scholarly journals Short Communication: Weighted dual approach to the problem of equivalent replacement

2013 ◽  
Vol 35 (2) ◽  
pp. 169-173
Author(s):  
N. D. Anh
Keyword(s):  
Short Communication ◽  
Main Idea ◽  
Mean Square ◽  
Dual Approach ◽  
Object A ◽  
The Mean ◽  
Linear And Nonlinear ◽  
The Difference ◽  
Improved Accuracy ◽  
Linear And Nonlinear Systems

The problem of equivalent replacement plays a basic role in many fields of science and technology. In the classical approach the original object A is to be replaced by an equivalent object kB using the mean square minimum criterion. When the difference between A and kB is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. The main idea of this short communication is to propose a special form of weighted dual mean square criterion. Numerical results are carried out for linear and nonlinear systems to show an improved accuracy of the proposed criterion.

scholarly journals On an extension of the stochastic linearization

1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Equation ◽  
Random Excitation ◽  
Linearization Method ◽  
Mean Square ◽  
Fundamental Idea ◽  
Stochastic Linearization ◽  
The Mean ◽  
The Difference

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.

scholarly journals INFLUENCE OF DIFFERENT VERSIONS ARTIFICIAL INSEMINATION OF GILTS OF THEIR TRAITS OF THE REPRODUCTIVE ABILITY CONSOLIDATION

2018 ◽  
Vol 56 ◽  
pp. 130-135
Author(s):  
M. V. Tserenyuk ◽  
O. M. Tserenyuk
Keyword(s):  
Artificial Insemination ◽  
Reproductive Capacity ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Reproductive Ability ◽  
Coefficient Of Variability ◽  
Current Instruction ◽  
The Mean ◽  
The Difference ◽  
The Impact

In addition to assessing the absolute performance of animals, the impact of certain technological approaches, breeding influence and other external organized factors on the consolidation of pigs groups on certain grounds should be evaluated. Breeding consolidation is a desirable breeding process that is realized through more motivated consolidation of intra-breeding structural units for maintaining a significant level of intergroup differentiation and variability. If the issue relates to the rearing young animals that are introduced into the herd, this is the most urgent issue that needs to be monitored. The purpose of the research is to determine the consociality of the main signs of reproductive ability of the gilts, which are checked at different rates of artificial insemination of sows of the main herd. The research was carried out at the Shubs`ke farm in the Bogoduhivsky District of Kharkiv Oblast at the pig farm for the pure breeding of the Welsh breed pigs (breeding reproductive status from 2014). In order to evaluate the optimal multiplicity (from single to triple), a gilts with a total of 30 heads was selected. The main indicators of reproductive ability of gilts (multiplicity, weight of nest at birth and excommunication and keeping piglets before weaning on day 28) were evaluated. Recalculation on the weight of the litter at weaning at the weight of the nest at extermination in 60 days was carried out in accordance with the current instruction on the boning of pigs. The results of researches were worked out according to traditional methods by the method of variation statistics. Consolidation of individual indicators of reproductive capacity of gilts was calculated to the total number of evaluated animals. In the previous stage of the research, it was found that the use of multiple insemination of gilts compared to single insemination is positively reflected at the level of their reproductive ability. A decrease in the percentage of non-productive inseminants in animal groups has been established. Triple insemination of gilts allows for 1.14 piglets to be obtained more compared to single insemination of the same pigs (p < 0.01). Also, for three times insemination of gilts, in comparison with single insemination, larger nest for weaning were obtained (by 14.24 kg, converted to 60th day p < 0.01). At the same time, the reduction in the keeping of piglets to weaning for increase frequency of insemination of gilts. According to the multiplicity of gilts, the most consolidated level of symptoms per group was obtained for single insemination. Increasing the multiplicity of insemination negatively affected the consolidation of the multiplicity of the piglets (as for determining the coefficients of phenotypic consolidation due to the mean square deviation, so, and for determining the coefficient of variability). The least consolidated in terms of multiplicity were uterus for double insemination. It should also be noted that there is little difference, in general, on the indicators of the theonotypical consolidation of the multiplicity of piglets between different groups of animals. So this difference between the most contrasting groups was 0.447 points for determining the coefficients due to the mean square deviation and 0.397 points for the determination due to the coefficient of variability, respectively. By weight of the same litters at birth, the most consolidated group was gilts, which was inseminated twice. The least consolidated are trimmed three times, respectively. The difference as a whole, according to the indicators of the theonotype consolidation of the mass of the litter’s piglets at birth, between different groups of pigs was even smaller. The difference between the most contrasting groups was 0.270 points for determining the coefficients due to the mean square deviation and 0.260 points for the determination due to the coefficient of variability, respectively. On the basis of the mass of the litter at weaning, the most consolidated level of symptoms was obtained in the group of gilts for triple insemination. The least consolidated group, respectively, was gilts for single insemination. At the same time, on the basis of the weight of the litter at weaning, the slightest differences were obtained after the consolidation of the signs between different groups of pigs. The difference between the most contrasting groups was 0.173 points for determining the coefficients due to the mean square deviation and 0.248 points for the determination due to the coefficient of variation, respectively. At different rates of insemination of gilts, there are no significant differences between the groups between the groups in terms of the consolidation of signs of reproductive ability. Also, there was no clear effect on increasing the multiplicity of insemination of gilts to the consolidation of their signs of reproductive qualities.

scholarly journals The nth-order moment of the nuclear charge density and contribution from the neutrons

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Haruki Kurasawa ◽  
Toshio Suzuki
Keyword(s):  
Charge Density ◽  
Electron Scattering ◽  
Nuclear Charge ◽  
Order Moment ◽  
Proton Density ◽  
Neutron Density ◽  
Mean Square ◽  
Relativistic Expression ◽  
The Mean ◽  
The Difference

Abstract The relativistic expression for the $n$th-order moment of the nuclear charge density is presented. For the mean square radius (msr) of the nuclear charge density, the non-relativistic expression, which is equivalent to the relativistic one, is also derived consistently up to $1/M^2$ with use of the Foldy–Wouthuysen transformation. The difference between the relativistic and non-relativistic expressions for the msr of the point proton density is also discussed. The $n(\ge 4)$th-order moment of the nuclear charge density depends on the point neutron density. The fourth-order moment yields useful information on the msr of the point neutron density, and is expected to play an important role in electron scattering off neutron-rich nuclei.

scholarly journals Dual approach to averaged values of functions: A form for weighting coefficient

2015 ◽  
Vol 37 (2) ◽  
pp. 145-150 ◽  
Author(s):  
N. D. Anh
Keyword(s):  
Short Communication ◽  
Duffing Oscillator ◽  
Main Idea ◽  
Weighting Coefficient ◽  
Dynamic Processes ◽  
Equivalent Linearization ◽  
Dual Approach ◽  
Classical Criterion ◽  
New Form ◽  
Constant Characteristics

Averaged values play major roles in the study of dynamic processes. The use of those values allows transforming varying processes to some constant characteristics that are much easier to be investigated. In order to extend the use of averaged values one may apply the dual approach which suggests a consideration of two different aspects of a problem in question. In this short communication the main idea of the dual conception is further extended to suggest a new form for weighting coefficient and then a new averaged value of functions. This new averaged value depends on the parameter \(s\) and contains the classical averaged value when \(s=0\). In the example of Duffing oscillator it is shown that the parameter \(s\) can be chosen as \(s=n/(2\pi)\) and for \(n=4\) one gets the solution that is much accurate than the conventional one obtained by the classical criterion of equivalent linearization.

Modeling relative error in stem basal area estimates

1990 ◽  
Vol 20 (5) ◽  
pp. 496-502 ◽  
Author(s):  
T. G. Gregoire ◽  
S. M. Zedaker ◽  
N. S. Nicholas
Keyword(s):  
Basal Area ◽  
Field Measurements ◽  
Mean Square ◽  
Interval Estimates ◽  
Tree Diameter ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
The Mean ◽  
The Difference ◽  
Relative Errors

The computed estimate of basal area was the focus of this investigation into the accuracy of tree diameter measurements. Diameter at breast height was measured on 101 trees, the breast height disc was removed from the stem, and each disc outline was then digitized to determine its actual area. Actual areas were compared with the basal areas computed with the field measurements of diameter by expressing the deviations as a proportion of the actual areas. These relative errors averaged 3.1% when basal area was computed with a taped diameter at breast height, and they averaged −2.5% when the mean of two calipered, perpendicular diameter at breast height measurements were used. Noncircularity accounted for about 2.6% of the bias, on average, in basal areas from taped diameters. Root mean square error of relative basal area errors ranged from 7.3 to 7.9% among these methods. The difference between basal areas computed with a taped diameter at breast height and with calipered diameter at breast height was computed and expressed as a proportion of the actual basal area. On average, a difference of 5% was observed. Interval estimates for these differences are presented.

The investigations of pulsar integral radio luminosities

1996 ◽  
Vol 160 ◽  
pp. 59-60
Author(s):  
Igor’ F. Malov ◽  
Oleg I. Malov ◽  
Valerij M. Malofeev
Keyword(s):  
Mean Value ◽  
Main Mechanism ◽  
Square Root ◽  
Mean Square ◽  
Pulsar Period ◽  
Light Cylinder ◽  
Curvature Radiation ◽  
The Mean ◽  
The Difference ◽  
Integral Radio

We have calculated accurate integral radio luminositiesLfor 232 pulsars (Malov et al., 1994) using new average spectra of these objects. Histogram ofL-distribution is characterized by the mean value &lt; logL&gt;= 28.45 and by the mean-square-root deviationS= 1.0. We have analysed also data for short-periodic pulsars (P &lt; 0.1 s) and long-periodic ones (P &gt; 1 s) separately.The main goal of such separation was to test the hypothesis on two types of pulsars (Malov, 1987): i) for the first group of objects radiation is emitted from the neighbourhood of the light cylinder (r=rLC=cP/2π, P is the pulsar period), ii) for the second one emission is generated at distancesr≪rLC. In the second case the main mechanism of radiation is curvature radiation. For the first group of pulsars the radiation is connected with the cyclotron mechanism. The difference between two basic mechanisms and the locations of the emission generation regions must cause some differences in the observable features for these two classes of pulsars.

scholarly journals A FULL DUAL MEAN SQUARE ERROR CRITERION FOR THE EQUIVALENT LINEARIZATION

2016 ◽  
Vol 54 (4) ◽  
pp. 557
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Minh Triet
Keyword(s):  
Mean Square Error ◽  
Nonlinear Function ◽  
Approximate Solutions ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Approximate Methods ◽  
Dual Approach ◽  
The Difference ◽  
Mean Square Error Criterion

Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of implementing this method is that the coefficients of linearization are to be found from a criterion of equivalence. When the difference between the nonlinear function and equivalent linear one is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems.

ISOSPIN DEPENDENT OSCILLATOR SPACING FOR NEUTRONS AND PROTONS IN NUCLEI USING HF-BCS RADII

1996 ◽  
Vol 05 (04) ◽  
pp. 669-679 ◽  
Author(s):  
G.A. LALAZISSIS ◽  
C.P. PANOS
Keyword(s):  
Root Mean Square ◽  
Neutron Number ◽  
Asymptotic Formulas ◽  
Mean Square ◽  
Heavy Nuclei ◽  
Nuclear Radius ◽  
Proton Number ◽  
The Mean ◽  
The Difference

The oscillator spacing for neutrons (ħωn) and protons (ħωp) is calculated as a function of the neutron number N and the proton number Z. The dependence of ħωn(ħωp) on N and Z is established employing a parametrization for the mean square nuclear radius obtained from HF-BCS calculations. It turns out that the difference ħωn−ħωp is appreciable, because ħω amplifies small differences of root mean square radii. It is also seen that the correction due to valence nucleons is important for relatively light and medium heavy nuclei. Satisfactory and simple approximate asymptotic formulas for ħωn(N, Z) and ħωp(N, Z) are also derived, which can be used in practice. Finally, the validity of our various approaches is checked and a possible application is also discussed.

scholarly journals Contribution Degree of Different Surface Factors in Urban Interior to Urban Thermal Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jikang Wan ◽  
Min Zhu
Keyword(s):  
Regression Analysis ◽  
Thermal Environment ◽  
Linear Regression Analysis ◽  
Multiple Linear Regression Analysis ◽  
Linear Analysis ◽  
Mean Square ◽  
Ground Object ◽  
The Mean ◽  
The Difference ◽  
Urban Thermal Environment

The contribution degree of different surface factors (complexity and heterogeneity) in the urban interior to the urban thermal environment has become an issue of increasing concern under changing climate. In this paper, the multiple linear regression analysis methods to analyze the contribution degree of different surface factors to the urban thermal environment were based on seven urban built-up areas. At the same time, the LST of the same type of factors in the same city will have a difference of ±2.5°C due to the different surrounding features. At the same time, the LST of the same ground object in the same city will be ±2.5°C different because of the difference of the surrounding ground object. The environmental LST and the mean LST of other surface factors were significantly correlated, and the root mean square error was 3.52. This study first classifies the ground features with different attributes, conducts LST statistics for each category, and conducts multivariate linear analysis, instead of setting some fuzzy exponent and forcing a threshold to calculate. The purpose is to explore the contribution of different reflectivity ground objects to the urban thermal environment.

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