Next to the result of equal-precision vimіryuvan we start with the Gauss formula:

m = (12.2) ,

de Δ i - Help for a hitch.

In geodesic practice, there is no real significance of a certain magnitude in a large number of countries in the past unavoidably. Todi the average quadratic abduction around the result of vimiriv is counted as the average abduction ( δ ) Approximate results in vimiryuvan ( l i ); behind the Bessel formula:

m = (12.3)

Devotionality ( δ i ) It starts when the results are displayed as the arithmetic mean

δ i = l i - µ

Often instructing people to write down the mean square deduction ( m), For example 70 ° 05 "± 1". It means that the exact value of the kuta can be more or less than the indicated one by 1 ".

An analysis of the crooked normal growth of Gauss shows how, when reaching a great number of vimiruvan, one and the same magnitude of vipadkova can be inferred:

more mean square m in 32 vipad s 100;
more baseline mean square 2m in 5 vipad s 100;
more giblet mean square 3m in 3 vipad s 1000.

Maloimovirno, the vipadkova's mistake appeared to be a bigger mean square, that I will use the average quadratic hack, but I will use the boundary:

Δ poper. = 3m

To be called a borderline abusiveness is the same meaning of a vipadkoy abduction, when it is said that for the gifts of minds, it is not enough.

Yak borderline also accept the average quadratic misbehavior, equal

Δ in front = 2.5m ,

The amount of pardon is close to 1%.

The mean quadratic calculation of the sum of the variable values

The square of the mean squares of the algebraic sums to the argument

m S 2 = m 1 2 + m 2 2 + m 3 2 + ..... + m n 2

In the near vipad, if m 1 = m 2 = m 3 = m n= m for the mean value of the arithmetic mean, use the formula

m S =

The mean quadratic misbehavior of the algebraic sumi of the equal points is in times greater than the mean deduction of one dodank.

Butt.
Yaksho vimiryana 9 kutiv with a 30-second theodolite, then the average quadratic pickup of kutov vimiriv in the warehouse

m kut = 30 " = ± 1.5 "

Mean quadratic tweak of arithmetic mean
(The accuracy of the value of the arithmetic mean)

The mean is quadratic, the calculation of the arithmetic mean (mµ )times less than the mean square one vimir.

The power of the mean deviation of the arithmetic mean allowance to adjust the accuracy of the mean increase in the number of vimiryuvan .

by the way, It is necessary to determine the value of the cut with an accuracy of ± 15 seconds with the presence of a 30-second theodolite.

Yaksho vimiryati kut 4 times ( n) І, if the arithmetic mean is greater than the mean, then the mean is quadratic, and the arithmetic mean ( mµ ) Stock ± 15 seconds.

The mean is quadratic, the calculation of the arithmetic mean ( m µ ) I will show what kind of world it is to fall in the inflow of vypadkovyh mischiefs with bagatorazovy vimir.

butt
Vyrobleno 5 times vimіryuvannya per genie of one line.
According to the results, count vimiryuvan: the most probable significance of її dozhini L(mean); Ymovіrno hiccups (vіdhilennya from the arithmetic mean); average quadratic misbehavior of one vimir m; the accuracy of the value of the arithmetic mean mμ, I the most probable value of the line from the mean square deviation of the mean arithmetic ( L).

Processing of results

Table 12.1.

imovіrno tweaks di, cm	The square is the size of the hand, cm 2	characteristic accuracy
		m= ± = ± 19 cm mµ = 19 cm / = ± 8 cm




Σ di = 0	[Σ di]2 = 1446	L= (980.65 ± 0.08) m

12.4. VAGI RESULTS IN Unequal Measurements

In case of unequal values, if the results of the skin visualization cannot be matched equally to the superior ones, it is still impossible to do with the values of a simple arithmetic mean. In such cases, the dermal results are more likely to be damaged.
The majority of the results in vimiryuvan turn in a single number, we call vagoyu ts'go vimir ... Obviously, the arithmetic mean is greater than the average in the case of a single one, but in the case of victorious, I will be more accurate and accurate, there will be more steps to be taken, in the least
Oskilki think vimiryuvan viznachyut the value of the average abduction, then it will be left and accepted yak the basics of assessing car values, conducted vimiryuvan. With a wide range of results, we will take wrapped in the proportional squares of the mean squares .
So, how do you mean through Rі R Vagi vimiriv, may be the mean-square error as per mі µ , Then you can write down the proportions:

Forward, yaksho µ the mean is the quadratic subtraction of the arithmetic mean, and m - apparently, one vimir, then, like vipliv z

you can write:

i.e. wag of arithmetic mean in n times more than a single vimіryuvannya vagi.

An analogous rank can be set up, where a whale of a kut vimiruvannya, viconated with a 15-second theodolite, in the form of a wha of a kutovy vimіryuvannya, viconated with a 30-second adjuster, can be installed.

With practical calculations, make sure to count the same size as one, and when you count, consider the number of the same size. So, in the last butt, you can take the result of a cut-and-go vimiruvannya with a 30-second theodolite for R= 1, then the car is given the result of a 15-second theodolite warehouse R = 4.

12.5. VIMOGS BEFORE REGISTRATION OF THE RESULTS IN THE SEXUAL MEASUREMENTS І Х TREATMENT

All materials of geodetic surveys are stored from Polish documentation, as well as documentation from numerical and graphical robots. Bagatorial reports of geodetic surveys and revisions allowing the development of the rules for maintaining the documentation.

Registration of Polish documents

Prior to Polish documents, there are materials of revisions of geodetic attachments, journals and forms of special forms, sketches, marketing journals. All Polish documentation is used only in originals. You can store it in a single copy, and at the same time it can be renewed only by repeated copies, which is practically impossible.

The rules for polish magazines are published before the coming.

1. Memorize polovi magazines carefully, all numbers and letters are written down clearly and freely.
2. Correcting digits and cleaning, as well as writing digits by digits are not allowed.
3. Pomilkovy records of vіdlіkіv zashlyuyutsya with one rice і right-handers vkazutsya "pomilkovo" or "typo", and the correct results are inscribed above.
4. All entries in the journals are kept by an old man of average hardness, blackened with a paper bag; victorian for all chemists and color olivts is not recommended.
5. In the case of a dermal appearance of geodesic chimneys, the recording of the results in vimiryuvannya to be recorded in the general journals of the established form. Until the earliest, the pages of the journals are numbered and the number of the singers.
6. In the process of polovy robots with rejected results, check the diagonal with one rice, indicate the reason for the loader and the number of the line, so as to revenge the results and repeated vimiriv.
7. In the skin magazine, on the headline archives, write down the information about the geodetic attachment (brand, number, average quadratic error), write down the date and hour warning, meteorological information (weather, visibility, etc.), and remarks.
8. The magazine is of such a rank, that he is a visitor who does not take part in Polish robots, and I will send a sample of the results to the polish robots. When storing Polish journals, following the offensive recording forms:
a) the numbers in the hundredths should be written in such a way that all the digits of the same lines were rejected one without a change.
b) all the results of the test, registered with the same accuracy, should be written down with the same number of characters written by the Komi.

butt
356.24 і 205.60 m - correct,
356.24 and 205.6 m - wrong;
c) the value of quills and seconds in case of kutovnyh vimirs and calculations should be written down in two digits.

butt
127 ° 07'05 " , Not 127º7 "5 " ;

d) in the numerical values of the results in a certain period, write down as many numbers as possible, as it is allowed to correct the display of an example of a certain number of figures. For example, if the line is to be measured with a tape measure with millimeter rosettes and when it is carried out with an accuracy of up to 1 mm, then the record is blamed for 27,400 m, and not 27.4 m. , not 47º or 47º00 "00".

12.5.1. Understanding the rules of geodetic calculation

Prior to the revision of the results, we start to revise all the Polish materials. At the same time, the practice of using the rules and accepting the rules, taking care of the rules and taking advantage of the rules and allowing them to rationalize the calculation of the technology and the additional assistance.
1. Before the cob of the crumbled results of geodesic surveys, a detailed numerical scheme should be developed, in which the last of the events should be taken into account, so that the results can be rejected, we will forgive the best and the quickest way.
2. With regard to the calculation of calculating robots, select the most optimal ways and methods of calculating those who use vitrates if they do not have the necessary accuracy.
3. The accuracy of the results cannot be ascertained from the accuracy of the calculation. To him zdalegіd went to the prosperous, rather not overwhelming accuracy of the enumeration actions.
4. When calculating, it is possible to use black cocks, since rewriting digital material takes away a lot of an hour and is often supervised by pardons.
5. For recording the results of the calculation, it is recommended to register special schemes, forms and houses, to start the order of registrations and to ensure the intermediate and general control.
6. Without the control of the calculation, we can’t get it done. The control can be performed by the visitor, the visitor is able to solve the problem, or if it is repeated by the visitor (in the "two hands").
7. The calculation will eventually end on the basis of the errors and the binding tolerances, which are transferred by the appropriate instructions.
8. Especially in the case of calculating robots, it is necessary to record the numbers in the calculating forms before they are accurate and readable, and if they are not worthless in the records, they must be made until the pardons.
Yak i in Polish journals, when writing a hundred numbers in numerical schemes, the numbers of the same series are followed by one after one. With a large shot, a part of the number appears in a lump; bagatorazryadnі numbers are recorded with intervals, for example 2 560 129.13. Records of the number of slid should be kept only in chornil rectangular type; pardon the results and carefully pereklyuvat і from the top of the writing to correct the meaning.
When the materials are processed, the nobility is slid by the nobility, because of the accuracy of the guilt, the results are rejected, so do not operate because of the number of signs; If the residual result of the calculation comes with a large number of signs, it is not necessary, then the rounding of the numbers should be rotated.

12.5.2. rounding numbers

Round the number to n signs - mean safety in new pershі n significant digits.
Significant digits of the number - all of the first digits are from the first evil, from zero, until the last recorded digit is right-handed. With a full zero on the right, it does not sound like significant digits, as the stench replaces the unavailable digits or the substitution of the other digits when the given number is rounded.
For example, the number 0.027 is two significant digits, and the number 139.030 is the number of significant digits.

When the numbers are rounded off, follow the offensive rules.
1. If the first digit is less than 5, then the left digit is saved without a change.
For example, the number 145.873 is rounded to five significant digits for 145.87.
2. If the first digit is more than 5, then the left digit is changed to one.
For example, the number 73.5672 is rounded to the most significant digits for 73.57.
3. If the last digit to round off the number є digit 5 and won’t be guilty of being shown, then the preceding figure in the number is increased by one only in the same way, if it’s unpaired (the rule of pair numbers).
For example, the numbers 45.175 and 81.325 will be approximately 45.18 and 81.32 if rounded to 0.01.

12.5.3. graphic robots

The value of graphic materials (plans, maps and profiles), as well as the final result of geodetic zyomok, in the meaning of the world, it is not only the exactness of the polish that is needed, but the correct number of numerical Graphic robots are responsible for the additional retrofitting of armchair instruments: lines, robots, geodesic transports, compasses-vimіryuvachіv, hospitality іnіvtsіh olivtsіv (T and P. TM) Kreslyarsky robots guilty vikonuvatisya on the arches of the yakisky kreslyarsky paper, fastened on the ravny table or on the special kreslyarskoy dooshtsi. The copy of the original of the graphic document for the retranslation and registration is made out in ink according to the original signs.

Nutrition and staff for self-control

What does viraz mean: "be-like size"?
Yak clasify vimiryuvannya?
Yak klasifіkuyut vimіryuvalnі attach?
How do you classify the results and the accuracy?
Do you call Yaki vimiryuvannya equal?
Scho means to understand: " necessary і surplus the number of vimiryuvan "?
How to classify the pardons vimiryuvannya?
Why are there systematic abductions?
By the powers of power, who are they wrong?
What is called absolute (іtinnoї) wickedness?
What do you call an admirable bribe?
How do they call the arithmetic mean in the theory?
What is called in the theory of misbehavior the mean-square misbehavior?
Why is the borderline mean quadratic error?
How is the average quadratic calculation of the algebraic sum of equidistant values?
How does one correlate the mean quadratic?
How do I show the mean, is the arithmetic mean?
What parameter is taken in the basis of the assessment of the car values?
How can we talk about an arithmetic mean and a single one?
What are the rules adopted in geodesy for keeping Polish journals?
Check out the basic rules of geodetic calculation.
Round up to 0.01 for 31.185 і 46.575.
Check out the basic rules for the visibility of graphic robots.

Accumulation of mischief. Mathematical processing of results in equal-precision values ​​of the same quantity

"ACCUMULATED KHIBKI" in books

Technical troubles

Technical troubles

Grishki and infidels

First accumulated capital. The rapist is the landlessness of the villagers. Accumulation of riches.

Socialistic accumulation. Accumulation and living in the socialist suspension.

abductions vimiryuvan

Hijacking with the help of vimiruval technology

uzd tweaks

Dodatok 13 Movements

movnі chibi

mouthful

Abductions in the event of an accident

Hobbies: Philosophy

Hobbies: models

Hobbies: scho i yak control

marvel at the meaning accumulation of Pohibka in the last dictionaries

12.1. Vimiru and їkh KLASIFIKATSIYA

12.2. MEASUREMENT BUCKETS

12.3 MATHEMATICAL REDUCTION OF THE RESULTS IN EQUAL ACCURATE MEASUREMENTS OF ONE VALUE

The mean quadratic calculation of the sum of the variable values

The mean is quadratic, the calculation of the arithmetic mean (mµ )times less than the mean square one vimir.

The power of the mean deviation of the arithmetic mean allowance to adjust the accuracy of the mean increase in the number of vimiryuvan .

12.4. VAGI RESULTS IN Unequal Measurements

12.5. VIMOGS BEFORE REGISTRATION OF THE RESULTS IN THE SEXUAL MEASUREMENTS І Х TREATMENT

Registration of Polish documents

12.5.1. Understanding the rules of geodetic calculation

12.5.2. rounding numbers

12.5.3. graphic robots

Accumulation of mischief. Mathematical processing of results in equal-precision values of the same quantity