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In this paper, we generalize the main results of Guo and Isaacs, Archiv der Mathematik 105 (2015) 215-222. We also obtain some criteria for -nilpotency of a finite group. [ABSTRACT FROM AUTHOR]

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [ABSTRACT FROM AUTHOR]

In an earlier paper, we defined a degree stable Lie algebra, and determined the Lie algebra automorphism group AutLie(S+(2)) of the Lie algebra S+(2). In this paper, we determine the Lie algebra automorphism group AutLie(S(1,0,2)) of the Lie algebra S(1,0,2). [ABSTRACT FROM AUTHOR]

In this paper, some methods are given to construct dipolarizations in Kac–Moody algebras as well as their some subalgebras, and an illustrative example is provided. The dipolarizations found in this paper include symmetric and non-symmetric ones. [ABSTRACT FROM AUTHOR]

This is a reply to Ramon Ferrer-I-Cancho's paper in this issue "Some Word Order Biases from Limited Brain Resources: A Mathematical Approach." In this reply, I challenge the Euclidean distance model proposed in that paper by proposing a simple alternative model based on linear ordering. [ABSTRACT FROM AUTHOR]

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin–Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even "small" spanning sets of these spaces. In this paper, we prove presentations of the principal subspaces of the basic $A_{1}^{(1)}$-modules. These convenient presentations were previously used in work of Capparelli–Lepowsky–Milas for the purpose of obtaining the classical Rogers–Ramanujan recursion for the graded dimensions of the principal subspaces. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous work [10]. By GAERS-1, we denote the class of generalized abelian exchange rings with stable range 1. In this paper, we first prove that for any ring R ∈ GAERS-1 and any ideal I of R, K0(R/I) is an archimedean ℓ-group, which is a natural generalization of [10, Theorem 5.3]. As applications, we establish explicit characterizations for the K0-simplicity of such rings in the sense of [3], and investigate the norm completeness of their K0-groups. Finally, we characterize the primitive idempotents in R by K0(R) with ordered structure, from which we can further determine completely the structure of K0(R). [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that, for some parameters, a two-dimensional cardiovascular system model can exhibit intrinsic equilibrium multiplicity generated by a backward bifurcation, regardless of the baroreflex effect. The model considers the dynamics of arterial and venous compartments and a feedback effect in the stroke volume induced by venous pressure changes. The results of the mathematical analysis indicate that multiple non-trivial equilibrium points exist when the stroke volume function is convex around the origin. Interestingly, this equilibrium point structure would imply that under certain stroke volume functions, the baroreflex system would have to stabilize and regulate an unstable operating condition produced by certain values of the stroke volume. The paper ends with the discussion of some implications for the reliability and robustness of the baroreflex-feedback mechanism. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a model of urban dynamics, which was proposed by Miyata and Yamaguchi in the context of a region of Japan. The model is a complex system of first-order nonlinear ordinary differential equations. The study undertaken by Miyata and Yamaguchi is essentially computational, while an extensive study of the asymptotic behavior of the solutions is performed in this paper related to a detailed analysis of the qualitative properties of the system. [ABSTRACT FROM AUTHOR]

In a recent paper, Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Büchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length ω2. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length ω2 are Büchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wöhrle, showing that it is undecidable whether a Büchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). [ABSTRACT FROM AUTHOR]

For any C¹ differential system S on a compact Riemannian manifold M of dimension d with d ≥= 2, this paper studies the Liao style numbers, κ(S) (or respectively, κ*(S)) of S from the view-point of ergodic theory. Here κ(S) (κ* (S)) is the largest number of moving vectors (or respectively, conjugate-) of the differential system S that are mean linearly independent. For any ergodic measure v of S, two positive integers κ* (v) and κ(v), called the reduced and non-reduced style number of v respectively, are introduced. The connection between the style numbers of the system (M, S) and ones of the ergodic system (M, S; v) are discovered by the variational principle of style number proved in the paper. Several characterization theorems with respect to the style numbers κ* (S), κ*(v), κ(S) and κ(v) are presented respectively. [ABSTRACT FROM AUTHOR]

The structure of groups in which many subgroups have a certain property χ has been investigated for several choices of the property χ. In particular, groups whose non-normal subgroups are supersoluble are studied in this paper. Moreover, groups with only finitely many normalizers of non-supersoluble groups are considered. [ABSTRACT FROM AUTHOR]

Fix , let be the loop Lie algebra over with basis and relations , where . In this paper, a formal distribution Lie algebra of is constructed. Then the associated conformal algebra is studied, where has a -basis with -brackets and . In particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules. [ABSTRACT FROM AUTHOR]

In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient condition is given for the graded path category to admit a DG category structure. [ABSTRACT FROM AUTHOR]

An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A=AI and B=BI, if 2A ≅ A ⊕ B, then A ≅ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a ∈ 1+I satisfying (1-a)R ∝ r(a) is unit-regular, if and only if each a ∈ 1+I satisfying (1-a2)R ∝ r(a2) is unit-regular, if and only if each a ∈ 1+I satisfying R(1-a)R=R r(a) is unit-regular, if and only if each a ∈ 1+I satisfying R(1-a2)R=R r(a2) is unit-regular. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of non-weight modules for some algebras related to the Virasoro algebra: The algebra (a, b), the twisted deformative Schrödinger-Virasoro Lie algebras and the Schrödinger algebra. We study the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank 1 for these algebras. Moreover, the simplicities of these modules are determined. [ABSTRACT FROM AUTHOR]

In the present paper, the σ-derivations of ℂ[x±1,y±1] are determined, and their applications are considered. [ABSTRACT FROM AUTHOR]

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied. [ABSTRACT FROM AUTHOR]

Ramanujan's formula for the number r24(n) of representations of a positive integer n as a sum of 24 squares asserts that where and Ramanujan's function τ(n) is given by In this paper, we determine a class of formulae analogous to Ramanujan's formula for r24(n). [ABSTRACT FROM AUTHOR]

The unicyclic graph Cn,g obtained by appending a cycle Cg of length g to a pendent vertex of a path on n - g vertices is the lollipop graph on n vertices. In [Algebraic connectivity of lollipop graphs, Linear Algebra Appl.434 (2011) 2204–2210], Guo et al. proved that a(Cn,g-1) < a(Cn,g) for g ≥ 4, where a(Cn,g) is the algebraic connectivity of Cn,g. In this paper, we present a new approach which is quite different from that of Guo et al. in proving a(Cn,g-1) < a(Cn,g) for g ≥ 4. [ABSTRACT FROM AUTHOR]

In this paper we mainly study sporadic groups in terms of p-local rank, especially, the 2-local ranks of some sporadic groups are given. [ABSTRACT FROM AUTHOR]

In this short paper, it is proved that every pair of large positive odd integers satisfying some necessary conditions can be represented in the form of a pair of one prime, two prime squares and k powers of 2. In particular, we have k -- 332. [ABSTRACT FROM AUTHOR]

In this paper we establish interrelations between fuzzy direct revelation axiom (FDRA), fuzzy transitive-closure coherence axiom (FTCCA), fuzzy consistent-closure coherence axiom (FCCCA) and fuzzy intermediate congruence axiom (FICA). We also establish their relationships with weak fuzzy congruence axiom (WFCA), strong fuzzy congruence axiom (SFCA) and weak axiom of fuzzy revealed preference (WAFRP). Condition for equivalence of fuzzy Arrow axiom (FAA) and weak fuzzy congruence axiom (WFCA) on arbitrary domain is also given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce intuitionistic fuzzy derivative, intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative and some of their properties are studied. The relations between intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative are studied. [ABSTRACT FROM AUTHOR]

In this paper we define prime, strongly prime and semiprime k-bi-ideals of a hemiring. We also define their fuzzy versions and characterize hemirings by the properties of these k-bi-ideals. [ABSTRACT FROM AUTHOR]

A module M is called a dimension module if the Goldie (uniform) dimension satisfies the formula u(A + B) + u(A ∩ B) = u(A) + u(B) for arbitrary submodules A, B of M. Dimension modules and related notions were studied by several authors. In this paper, we study them in a more general context of modular lattices with 0 to which the notion of dimension modules can be extended in an obvious way. Some constructions available in the lattice theory framework make it possible to identify several new aspects concerning the nature of dimension lattices and modules as well as to describe a number of related properties. In particular we find a lattice which can be used to test whether a given lattice or a module satisfies the studied properties. Most of the results are obtained for lattices and then they are applied to modules. However the examples are given, when possible, in the more restrictive case of modules. [ABSTRACT FROM AUTHOR]

Let two nonperiodic binary morphisms ... be given. A word w is called a solution of g and h if g(w) = h(w). We say that a solution w is simple if whenever ... are prefixes of wu such that ... for some word z, then |u| = |u'| = k|w|, for some k ∈ N. In this paper we will study simple solutions and show that if a word w is a simple solution containing at least nine occurrences of the letter a and at least nine occurrences of the letter b, then either w = (ab)ia, or w = ajbk with gcd (j, k) = 1, up to the exchange of letters a and b. [ABSTRACT FROM AUTHOR]

In this paper we investigate the factorization of trinomials of the form xn + cxn-1 + d ∈ ℤ[x]. We then use these results about trinomials to prove results about the factorization of polynomials of the form xn + c(xn-1 +⋯+ x + 1) ∈ ℤ[x]. [ABSTRACT FROM AUTHOR]

Partially peripheral 3-manifolds and homologically peripheral 3-manifolds are defined by generalizing the notion of totally peripheral 3-manifolds. The aim of this paper is to provide a method for constructing hyperbolic links in 3-manifolds whose exteriors are not partially peripheral but homologically peripheral, and to prove that the connected sum with a homology 3-sphere enables every closed connected orientable 3-manifold to contain infinitely many such hyperbolic links. [ABSTRACT FROM AUTHOR]

In this paper, from the viewpoint of quandle construction we prove that for any link type L and any diagram of it, there exists another diagram of L such that these two diagrams are Ω1-dependent, Ω2-dependent and Ω3-dependent. [ABSTRACT FROM AUTHOR]

In this paper, we study the class of Jordan dialgebras (also called quasi-Jordan algebras). We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we prove dialgebraic analogues of these statements. Also, we study multilinear special identities which hold in all special Jordan algebras and do not hold in all Jordan algebras. We find a natural correspondence between special identities for ordinary algebras and dialgebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider GC-projective, injective and flat modules and dimensions under change of rings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize the formal power series which have purely periodic β-expansions in Pisot or Salem unit base under some condition. Furthermore, we will prove that if β is a quadratic Pisot unit base, then every rational f in the unit disk has a purely periodic β-expansion and discuss their periods. [ABSTRACT FROM AUTHOR]

In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their attached (φ, Γ)-modules by writing down explicit matrices for φ and for the action of Γ, and finally to determine which of these are trianguline. [ABSTRACT FROM AUTHOR]

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander-Reiten components. [ABSTRACT FROM AUTHOR]

The quasi-Baer condition of R/P(R) is investigated when R is a quasi-Baer ring, where P(R) is the prime radical of R. We provide an example of quasi-Baer ring R such that R/P(R) is not quasi-Baer. However, when P(R) is nilpotent, we prove that if R is a quasi-Baer (resp., Baer) ring, then R/P(R) is quasi-Baer (resp., Baer). Examples which illustrate and delimit the results of this paper are provided. [ABSTRACT FROM AUTHOR]

The paper investigates classes of words equivalent under different ways of counting subwords. We present a general method of constructing sequences of equivalent words. Apart from obtaining numerical characterizations of words, we also construct sequences of words generating equal arithmetical power sums. Our notions of equivalence include the Parikh equivalence resulting from Parikh matrices, recently widely studied. Consequently, we are able to settle some open problems in this area. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a pseudo-metric on the space of all m × s matrices with entries from the finite ring Zq, generalizing the classical Lee metric and the array RT metric, and name this pseudo-metric as the generalized Lee-RT pseudo-metric (or the GLRTP-metric). We also obtain some bounds on the parameters of array codes equipped with the GLRTP-metric. [ABSTRACT FROM AUTHOR]

It is well known that there are several non-equivalent types of prime near-rings which are all equivalent in the case of associative rings. In this paper we introduce various characterizations of prime modules in a zero-symmetric near-ring R. The connection of a prime R-ideal P of a module M and the ideal (P:M) of the near-ring R is also investigated. [ABSTRACT FROM AUTHOR]

Let R be a ring and α,β be endomorphisms of R. An additive mapping F: R → R is called a generalized (α,β)-derivation on R if there exists an (α,β)-derivation d: R → R such that F(xy)=F(x) α(y) + β(x)d(y) holds for all x, y ∈ R. In the present paper, we discuss the commutativity of a prime ring R admitting a generalized (α,β)-derivation F satisfying any one of the properties: (i) [F(x),x]α,β=0, (ii) F([x,y])=0, (iii) F(x ◦ y)=0, (iv) F([x,y])=[x,y]α,β, (v) F(x ◦ y)=(x ◦ y)α,β, (vi) F(xy)- α(xy) ∈ Z(R), (vii) F(x)F(y)- α(xy) ∈ Z(R) for all x, y in an appropriate subset of R. [ABSTRACT FROM AUTHOR]

In this paper, we deal with commutative algebras A satisfying the identity 2β{(xy)2 - x2y2} + γ{((xy)x)y + ((xy)y)x - (y2x)x - (x2y)y} = 0, where β, γ are scalars. These algebras appeared as one of the four families of degree four identities in Carini, Hentzel and Piacentini-Cattaneo [2]. We prove that if the algebra A admits an identity element, then A is associative. We also prove that there exist trace forms on A. Finally, we prove that if A has a non-degenerate trace form, then A satisfies the identity ((yx)x)x = y((xx)x), a generalization of right alternativity. Our results require characteristic ≠ 2, 3. [ABSTRACT FROM AUTHOR]

In this paper we study flexible algebras (possibly infinite-dimensional) satisfying the polynomial identity x(yz) = y(zx). We prove that in these algebras, products of five elements are associative and commutative. As a consequence of this, we get that when such an algebra is a nil-algebra of bounded nil-index, it is nilpotent. Furthermore, we obtain optimal bounds for the index of nilpotency. Another consequence that we get is that these algebras are associative when they are semiprime. [ABSTRACT FROM AUTHOR]

It is well known that Jones polynomial (hence, Kauffman bracket polynomial) of links is, in general, hard to compute. By now, Jones polynomials or Kauffman bracket polynomials of many link families have been computed, see [4, 7–11]. In recent years, the computer algebra (Maple) techniques were used to calculate link polynomials for various link families, see [7, 12–14]. In this paper, we try to design a maple program to calculate the explicit expression of the Kauffman bracket polynomial of Montesinos links. We first introduce a family of "ring of tangles" links, which includes Montesinos links as a special subfamily. Then, we provide a closed-form formula of Kauffman bracket polynomial for a "ring of tangles" link in terms of Kauffman bracket polynomials of the numerators and denominators of the tangles building the link. Finally, using this formula and known results on rational links, the Maple program is designed. [ABSTRACT FROM AUTHOR]

In this paper, with the study of combinatorial Dyson–Schwinger equations at the level of the universal Hopf algebra of renormalization and with the extension of the universality of this specific Hopf algebra and also category of flat equisingular vector bundles to the level of these equations, we are going to consider the notion of a geometric description from nonperturbative theory. [ABSTRACT FROM AUTHOR]

The most important families of nonlinear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the black-box complexity model, the check is optimal among closest-pair algorithms. In this paper, we provide a Gröbner basis technique to compute the weight/distance distribution of any systematic nonlinear code. Also our technique outputs all closest pairs. Unlike the check, our method can be extended to work on code families. [ABSTRACT FROM AUTHOR]

In this paper, we study the structure of finite groups G under the assumption that certain abelian subgroups of largest possible exponent of prime power order lie in the 픉-hypercenter of G. We improve and extend some results of Ezzat, Shaalan, Elashiry, Asaad, Ramadan, and Buckley. [ABSTRACT FROM AUTHOR]

In this paper we prove that a finite p-solvable group G is solvable if its every conjugacy class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every conjugacy class size of 2′-elements with prime power order. [ABSTRACT FROM AUTHOR]

Let (W,S) be a Weyl group of type Bn. In this paper, we find certain nontrivial distinguished involutions in the two-sided cell Ωt of W with a-value $\frac12(n^2-n+4t^2+2t)$ for 1≤ 2t ≤ n and n even (resp., $\frac12(n^2-n+4t^2-2t)$ for 1≤ 2t < n and n odd). Besides, for 1≤ i1< ⋯ < it≤ n-1, let Li1⋯ it be a left cell of W with a-value t2 and R(Li1⋯ it) ={si1,...,sit}. There are only two involutions y(i1,i1)⋯ y(it-1,it-1) sit and y(i1,i1)⋯ y(it,it) in the left cell Li1⋯ it. We prove that the former (resp., latter) is a distinguished involution in the left cell Li1⋯ it for t odd (resp., even). [ABSTRACT FROM AUTHOR]

Linton in 1978 proved that a λ-large subgroup of an abelian p-group A is totally projective if and only if A is totally projective. In this paper it will be shown that a special λ-large subgroup of a CΩ-p-group A is summable if and only if A is summable. [ABSTRACT FROM AUTHOR]