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 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.

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.

EFFECT OF ELEVATED TEMPERATURE ON CONCRETE STRUCTURES BY BOUNDARY ELEMENTS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240014 ◽  
Author(s):  
PETR P. PROCHAZKA ◽  
TAT S. LOK
Keyword(s):  
Elevated Temperature ◽  
Boundary Element Method ◽  
Nonlinear System ◽  
Time Dependent ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear System ◽  
Long Time ◽  
Large Systems

Extreme elevation of temperature principally threatens tunnel linings and may cause fatal disaster; the recovery of it may take a long time and significant traffic troubles. System of equations is to be described and solution in terms of boundary element method (BEM) is suggested. Moreover, a technique of time-dependent eigenparameters enables one to apply parallel computations and converts the strongly nonlinear system to pseudo-linear one using the influence and polarization tensors. Consequently, instead of repeated solution of large systems of equations, the multiplication of pre-calculated influence matrices has to be carried out instead. In order to properly create the above-outlined procedure, internal cells are selected in the regions primarily connected by the change of temperature. Some examples follow the theory.

scholarly journals New iterative methods for dense linear systems

2021 ◽  
Vol 293 ◽  
pp. 02013
Author(s):  
Jinmei Wang ◽  
Lizi Yin ◽  
Ke Wang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Iterative Methods ◽  
Parallel Implementation ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Linear System Of Equations ◽  
Dense Linear System ◽  
Linear Systems Of Equations

Solving dense linear systems of equations is quite time consuming and requires an efficient parallel implementation on powerful supercomputers. Du, Zheng and Wang presented some new iterative methods for linear systems [Journal of Applied Analysis and Computation, 2011, 1(3): 351-360]. This paper shows that their methods are suitable for solving dense linear system of equations, compared with the classical Jacobi and Gauss-Seidel iterative methods.

scholarly journals On some classes of coefficient inverse problems for parabolic systems of equations with the ovedetermination date of evolutionary type

2015 ◽  
Vol 11 (3) ◽  
pp. 51-57
Author(s):  
Ekaterina M Korotkova
Keyword(s):  
Inverse Problems ◽  
Parabolic System ◽  
Local Existence ◽  
Parabolic Systems ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Local Existence Theorem ◽  
Coefficient Inverse Problems ◽  
Boundary Operators ◽  
Parabolic System Of Equations

The article is devoted to the question of wellposedness in the Sobolev spaces of inverse problems on determining the righthand side and coefficients in a parabolic system of equations. The overdetermination conditions are the values of a part of the vector of solutions on some system of surfaces. Under special conditions on the boundary operators the local existence theorem of solutions to the problem is established.

My Equations Are the Same as Yours!

2012 ◽  
pp. 259-273
Author(s):  
M Badger ◽  
C J Sangwin
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Computer Aided ◽  
Two Systems

In this chapter we explain how computer aided assessment (CAA) can automatically assess an answer that consists of a system of equations. In particular, we will use a computer algebra system (CAS) and Buchberger’s Algorithm to establish when two systems of equations are the “same.”

The effective ellipsoid: a method for calculating the permittivity of composites with multilayer ellipsoids

2018 ◽  
Vol 25 (5) ◽  
pp. 1031-1038
Author(s):  
Liming Yuan ◽  
Yonggang Xu ◽  
Fei Dai ◽  
Deyuan Zhang
Keyword(s):  
Boundary Condition ◽  
Linear System ◽  
Effective Permittivity ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Linear System Of Equations ◽  
Consistent Approximation ◽  
Self Consistent ◽  
Linear Systems Of Equations ◽  
Good Agreement

AbstractIn order to calculate the effective permittivity of a mixture with multilayer ellipsoids, this paper presents a self-consistent approximation (SCA) on the basis of the Bruggeman’s analytical model. The effective permittivity of a mixture with aligned multilayer ellipsoids is derived directly from the linear system of equations, which are built using the boundary condition of the electric field on the confocal ellipsoidal interface in the ellipsoidal coordinate system. Furthermore, for a mixture with multilayer ellipsoids oriented randomly, an effective ellipsoid is introduced to substitute the original multilayer ellipsoid, and the permittivity of the effective ellipsoid is derived by jointly solving the two linear systems of equations for the situation of the original multilayer ellipsoid and that of the effective ellipsoid, then the effective permittivity of the mixture can be calculated by the existing Maxwell-Garnett formula. After comparisons, it is revealed that there is a good agreement between this SCA method and existing theories.

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.

scholarly journals Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Manuel F. Abad ◽  
Alicia Cordero ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Global Positioning System ◽  
Positioning System ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Nonlinear System Of Equations ◽  
Global Positioning ◽  
Order Four ◽  
Fifth Order

Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. Numerical comparisons are made with other existing second- and fourth-order schemes to solve the nonlinear system of equations of theGlobal Positioning Systemand some academic nonlinear systems.

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