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| 1 | A Characterization of $\mathcal{M}$-harmonicity | |
| | | Author(s) | : | Jaesung Lee |
| | | Keyword(s) | : | $; mathcal{M}$-harmonic function; weighted Berezin transform; Gelfand transform |
| | | Abstract | : | If $f$ is $\mathcal{M}$-harmonic and integrable with respect to a weighted radial measure $\nu_{\h}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n} (f\circ\psi)\ d\nu_{\h}=f(\psi(0))$ for every $\psi \in {\hbox{Aut}(B_n)}$. Equivalently $f$ is fixed by the weighted Berezin transform; $T_{\h}f=f$. In this paper, we show that if a function $f$ defined on $B_n$ satisfies $R(f \circ \phi) \in L^{\infty}(B_{n})$ for every $\phi \in {\hbox{Aut}(B_n)}$ and $Sf=rf$ for some $|r|=1$, where $S$ is any convex combination of the iterations of ${T_{\h}}'s$, then $f$ is $\mathcal{M}$-harmonic. |
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| 2 | A Classification of prime-valent Regular Cayley Maps on Abelian, Dihedral and Dicyclic Groups | |
| | | Author(s) | : | Dongseok Kim; Young Soo Kwon; Jaeun Lee |
| | | Keyword(s) | : | Cayley map; regular embedding |
| | | Abstract | : | A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are balanced and all prime-valent regular Cayley maps on abelian groups are either balanced or anti-balanced. Furthermore, we prove that there is no prime-valent regular Cayley map on any dicyclic group. |
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| 3 | A Note on Functions of Mean Bloch Types | |
| | | Author(s) | : | Hong Rae Cho; Youn Ki Kim; Ern Gun Kwon; Jin Kee Lee |
| | | Keyword(s) | : | $H^p$ space; Bloch space; mean Lipschitz space |
| | | Abstract | : | A characterization of the holomorphic function spaces of me\-an Bloch type on the unit disc is deduced in terms of the induced distance. |
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| 4 | A Polar, the Class and Plane Jacobian Conjecture | |
| | | Author(s) | : | Dosang Joe |
| | | Keyword(s) | : | polar; class of plane curve; plane Jacobian conjecture |
| | | Abstract | : | Let $P$ be a Jacobian polynomial such as $\deg P=\deg_y P$. Suppose the Jacobian polynomial $P$ satisfies the intersection condition satisfying $\dim_{\CC} \CC[x,y]/\langle P, P_y\rangle=\deg P-1$, we can prove that the Keller map which has $P$ as one of coordinate polynomial always has its inverse. |
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| 5 | Approximate bi-homomorphisms and bi-derivations in $C^*$-ternary Algebras | |
| | | Author(s) | : | Jae-Hyeong Bae ; Won-Gil Park |
| | | Keyword(s) | : | bi-additive mapping; $C^*$-ternary algebra |
| | | Abstract | : | In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $C^*$-ternary algebras and of bi-derivations on $C^*$-ternary algebras for the following bi-additive functional equation $$f(x+y,z-w)+f(x-y,z+w)=2f(x,z)-2f(y,w).$$ This is applied to investigate bi-isomorphisms between $C^*$-ternary algebras. |
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| 6 | Characterizations of Real Hypersurfaces of Type a in a Complex Space Form | |
| | | Author(s) | : | U-Hang Ki; In-Bae Kim; Dong Ho Lim |
| | | Keyword(s) | : | real hypersurface; structure Jacobi operator; Hopf hypersurface |
| | | Abstract | : | Let $M$ be a real hypersurface with almost contact metric structure $(\phi, g, \xi, \eta)$ in a complex space form $\mn$, $c \neq 0$. In this paper we prove that if $\rx\lx g=0$ holds on $M$, then $M$ is a Hopf hypersurface in $\mn$, where $\rx$ and $\lx$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\xi$ respectively. We characterize such Hopf hypersurfaces of $\mn$. |
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| 7 | Global Robust Stability of time-delay Systems with Discontinuous Activation Functions under Polytopic Parameter Uncertainties | |
| | | Author(s) | : | Zengyun Wang; Lihong Huang; Yi Zuo; Lingling Zhang |
| | | Keyword(s) | : | global robust stability; delayed neural network; delay-independ; -ent condition; delay-dependent condition; linear matrix inequality; discontinuous neuron activation |
| | | Abstract | : | This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of $M$-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria. |
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| 8 | Impersonation Attack on the Strong Identification Based on a hard-on-average Problem | |
| | | Author(s) | : | Bonwook Koo; Daesung Kwon; Jooyoung Lee; Jung Hwan Song |
| | | Keyword(s) | : | cryptography; authentication; zero-knowledge identification |
| | | Abstract | : | In this paper, we analyze a zero-knowledge identification scheme presented in~\cite{Cab05}, which is based on an average-case hard problem, called \emph{distributional matrix representability problem}. On the contrary to the soundness property claimed in~\cite{Cab05}, we show that a simple impersonation attack is feasible. \keywords{zero-knowledge, computational complexity, matrix representability problem} |
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| 9 | Integration with Respect to Analogue of Wiener Measure over Paths in Abstract Wiener Space and its Applications | |
| | | Author(s) | : | Kun Sik Ryu |
| | | Keyword(s) | : | analogue of Wiener measure; measure-valued measure; Bartle integral; Bochner integral; stochastically independent; conditional expectation |
| | | Abstract | : | In 1992, the author introduced the definition and the properties of Wiener measure over paths in abstract Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in abstract Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae. |
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| 10 | Invariance of Domain Theorems for Condensing Multivalued Vector Fields | |
| | | Author(s) | : | In-Sook Kim |
| | | Keyword(s) | : | invariance of domain; countably condensing; multivalued vector fields; degree theory |
| | | Abstract | : | Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably $k$-contractive multivalued vector fields. |
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| 11 | Left Jordan Derivations on Banach Algebras and Related Mappings | |
| | | Author(s) | : | Yong-Soo Jung ; Kyoo-Hong Park |
| | | Keyword(s) | : | (generalized) left Jordan derivation; (generalized) left derivation; derivation; spectral boundedness; Jacobson radica |
| | | Abstract | : | In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\d$ be a spectrally bounded left Jordan derivation on a Banach algebra $A$. Then $\d$ maps $A$ into its Jacobson radical. (ii) Let $\d$ be a left Jordan derivation on a unital Banach algebra $A$ with the condition sup$\{r(c^{-1}\d(c)): c \in A \text{ invertible} \}< \infty$. Then $\d$ maps $A$ into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in \cite[p.\,260]{Ash08}: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation. |
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| 12 | Nontrivial Solutions for boundary-value Problems of Nonlinear Fractional Differential Equations | |
| | | Author(s) | : | Yingxin Guo |
| | | Keyword(s) | : | standard Riemann-Liouville differentiation; fractional differential equation; boundary-value problem; nontrivial solution; Leray-Schauder nonlinear alternative |
| | | Abstract | : | In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem (BVP) \begin{gather*} -\mathbf{D}_{0+}^\alpha u(t)=\lambda [f(t,u(t))+q(t)],\quad 00$ is a parameter, $1<\alpha\leq 2$, $\mathbf{D}_{0+}^\alpha$ is the standard Riemann-Liouville differentiation, $f:[0,1]\times \mathbb{R}\to \mathbb{R}$ is continuous, and $q(t):(0,1)\to [0, +\infty)$ is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on $f$. |
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| 13 | Notes on Critical almost Hermitian Structures | |
| | | Author(s) | : | Jung Chan Lee; Jeong Hyeong Park; Kouei Sekigawa |
| | | Keyword(s) | : | critical almost Hermitian structure; Einstein-Hilbert functional |
| | | Abstract | : | We discuss the critical points of the functional $\mathcal {F}_{\lambda, \mu} (J, g) = \int_M (\lambda \tau + \mu \tau^* ) dv_g$ on the spaces of all almost Hermitian structures $\mathcal{AH}(M)$ with ${(\lambda, \mu)} \in \mathbb{R}^2 - (0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the $*$-scalar curvature of $(J, g)$, respectively. We shall give several characterizations of K\"{a}hler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $\mathcal {F}_{\lambda, \mu} (J, g)$ on $\mathcal{AH}(M)$. Further, we provide the almost Hermitian analogy of the Hilbert's result. |
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| 14 | Self-similar Solutions for the 2-D Burgers System in Infinite Subsonic Channels | |
| | | Author(s) | : | Kyungwoo Song |
| | | Keyword(s) | : | changing-type equations; degenerating quasilinear elliptic equations; self-similar solutions; 2-D full Euler equations |
| | | Abstract | : | We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp. |
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| 15 | The Moments of the Riesz-N{\'a}gy-Tak{\'a}cs Distribution over a General Interval | |
| | | Author(s) | : | In Soo Baek |
| | | Keyword(s) | : | Riemann-Stieltjes integral; moment; interval of orthogonality; singular distribution function; metric number theory |
| | | Abstract | : | In this paper, the moments of the Riesz-N{\'a}gy-Tak{\'a}cs(RNT) distribution over a general interval $[a,b]\subset [0,1]$, are found through the moments of the RNT distribution over the unit interval, $[0,1]$. This is done using some special features of the distribution and the fact that $[0,1]$ is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval. |
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| 16 | The Motion of Point Vortex Dipole on the Ellipsoid of Revolution | |
| | | Author(s) | : | Sun-Chul Kim |
| | | Keyword(s) | : | point vortex; ellipsoid of revolution; perturbation expansion; geodesic; vortex dipole |
| | | Abstract | : | A pair of point vortices of the same strength but opposite sign is called a vortex dipole. We consider the limiting case where two vortices approach infinitely close while the ratio of the strength to the distance kept constant. The motion of such {\em point} vortex dipole on the ellipsoid of revolution is investigated geometrically to conclude that the trajectory draws a geodesic up to the leading order of perturbation, whose direction is determined by the initial orientation of the dipole. Related issues are also remarked. |
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| 17 | The Propagation Phenomenon of Weighted Shifts | |
| | | Author(s) | : | An-Hyun Kim ; Eun-Young Kwon |
| | | Keyword(s) | : | weighted shifts; subnormal; $k$-hyponormal; quadratically hyponormal; cubically hyponormal |
| | | Abstract | : | This paper concerns the propagation phenomenon of weight\-ed shifts. We here establish the existence of positive real numbers $b$ and $c$ ($1 |
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| 18 | The Reflective Function Represented by Three Exponential Matrixes | |
| | | Author(s) | : | Zhengxin Zhou |
| | | Keyword(s) | : | reflecting function; periodic system; asymptotic behavior |
| | | Abstract | : | In this article, we discuss the reflective function which can be represented by three exponential matrixes and apply the results to studying the existence of periodic solutions of these systems. The obtained conclusions extend and improve the foregoing results. |
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| 19 | The Uniform CLT for Martingale Difference Arrays under the Uniformly Integrable Entropy | |
| | | Author(s) | : | Jongsig Bae; Doobae Jun; Shlomo Levental |
| | | Keyword(s) | : | uniform CLT; martingale difference array; uniformly integrable entropy; restricted chaining; sequential empirical process |
| | | Abstract | : | In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler~\cite{ReferZIEGLER} did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler~\cite{ReferZIEGLER} and other results of independent problems. The results also generalizes those of Bae and Choi~\cite{ReferBAECHOI} to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with $n$ is given. |
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| 20 | Two New Proofs of the Complete Monotonicity of a Function Involving the Psi Function | |
| | | Author(s) | : | Bai-Ni Guo ; Feng Qi |
| | | Keyword(s) | : | new proof; completely monotonic function; psi function; inequality |
| | | Abstract | : | In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha\le1$ such that the function $x^\alpha[\ln x-\psi(x)]$ is completely monotonic on $(0,\infty)$. |
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