Showing papers in "Asian-european Journal of Mathematics in 2009"
TL;DR: In this paper, a complete characterization of all orthogonality-preserving operators from a JB*-algebra to a jb*-triple is given.
Abstract: We obtain a complete characterization of all orthogonality preserving operators from a JB*-algebra to a JB*-triple. If T : J → E is a bounded linear operator from a JB*-algebra (respectively, a C*-algebra) to a JB*-triple and h denotes the element T**(1), then T is orthogonality preserving, if and only if, T preserves zero-triple-products, if and only if, there exists a Jordan *-homomorphism such that S(x) and h operator commute and T(x) = h•r(h) S(x), for every x ∈ J, where r(h) is the range tripotent of h, is the Peirce-2 subspace associated to r(h) and •r(h) is the natural product making a JB*-algebra. This characterization culminates the description of all orthogonality preserving operators between C*-algebras and JB*-algebras and generalizes all the previously known results in this line of study.
49 citations
28 citations
TL;DR: In this paper, the authors define prime, semiprime and irreducible ideals in ternary semigroups and prove that a semigroup is semisimple if and only if each of its ideals is semi-prime.
Abstract: In this paper we define prime, semiprime and irreducible ideals in ternary semigroups. We also define semisimple ternary semigroups and prove that a ternary semigroup is semisimple if and only if each of its ideals is semiprime.
17 citations
TL;DR: In this paper, the notion of isoclinism on a pair of Lie algebras, which forms an equivalence relation, was studied and it was shown that each equivalence class contains a stem pair of LAs.
Abstract: In 1940, P. Hall introduced the concept of isoclinism on the class of all groups. In the present article we study the notion of isoclinism on a pair of Lie algebras, which forms an equivalence relation and show that each equivalence class contains a stem pair of Lie algebras, which has minimal dimension among the finite dimensional pairs of Lie algebras. Finally, some more results are obtained when two isoclinic pairs of Lie algebras are given.
14 citations
TL;DR: In this paper, several open problems on spectrally bounded operators are discussed, some new, some old, adding in a few new insights, and some new insights are discussed.
Abstract: We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
12 citations
TL;DR: In this paper, new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established, which generalize some recent well known comparable results in the literature.
Abstract: Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.
12 citations
TL;DR: In this article, it was proved that every law of the lattice of all τ-closed n-multiply ω-saturated formations of finite groups is fulfilled in the lattices of all ε-closed groups.
Abstract: It is proved that every law of the lattice of all τ-closed formations of finite groups is fulfilled in the lattice of all τ-closed n-multiply ω-saturated formations of finite groups, for every subgroup functor τ and every natural number n.
11 citations
TL;DR: In this paper, a new convolution was defined for the dual wavelet transform and the wavelet transformation in the context of tempered distributions, and a new Boehmian space containing the tempered distributions was constructed.
Abstract: We define a new convolution ⊗ : 𝒮'(ℝ × ℝ+) × 𝒟(ℝ) → 𝒮'(ℝ × ℝ+) and derive the convolution theorems for wavelet transform and dual wavelet transform in the context of tempered distributions. By using the new convolution, we construct a Boehmian space containing the tempered distributions on ℝ × ℝ+. Applying the convolution theorems in the context of tempered distributions, we also extend the wavelet transform and dual wavelet transform between the tempered Boehmian space and the new Boehmian space as linear continuous maps with respect to δ-convergence and Δ-convergence, satisfying the convolution theorems.
11 citations
TL;DR: In this paper, the authors consider finite groups in which every triple of distinct conjugacy class sizes greater than one has a pair which is coprime and prove such a group is soluble and has conjugate rank at most three.
Abstract: We consider finite groups in which every triple of distinct conjugacy class sizes greater than one has a pair which is coprime. We prove such a group is soluble and has conjugate rank at most three.
9 citations
TL;DR: In this paper, a non-flat Riemannian manifold called pseudo cyclic Ricci symmetric manifold was introduced and its geometric properties were studied. And it was shown that such a manifold can be isometrically immersed in a Euclidean manifold as a hypersurface.
Abstract: The object of the present paper is to introduce a type of non-flat Riemannian manifold called pseudo cyclic Ricci symmetric manifold and study its geometric properties. Among others it is shown that a pseudo cyclic Ricci symmetric manifold is a special type of quasi-Einstein manifold. In this paper we also study conformally flat pseudo cyclic Ricci symmetric manifolds and prove that such a manifold can be isometrically immersed in a Euclidean manifold as a hypersurface.
8 citations
TL;DR: In this article, it was shown that simple digraphs are isomorphic as semigroups if and only if W(D1/D2) and D(D2/D3) are digraph isomorphic.
Abstract: For each simple digraph D, we introduce its associated semigroup S(D) and its widened digraph W(D). We show that, for any two finite simple digraphs D1 and D2, S(D1) and S(D2) are isomorphic as semigroups if and only if W(D1) and W(D2) are isomorphic as digraphs.
TL;DR: In this article, the structure of separating linear maps between continuous fields of Banach spaces is described and some automatic continuity results are obtained, and a complete description of the structure is given.
Abstract: In this paper, we give a complete description of the structure of separating linear maps between continuous fields of Banach spaces. Some automatic continuity results are obtained.
TL;DR: The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
Abstract: Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
TL;DR: In this paper, a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations is given.
Abstract: This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the lp-real and complex stability radii of these systems coincide and they are given by a formula of input-output operators. The result is an extension of a previous result for time-varying ordinary differential equations [7].
TL;DR: In this paper, the homotopy perturbation method (HPM) was applied for solving systems of partial differential equations without any discretization, linearization or restrictive assumptions.
Abstract: In this paper, we apply the homotopy perturbation method (HPM) for solving systems of partial differential equations. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the suggested technique solves nonlinear problems without using the Adomian's polynomials is an advantage of this algorithm over the decomposition method.
TL;DR: In this article, a decomposition of the q-oscillator is considered and the rate of such decomposition is shown to be exponential in the number of discrete-time rotators, where a rotator is a system consisting of a particle rotating on a circle with a constant angular rate.
Abstract: A decomposition of a simplest mechanical system – a q-oscillator, is considered. A q-oscillator (quasi-oscillator) is defined as a system consisting of a particle moving on a linear segment with a constant speed and reflecting from the segment's end-points. A theorem, stating that a discrete-time version of q-oscillator can be decomposed into a countable set of discrete-time rotators (a rotator consists of a particle rotating on a circle with a constant angular rate) as well as a metrical theorem, concerning the rate of such decomposition, are proved. Some physics-related examples are discussed. A phase-shifting perturbed rotator and a number-theoretical matrix system modelling the quantum oscillator, are presented.
TL;DR: In this paper, it was shown that the conjugacy problem is undecidable (in the case a ≠ 0) and the proportion of the elements of a group for which it is known whether two elements are conjugate is strictly less than l 2/(2λ - 1)l where λ > 4.
Abstract: The algorithmic unsolvability of the conjugacy problem for finitely presented groups was demonstrated by Novikov in the early 1950s. Various simplifications and alternative proofs were found by later researchers and further questions raised. Recent work by Borovik, Myasnikov and Remeslennikov has considered the question of what proportion of the number of elements of a group (obtained by standard constructions) falls into the realm of unsolvability. In this paper we provide a straightforward construction, as a Britton tower, of a finitely presented group with solvable word problem but unsolvable conjugacy problem of any r.e. (recursively enumerable) Turing degree a. The question of whether two elements are conjugate is bounded truth-table reducible to the question of whether the elements are both conjugate to a single generator of the group. We also define computable normal forms, based on the method of Bokut', that are suitable for the conjugacy problem. We consider (ordered) pairs of normal words U, V for the conjugacy problem whose lengths add to l and show that the proportion of such pairs for which conjugacy is undecidable (in the case a ≠ 0) is strictly less than l2/(2λ - 1)l where λ > 4. The construction is based on modular machines, introduced by Aanderaa and Cohen. For the purposes of this construction it was helpful to extend the notion of configuration to include pairs of m-adic integers. The notion of computation step was also extended and is referred to as s-fold computation where s ∈ ℤ (the usual notion coresponds to s = 1). If gcd(m, s) = 1 then determinism is preserved, i.e., if the modular machine is deterministic then it remains so under the extended notion. Furthermore there is a simple correspondence between s-fold and standard computation in this case. Otherwise computation is non-deterministic and there does not seem to be any straightforward correspondence between s-fold and standard computation.
TL;DR: For an arbitrary binary word ω of Arnold complexity A(ω) it is proved that the number of steps in computing A( ω) can be lowered from A (ω) to ν(A(ω).
Abstract: For an arbitrary binary word ω of Arnold complexity A(ω) we prove that the number of steps in computing A(ω) can be lowered from A(ω) to ν(A(ω)) where ν(A(ω)) is the number of occurrences of the digit 1 in A(ω). For a class of words we obtain an explicit algorithm for computing A(ω). We illustrate the efficacy of our construction by determining the Arnold complexity of the Thue–Morse sequence.
TL;DR: In this article, the Laplacian eigenvalues of graphs on n vertices with domination number γ were studied and upper bounds for the spectral radius and algebraic connectivity were obtained.
Abstract: In this paper, we study the Laplacian eigenvalues of graphs on n vertices with domination number γ and present upper bounds for the Laplacian spectral radius and algebraic connectivity as well, which improve old results apparently.
TL;DR: In this paper, the identity of a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A(G) satisfies s = t for all G ∈ V.
Abstract: Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = ModgΣ where Σ is a subset of T(X) × T(X). A graph variety V' = ModgΣ' is called a biregular leftmost graph variety if Σ' is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety V if G satisfies s ≈ t for all G ∈ V. In this paper we characterize identities in each biregular leftmost graph variety. For identities, varieties and other basic concepts of universal algebra see e.g. [1].
TL;DR: In this article, it was shown that an isotope of a JB*-triple is also a JEB* -triple, and the Russo-Dye theorem for JBW* triples was proved.
Abstract: In this note, we look at homotopes of Jordan triple structures and show that, following a renorming, an isotope of a JB*-triple is also a JB*-triple. We also provide a proof of the Russo—Dye theorem for JBW*-triples.
TL;DR: In particular, all infinitely-dimensional finitely generated K-algebras have exponential growth as discussed by the authors, where the number of homogeneous generic relations in A of degrees smaller than n grows exponentially with n.
Abstract: Let K be a field of infinite transcendence degree and let A be a finitely generated K-algebra. Suppose that the number of homogeneous generic relations in A of degrees smaller than n grows exponentially with n. Then all infinitely-dimensional finitely generated A-modules have exponential growth. In particular there are Golod-Shafarevich algebras all of whose finitely generated modules either have exponential growth or are finite-dimensional.
TL;DR: In this paper, it was shown that every simple abelian real Hilbert ternary algebra is isomorphic to the algebra of Hilbert-Schmidt operators between two real, complex or quaternionic Hilbert spaces, up to a positive multiple of the inner product.
Abstract: We show that every simple abelian real Hilbert ternary algebra is isomorphic to the algebra of Hilbert-Schmidt operators between two real, complex or quaternionic Hilbert spaces, up to a positive multiple of the inner product.
TL;DR: In this article, the authors studied the super minimizers of the sum F1 + F2 related to the concept of super efficiency in constrained problems of multiobjective optimization, where each cost mapping Fi is generally set-valued for i = 1, 2.
Abstract: The primary goal of this paper is to study the so-called super minimizers of the sum F1 + F2 related to the concept of super efficiency in constrained problems of multiobjective optimization, where each cost mapping Fi is generally set-valued for i = 1, 2 We will derive necessary conditions (of the subdifferential type) for super minimizers of the sum F1 + F2 on the basis of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives
TL;DR: An adaptive estimator based on wavelet block thresholding is developed and it is proved that it attains near optimal rates of convergence under the minimax approach.
Abstract: We consider a density estimation problem with a change-point. The contribution of the paper is theoretical: we develop an adaptive estimator based on wavelet block thresholding and we evaluate these performances via the minimax approach under the 𝕃p risk with p ≥ 1 over a wide range of function classes: the Besov classes, $B_{\pi, r}^s$ (with no particular restriction on the parameters π and r). Under this general framework, we prove that it attains near optimal rates of convergence.
TL;DR: In this paper, the authors investigated generalizations of D11 and modules, namely δ-D11, and proved that any δ -D11 module M has a decomposition M = M1 ⊕ M2 with δ(M1) ≪δ M1 and δ (M2) = M2.
Abstract: Let M be a module. Then M is called a D11 module if any submodule of M has a supplement which is a direct summand of M. Also M is called if every direct summand of M is D11. In this paper we investigate generalizations of D11 and modules, namely δ-D11 and modules. We will prove that any δ-D11 module M has a decomposition M = M1 ⊕ M2 with δ(M1) ≪δ M1 and δ(M2) = M2.
TL;DR: In this paper, a kind of analytical technique called Exp-Function method is implemented to find the solitary wave solution of the Kuramoto-Sivashinsky equation and some of the most useful equations in physics, the Camassa-Holm equation and the reduced Ostrovsky equation (ROE).
Abstract: In this paper, a kind of analytical technique, called Exp-Function method is implemented to find the solitary wave solution of the Kuramoto-Sivashinsky equation and some of the most useful equations in physics, the Camassa-Holm equation and the reduced Ostrovsky equation (ROE). This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of the Exp-Function method. It is predicted that Exp-Function method can be found widely applicable in engineering.
TL;DR: The π-near-armendariz ring as mentioned in this paper is a generalization of both Armendariz rings and 2-primal rings and is a ring extension of the 2-parallel ring.
Abstract: In this note we introduce a concept, so-called π-Near-Armendariz ring, that is a generalization of both Armendariz rings and 2-primal rings We first observe the basic properties of π-Near-Armendariz rings, constructing typical examples We next extend the class of π-Near-Armendariz rings, through various ring extensions
TL;DR: In this paper, a generalised trapezoidal rule is considered and error estimates for functions of bounded variation are given for some particular cases of interest as well as applications for particular problems of interest.
Abstract: A generalised trapezoidal rule is considered. Error estimates for functions of bounded variation are given. Applications for some particular cases of interest are provided as well.