scholarly journals Mathematical Problems in Creating Large Astronomical Catalogs

2016 ◽  
Vol 25 (4) ◽  
Author(s):  
M. E. Prokhorov ◽  
A. I. Zakharov ◽  
N. L. Kroussanova ◽  
M. S. Tuchin ◽  
P. V. Kortunov
Keyword(s):  
Systematic Errors ◽  
Specific Form ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Mathematical Methods ◽  
Data Set ◽  
Astronomical Catalogs ◽  
Mathematical Problems ◽  
Primary Reduction ◽  
Star Catalogs

AbstractThe next stage after performing observations and their primary reduction is to transform the set of observations into a catalog. To this end, objects that are irrelevant to the catalog should be excluded from observations and gross errors should be discarded. To transform such a prepared data set into a high-precision catalog, we need to identify and correct systematic errors. Therefore, each object of the survey should be observed several, preferably many, times. The problem formally reduces to solving an overdetermined set of equations. However, in the case of catalogs this system of equations has a very specific form: it is extremely sparse, and its sparseness increases rapidly with the number of objects in the catalog. Such equation systems require special methods for storing data on disks and in RAM, and for the choice of the techniques for their solving. Another specific feature of such systems is their high “stiffiness”, which also increases with the volume of a catalog. Special stable mathematical methods should be used in order not to lose precision when solving such systems of equations. We illustrate the problem by the example of photometric star catalogs, although similar problems arise in the case of positional, radial-velocity, and parallax catalogs.

Families of quasigroup operations satisfying the generalized distributive law

2020 ◽  
Vol 30 (3) ◽  
pp. 187-202
Author(s):  
Sergey V. Polin
Keyword(s):  
System Of Equations ◽  
Systems Of Equations ◽  
The Family ◽  
Distributive Law ◽  
Elimination Of Variables

AbstractThe previous paper was concerned with systems of equations over a certain family 𝓢 of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family 𝓢 of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families 𝓢 that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.

BATCH DOUGH VISCOSITY INFLUENCE ON FLOW-PRESSURE CHARACTERISTICS OF THE KNEADING MACHINE

2019 ◽  
Author(s):  
В.С. РУБАН ◽  
В.И. АЛЕШИН ◽  
Д.С. БЕЗУГЛЫЙ
Keyword(s):  
Batch Process ◽  
System Of Equations ◽  
Systems Of Equations ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Symmetric Form ◽  
Pressure Function ◽  
One Dimensional ◽  
Flow Pressure ◽  
Transport Problems

Рассмотрены уравнения баланса и концентрационных потоков, базирующихся на моделях, позволяющих анализировать одноименные модели реологии течения в канале шнека блока замеса тестомесильной машины. Анализ процесса транспортировки и замеса на основе одномерной модели выявил необходимость использования сигмоидальной функции коэффициента напоропроводности от давления. Переход от одномерных задач к многомерным задачам переноса связан с преобразованием систем уравнений к симметричному виду. Полученные системы уравнений после использования теоремы Грина могут быть решены методом конечных элементов. The balance equation and concentration flows based on the models which make it possible to analyze the eponymous models of flow rheology in the block screw channel in a dough mixing machine has been considered. The analysis of the transportation and batch process based on one-dimensional model proved the necessity to apply sigmoidal coefficient of pressure function. The transition from one-dimensional problems to multidimensional transport problems is associated with the transformation of systems of equations to a symmetric form. The resulting system of equations after using Green’s theorem can be solved by the finite element method.

scholarly journals Calculation of Maxwell’s Equations Using MATLAB

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Subhi Abdalazim Aljily Osman ◽  
Keyword(s):  
Mathematical Method ◽  
Analytical Solution ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
System Of Equations ◽  
First Order ◽  
Mathematical Programs ◽  
Mathematical Problems ◽  
Micro Radio

Maxwell’s equations describe electromagnetic Phenomena. This includes micro- , radio and radar waves .The Maxwell equations are discussed in more detail Faraday's and Amperes laws constitute a first - order hyperbolic system of equations .Matlab is one of the most famous mathematical programs in calculating mathematical problems .The aims of this study is to calculate Maxwell’s equations using Matlab .We followed the applied mathematical method by using Matlab .We found that the solution of Matlab is more accuracy and speed than the analytical solution.

scholarly journals COMPATIBILITY BETWEEN THE STEM VOLUME AND TAPER EQUATIONS VOLUME FOR BLACK WATTLE TREES

FLORESTA ◽  
2020 ◽  
Vol 50 (3) ◽  
pp. 1518
Author(s):  
Marcos Behling ◽  
Henrique Soares Koehler ◽  
Alexandre Behling
Keyword(s):  
Traditional Approach ◽  
Stem Volume ◽  
System Of Equations ◽  
Data Set ◽  
Taper Function ◽  
Black Wattle ◽  
Taper Equations ◽  
Volume Estimates ◽  
Forest Engineering

A system of equations widely used in Forest Engineering by the international community of researchers consists of a combination of a volumetric function and a taper function, with the purpose of making volume estimates compatible. When using the volume function and the taper function in a system, the result of the volume estimated by the two functions should be compatible, meaning that the volume estimated by the volumetric function should not differ from the volume obtained by integrating the taper function. Thus, the purpose of this paper was to develop and present the procedures of a system of equations to make volume estimates from both volume and taper equations compatible, and then compare it to the traditional approach, which is used in forestry companies. The procedures proposed were applied to a data set on the Acacia mearnsii De Wild. (black wattle) at sites where the plantation of this species is concentrated in the state of Rio Grande do Sul. The data set included 343 trees ranging from 5 to 10.75 years of age. It was noted that the lack of volume compatibility, in absolute terms, grows exponentially with the size of the tree. The quality of the estimates using the system of compatible equations did not differ from those obtained from the traditional model, therefore, the former is preferable. Furthermore, it was noted that the residuals from the volume and taper equations are correlated, which suggests that the system of equations be fitted simultaneously.

scholarly journals LISMA_HDS language for modeling heterogeneous dynamic systems

2021 ◽  
pp. 103-122
Author(s):  
Evgeny Popov ◽  
◽  
Yury Shornikov ◽  
Keyword(s):  
Dynamic Systems ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
System Of Equations ◽  
Modeling Languages ◽  
Cauchy Problems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Algebraic Systems ◽  
Different Types

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

scholarly journals The measurements results adjustment by the Least Square Method

2021 ◽  
Vol 1 ◽  
pp. 1-8
Author(s):  
Oleksandr Samoilenko ◽  
Yurii Kuzmenko
Keyword(s):  
Reference Value ◽  
Least Square Method ◽  
Systematic Errors ◽  
Least Square ◽  
Key Comparisons ◽  
System Of Equations ◽  
The Third ◽  
Measurement Results ◽  
Free Case ◽  
Degrees Of Equivalence

The method for processing of the measurement results obtained from Comite International des Poids et Measures (CIPM) Key, Regional Metrology Organizations (RMO) or supplementary comparisons, from the proficiency testing by interlaboratory comparisons and the calibrations is proposed. It is named by authors as adjustment by least square method (LSM). Additive and multiplicative parameters for each measuring standard of every particular laboratory will be the results of this adjustment. As well as the parameters for each artifact. The parameters of the measurements standards are their additive and multiplicative degrees of equivalence from the comparison and the estimations of the systematic errors (biases) from calibrations. The parameters of the artifacts are the key comparisons reference value from the comparison and the assigned quantity values from the calibrations. The adjustment is considered as a way to solving a problem of processing the great amount of homogeneous measurements with many measuring standards at a different comparison levels (CIPM, RMO or supplementary), including connected problems. Four different cases of the adjustments are considered. The first one is a free case of adjustment. It was named so because of the fact that none of participants has any advantage except their uncertainties of measurements. The second one is a fixed case of adjustment. Measuring results of RMO and supplementary comparisons are rigidly linked to additive and multiplicative parameters of measuring standards of particular laboratories participated in CIPM key comparisons. The third one is a case of adjustment with dependent equations. This one is not so rigidly linked of the new comparisons results to previous or to some other comparisons as for fixed case. It means that the new results of comparisons are influenced by the known additive and multiplicative parameters and vice versa. The fourth one is a free case of adjustment with additional summary equations. In that case certain checking equations are added to the system of equations. So, the sum of parameters multiplied by their weights of all measurement standards for particular laboratories participated in comparisons should be equal to zero.

On predicted R factors for dynamic structure crystallography

2018 ◽  
Vol 233 (9-10) ◽  
pp. 689-694 ◽  
Author(s):  
Julian Henn
Keyword(s):  
Dynamic Structure ◽  
Systematic Errors ◽  
Data Sets ◽  
Data Set ◽  
Evaluation Of Data ◽  
R Factors

Abstract For the evaluation of data sets from dynamic structure crystallography, it may be helpful to predict expected $R = {{{I_{ON}}} \over {{I_{OFF}}}}$ -based agreement factors from the observed intensities and their corresponding standard uncertainties with laser ON and with laser OFF. The predicted R factors serve three purposes: (i) they indicate, which data sets are suitable and promising for further evaluation, (ii) they give a reference R value for the case of absence of systematic errors in the data and (iii) they can be compared to the corresponding predicted F2-based R factors. For point (ii) it is inevitable, that the standard uncertainties from the experiment are adequate, i.e. they should adequately describe the noise in the observed intensities and must not be systematically over- or under estimated for a part of the data or the whole data set. It may be this requirement, which is currently the largest obstacle for further progress in the field of dynamic structure crystallography.

Application of Information and Communication Technology to Create E-Learning Environments for Mathematics Knowledge Learning to Prepare for Engineering Education

2014 ◽  
pp. 345-373
Author(s):  
Tianxing Cai
Keyword(s):  
Engineering Education ◽  
Learning Environments ◽  
Teaching And Learning ◽  
Engineering Application ◽  
Mathematical Practice ◽  
Mathematical Methods ◽  
Mathematics Knowledge ◽  
Mathematical Problems ◽  
Information And Communication ◽  
E Learning

The standards for mathematical practice describe varieties of expertise that mathematics educators should develop in their students, including NCTM process standards (problem solving, reasoning and proof, communication, representation, and connections), NRC's report “Adding It Up” (adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition), common core state standards in mathematics (ICT application) to support mathematics teaching and learning. There is a need to provide effective ways that technology can be integrated into mathematics classrooms. Mathematical methods and techniques are typically used in engineering and industrial fields. It can also become an interdisciplinary subject motivated by engineers' needs. Mathematical problems in engineering result in rigorous engineering application carried out by mathematical tools. Therefore, a solid understanding and command of mathematical knowledge is very necessary. This chapter presents the introduction of currently available ICTs and their application of to create e-learning environments to prepare for the students' future engineering education.

scholarly journals Precision vs. Accuracy in Star Catalogs

1995 ◽  
Vol 166 ◽  
pp. 372-372
Author(s):  
L. G. Taff ◽  
J. E. Morrison ◽  
R. L. Smart
Keyword(s):  
Random Error ◽  
A Priori ◽  
Systematic Errors ◽  
A Posteriori ◽  
New Techniques ◽  
Star Catalog ◽  
True Value ◽  
Reduction Methods ◽  
Star Catalogs ◽  
Comparable Amplitude

As better precision is achieved and more sophisticated reduction methods are created previously invisible biases surface. This has been especially true in astrometric Schmidt plate work. The problem of their amelioration is not fully solved and precision per se is meaningless in the presence of poor accuracy of comparable amplitude. Continuing to benignly neglect this issue puts us in the position of standing on only one statistical leg. New techniques have been designed to further minimize systematic errors. Of especial interest to star catalog analysis is the method of infinitely overlapping circles (Taff, Bucciarelli & Lattanzi, ApJ 361, 667, 1990; Taff, Bucciarelli & Lattanzi, ApJ 392, 746 1992; Bucciarelli, Taff & Lattanzi, J. Stat. Comp. and Sim. 48, 29 1993). With it almost complete success has occurred with regard to the removal of systematic errors which creep into compilation catalogs as a result of inadequate treatment of catalog-to-catalog systematic errors; they can essentially be eliminated a priori or a posteriori (Bucciarelli, Lattanzi & Taff, in press in ApJ 1994; Taff & Bucciarelli, in press in ApJ 1994). What infinitely overlapping circles does can be briefly described as follows: Let X (x) be the measured (true) value of a standard coordinate, S(x,y) (ε) be the systematic (random) error in x at this point, let w∞ be the infinitely overlapping circle weight, a be the standard deviation of the random error in x, N be the total number of stars in this circle which has radius R, and x0,y0 be the coordinates of the center of this circle.

On a Maximality Property of Partition Regular Systems of Equations

1993 ◽  
Vol 36 (1) ◽  
pp. 96-102
Author(s):  
Hanno Lefmann ◽  
Hamza Si Kaddour
Keyword(s):  
Regular System ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Augmented System ◽  
Maximality Property ◽  
Finite Sums ◽  
New Variables

AbstractIn this note we will study the following problem. For a given partition regular system of equations, which equations can be added to this system without introducing new variables, such that the new augmented system is again partition regular. It turns that the Hindman system on finite sums as well as the Deuber-Hindman system on finite sums of (m, p, c)-sets are maximal in this sense.

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