Hypersatisfaction of quantifier free formulas in algebraic systems

2016 ◽  
Vol 09 (03) ◽  
pp. 1650057
Author(s):  
Dara Phusanga ◽  
Jintana Joomwong
Keyword(s):  
Algebraic System ◽  
Solid Model ◽  
Algebraic Systems ◽  
General Algebra

In [Hyperformulas and solid algebraic systems, Studia Logica 90(2) (2008) 263–286], the theory of hyperidentities and solid varieties (see [K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hyperidentities, hyperequational classes, and clone congruences, in Contributions to General Algebra, Vol. 7 (Verlag Hölder-Pichler-Tempsky, Wien, 1991), pp. 97–118]) was extended to algebraic systems and solid model classes of algebraic system. In this paper, we will present a different approach which is based on the concept of the term operations and the realization of quantifier free formulas.

n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules

2020 ◽  
pp. 81-95
Author(s):  
admin admin ◽  
Keyword(s):  
Algebraic System ◽  
Algebraic Systems

Refining the indeterminate I into many levels of indeterminacy is a way to explore many neutrosophic algebraic structures.This paper introduces the concept of n-cyclic refined algebraic system of sub-indeterminacies as a new way to refine a neutrosophic indeterminate I. This idea will be used to introduce the notion of n-cyclic refined neutrosophic ring and to study its AH-substructures. Also, this work presents the concept of n-cyclic refined neutrosophic modules with many related structures.

scholarly journals On Meromorphisms of Algebraic Systems

1966 ◽  
Vol 27 (2) ◽  
pp. 559-569 ◽  
Author(s):  
Junji Hashimoto
Keyword(s):  
Algebraic System ◽  
Algebraic Systems

In the present paper by an algebraic system (algebra) A we shall mean a system with a set F of operations fλ: (x1,…, xn) ∈ A × · · · × A → fλ(x1,…, xn) ∈ A. A polynomial p(x1, …, xr) is a function of variables x1,…, xr which is either one of the xi, or (recursively) a result of some operation fλ(p1,…, pn) performed on other polynomials pi. An algebra A may satisfy a set R of identities p(x1,…, xr) = q(x1,…, xs), and then A shall be called an (F, R)-algebra.

All idempotent and regular elements in the monoid of generalized hypersubstitutions for algebraic systems of type (2; 2)

2019 ◽  
pp. 2150015
Author(s):  
D. Phusanga ◽  
J. Joomwong ◽  
S. Jino ◽  
J. Koppitz
Keyword(s):  
The Other ◽  
Algebraic Systems ◽  
General Algebra ◽  
Regular Elements ◽  
Other Hand

There are two different concepts for hypersubstitutions for algebraic systems [K. Denecke and D. Phusanga, Hyperformulas and solid algebraic systems, Studia Logica 90(2) (2008) 263–286; J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. In this paper, we follow the more natural and practicable one given in [J. Koppitz and D. Phusanga, The monoid of hypersubstitutions for algebraic systems, J. Announcements Union Sci. Sliven 33(1) (2018) 120–127]. On the other hand, in [S. Leeratanavalee and K. Denecke, Generalized hypersubstitutions and strongly solid varieties, General Algebra and Applications[Formula: see text] Proc. of 59th Workshop on General Algebra[Formula: see text] 15th Conf. for Young Algebraists Potsdam 2000 (Shaker Verlag, 2000), pp. 135–145], the concept of the monoid of generalized hypersubstitutions was introduced. Following both ideas, one obtains the concept of a monoid of generalized hypersubstitutions for algebraic systems in a canonical way. The purpose of this paper is the study of the monoid of generalized hypersubstitutions for algebraic systems. We characterize the idempotent as well as regular elements in this monoid.

Some varieties of algebraic systems of type ((n),(m))

2019 ◽  
Vol 12 (01) ◽  
pp. 1950005
Author(s):  
D. Phusanga ◽  
J. Koppitz
Keyword(s):  
Algebraic System ◽  
Natural Numbers ◽  
Algebraic Systems ◽  
Term Operation ◽  
Type Formula

In the present paper, we classify varieties of algebraic systems of the type [Formula: see text], for natural numbers [Formula: see text] and [Formula: see text], which are closed under particular derived algebraic systems. If we replace in an algebraic system the [Formula: see text]-ary operation by an [Formula: see text]-ary term operation and the [Formula: see text]-ary relation by the [Formula: see text]-ary relation generated by an [Formula: see text]-ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.

H∞Control of Fractional Nonlinear Differential Systems

2014 ◽  
Vol 945-949 ◽  
pp. 2737-2740
Author(s):  
Li Li
Keyword(s):  
Control Strategy ◽  
Algebraic System ◽  
Structural Characteristics ◽  
Robust Controller ◽  
Differential Systems ◽  
Algebraic Systems ◽  
Differential Algebraic System ◽  
Fractional Differential ◽  
Fractional Control ◽  
Nonlinear Differential Systems

In this paper, the stabilization of nonlinear fractional differential algebraic system is constructed. The fractional nonlinear differential algebraic systems (FNDAS) in presence of disturbance, we construct a fractional control strategy. The proposed stabilization and robust controller effectively take advantage of the structural characteristics of FNDAS and is simple in form.

scholarly journals ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS

2019 ◽  
Vol 7 ◽  
Author(s):  
ZIYANG GAO
Keyword(s):  
Algebraic System ◽  
Shimura Varieties ◽  
Algebraic Systems

We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the logarithmic Ax theorem and the Ax-Lindemann theorem which we shall prove. All these bi-algebraic and transcendental results extend their counterparts for mixed Shimura varieties. In the end we briefly discuss the André–Oort and Zilber–Pink type problems for enlarged mixed Shimura varieties.

scholarly journals On finite approximations of topological algebraic systems

2007 ◽  
Vol 72 (1) ◽  
pp. 1-25 ◽  
Author(s):  
L. Yu. Glebsky ◽  
E. I. Gordon ◽  
C. Ward Henson
Keyword(s):  
Algebraic System ◽  
Nonstandard Analysis ◽  
Space Structures ◽  
Locally Compact ◽  
Algebraic Systems ◽  
Finite Approximations ◽  
Similar Characterization ◽  
Compact Field ◽  
Associative Rings

AbstractWe introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class . If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class of algebraic systems. One characterization of this concept states that A is locally embedded in iff it is a subsystem of an ultraproduct of systems from . In this paper we obtain a similar characterization of approximability of a locally compact system A by systems from using the language of nonstandard analysis.In the signature of A we introduce positive bounded formulas and their approximations; these are similar to those introduced by Henson [14] for Banach space structures (see also [15, 16]). We prove that a positive bounded formula φ holds in A if and only if all precise enough approximations of φ hold in all precise enough approximations of A.We also prove that a locally compact field cannot be approximated arbitrarily closely by finite (associative) rings (even if the rings are allowed to be non-commutative). Finite approximations of the field ℝ can be considered as possible computer systems for real arithmetic. Thus, our results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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