Showing papers in "Journal of The Korean Mathematical Society in 2006"
73 citations
TL;DR: The existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes are discussed in this paper, and the results presented in this paper extend, improve and unify the results due to Bellman [2, 3], Bhakta-Choudhury [6], Bhaka-Mitra [7], and Liu [12].
Abstract: The existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes are discussed. The results presented in this paper extend, improve and unify the results due to Bellman [2, 3], Bhakta-Choudhury [6], Bhakta-Mitra [7], and Liu [12].
64 citations
TL;DR: In this article, the authors studied both slant and semi-slant submanifolds of an almost product Riemannian manifold and gave characterization theorems for them.
Abstract: In this paper, we study both slant and semi-slant sub- manifolds of an almost product Riemannian manifold. We give characterization theorems for slant and semi-slant submanifolds and investigate special class of slant submanifolds which are product version of Kaehlerian slant submanifold. We also obtain integrabil- ity conditions for the distributions which are involved in the defl- nition of a semi-slant submanifold. Finally, we prove a theorem on the geometry of leaves of distributions under a condition.
55 citations
TL;DR: In this paper, the authors obtained several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness.
Abstract: The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.
40 citations
TL;DR: In this article, q-extensions of Genocchi numbers and polynomials are used to construct p-adic inter-polation functions for q-Genocchi number.
Abstract: In this paper q-extensions of Genocchi numbers are de- flned and several properties of these numbers are presented. Prop- erties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic inter- polation functions for q-Genocchi numbers. As an application, gen- eral systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.
33 citations
TL;DR: In this paper, the authors obtained a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for f(z) = P1=1 Pnk (z) satisfying nk+1=nk > 1 for all k 2 N, to belong to the weighted Bergman space.
Abstract: In this paper we obtain a su-cient and necessary con- dition for an analytic function f on the unit ball B with Hadamard gaps, that is, for f(z) = P1=1 Pnk (z) (the homogeneous polyno- mial expansion of f) satisfying nk+1=nk ‚ ‚ > 1 for all k 2 N; to belong to the weighted Bergman space A p(B) = ' f j Z B jf(z)j p (1 i jzj 2 ) fi dV (z) < 1; f 2 H(B) " : We flnd a growth estimate for the integral mean µZ @B jf(r‡)j p dae(‡) ¶1=p ; and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space Hp;q;fi(B) and weighted Bergman space on polydisc A p (U n ) are also given.
23 citations
TL;DR: In this article, the topological entropy of a sequence of equi-continuous monotone maps on circles is shown to be Ω( √ √ log n) for skew products on annular and torus.
Abstract: In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps on circles is . As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.Ā搀會Ā搀肔�⨀烈ĀĀĀ會ĀĀ⨀䁩ĀĀĀ會ĀĀゕ�⨀预烈ЀĀЀ會ĀЀ袕�⨀㢅烈Ā會Ā�⨀�烈ࠀĀࠀ會Āࠀ㢖�⨀ạĀ᐀會Ā᐀邖�⨀䢫ạᄀĀ저會Ā저�⨀炆烈Ā᐀會Ā᐀䂗�⨀ࢇ烈Ā᐀會Ā᐀颗�⨀킈烈瀀ꀏ會Ā�⨀ạĀ᐀會Ā᐀䢘�⨀碬ạĀ㰀
22 citations
TL;DR: The developed lumped model of circulation in normal case is extended into a speciflc model for arrhythmia and provides valuable tools in examining and understanding cardiovascular diseases.
Abstract: A new mathematical model of pumping heart coupled to lumped compartments of blood circulation is presented. This lumped pulsatile cardiovascular model consists of eight compart- ments of the body that include pumping heart, the systemic circu- lation, and the pulmonary circulation. The governing equations for the pressure and volume in each vascular compartment are derived from the following equations: Ohm's law, conservation of volume, and the deflnition of compliances. The pumping heart is modeled by the time-dependent linear curves of compliances in the heart. We show that the numerical results in normal case are in agree- ment with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a speciflc model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.
21 citations
TL;DR: In this article, the Briot-Bouquet differential equations of the form given in [1] were reduced to where, and conditions were given in order that if u and v satisfy, respectively, the equations, with certain conditions on the functions F and G applying the concept of strong subordination, implies that indicates subordination.
Abstract: For the Briot-Bouquet differential equations of the form given in [1] we can reduce them to where . In this paper we are going to give conditions in order that if u and v satisfy, respectively, the equations (1) , with certain conditions on the functions F and G applying the concept of strong subordination given in [2] by the author, implies that indicates subordination.
20 citations
TL;DR: In this article, the main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results, which are discussed in detail.
Abstract: The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.
19 citations
TL;DR: In this paper, it was shown that if T is a quasi-class A operator and f is a function analytic on a neigh-borhood of T, then f(T) satisfies Weyl's theorem and f (T ⁄ ) satisfies a-Weyl's conjecture.
Abstract: Let T be a bounded linear operator on a complex in- flnite dimensional Hilbert space H. We say that T is a quasi-class A operator if T ⁄ jT 2 jT ‚ T ⁄ jTj 2 T. In this paper we prove that if T is a quasi-class A operator and f is a function analytic on a neigh- borhood of the spectrum of T, then f(T) satisfles Weyl's theorem and f(T ⁄ ) satisfles a-Weyl's theorem.
TL;DR: In this paper, a contact strongly pseudo-convex CR-space form (of con- stant pseudo-holomorphic sectional curvature) was defined by using the Tana- ka-Webster connection.
Abstract: As a natural generalization of a Sasakian space form, we deflne a contact strongly pseudo-convex CR-space form (of con- stant pseudo-holomorphic sectional curvature) by using the Tana- ka-Webster connection, which is a canonical a-ne connection on a contact strongly pseudo-convex CR-manifold In particular, we classify a contact strongly pseudo-convex CR-space form (M;·;') with the pseudo-parallel structure operator h(= 1=2L»'), and then we obtain the nice form of their curvature tensors in proving Schur- type theorem, where L» denote the Lie derivative in the character- istic direction »
TL;DR: The moduli spaces of stable vector bundles of rank 2 on Enriques surfaces are described, which all have the structure of the fibrations reflecting those of Enrique surfaces.
Abstract: We describe the moduli spaces of stable vector bundles of rank 2 on Enriques surfaces. They all have the structure of the fibrations reflecting those of Enriques surfaces.
TL;DR: In this paper, it was shown that the Cauchy-Rassias stability of the functional equation in Banach modules over a unital or a Lie vector space is robust.
Abstract: Let X and Y be vector spaces. It is shown that a mapping satisfies the functional equation $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1 is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital . Let A and B be unital or Lie . As an application, we show that every almost homomorphism h : of A into B is a homomorphism when for all unitaries , and d = 0,1,2,..., and that every almost linear almost multiplicative mapping is a homomorphism when h(2x)=2h(x) for all . Moreover, we prove the Cauchy-Rassias stability of homomorphisms in or in Lie , and of Lie derivations in Lie .
TL;DR: In this paper, the authors show further results concerning the problem of extending total preorders from a sub-set of a topological space to the entire space using the approach introduced by Gyoseob Yi.
Abstract: ain Abstract. The objective of this paper is to show further results concerning the problem of extending total preorders from a sub- set of a topological space to the entire space using the approach introduced by Gyoseob Yi.
TL;DR: For double arrays of constants and sequences of negatively orthant dependent random variables, the conditions for strong law of large number of are given in this paper, and both cases are treated.
Abstract: For double arrays of constants and sequences of negatively orthant dependent random variables , the conditions for strong law of large number of are given. Both cases are treated.
TL;DR: In this article, a subspace lattice on a Hilbert space H and X and Y operators acting on H were considered and the assertion that there exists an operator A in AlgL such that Ax = y is equivalent to the condition $$K_0\;:\;=\;sup\{{\parallel}E^{\bot}y{\parallel]/{\ parallel}x\;:/;E{\in}L}= whose norm is under this case.
Abstract: Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. Let P be the projection onto , where RX is the range of X. If PE = EP for each , then there exists an operator A in AlgL such that AX = Y if and only if $$sup\{{\parallel}E^{\bot}Yf{\parallel}/{\parallel}E^{\bot}Xf{\parallel}\;:\;f{\in}H,\; E{\in}L}=K\; Let x and y be vectors in H and let be the projection onto the singlely generated space by x. If for each , then the assertion that there exists an operator A in AlgL such that Ax = y is equivalent to the condition $$K_0\;:\;=\;sup\{{\parallel}E^{\bot}y{\parallel}/{\parallel}E^{\bot}x\;:\;E{\in}L}= whose norm is under this case.
TL;DR: In this article, the authors give some rather weak size conditions implying the L p boundedness of the multiple Marcin- kiewicz integrals for some flxed 1 < p < 1, which essentially prove and extend some known results.
Abstract: This paper is concerned with giving some rather weak size conditions implying the L p boundedness of the multiple Marcin- kiewicz integrals for some flxed 1 < p < 1, which essentially im- prove and extend some known results. ›(x 0 ; x 0 )dae(x 0 ) = Z S ni1 ›(x 0 ; x 0 )dae(x 0 ) = 0:
TL;DR: In this article, the p-adic q-higher-order Dedekind sums were constructed for an odd prime and the properties of these sums were established by using Bernoulli functions, trigonometric functions and Lambert series.
Abstract: The goal of this paper is to deflne p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic con- tinuous functions for an odd prime. These functions contain p- adic q-analogue of higher-order Hardy-type sums. By using an in- variant p-adic q-integral on Zp, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.
TL;DR: For 3-dimensional Bieberbach groups, the authors studied the deformation spaces in the group of isometries of R 3, and gave complete descrip- tions of Teichmuller spaces, Chabauty spaces, and moduli spaces.
Abstract: For 3-dimensional Bieberbach groups, we study the de- formation spaces in the group of isometries ofR 3 . First we calculate the discrete representation spaces and the automorphism groups. Then for each of these Bieberbach groups, we give complete descrip- tions of Teichmuller spaces, Chabauty spaces, and moduli spaces.
TL;DR: In this article, it was shown that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomial for G to the function of the re∞exive Smirnov-Orlicz class EM (G) is equivalent to the best approximat- ing poinomial rate in EM(G).
Abstract: Let i be a bounded rotation (BR) curve without cusps in the complex plane C and let G := inti. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials Fn for G to the function of the re∞exive Smirnov-Orlicz class EM (G) is equivalent to the best approximat- ing polynomial rate in EM (G).
TL;DR: In this article, the authors restrict regularity to normal subgroups of finite index, which generalises the notion of regularity for some non-regular objects, such as subgroups with symmetries.
Abstract: Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product . In this correspondence, hypermaps correspond to conjugacy classes of subgroups of , and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out of the triangle group . This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups of of finite index. This generalises the notion of regularity to some non-regular objects.
TL;DR: In this article, a complete convergence result for weighted sums of the form P1=1 ankVnk was obtained for the weighted sum of P1 = 1 ank Vnk.
Abstract: Let fVnk;k ‚ 1;n ‚ 1g be an array of rowwise inde- pendent random elements which are stochastically dominated by a random variable X with EjXj fi ∞ +µ log ‰ (jXj) 0;fi > 0;∞ > 0;µ > 0 such that µ+fi=∞ < 2: Let fank;k ‚ 1;n ‚ 1g be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form P1=1 ankVnk:
TL;DR: In this article, a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk is given, and some results for special types of semi-commutators are included.
Abstract: We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.
TL;DR: In this paper, conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I inveXity of both the objective function and the constraint functions on the feasible set of the program are given.
Abstract: This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.
TL;DR: In this paper, a cubic difierential system is proposed, which can be considered a generalization of the predator-prey models, studied by many authors recently (see (18, 20), for instance).
Abstract: We propose a cubic difierential system, which can be considered a generalization of the predator-prey models, studied by many authors recently (see (18, 20), for instance). The properties of the equilibrium points, the existences, nonexistence, the uniqueness conditions and the relative positions of the limit cycles are inves- tigated. An example is used to show our theorems are easy to be used in applications.
TL;DR: In this article, the identifcation problem of constant pa-rameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition was studied, and necessary conditions were established for several types of observations by utilizing quadratic optimal control theory due to lions.
Abstract: We study the identiflcation problems of constant pa- rameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parame- ters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions (13).
TL;DR: This work calculates m's which correspond to the nonexistence of some extremal self-dual binary linear codes and proves that there are inflnitely many such m's.
Abstract: It is known that if C is an (24m + 2l;12m + l;d ) self- dual binary linear code with 0 • l < 11, then d • 4m + 4. We present a su-cient condition for the nonexistence of extremal self- dual binary linear codes with d = 4m + 4;l = 1;2;3;5. From the su-cient condition, we calculate m's which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are inflnitely many such m's. We also give similar results for additive self-dual codes over GF(4) of length n = 6m + 1.
TL;DR: In this paper, the concept of self homotopy equivalences of a space X to that of an object in the category of pairs was extended to the special case of the CW-pair (X, A).
Abstract: In this paper, we extend the concept of the group of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence where G is a subgroup of . Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence provided the two sets and [X, Y] are trivial.
TL;DR: In this paper, the existence theorem for measure-valued Dyson series was established and it satisfies the Volterra-type integral equation, and it was shown that the stability of the stability result is also satisfied.
Abstract: In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfles the Volterra- type integral equation. Furthermore, we prove the stability theo- rems for measure-valued Dyson series.