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In this paper, we characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ, ψ ∈ W , S S = S S on ( D ) if and only if φ and ψ satisfy one of the following conditions: (1) Both φ and ψ are harmonic functions; (2) There exist complex constants α and β, not both 0, such that φ = αψ+ β. [ABSTRACT FROM AUTHOR]

There is a large body of evidence showing that the existence of a suitably-constrained derivation on a 3-prime near-ring forces the near-ring to be a commutative ring. The purpose of this paper is to study generalized semiderivations which satisfy certain identities on 3-prime near-ring and generalize some results due to [H. E. Bell and G. Mason, On derivations in near-rings, North-Holland Math. Stud. 137 (1987) 31-35; H. E. Bell, On prime near-rings with generalized derivation, Int. J. Math. Math. Sci. 2008 (2008), Article ID: 490316, 5pp; A. Boua and L. Oukhtite, Some conditions under which near-rings are rings, Southeast Asian Bull. Math. 37 (2013) 325-331]. Moreover, an example is given to prove that the necessity of the 3-primeness hypothesis imposed on the various theorems cannot be marginalized. [ABSTRACT FROM AUTHOR]

In this paper we investigate the commutativity of prime rings (R, *) with involution of second kind which admits a gen-eralized derivation satisfying certain algebraic identities on ideals of R. We also give classifications of some functions. Finally, we provide examples to show that various restrictions imposed in the hypothesis of our theorems are not superfluous. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the commutativity of a two-torsion free prime ring R provided with generalized derivations, and some well-known results that characterize the commutativity of prime rings through generalized derivations have been generalized. Moreover, we provide some examples to testify that the assumed restriction in our theorems cannot be omitted.

In the present paper it is shown that 3-prime left near-rings satisfying certain identities involving generalized derivations are commutative rings. Moreover, examples proving the necessity of the 3-primeness hypothesis in various theorems are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study derivations and generalized derivations satisfying certain identities on semigroup ideals of near-rings. Some well-known results characterizing commutativity of 3-prime near-rings by derivations have been generalized by using semigroup ideals. Moreover, examples proving the necessity of the 3-primeness hypothesis are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study derivations satisfying certain differential identities on Jordan ideals of prime rings. Some well known results characterizing commutativity of prime rings by derivations have been generalized by using Jordan ideals. Moreover, we provide examples to show that our results cannot be extended to semi-prime rings. [ABSTRACT FROM AUTHOR]

In this paper we investigate commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy certain algebraic identities. Furthermore, we provide examples to show that the various restrictions imposed by the hypotheses of our theorems are not superfluous. [ABSTRACT FROM AUTHOR]

Let R be a prime ring of characteristic different from 2 with involution '* ' of the second kind and n ≥ 1 be a fixed positive integer. In the present paper it is shown that if R admits nonzero left multipliers S and T, then the following conditions are equivalent: .....The existence of hypotheses in various theorems have been justified by the examples. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain the structure of certain near-rings satisfying the following conditions: (i) d(I) ⊆ Z(N); (ii) d(-I) ⊆ Z(N); (iii) d([x; y]) = 0; (iv) d([x; y]) = [x; y]; (v) d(x ∘ y) = 0; (vi) d(x ∘ y) = x ∘ y for all x; y ∈ I, with I is a semigroup ideal and d is a semiderivation associated with an automorphism. Furthermore; an example is given to illustrate that the 3-primeness hypothesis is not superfluous. [ABSTRACT FROM AUTHOR]

The paper examines existence and properties about average Floquet factorisations, determined via average integration instead of matrix logarithms, for the transition matrices of finite-dimensional linear continuous-time periodic (FDLCP) systems. We talk about the following aspects about average Floquet factorisations: existence conditions, properties and relationships with the conventional Floquet factorisations. We reveal that average scaling and modelling may be incomplete or even incorrect for reflecting dynamics in general FDCLP systems, compared to the Floquet factorisations defined through matrix logarithms. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with characteristic not 2 and I, J ideals of R. Let $${h:R\longrightarrow R}$$ be a generalized (1, τ)-derivation associated with a nonzero ( λ, γ)-derivation d. In this paper we proved that, if one of the following conditions holds then R is commutative. (i) h[ x, y] α,β = [ x, y] α,μ, for all $${ x\in I,y\in J}$$ (or h[ x, y] α,β = −[ x, y] α,μ). (ii) h( x, y) α,β = ( x, y) α,μ, for all $${x\in I,y\in J}$$ (or h( x, y) α,β = ( x, y) α,μ). We also prove some results in prime rings with generalized ( σ, τ)-derivation. [ABSTRACT FROM AUTHOR]

Let R be an associative ring and let x, y ∈ R. Define the generalized commutators as follows: [x, 0y] = x and [x, ky] = [x, k-1y]y - y[x, k-1y](k = 1, 2, ...). In this paper we study some generalized Engel rings, i.e. -rings (satisfying [xm(x, y), k(x, y)y] = 0), -rings (satisfying [xm(x, y), k(x, y)yn(x, y)] = 0) and -rings (satisfying [xm(x, y), k(x, y)yn(x, y)]r(x, y) = 0). Among other results, it is proved that every Artinian -ring is strictly Lie-nilpotent. Also, we show that in each of the following cases R has nil commutator ideal: (1) if R is a -ring with unity and k, n independent of y; (2) if R is a locally bounded -ring (defined below); (3) if R is an algebraic algebra over a field in which R* is a bounded Engel group or a soluble group. [ABSTRACT FROM AUTHOR]

Operator fractional Brownian motions (OFBMs) are zero mean, operator self-similar (o.s.s.) Gaussian processes with stationary increments. They generalize univariate fractional Brownian motions to the multivariate context. It is well-known that the so-called symmetry group of an o.s.s. process is conjugate to subgroups of the orthogonal group. Moreover, by a celebrated result of Hudson and Mason, the set of all exponents of an operator self-similar process can be related to the tangent space of its symmetry group. In this paper, we revisit and study both the symmetry groups and exponent sets for the class of OFBMs based on their spectral domain integral representations. A general description of the symmetry groups of OFBMs in terms of subsets of centralizers of the spectral domain parameters is provided. OFBMs with symmetry groups of maximal and minimal types are studied in any dimension. In particular, it is shown that OFBMs have minimal symmetry groups (and thus unique exponents) in general, in the topological sense. Finer classification results of OFBMs, based on the explicit construction of their symmetry groups, are given in the lower dimensions 2 and 3. It is also shown that the parametrization of spectral domain integral representations are, in a suitable sense, not affected by multiplicity of exponents, whereas the same is not true for time domain integral representations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give sufficient conditions on two normal operators (bounded or not), defined on a Hilbert space, which make their algebraic sum normal. The results are accompanied by some interesting examples and counter examples. [ABSTRACT FROM AUTHOR]

It is proven that the transitivity property of commutativity is always valid for second-order linear time-varying analog systems whether their initial states are zero or not. Throughout the study, it is assumed that the subsystems considered cannot be obtained from each other by any feed-forward and feedback structure. The results are well validated by MATLAB simulations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce dual g-frames for a closed subspace in a separable Hilbert space and also give a characterization. Generally dual g-frames for a closed subspace are non-commutative. Therefore, we construct dual g-frames for closed subspaces from two aspects and give the corresponding formulas, respectively. Finally, we give a necessary and sufficient condition for commutative dual g-frame pairs for closed subspaces under certain conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball. [ABSTRACT FROM AUTHOR]

In this paper, we study the commutativity of prime rings admit- ting automorphisms which satisfy certain identities. [ABSTRACT FROM AUTHOR]

complex square matrix A is called an orthogonal projector if A = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we derive necessary and sufficient conditions for various equalities for orthogonal projectors and their operations to hold. [ABSTRACT FROM AUTHOR]

The equivalence between various types of moduli of smoothness and respective Peetre K-functionals has been actively explored since the 1960s, in view of the importance of this topic for revealing connections among approximation theory, functional analysis and operator theory. The existence of the embedding constants in this equivalence relation (together with one-sided estimates for these constants) has been established in great generality, but the derived one-sided bounds are rather coarse (see, e.g., Johnen and Scherer, in Constructive Theory of Functions of Several Variables. Proc. Conf., Math. Res. Inst. Oberwolfach, 1976, pp. 119–140, Springer, Berlin, and the references therein). The problem of finding the sharp embedding constants for this equivalence was posed in Dechevsky, C. R. Acad. Bulg. 42(2), 21–24, and Int. J. Pure Appl. Math. 33(2), 157–186, , where this problem was solved in the particular case of L2-metric, for real-valued and complex-valued functions of one real variable, with definition domain Ω=ℝ or $\varOmega =\mathbb{T}$ (the periodic case). In the present paper we extend the results of Dechevsky to the case of several real variables: Ω=ℝ n or $\varOmega =\mathbb{T}^{n}$ , n∈ℕ. We consider two different types of equivalent norms for the Sobolev spaces involved in the K-functional (with and without intermediate mixed partial derivatives) and obtain a separate set of sharp two-sided bounds for the embedding constants in each of these two cases. We also briefly outline how the approach of the present study can be extended to the case of n-dimensional Lie (semi)groups. [ABSTRACT FROM AUTHOR]

How should we respond to cases of disagreement where two epistemic agents have the same evidence but come to different conclusions? Adam Elga has provided a Bayesian framework for addressing this question. In this paper, I shall highlight two unfortunate consequences of this framework, which Elga does not anticipate. Both problems derive from a failure of commutativity between application of the equal weight view and updating in the light of other evidence. [ABSTRACT FROM AUTHOR]

Abstract: For a connected Lie group G, the homotopy set inherits the group structure by the pointwise multiplication and is called by the self homotopy group of G. In this paper we work with the case . It was shown by McGibbon that and themselves are homotopy commutative when they are localized at p and . Thus the p-localized self homotopy groups of and are commutative, if . Then the converse is true? In this paper, we completely determine, for which p, the p-localized self homotopy group of G is commutative, in the case or where H is a subgroup of the center of . [Copyright &y& Elsevier]

Providing efficient access to XML documents is crucial, as XML has become the most important technique to exchange data in WWW. DOM is a popular object-oriented user interface to manipulate XML documents. Several concurrency control protocols have been proposed for DOM by analyzing the read/write behaviors of DOM operations. However, none of them exploit the semantics of DOM operations for enhancing concurrency. Semantics were introduced in object databases to develop concurrency control protocols. And this research is motivated by the success of this approach on object databases. In this paper, we analyze the commutativity relationship between DOM operations and propose a new semantic-based protocol for DOM, namely the SCD protocol. SCD not only allows non-serializable schedules to be executed, but also preserves the correctness of the resulting schedules. Our simulation results show that SCD outperforms other DOM-based protocols in its higher throughput and shorter response time. There are two major contributions in this paper. First, the semantics of DOM operations are analyzed formally. Second, based on the semantic analysis, a new way to design DOM-based concurrency control protocol is presented. [ABSTRACT FROM AUTHOR]

The problem of state space search is fundamental to many areas of computer science, such as, e.g., AI and formal methods. Often, the state space to be searched is huge, so optimizing the search is an important issue. In this paper, we consider the problem of visiting all states in the setting where transitions between states are generated by actions, and the (reachable) states are not known in advance. Some of the actions may commute, i.e., they result in the same state for every order in which they are taken. We show how to use commutativity to achieve full coverage of the states, while traversing a relatively small number of edges. [ABSTRACT FROM AUTHOR]

It is well-known that some of the most basic properties of words, like the commutativity (xy = yx) and the conjugacy (xz = zy), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation xmyn = zp has only periodic solutions in a free monoid, that is, if xmyn = zp holds with integers m, n, p ≥ 2, then there exists a word w such that x, y, z are powers of w. This result, which received a lot of attention, was first proved by Lyndon and Schützenberger for free groups. In this paper, we investigate equations on partial words. Partial words are sequences over a finite alphabet that may contain a number of "do not know" symbols. When we speak about equations on partial words, we replace the notion of equality (=) with compatibility (↑). Among other equations, we solve xy ↑ yx, xz ↑ zy, and special cases of xmyn ↑ zp for integers m, n, p ≥ 2. [ABSTRACT FROM AUTHOR]

Abstract: Rabi and Sherman [M. Rabi, A. Sherman, An observation on associative one-way functions in complexity theory, Information Processing Letters 64 (5) (1997) 239–244; M. Rabi, A. Sherman, Associative one-way functions: A new paradigm for secret-key agreement and digital signatures, Tech. Rep. CS-TR-3183/UMIACS-TR-93-124, Department of Computer Science, University of Maryland, College Park, MD, 1993] proved that the hardness of factoring is a sufficient condition for there to exist one-way functions (i.e., p-time computable, honest, p-time noninvertible functions; this paper is in the worst-case model, not the average-case model) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to . More generally, in this paper we completely characterize which types of one-way functions stand or fall together with (plain) one-way functions—equivalently, stand or fall together with . We look at the four attributes used in Rabi and Sherman’s seminal work on algebraic properties of one-way functions (see [M. Rabi, A. Sherman, An observation on associative one-way functions in complexity theory, Information Processing Letters 64 (5) (1997) 239–244; M. Rabi, A. Sherman, Associative one-way functions: A new paradigm for secret-key agreement and digital signatures, Tech. Rep. CS-TR-3183/UMIACS-TR-93-124, Department of Computer Science, University of Maryland, College Park, MD, 1993]) and subsequent papers–strongness (of noninvertibility), totality, commutativity, and associativity–and for each attribute, we allow it to be required to hold, required to fail, or “don’t care”. In this categorization there are potential types of one-way functions. We prove that each of these 81 feature-laden types stands or falls together with the existence of (plain) one-way functions. [Copyright &y& Elsevier]

In this paper, we analyze from a geometric perspective the meaningful relations taking place between belief and probability functions in the framework of the geometric approach to the theory of evidence. Starting from the case of binary domains, we identify and study three major geometric entities relating a generic belief function (b.f.) to the set of probabilities P: 1) the dual line connecting belief and plausibility functions; 2) the orthogonal complement of P; and 3) the simplex of consistent probabilities. Each of them is in turn associated with a different probability measure that depends on the original b.f. We focus in particular on the geometry and properties of the orthogonal projection of a b.f. onto P and its intersection probability, provide their interpretations in terms of degrees of belief, and discuss their behavior with respect to affine combination. [ABSTRACT FROM AUTHOR]

We study pseudo MV-algebras introduced recently by Georgescu and Iorgulescu as a non-commutative generalization of MV-algebras. We introduce a partial binary operation which model the addition in pseudo MV-algebras. In the paper, we give basic properties of such an addition. We find conditions which entail the commutativity of pseudo MV-algebras, i.e., when they are classical MV-algebras. We study ideals and the conditions when a pseudo MV-algebra is representable. Finally, we introduce states and show how they are connected with the normal ideals. [ABSTRACT FROM AUTHOR]

Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping Hon R is called a homoderivation if H(xy) =H(x)H(y)+H(x)y+xH(y)for all x, y∈R. In this paper we investigate homoderivations satisfying certain differential identitieson square closed Lie ideals of prime rings.

Until now, it was believed that, unlike real and complex numbers, the construction of a commutative algebra of quaternions or octonions with division over the field of real numbers is impossible in principle. No one questioned the existing theoretical assertion that quaternions, octonions, and other hypercomplex numbers cannot have the commutativity property. This article demonstrates the following for the first time: (1) the possibility of constructing a normed commutative algebra of quaternions and octonions with division over the field of real numbers; (2) the possibility of constructing a normed commutative algebra of six-dimensional and ten-dimensional hypercomplex numbers with division over the field of real numbers; (3) a method for constructing a normed commutative algebra of N-dimensional hypercomplex numbers with division over the field of real numbers for even values of N; and (4) the possibility of constructing a normed commutative algebra of other N-dimensional hypercomplex numbers with division over the field of real numbers. The article also shows that when using specific forms of representation of unit vectors, the product of vectors has the property of commutativity. Normed commutative algebras of N-dimensional hypercomplex numbers can be widely used to solve many topical scientific problems in the field of theoretical physics for modeling force fields with various types of symmetry, in cryptography for developing a number of new cryptographic programs using hypercomplex number algebras with different values of dimension, and in many other areas of fundamental and applied sciences. [ABSTRACT FROM AUTHOR]

Let A be a ring with its center Z (A). An additive mapping ξ: A → A is called a homoderivation on A if ∀ a, b ∈ A: ξ(ab) = ξ(a)ξ(b) + ξ(a)b + aξ(b). An additive map ψ: A → A is called a generalized homoderivation with associated homoderivation ξ on A if ∀ a, b ∈ A: ψ(ab) = ψ(a)ψ(b) + ψ(a)b + aξ(b). This study examines whether a prime ring A with a generalized homoderivation ψ that fulfils specific algebraic identities is commutative. Precisely, we discuss the following identities: ψ(a)ψ(b) + ab ∈ Z (A), ψ(a)ψ(b) - ab ∈ Z (A), ψ(a)ψ(b) + ab ∈ Z (A), ψ(a)ψ(b) - ab ∈ Z (A), ψ(ab) + ab ∈ Z (A), ψ(ab) - ab ∈ Z (A), ψ(ab) + ba ∈ Z (A), ψ(ab) - ba ∈ Z (A) (∀ a, b ∈ A). Furthermore, examples are given to prove that the restrictions imposed on the hypothesis of the various theorems were not superfluous. [ABSTRACT FROM AUTHOR]

Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε -commutativity), we introduce almost mediality ("commutativity-to-mediality" ansatz). Higher graded twisted products and "deforming" brackets (being the medial analog of Lie brackets) are defined. Toyoda's theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. A polyadic (non-strict) tensor category has an n-ary tensor product as an additional multiplication with n − 1 associators of the arity 2 n − 1 satisfying a n 2 + 1 -gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called groupal) is defined: they are close to monoidal categories but may not contain units: instead the querfunctor and (natural) functorial isomorphisms, the quertors, are considered (by analogy with the querelements in n-ary groups). The arity-nonreducible n-ary braiding is introduced and the equation for it is derived, which for n = 2 coincides with the Yang–Baxter equation. Then, analogously to the first part of the paper, we introduce "medialing" instead of braiding and construct "medialed" polyadic tensor categories. [ABSTRACT FROM AUTHOR]

Commutativity is an important property in two-step information merging procedure. It is shown that the result obtained from the procedure should not depend on the order in which signal steps are performed. In the case of a bisymmetric aggregation operator with the neutral element, Saminger et al. have provided a full characterization of commutative n -ary operator by means of unary distributive functions. Further, characterizations of these unary distributive functions can be viewed as resolving a kind of the Cauchy-like equations f ( x ⊕ y ) = f ( x ) ⊕ f ( y ) , where f : [ 0 , 1 ] → [ 0 , 1 ] is a monotone function, ⊕ is a bisymmetric aggregation operator with the neutral element. In this paper, we are still devoted to investigating and fully characterizing the Cauchy-like equation f ( U ( x , y ) ) = U ( f ( x ) , f ( y ) ) , where f : [ 0 , 1 ] → [ 0 , 1 ] is an unknown function but not necessarily monotone, U is a uninorm continuous in ( 0 , 1 ) 2 . These results show the key technology is how to find a transformation from this equation into several known cases. Moreover, this equation has completely different and non-monotone solutions in comparison with the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we consider a graph G, a partition P = [V1, V2, ..., Vk} of V (G) and the generalized complements GkP and Gk(i)P with respect to the partition P. We derive conditions to be satisfied by P so that G commutes with its generalized complements. Apart from the general characterization, we also obtain conditions on P = [V1, V2, ...,Vk} so that G commutes with its generalized complements for certain classes of graphs namely complete graphs, cycles and generalized wheels. In the process we obtain a commuting decomposition of regular complete k-partite graph ... in terms of a Hamiltonian cycle and its k-complement. We also get a commuting decomposition of a complete k-partite graph ... in terms of a generalized wheel and its k-complement, where n1, n2, ..., nk satisfy some conditions. [ABSTRACT FROM AUTHOR]

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant. [ABSTRACT FROM AUTHOR]

Extending the notion of probability to the automorphisms of a group, we find the probability of an arbitrarily chosen automorphism of a group fixing an arbitrary element of the group. [ABSTRACT FROM PUBLISHER]

We introduce the notion of -derivations in rings and obtain commutativity results in a prime ring R admitting multiplicative -derivations. We show that the symmetry of Ƴ with various conditions on Lie products and Jordan products gives rise to commutativity of R. We obtain (i) a characterization of Galois field of any characteristic by using Lie product and - derivation, and (ii) a characterization of Galois field of characteristic 2 by using Jordan product and Ƴ-derivation. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of quasi-static evolution problems involving oscillating energies E ε and dissipations D ε . Even though we have separate Γ -convergence of E ε and D ε , the Γ -limit F of the sum does not agree with the sum of the Γ -limits. Nevertheless, F can still be viewed as the sum of an internal energy and a dissipation, and the corresponding quasi-static evolution is the limit of the quasi-static evolutions related to E ε and D ε . This result contributes to the analysis of the interaction between Γ -convergence and variational evolution, which has recently attracted much interest both in the framework of energetic solutions and in the theory of gradient flows. [ABSTRACT FROM AUTHOR]

This paper deals with estimability of variance components in mixed models when all model matrices commute. In this situation, it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators. If, in addition, the family of possible variance–covariance matrices forms an orthogonal block structure, then there are the same number of variance components as strata, and the variance components are all estimable if and only if there are non-zero residual degrees of freedom in each stratum. We investigate the case where the family of possible variance–covariance matrices, while still commutative, no longer forms an orthogonal block structure. Now the variance components may or may not all be estimable, but there is no clear link with residual degrees of freedom. Whether or not they are all estimable, there may or may not be uniformly best unbiased quadratic estimators of those that are estimable. Examples are given to demonstrate all four possibilities. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the commutativity of H-Toeplitz operators with quasihomogeneous symbols on the Bergman space, which is different from the case of Toeplitz operators with same symbols on the Bergman space.

We consider some generalizations of BCK algebras (RML, BE, aBE, BE** and aBE** algebras). We investigate the property of implicativity for these algebras. We prove that for any implicative BE** algebra the commutativity property is equivalent to the property of antisymmetry and show that implicative aBE** algebras are commutative BCK algebras. We also show that the class of implicative BE** algebras is a variety. [ABSTRACT FROM AUTHOR]