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Статті в журналах з теми "Finite algebraic structures"

Автор: Grafiati

Опубліковано: 18 листопада 2023

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1

Aichinger, Erhard, Peter Mayr, and Ralph McKenzie. "On the number of finite algebraic structures." Journal of the European Mathematical Society 16, no. 8 (2014): 1673–86. http://dx.doi.org/10.4171/jems/472.

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2

Milani, Vida, Seyed M. H. Mansourbeigi, and Hossein Finizadeh. "Algebraic and topological structures on rational tangles." Applied General Topology 18, no. 1 (April 3, 2017): 1. http://dx.doi.org/10.4995/agt.2017.2250.

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<p>In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.</p>

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3

Campercholi, Miguel, Mauricio Tellechea, and Pablo Ventura. "Deciding Quantifier-free Definability in Finite Algebraic Structures." Electronic Notes in Theoretical Computer Science 348 (March 2020): 23–41. http://dx.doi.org/10.1016/j.entcs.2020.02.003.

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4

Levitskaya, A. A. "Systems of Random Equations over Finite Algebraic Structures." Cybernetics and Systems Analysis 41, no. 1 (January 2005): 67–93. http://dx.doi.org/10.1007/s10559-005-0042-7.

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5

Shevlyakov, Artyom N. "Direct powers of algebraic structures and equations." Prikladnaya Diskretnaya Matematika, no. 58 (2023): 31–39. http://dx.doi.org/10.17223/20710410/58/4.

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We study systems of equations over graphs, posets and matroids. We give the criteria when a direct power of such algebraic structures is equationally Noetherian. Moreover, we prove that any direct power of any finite algebraic structure is weakly equationally Noetherian.

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6

Laskowski, Michael C. "Mutually algebraic structures and expansions by predicates." Journal of Symbolic Logic 78, no. 1 (March 2013): 185–94. http://dx.doi.org/10.2178/jsl.7801120.

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AbstractWe introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion (M, A) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.

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7

Lin, Zhe, Mihir Kumar Chakraborty, and Minghui Ma. "Residuated Algebraic Structures in the Vicinity of Pre-rough Algebra and Decidability." Fundamenta Informaticae 179, no. 3 (April 15, 2021): 239–74. http://dx.doi.org/10.3233/fi-2021-2023.

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Varieties of topological quasi-Boolean algebras in the vicinity of pre-rough algebras [28, 29] are expanded to residuated algebraic structures by introducing a new implication operation and its residual in these structures. Sequent calculi for some classes of residuated algebraic structures are established. These sequent calculi have the strong finite model property which yields the decidability of the word problem for corresponding classes of algebraic structures.

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8

García, Darío, Dugald Macpherson, and Charles Steinhorn. "Pseudofinite structures and simplicity." Journal of Mathematical Logic 15, no. 01 (June 2015): 1550002. http://dx.doi.org/10.1142/s0219061315500026.

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We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted.

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9

Rybalov, Alexander. "On generic complexity of theories of finite algebraic structures." Journal of Physics: Conference Series 1901, no. 1 (May 1, 2021): 012046. http://dx.doi.org/10.1088/1742-6596/1901/1/012046.

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10

Hambleton, Ian, and Matthias Kreck. "Smooth structures on algebraic surfaces with finite fundamental group." Inventiones Mathematicae 102, no. 1 (December 1990): 109–14. http://dx.doi.org/10.1007/bf01233422.

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11

Farsi, Carla, and Christopher Seaton. "Algebraic Structures Associated to Orbifold Wreath Products." Journal of K-Theory 8, no. 2 (August 3, 2010): 323–38. http://dx.doi.org/10.1017/is010006009jkt121.

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AbstractWe present structure theorems in terms of inertial decompositions for the wreath product ring of an orbifold presented as the quotient of a smooth, closed manifold by a compact, connected Lie group acting almost freely. In particular we show that this ring admits λ-ring and Hopf algebra structures both abstractly and directly. This generalizes results known for global quotient orbifolds by finite groups.

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12

Markhabatov, N. D. "APPROXIMATIONS OF THE THEORIES OF STRUCTURES WITH ONE EQUIVALENCE RELATION." Herald of the Kazakh-British technical university 20, no. 2 (July 2, 2023): 67–72. http://dx.doi.org/10.55452/1998-6688-2023-20-2-67-72.

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Анотація:

Recently, various methods similar to the “transfer principle” have been rapidly developing, where one property of a structure or pieces of this structure is satisfied in all infinite structures or in another algebraic structure. Such methods include smoothly approximable structures, holographic structures, almost sure theories, and pseudofinite structures approximable by finite structures. Pseudofinite structures are mathematical structures that resemble finite structures but are not actually finite. They are important in various areas of mathematics, including model theory and algebraic geometry. Pseudofinite structures are a fascinating area of mathematical logic that bridge the gap between finite and infinite structures. They allow studying infinite structures in ways that resemble finite structures, and they provide a connection to various other concepts in model theory. Further studying pseudofinite structures will continue to reveal new insights and applications in mathematics and beyond. Pseudofinite theory is a branch of mathematical logic that studies structures that are similar in some ways to finite structures, but can be infinitely large in other ways. It is an area of research that lies at the intersection of model theory and number theory and deals with infinite structures that share some properties with finite structures, such as having only finitely many elements up to isomorphism. A. Lachlan introduced the concept of smoothly approximable structures in order to change the direction of analysis from finite to infinite, that is, to classify large finite structures that seem to be smooth approximations to an infinite limit. The theory of pseudofinite structures is particularly relevant for studying equivalence relations. In this paper, we study the model-theoretic property of the theory of equivalence relations, in particular, the property of smooth approximability. Let L = {E}, where Е is an equivalence relation. We prove that an any ω-categorical L-structure M is smoothly approximable. We also prove that any infinite L-structure M is pseudofinite.

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13

Evans, David M., та M. E. Pantano. "ℵ0-categorical structures with arbitrarily fast growth of algebraic closure". Journal of Symbolic Logic 67, № 3 (вересень 2002): 897–909. http://dx.doi.org/10.2178/jsl/1190150137.

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Анотація:

Various results have been proved about growth rates of certain sequences of integers associated with infinite permutation groups. Most of these concern the number of orbits of the automorphism group of an ℵ0-categorical structure on the set of unordered n-subsets or on the set of n-tuples of elements of . (Recall that by the Ryll-Nardzewski Theorem, if is countable and ℵ0-categorical, the number of the orbits of its automorphism group Aut() on the set of n-tuples from is finite and equals the number of complete n-types consistent with the theory of .) The book [Ca90] is a convenient reference for these results. One of the oldest (in the realms of ‘folklore’) is that for any sequence (Kn)n∈ℕ of natural numbers there is a countable ℵ0-categorical structure such that the number of orbits of Aut() on the set of n-tuples from is greater than kn for all n.These investigations suggested the study of the growth rate of another sequence. Let be an ℵ0-categorical structure and X be a finite subset of . Let acl(X) be the algebraic closure of X, that is, the union of the finite X-definable subsets of . Equivalently, this is the union of the finite orbits on of Aut()(X), the pointwise stabiliser of X in Aut(). Define

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14

Matrassulova, Dinara Kutlimuratovna, Yelizaveta Sergeevna Vitulyova, Sergey Vladimirovich Konshin, and Ibragim Esenovich Suleimenov. "Algebraic fields and rings as a digital signal processing tool." Indonesian Journal of Electrical Engineering and Computer Science 29, no. 1 (January 1, 2022): 206. http://dx.doi.org/10.11591/ijeecs.v29.i1.pp206-216.

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It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as a model of a signal reduced to a discrete form. A special case of such a signal model are functions that take values in Galois fields. It is shown that, along with Galois fields, in certain cases, algebraic rings contain zero divisors can be used to construct signal models. This representation is convenient because in this case it becomes possible to independently operate with the digits of the number that enumerates the signal levels. A simple and intuitive method for constructing rings is proposed, based on an analogy with the method of algebraic extensions.

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15

Mude, Lao Hussein, Owino Maurice Oduor, and Ojiema Michael Onyango. "Automorphisms of Zero Divisor Graphs of Power Four Radical Zero Completely Primary Finite Rings." Asian Research Journal of Mathematics 19, no. 8 (June 19, 2023): 108–13. http://dx.doi.org/10.9734/arjom/2023/v19i8693.

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Let R be a commutative unital finite rings and Z(R) be its set of zero divisors. The study of automorphisms of algebraic structures via zero divisor graphs is still an active area of research. Perhaps, because of the fact that automorphisms have got real life application in capturing the symmetries of algebraic structures. In this study, the automorphisms zero divisor graphs of such rings in which the product of any four zero divisor is zero has been determined.

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16

Ayoub, Ettaki, Elomary Mohamed Abdou, and Mamouni My Ismail. "On the Finite Presentation of Operads." WSEAS TRANSACTIONS ON SYSTEMS 22 (June 19, 2023): 622–35. http://dx.doi.org/10.37394/23202.2023.22.63.

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Operads were introduced to describe compositional structures arising in algebraic topology. Recently, some researches were interested in using operads in applied mathematics, to model composition of structures in logic, databases, and dynamical systems. In, we focus on finite presentation of an operad and its associated algebra. More precisely, we prove the general result stating that if an operad O has a finite presentation, then the associate O-algebra has also a corresponding one. Some application in physics, especially in wiring diagrams will be discussed.

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17

Schmitt, William R. "Hopf Algebras of Combinatorial Structures." Canadian Journal of Mathematics 45, no. 2 (April 1, 1993): 412–28. http://dx.doi.org/10.4153/cjm-1993-021-5.

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AbstractA generalization of the definition of combinatorial species is given by considering functors whose domains are categories of finite sets, with various classes of relations as moronisms. Two cases in particular correspond to species for which one has notions of restriction and quotient of structures. Coalgebras and/or Hopf algebras can be associated to such species, the duals of which provide an algebraic framework for studying invariants of structures.

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18

Chiaselotti, G., T. Gentile, and F. Infusino. "Local dissymmetry on graphs and related algebraic structures." International Journal of Algebra and Computation 29, no. 08 (October 24, 2019): 1499–526. http://dx.doi.org/10.1142/s0218196719500607.

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We use the set symmetric difference between vertex subsets of a finite undirected simple graph [Formula: see text] to define a binary operation ∘ on the vertex set of a new graph [Formula: see text], that contains [Formula: see text] as subgraph and whose vertices are non-empty vertex subsets of [Formula: see text]. We show how the binary operation ∘ determines an algebraic structure on [Formula: see text] that is strictly related to the graph structure of [Formula: see text]. In fact, we show that [Formula: see text] agrees with [Formula: see text] and, next, we provide several characterizations for the algebraic structure [Formula: see text] when the graph [Formula: see text] is connected and locally dissymmetric.

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19

Wencel, Roman. "Small theories of Boolean ordered o-minimal structures." Journal of Symbolic Logic 67, no. 4 (December 2002): 1385–90. http://dx.doi.org/10.2178/jsl/1190150291.

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AbstractWe investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are ℵ0-categorical. We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.

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20

Ejima, Ojonugwa, Abor Isa Garba, and Kazeem Olalekan Aremu. "Subgroup Graphs of Finite Groups." International Journal of Applied Sciences and Smart Technologies 3, no. 2 (December 31, 2021): 225–40. http://dx.doi.org/10.24071/ijasst.v3i2.3765.

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Let G be a fnite group with the set of subgroups of G denoted by S(G), then the subgroup graphs of G denoted by T(G) is a graph which set of vertices is S(G) such that two vertices H, K in S(G) (H not equal to K)are adjacent if either H is a subgroup of K or K is a subgroup of H. In this paper, we introduce the Subgroup graphs T associated with G. We investigate some algebraic properties and combinatorial structures of Subgroup graph T(G) and obtain that the subgroup graph T(G) of G is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups. Let be a finite group with the set of subgroups of denoted by , then the subgroup graphs of denoted by is a graph which set of vertices is such that two vertices , are adjacent if either is a subgroup of or is a subgroup of . In this paper, we introduce the Subgroup graphs associated with . We investigate some algebraic properties and combinatorial structures of Subgroup graph and obtain that the subgroup graph of is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups.

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21

Akra, U. P., O. E. Ntekim, R. S. Ndah, and A. C. Etim. "Evaluation of Some Algebraic Structures in Balanced Incomplete Block Design." African Journal of Mathematics and Statistics Studies 6, no. 4 (September 22, 2023): 34–43. http://dx.doi.org/10.52589/ajmss-tqisir8c.

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Balanced incomplete block design is an incomplete block design in which any two varieties appear together an equal number of times. In algebra, the existence of block design is closely related to balanced incomplete block design. To ascertain the claim, this research aim to employ some algebraic structures to examine whether or not balanced incomplete block design is related to the above statement. The methods adopted are finite group, ring and field algebra. The result shows that balanced incomplete block design (BIBD) cannot form a finite group under multiplication binary operation, but it is for additive case. It is also revealed that balanced incomplete block design is not a field algebra in both binary operations no matter the size of the design, but it is a ring in all cases. In conclusion, BIBD of the form (X,B) is a semigroup, commutative group, semiring, commutative ring and subfield in both binary operations. Several theorems with proofs have been established in harmony with the algebraic structure mentioned above.

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22

Shah, Dawood, and Tariq Shah. "A novel discrete image encryption algorithm based on finite algebraic structures." Multimedia Tools and Applications 79, no. 37-38 (July 31, 2020): 28023–42. http://dx.doi.org/10.1007/s11042-020-09182-0.

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23

Glebsky, L. Yu, E. I. Gordon, and C. Ward Henson. "On finite approximations of topological algebraic systems." Journal of Symbolic Logic 72, no. 1 (March 2007): 1–25. http://dx.doi.org/10.2178/jsl/1174668381.

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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.

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24

BERGMAN, CLIFFORD, DAVID JUEDES, and GIORA SLUTZKI. "COMPUTATIONAL COMPLEXITY OF TERM-EQUIVALENCE." International Journal of Algebra and Computation 09, no. 01 (February 1999): 113–28. http://dx.doi.org/10.1142/s0218196799000084.

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Two algebraic structures with the same universe are called term-equivalent if they have the same clone of term operations. We show that the problem of determining whether two finite algebras of finite similarity type are term-equivalent is complete for deterministic exponential time.

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25

Protasov, I., and K. Protasova. "Coarse structures on groups defined by conjugations." Algebra and Discrete Mathematics 32, no. 1 (2021): 65–75. http://dx.doi.org/10.12958/adm1737.

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For a group G, we denote by G↔ the coarse space on G endowed with the coarse structure with the base {{(x,y)∈G×G:y∈xF}:F∈[G]<ω}, xF={z−1xz:z∈F}. Our goal is to explore interplays between algebraic properties of G and asymptotic properties of G↔. In particular, we show that asdim G↔=0 if and only if G/ZG is locally finite, ZG is the center of G. For an infinite group G, the coarse space of subgroups of G is discrete if and only if G is a Dedekind group.

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26

NELSON, SAM, and EMILY WATTERBERG. "BIRACK DYNAMICAL COCYCLES AND HOMOMORPHISM INVARIANTS." Journal of Algebra and Its Applications 12, no. 08 (July 31, 2013): 1350049. http://dx.doi.org/10.1142/s0219498813500497.

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Biracks are algebraic structures related to knots and links. We define a new enhancement of the birack counting invariant for oriented knots and links via algebraic structures called birack dynamical cocycles. The new invariants can also be understood in terms of partitions of the set of birack labelings of a link diagram determined by a homomorphism p : X → Y between finite labeling biracks. We provide examples to show that the new invariant is stronger than the unenhanced birack counting invariant and examine connections with other knot and link invariants.

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27

Mainhardt, Gunther. "P versus NP and computability theoretic constructions in complexity theory over algebraic structures." Journal of Symbolic Logic 69, no. 1 (March 2004): 39–64. http://dx.doi.org/10.2178/jsl/1080938824.

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AbstractWe show that there is a structure of countably infinite signature with P = N2P and a structure of finite signature with P = N1P and N1P ≠ N2P. We give a further example of a structure of finite signature with P ≠ N1P and N1P ≠ N1P. Together with a result from [10] this implies that for each possibility of P versus NP over structures there is an example of countably infinite signature. Then we show that for some finite the class of -structures with P = N1P is not closed under ultraproducts and obtain as corollaries that this class is not ∆-elementary and that the class of -structures with P ≠ N1P is not elementary. Finally we prove that for all ƒ dominating all polynomials there is a structure of finite signature with the following properties: P ≠ N1P, N1P ≠ N2P, the levels N2TIME(ni) of N2P and the levels N1TIME(ni) of N1P are different for different i, indeed DTIME(ni′) ⊈ N2TIME(ni) if i ′ > i; DTIME(ƒ) ⊈ N2P, and N2P ⊈ DEC. DEC is the class of recognizable sets with recognizable complements. So this is an example where the internal structure of N2P is analyzed in a more detailed way. In our proofs we use methods in the style of classical computability theory to construct structures except for one use of ultraproducts.

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28

Arnold, Douglas N., Richard S. Falk, and Ragnar Winther. "Finite element exterior calculus, homological techniques, and applications." Acta Numerica 15 (May 2006): 1–155. http://dx.doi.org/10.1017/s0962492906210018.

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Анотація:

Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the PDE problem being solved. In the finite element exterior calculus, many finite element spaces are revealed as spaces of piecewise polynomial differential forms. These connect to each other in discrete subcomplexes of elliptic differential complexes, and are also related to the continuous elliptic complex through projections which commute with the complex differential. Applications are made to the finite element discretization of a variety of problems, including the Hodge Laplacian, Maxwell’s equations, the equations of elasticity, and elliptic eigenvalue problems, and also to preconditioners.

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29

Kovalenko, I. N., and A. A. Levitskaya. "Probabilistic properties of systems of random linear equations over finite algebraic structures." Cybernetics and Systems Analysis 29, no. 3 (1993): 385–90. http://dx.doi.org/10.1007/bf01125544.

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30

Planat, Michel, Haret C. Rosu, and Serge Perrine. "A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements." Foundations of Physics 36, no. 11 (November 14, 2006): 1662–80. http://dx.doi.org/10.1007/s10701-006-9079-3.

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31

Shevlyakov, A. "EQUATIONS OVER DIRECT POWERS OF ALGEBRAIC STRUCTURES IN RELATIONAL LANGUAGES." Prikladnaya Diskretnaya Matematika, no. 53 (2021): 5–11. http://dx.doi.org/10.17223/20710410/53/1.

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Анотація:

For a semigroup S (group G) we study relational equations and describe all semigroups S with equationally Noetherian direct powers. It follows that any group G has equationally Noetherian direct powers if we consider G as an algebraic structure of a certain relational language. Further we specify the results as follows: if a direct power of a finite semigroup S is equationally Noetherian, then the minimal ideal Ker(S) of S is a rectangular band of groups and Ker(S) coincides with the set of all reducible elements

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32

Shabat, George. "On the elliptic time in the adelic gravity." Facta universitatis - series: Physics, Chemistry and Technology 14, no. 3 (2016): 307–18. http://dx.doi.org/10.2298/fupct1603307s.

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Анотація:

The paper is devoted to the algebraic and arithmetic structures related to the two-body problem and discuss the possible generalizations. The role of the points of finite order on the elliptic curves is emphasized.

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33

MYASNIKOV, ALEXEI G., та MAHMOOD SOHRABI. "ω-STABILITY AND MORLEY RANK OF BILINEAR MAPS, RINGS AND NILPOTENT GROUPS". Journal of Symbolic Logic 82, № 2 (червень 2017): 754–77. http://dx.doi.org/10.1017/jsl.2016.29.

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Анотація:

AbstractIn this paper we study the algebraic structure of ω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

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34

Alcaraz, Ainhoa Berciano, Julio Rubio та Francis Sergeraert. "A case study of 𝐴∞-structure". gmj 17, № 1 (березень 2010): 57–77. http://dx.doi.org/10.1515/gmj.2010.003.

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Abstract The computer program Kenzo is used to study complex 𝐴∞-structures coming from iterated loop spaces. The methods of constructive algebraic topology, due to the authors, do produce chain complexes of finite type and chain equivalences with the Hopf algebras canonically associated to the loop spaces. These chain complexes of finite type are therefore endowed with 𝐴∞-structures. It is then experimentally observed, using the Kenzo program, that 𝐴∞-structures of arbitrarily high orders are nontrivial in these objects. This case study is a good illustration of the computing tools given to the topologists by the Kenzo program.

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35

Khimshiashvili, G., and R. Przybysz. "On Generalized Sklyanin Algebras." Georgian Mathematical Journal 7, no. 4 (December 2000): 689–700. http://dx.doi.org/10.1515/gmj.2000.689.

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Анотація:

Abstract A class of algebraic Poisson structures on R 4 is introduced which contains the well-known Sklyanin algebras. For this class, an effective algebraic method of computing Euler characteristics of Casimir levels is developed which enables us to compute them in the case of Sklyanin algebras. It is also shown that one may associate a finite graph with every generalized Sklyanin algebra. Some related results and open problems are also presented.

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36

T. G, ALABI. "Direct Product of Finite Abelian Group." International Journal of Applied Science and Research 05, no. 05 (2023): 166–73. http://dx.doi.org/10.56293/ijasr.2022.5443.

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Анотація:

In this project, finite abelian groups with some theoretical and algebraic structures are considered. The order of each group is factorized completely with factor of higher multiplicity where necessary. This unique factorization will allow for a way of building new groups and understanding a given group better. Essentially, it provides a way of relating the given group to the direct products of some of its subgroups. Finally, it also reveals how a group of a finite order is isomorphically related to one of the direct products satisfying certain relatively prime condition.

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37

Boukraa, Salah, and Jean-Marie Maillard. "Symmetries of Non-Linear ODEs: Lambda Extensions of the Ising Correlations." Symmetry 14, no. 12 (December 11, 2022): 2622. http://dx.doi.org/10.3390/sym14122622.

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Анотація:

This paper provides several illustrations of the numerous remarkable properties of the lambda extensions of the two-point correlation functions of the Ising model, shedding some light on the non-linear ODEs of the Painlevé type they satisfy. We first show that this concept also exists for the factors of the two-point correlation functions focusing, for pedagogical reasons, on two examples, namely C(0,5) and C(2,5) at ν=−k. We then display, in a learn-by-example approach, some of the puzzling properties and structures of these lambda extensions: for an infinite set of (algebraic) values of λ these power series become algebraic functions, and for a finite set of (rational) values of lambda they become D-finite functions, more precisely polynomials (of different degrees) in the complete elliptic integrals of the first and second kind K and E. For generic values of λ these power series are not D-finite, they are differentially algebraic. For an infinite number of other (rational) values of λ these power series are globally bounded series, thus providing an example of an infinite number of globally bounded differentially algebraic series. Finally, taking the example of a product of two diagonal two-point correlation functions, we suggest that many more families of non-linear ODEs of the Painlevé type remain to be discovered on the two-dimensional Ising model, as well as their structures, and in particular their associated lambda extensions. The question of their possible reduction, after complicated transformations, to Okamoto sigma forms of Painlevé VI remains an extremely difficult challenge.

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38

Xia, Changchun. "On the finite embeddability property for quantum B-algebras." Mathematica Slovaca 69, no. 4 (August 27, 2019): 721–28. http://dx.doi.org/10.1515/ms-2017-0263.

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Анотація:

Abstract After the establishment of the finite embeddability property for integral and commutative residuated ordered monoids by Blok and Van Alten in 2002, the finite embeddability property for some other types of residuated ordered algebraic structures have been extensively studied. The main purpose of this paper is to construct a finite quantale X̂F from a finite partial subalgebra F of an increasing quantum B-algebra X so that F can be embedded into X̂F, that is, the class of increasing quantum B-algebras has the finite embeddability property.

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39

Hrushovski, Ehud, and James Loveys. "Strongly and co-strongly minimal abelian structures." Journal of Symbolic Logic 75, no. 2 (June 2010): 442–58. http://dx.doi.org/10.2178/jsl/1268917489.

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AbstractWe give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems:1. when the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case);2. when the theory of the structure is strongly minimal.In the first case, we identify the abelian structure as a “near-subspace” A of a vector space V over a division ring D with its induced structure, with possibly some collection of distinguished subgroups of A of finite index in A and (up to acl(∅)) no further structure. In the second, the structure is that of V/A for a vector space and near-subspace as above, with the only further possible structure some collection of distinguished points. Here a near-subspace of V is a subgroup A such that for any nonzero d ∈ D. the index of A ∩ dA, in A is finite. We also show that any weakly minimal abelian structure is a reduct of a weakly minimal module.

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40

Schwidefsky, Marina, and Anna Zamojska-Dzienio. "Lattices of subclasses. II." International Journal of Algebra and Computation 24, no. 08 (December 2014): 1099–126. http://dx.doi.org/10.1142/s0218196714500489.

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Анотація:

We prove that the class K(σ) of all algebraic structures of signature σ is Q-universal if and only if there is a class K ⊆ K(σ) such that the problem whether a finite lattice embeds into the lattice of K-quasivarieties is undecidable.

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41

Ebas, Nur Ain, Nor Shamsidah Amir Hamzah, Kavikumar Jacob, and Mohd Saifullah Rusiman. "Fuzzy Finite Switchboard Automata with Complete Residuated Lattices." International Journal of Engineering & Technology 7, no. 4.30 (November 30, 2018): 160. http://dx.doi.org/10.14419/ijet.v7i4.30.22099.

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The theory of fuzzy finite switchboard automata (FFSA) is introduced by the use of general algebraic structures such as complete residuated lattices in order to enhance the process ability of FFSA. We established the notion of homomorphism, strong homomorphism and reverse homomorphism and shows some of its properties. The subsystem of FFSA is studied and the set of switchboard subsystem-forms a complete -sublattices is shown. The algorithm of FFSA with complete residuated lattices is given and an example is provided.

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42

Beygi, M., S. Namazi, and H. Sharif. "Algebraic Structures of Constacyclic Codes Over Finite Chain Rings and Power Series Rings." Iranian Journal of Science and Technology, Transactions A: Science 43, no. 5 (June 14, 2019): 2461–76. http://dx.doi.org/10.1007/s40995-019-00722-4.

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43

GECK, MEINOLF. "Some applications of CHEVIE to the theory of algebraic groups." Carpathian Journal of Mathematics 27, no. 1 (2011): 64–94. http://dx.doi.org/10.37193/cjm.2011.01.07.

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The computer algebra system CHEVIE is designed to facilitate computations with various combinatorial structures arising in Lie theory, like finite Coxeter groups and Hecke algebras. We discuss some recent examples where CHEVIE has been helpful in the theory of algebraic groups, in questions related to unipotent classes, the Springer correspondence and Lusztig families.

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44

Cheng, Eugenia. "Distributive laws for Lawvere theories." Compositionality 2 (May 25, 2020): 1. http://dx.doi.org/10.32408/compositionality-2-1.

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Distributive laws give a way of combining two algebraic structures expressed as monads; in this paper we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches, involving profunctors, monoidal profunctors, an extension of the free finite-product category 2-monad from Cat to Prof, and factorisation systems respectively. We exhibit comparison functors between CAT and each of these new frameworks to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The different but equivalent formulations then provide, between them, a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws.

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45

Berak, E. G., and J. C. Gerdeen. "A Finite Element Technique for Limit Analysis of Structures." Journal of Pressure Vessel Technology 112, no. 2 (May 1, 1990): 138–44. http://dx.doi.org/10.1115/1.2928599.

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Анотація:

Limit analysis provides an alternative to incremental elastic-plastic analysis for determining a limit load. The limit load is obtained from the lower and upper-bound theorems. These theorems, which are based on variational principles, establish the static and kinematic methods, respectively, and are particularly attractive for finite element implementation. A finite element approach using the definition of the p-norm is developed for calculating upper and lower bounds of the limit load multiplier for two-dimensional, rigid perfectly plastic structures which obey the von Mises yield criterion. Displacement and equilibrium building block quadrilateral elements are used in these dual upper and lower-bound formulations, respectively. The nonlinear finite element equations are transformed into systems of linear algebraic equations during the iteration process, and the solution vectors are determined using a frontal equation solver. The upper and lower-bound solutions are obtained in a reasonable number of iteration steps, and provide a good estimate of the limit load multiplier. Numerical results are provided to demonstrate this finite element procedure. In addition, this procedure is particularly applicable to the solution of complex problems using parallel processing on a supercomputer.

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46

KOPONEN, VERA. "ON CONSTRAINTS AND DIVIDING IN TERNARY HOMOGENEOUS STRUCTURES." Journal of Symbolic Logic 83, no. 04 (December 2018): 1691–721. http://dx.doi.org/10.1017/jsl.2018.61.

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Анотація:

AbstractLet ${\cal M}$ be ternary, homogeneous and simple. We prove that if ${\cal M}$ is finitely constrained, then it is supersimple with finite SU-rank and dependence is k-trivial for some k < ω and for finite sets of real elements. Now suppose that, in addition, ${\cal M}$ is supersimple with SU-rank 1. If ${\cal M}$ is finitely constrained then algebraic closure in ${\cal M}$ is trivial. We also find connections between the nature of the constraints of ${\cal M}$, the nature of the amalgamations allowed by the age of ${\cal M}$, and the nature of definable equivalence relations. A key method of proof is to “extract” constraints (of ${\cal M}$) from instances of dividing and from definable equivalence relations. Finally, we give new examples, including an uncountable family, of ternary homogeneous supersimple structures of SU-rank 1.

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47

MILLIET, CÉDRIC. "GROUPES FINS." Journal of Symbolic Logic 79, no. 4 (December 2014): 1120–32. http://dx.doi.org/10.1017/jsl.2014.12.

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AbstractWe investigate some common points between stable structures and weakly small structures and define a structureMto befineif the Cantor-Bendixson rank of the topological space${S_\varphi }\left( {dc{l^{eq}}\left( A \right)} \right)$is an ordinal for every finite subsetAofMand every formula$\varphi \left( {x,y} \right)$wherexis of arity 1. By definition, a theory isfineif all its models are so. Stable theories and small theories are fine, and weakly minimal structures are fine. For any finite subsetAof a fine groupG, the traces on the algebraic closure$acl\left( A \right)$ofAof definable subgroups ofGover$acl\left( A \right)$which are boolean combinations of instances of an arbitrary fixed formula can decrease only finitely many times. An infinite field with a fine theory has no additive nor multiplicative proper definable subgroups of finite index, nor Artin-Schreier extensions.

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48

Richter, Wolf-Dieter. "On Complex Numbers in Higher Dimensions." Axioms 11, no. 1 (January 7, 2022): 22. http://dx.doi.org/10.3390/axioms11010022.

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Анотація:

The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is continued here in dimension four and above. To this end, the notions of geometric vector product and geometric exponential function are extended to arbitrary finite dimensions and some usual algebraic rules known from usual complex numbers are replaced with new ones. An application for the construction of directional probability distributions is presented.

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49

QUICK, MARTYN, and N. RUŠKUC. "GROWTH OF GENERATING SETS FOR DIRECT POWERS OF CLASSICAL ALGEBRAIC STRUCTURES." Journal of the Australian Mathematical Society 89, no. 1 (August 2010): 105–26. http://dx.doi.org/10.1017/s1446788710001473.

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Анотація:

AbstractFor an algebraic structure A denote byd(A) the smallest size of a generating set for A, and letd(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequenced(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite thend(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes thend(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.

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50

Kruis, J., T. Koudelka, and T. Krejcˇí. "Multi-Physics Analyses of Selected Civil Engineering Concrete Structures." Communications in Computational Physics 12, no. 3 (September 2012): 885–918. http://dx.doi.org/10.4208/cicp.031110.080711s.

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AbstractThis paper summarizes suitable material models for creep and damage of concrete which are coupled with heat and moisture transfer. The fully coupled approach or the staggered coupling is assumed. Governing equations are spatially dis-cretized by the finite element method and the temporal discretization is done by the generalized trapezoidal method. Systems of non-linear algebraic equations are solved by the Newton method. Development of an efficient and extensible computer code based on the C++ programming language is described. Finally, successful analyses of two real engineering problems are described.

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