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20 March 2012, Volume 32 Issue 2 Previous Issue    Next Issue

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COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJ´|ER POINTS ON A CURVE TU Tian-Liang, MO Jiong Acta mathematica scientia,Series B. 2012, 32 (2):  441-454.  DOI: 10.1016/S0252-9602(12)60028-9 Abstract ( 529 )   RICH HTML PDF (192KB) ( 962 )   Save The results of accurate order of uniform approximation and simultaneous ap-proximation in the early work “Jackson Type Theorems on Complex Curves” are improved from Fej´er points to disturbed Fej´er points in this article. Furthermore, the stability of convergence of T*n,ε(f, z) with disturbed sample values f(z*k) +εk are also proved in this article. References | Related Articles | Metrics

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BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR L.T. Rachdi, N. Msehli Acta mathematica scientia,Series B. 2012, 32 (2):  455-470.  DOI: 10.1016/S0252-9602(12)60029-0 Abstract ( 517 )   RICH HTML PDF (198KB) ( 1276 )   Save Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked. References | Related Articles | Metrics

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MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS CAO Fei-Long, LIN Shao-Bo Acta mathematica scientia,Series B. 2012, 32 (2):  471-482.  DOI: 10.1016/S0252-9602(12)60030-7 Abstract ( 566 )   RICH HTML PDF (199KB) ( 1082 )   Save Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the so-called multivariate weighted Bernstein, Nikol’skiÏ, and Ul’yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol’skiÏ-type and Ul’yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results. References | Related Articles | Metrics

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A NOTE ON THE DRAZIN INVERSE OF A MODIFIED MATRIX Dragana S. Cvetkovic, Jelena Ljubisavljevic Acta mathematica scientia,Series B. 2012, 32 (2):  483-487.  DOI: 10.1016/S0252-9602(12)60031-9 Abstract ( 922 )   RICH HTML PDF (114KB) ( 1185 )   Save In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9]. References | Related Articles | Metrics

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CONFOUNDING STRUCTURE OF TWO-LEVEL NONREGULAR FACTORIAL DESIGNS Ren Jun-Bai Acta mathematica scientia,Series B. 2012, 32 (2):  488-498.  DOI: 10.1016/S0252-9602(12)60032-0 Abstract ( 486 )   RICH HTML PDF (176KB) ( 1079 )   Save In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs? The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example. References | Related Articles | Metrics

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A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT#br# PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM LIU Min, ZHANG Shi-Sheng Acta mathematica scientia,Series B. 2012, 32 (2):  499-519.  DOI: 10.1016/S0252-9602(12)60033-2 Abstract ( 552 )   RICH HTML PDF (222KB) ( 722 )   Save In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone map-pings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Takahashi and Toyoda [9], Takahashi and Takahashi [10] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [11], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12]. References | Related Articles | Metrics

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SOME PROPERTIES OF m-ISOMETRIES AND m-INVERTIBLE OPERATORS ON BANACH SPACES Ould Ahmed Mahmoud Sid Ahmed Acta mathematica scientia,Series B. 2012, 32 (2):  520-530.  DOI: 10.1016/S0252-9602(12)60034-4 Abstract ( 602 )   RICH HTML PDF (160KB) ( 1865 )   Save This article has two purposes: the first is to give some structure results for the class of m-isometries, and the second purpose is to extend the notions of left and right inverses to m-left and m-right inverses respectively. References | Related Articles | Metrics

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MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS CUI Jian-Lian, Choonkil Park Acta mathematica scientia,Series B. 2012, 32 (2):  531-538.  DOI: 10.1016/S0252-9602(12)60035-6 Abstract ( 552 )   RICH HTML PDF (146KB) ( 1223 )   Save Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself. We prove that, if Φ satisfies that Φ(A)Φ(B) − Φ(B)Φ(A)* =AB − BA* for all A, B ∈ A, then there exist a linear bijective map  Ψ : A → A satisfying  (A) (B) −  (B) (A)* = AB − BA*  for A, B ∈ A and a real functional h on A with h(0) = 0 such that Φ(A) =  (A) + h(A)I for every A ∈ A. In particular, if A is a type I factor, then, Φ(A) = cA + h(A)I for every A ∈ A, where c = ±1. References | Related Articles | Metrics

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WEYL’S TYPE THEOREMS AND HYPERCYCLIC OPERATORS M.H. M. Rashid Acta mathematica scientia,Series B. 2012, 32 (2):  539-551.  DOI: 10.1016/S0252-9602(12)60036-8 Abstract ( 525 )   RICH HTML PDF (193KB) ( 1298 )   Save For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions: (i) If T or T*∈ SC, then generalized a-Browder’s theorem holds for f(T) for every f ∈Hol(σ(T)). (ii) If T or T* ∈ HC has topological uniform descent at all λ∈ iso(σ(T)), then generalized Weyl’s theorem holds for f(T) for every f ∈ Hol(σ(T)). (iii) If T ∈ HC has topological uniform descent at all λ∈ E(T), then T satisfies generalized Weyl’s theorem. (iv) Let T ∈HC. If T satisfies the growth condition Gd(d ≥ 1), then generalized Weyl’s theorem holds for f(T) for every f ∈ Hol(σ(T)). (v) If T ∈ SC, then, f(σSBF±(T)) = σSBF±(f(T)) for all f ∈ Hol(σ(T)). (vi) Let T be a-isoloid such that T* ∈ HC. If T − λI has finite ascent at every λ ∈ Ea(T) and if F is of finite rank on H such that TF = FT, then T +F obeys generalized a-Weyl’s theorem. References | Related Articles | Metrics

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DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES TIAN Xue-Ting, SUN Wen-Xiang Acta mathematica scientia,Series B. 2012, 32 (2):  552-558.  DOI: 10.1016/S0252-9602(12)60037-X Abstract ( 895 )   RICH HTML PDF (160KB) ( 1064 )   Save Let M be a smooth compact manifold and ∧ be a compact invariant set. In this article, we prove that, for every robustly transitive set ∧, f|∧ satisfies a C1-generic-stable shadowable property (resp., C1-generic-stable transitive specification property or C1-generic-stable barycenter property) if and only if ∧ is a hyperbolic basic set. In partic-ular, f|∧ satisfies a C1-stable shadowable property (resp., C1-stable transitive specification property or C1-stable barycenter property) if and only if ∧ is a hyperbolic basic set. Similar results are valid for volume-preserving case. References | Related Articles | Metrics

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EXTENDED CESÀRO OPERATORS AND MULTIPLIERS ON BMOA LV Xiao-Fen Acta mathematica scientia,Series B. 2012, 32 (2):  559-567.  DOI: 10.1016/S0252-9602(12)60038-1 Abstract ( 565 )   RICH HTML PDF (163KB) ( 908 )   Save In this article, we characterize the boundedness and compactness of extended Cesàro operators on the spaces BMOA by the Carleson measures in the unit ball. Mean-while, we study the pointwise multipliers on BMOA. References | Related Articles | Metrics

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Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP LI Peng-Tao, PENG Li-Zhong Acta mathematica scientia,Series B. 2012, 32 (2):  568-578.  DOI: 10.1016/S0252-9602(12)60039-3 Abstract ( 609 )   RICH HTML PDF (186KB) ( 1166 )   Save Let L = −△Hn+V be a Schr¨odinger operator on Heisenberg group Hn, where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class BQ/2, where Q is the homogeneous dimension of Hn. Let T1 = (−△Hn+V )−1V , T2 =(−△Hn+V )−1/2V 1/2, and T3 = (−△Hn+V )−1/2∇Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some Lp(Hn), where b ∈ BMO(Hn). Note that the kernel of Ti, i = 1, 2, 3 has no smoothness. References | Related Articles | Metrics

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REPRESENTATIONS OF A LOOP LIE ALGEBRA ASSOCIATED WITH QUANTUM PLANE LIANG Jun-Ping, WU Rue-Zhu Acta mathematica scientia,Series B. 2012, 32 (2):  579-585.  DOI: 10.1016/S0252-9602(12)60040-X Abstract ( 537 )   RICH HTML PDF (149KB) ( 921 )   Save In this article, some modules over a loop Lie algebra associated to quantum plane are constructed. The isomorphism classes among these modules are also determined. References | Related Articles | Metrics

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HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS TANG Dong-Mei, ZHONG Tong-De, QIU Chun-Hui Acta mathematica scientia,Series B. 2012, 32 (2):  586-604.  DOI: 10.1016/S0252-9602(12)60041-1 Abstract ( 575 )   RICH HTML PDF (242KB) ( 942 )   Save First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators ∂and ∂^ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace operator is argued. Then, the Borel-Pompeiu formulas for Wn-valued functions are derived through designing a matrix Dirac operator D and a 2× 2 matrix–valued invariant integral kernel with the Witt basis. References | Related Articles | Metrics

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INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE LI Fang, SUN Long-Gang Acta mathematica scientia,Series B. 2012, 32 (2):  605-618.  DOI: 10.1016/S0252-9602(12)60042-3 Abstract ( 508 )   RICH HTML PDF (210KB) ( 1250 )   Save The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type. First of all, we show that, if two finite-dimensional self-injective k-algebras are stably equivalent of Morita type, then their orbit algebras are isomorphic. Secondly, it is verified that the quasitilted property of an algebra is invariant under stable equivalences of Morita type. As an application of this result, it is obtained that if an algebra is of finite representation type, then its tilted property is invariant under stable equivalences of Morita type; the other application to partial tilting modules is given in Section 4. Finally, we prove that when two finite-dimensional k-algebras are stably equivalent of Morita type, their repetitive algebras are also stably equivalent of Morita type under certain conditions. References | Related Articles | Metrics

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ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES Ricardo Almeida, Rui A. C. Ferreira, Delfim F. M. Torres Acta mathematica scientia,Series B. 2012, 32 (2):  619-630.  DOI: 10.1016/S0252-9602(12)60043-5 Abstract ( 488 )   RICH HTML PDF (182KB) ( 1630 )   Save In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered. References | Related Articles | Metrics

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SOME PROPERTIES OF COMMUTING AND ANTI-COMMUTING m-INVOLUTIONS Mark Yasuda Acta mathematica scientia,Series B. 2012, 32 (2):  631-644.  DOI: 10.1016/S0252-9602(12)60044-7 Abstract ( 582 )   RICH HTML PDF (204KB) ( 1570 )   Save We define an m-involution to be a matrix K ∈ Cn×n for which Km = I. In this article, we investigate the class Sm (A) of m-involutions that commute with a diagonalizable matrix A ∈ Cn×n. A number of basic properties of Sm (A) and its related subclass Sm (A, X) are given, where X is an eigenvector matrix of A. Among them, Sm (A) is shown to have a torsion group structure under matrix multiplication if A has distinct eigenvalues and has non-denumerable cardinality otherwise. The constructive definition of Sm (A, X) allows one to generate all m-involutions commuting with a matrix with distinct eigenvalues. Some related results are also given for the class ˜ Sm (A) of m-involutions that anti-commute with a matrix A ∈ Cn×n. References | Related Articles | Metrics

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ON ALMOST PRIME SUBMODULES Hani A. Khashan Acta mathematica scientia,Series B. 2012, 32 (2):  645-651.  DOI: 10.1016/S0252-9602(12)60045-9 Abstract ( 588 )   RICH HTML PDF (133KB) ( 2452 )   Save In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules. References | Related Articles | Metrics

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UNIQUE CONTINUATION AND PERSISTENCE PROPERTIES OF SOLUTIONS OF THE 2-COMPONENT DEGASPERIS-PROCESI#br# EQUATIONS FU Ying, QU Chang-Zheng Acta mathematica scientia,Series B. 2012, 32 (2):  652-662.  DOI: 10.1016/S0252-9602(12)60046-0 Abstract ( 571 )   RICH HTML PDF (160KB) ( 1342 )   Save In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time. References | Related Articles | Metrics

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SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY CHENG Zhi-Yun, GAO Hong-Zhu Acta mathematica scientia,Series B. 2012, 32 (2):  663-671.  DOI: 10.1016/S0252-9602(12)60047-2 Abstract ( 558 )   RICH HTML PDF (204KB) ( 1177 )   Save The relationship between a link diagram and its corresponding planar graph is briefly reviewed. A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot. The relationship between planar graph and almost planar Seifert surface is discussed. Using planar graph, we construct an alternating amphicheiral prime knot with crossing number n for any even number n  4. This gives an affirmative answer to problem 1.66(B) on Kirby’s problem list. References | Related Articles | Metrics

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POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY Sma?l Djebali, Ouiza Sa?fi, YAN Bao-Qiang Acta mathematica scientia,Series B. 2012, 32 (2):  672-694.  DOI: 10.1016/S0252-9602(12)60048-4 Abstract ( 673 )   RICH HTML PDF (233KB) ( 995 )   Save In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi-demiology and combustion theory set on the positive half-line are investigated. We use upper and lower solution techniques combined with fixed point index on cones in appro-priate Banach spaces. The results complement recent ones in the literature. References | Related Articles | Metrics

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THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION WANG Ai-Feng, NI Ming-Kang Acta mathematica scientia,Series B. 2012, 32 (2):  695-709.  DOI: 10.1016/S0252-9602(12)60049-6 Abstract ( 557 )   RICH HTML PDF (227KB) ( 1077 )   Save In this article, the interior layer for a second order nonlinear singularly per-turbed differential-difference equation is considered. Using the methods of boundary func-tion and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = σ. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones. References | Related Articles | Metrics

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ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION YAN Wei, LI Yong-Sheng Acta mathematica scientia,Series B. 2012, 32 (2):  710-716.  DOI: 10.1016/S0252-9602(12)60050-2 Abstract ( 725 )   RICH HTML PDF (148KB) ( 847 )   Save In this article, we consider the Cauchy problems for the modified Kawahara equation ∂tu +μ∂x(u3) + α∂5xu + β∂3xu + γ∂xu = 0 and the Kaup-Kupershmidt equation ∂tu + μu∂2xu + α∂5xu + β∂3xu + γ∂xu = 0. Using the general well-posedness principle introduced by I. Bejenaru and T. Tao, we prove that the modified Kawahara equation is ill-posed for the initial data in Hs(R) with s < −1/4 and that the Kaup-Kupershmidt equation is ill-posed for the initial data in Hs(R) with s < 0. References | Related Articles | Metrics

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RESULTS ON A QUESTION OF ZHANG AND YANG LI Sheng, GAO Zong-Sheng Acta mathematica scientia,Series B. 2012, 32 (2):  717-723.  DOI: 10.1016/S0252-9602(12)60051-4 Abstract ( 678 )   RICH HTML PDF (143KB) ( 1045 )   Save For a meromorphic function f, let N(l+1(r, 1/f ) denote the counting function of zeros of f of order l at least. Let f be a nonconstant meromorphic function, such that N(r, f) = S(r, f). Denote F = fn. Suppose that F and F′ share 1 CM. If (1) n ≥ 3, or (2) n = 2 and N(r, 1/ f ) = O(N(3(r, 1/f )), then, F = F′, and f assumes the form f(z) = ce1/n z, where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved. References | Related Articles | Metrics

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ON PROPERTIES OF q-DIFFERENCE EQUATIONS ZHENG Xiu-Min, CHEN Zong-Xuan Acta mathematica scientia,Series B. 2012, 32 (2):  724-734.  DOI: 10.1016/S0252-9602(12)60052-6 Abstract ( 766 )   RICH HTML PDF (173KB) ( 1220 )   Save In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi. References | Related Articles | Metrics

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CONVERGENCE OF WEIGHTED AVERAGES OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES ZHANG Chao, HOU You-Liang Acta mathematica scientia,Series B. 2012, 32 (2):  735-744.  DOI: 10.1016/S0252-9602(12)60053-8 Abstract ( 539 )   RICH HTML PDF (172KB) ( 1171 )   Save Let x = (xn)n≥1 be a martingale on a noncommutative probability space (M, τ ) and (wn)n≥1 a sequence of positive numbers such that Wn = ∑nk=1 wk →∞ as n →1. We prove that x = (xn)n≥1 converges in E(M) if and only if (σn(x))n≥1 converges in E(M), where E(M) is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn(x) is given by σn(x) =1/Wn∑nk=1wkxk, n = 1, 2, · · · . If in addition, E(M) has absolutely continuous norm, then, (σn(x))n≥1 converges in E(M) if and only if x = (xn)n≥1 is uniformly integrable and its limit in measure topology x∞ ∈E(M). References | Related Articles | Metrics

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ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS MA Bing-Qing Acta mathematica scientia,Series B. 2012, 32 (2):  745-751.  DOI: 10.1016/S0252-9602(12)60054-X Abstract ( 479 )   RICH HTML PDF (132KB) ( 907 )   Save In this article, we study the first two eigenvalues of the higher order buckling problem on a domain in the unit sphere. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue. In particular, the estimate on first two eigenvalues of the higher order buckling problem of Huang, Li and Qi [5] is included in our results. References | Related Articles | Metrics

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THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER ON THE#br# UNIT POLYDISK IN Cn LIU Xiao-Song, LIU Tai-Shun Acta mathematica scientia,Series B. 2012, 32 (2):  752-764.  DOI: 10.1016/S0252-9602(12)60055-1 Abstract ( 587 )   RICH HTML PDF (199KB) ( 976 )   Save In this article, first, a sufficient condition for a starlike mapping of order f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f(z) =(f1(z), f2(z), · · · , fn(z))′ is a starlike mapping of order or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn, and D2fk(0)(z2)/2! = zk(∑nl=1aklzl), k =1, 2, · · · , n, here, akl = 1/2！∂2fk(0)/∂zk∂zl,k, l = 1, 2, · · · , n. Our result states that the Bieberbach conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order and biholomorphic starlike mappings) is partly proved. References | Related Articles | Metrics

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CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS J. Dziok Acta mathematica scientia,Series B. 2012, 32 (2):  765-774.  DOI: 10.1016/S0252-9602(12)60056-3 Abstract ( 612 )   RICH HTML PDF (160KB) ( 1162 )   Save The object of this article is to introduce new classes of meromorphic functions associated with conic regions. Several properties like the coefficient bounds, growth and distortion theorems, radii of starlikeness and convexity, partial sums, are investigated. Some consequences of the main results for the well-known classes of meromorphic functions are also pointed out. References | Related Articles | Metrics

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ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY M. Rahimi, A. Riazi Acta mathematica scientia,Series B. 2012, 32 (2):  775-782.  DOI: 10.1016/S0252-9602(12)60057-5 Abstract ( 505 )   RICH HTML PDF (147KB) ( 1173 )   Save In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional. References | Related Articles | Metrics

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APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS A. Ghaffari, S. Javadi, H. Khodaei Acta mathematica scientia,Series B. 2012, 32 (2):  783-792.  DOI: 10.1016/S0252-9602(12)60058-7 Abstract ( 1000 )   RICH HTML PDF (167KB) ( 940 )   Save For a Banach algebra A, we denote by A* and A the first and the second duals of A respectively. Let T be a mapping from A* to itself. In this article, we will investigate some stability results concerning the equations T(αf + βg) = αT(f) + βT(g), T(af) = aT(f) and T(αf + βg) + T(αf − βg) = 2α2T(f) + 2β2T(g) where f, g ∈ A*, a ∈ A, and α, β∈ Q \ {0}. References | Related Articles | Metrics

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SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION DING Hai-Yun, NI Ming-Kang, LIN Wu-Zhong, CAO Yang Acta mathematica scientia,Series B. 2012, 32 (2):  793-799.  DOI: 10.1016/S0252-9602(12)60059-9 Abstract ( 641 )   RICH HTML PDF (200KB) ( 1240 )   Save A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result. References | Related Articles | Metrics

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ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS GAO Ling-Yun Acta mathematica scientia,Series B. 2012, 32 (2):  800-806.  DOI: 10.1016/S0252-9602(12)60060-5 Abstract ( 514 )   RICH HTML PDF (144KB) ( 1183 )   Save In this article, we mainly investigate the growth and existence of meromor-phic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations. References | Related Articles | Metrics

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CONTINUOUS FRAME WAVELETS Ali Akbar Arefijamaal, Narguess Tavallaei Acta mathematica scientia,Series B. 2012, 32 (2):  807-812.  DOI: 10.1016/S0252-9602(12)60061-7 Abstract ( 578 )   RICH HTML Save Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector Ψ ∈ H is called a continuous frame wavelet if there exist A, B > 0 such that A||Φ||2 ≤∫G|<π(g)Ψ ,Φ|2dg ≤ B||Φ||2   (Φ ∈ H), in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components. References | Related Articles | Metrics

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ON REDUCIBILITY OF THE SELF-HOMOTOPY EQUIVALENCES OF WEDGE SPACES YU Hai-Bo, SHEN Wen-Huai Acta mathematica scientia,Series B. 2012, 32 (2):  813-817.  DOI: 10.1016/S0252-9602(12)60062-9 Abstract ( 413 )   RICH HTML PDF (136KB) ( 1106 )   Save Reducibility of the self-homotopy equivalences of wedge spaces is studied and some conditions implying the reducibility are obtained. References | Related Articles | Metrics

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COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS Boˇsko Damjanovi′c, Bessem Samet, Calogero Vetro Acta mathematica scientia,Series B. 2012, 32 (2):  818-824.  DOI: 10.1016/S0252-9602(12)60063-0 Abstract ( 881 )   RICH HTML PDF (133KB) ( 1889 )   Save We establish some results on coincidence and common fixed points for a two-pair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature. References | Related Articles | Metrics