201323

Code: 201323

A Compound Poisson Model for Learning Discrete Bayesian Networks

Abdelaziz Ghribi, Afif Masmoudi

 

Abstracts

We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks

 

201322

Code: 201322

Monotonicity and Inequalities for the Generalized Distortion Function

Xiaoyan Ma, Yuming Chu, Fei Wang

 

Abstracts

The authors prove some monotonicity properties of functions involving the generalized Agard distortion function η_K (a, t), and obtain some inequalities for η_K (a, t) and relative distortion functions

 

 

201321

Code: 201321

Some Convolution and Inclusion Properties for Subclasses of Meromorphic p-Valent Functions Involving Integral Operator

R. M. El-Ashawah

 

Abstracts

Making use of the linear operator <img height="39" border="0" style="vertical-align:bottom" width="291" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601204-si1.gif">${ℒ}_p^m\left(\lambda ,\mathcal{l}\right)f\left(z\right)=\frac{1}{z^p}+\sum _{k=1}^{\infty }{\left[\frac{\mathcal{l}}{\mathcal{l}+\lambda k}\right]}^m{a}_k{z}^{k-p,}$ where l>0,λ>0,p∈ℕ,m∈ℕ₀=ℕ∪{0},z∈U*$\mathcal{l}>0,\lambda >0,p\in \text{ℕ},m\in {\text{ℕ}}_0=\text{ℕ}\cup \left\{0\right\},z\in U*$ and f(z)∈Σp,$f\left(z\right)\in {\Sigma }_{\text{p}},$ we introduce two subclasses of meromorphic p-valent analytic functions and investigate convolution and inclusion properties for these classes

 

 

201320

Code: 201320

Renewal Theorem for (L, 1)-Random Walk in Random Environment

Wenming Hong, Hongyan Sun

 

Abstracts

We consider a random walk on ℤ in random environment with possible jumps {−L, …, −1, 1}, in the case that the environment {ω_i : i ∈ ℤ} are i.i.d.. We establish the renewal theorem for the Markov chain of “the environment viewed from the particle” in both annealed probability and quenched probability, which generalize partially the results of Kesten (1977) and Lalley (1986) for the nearest random walk in random environment on ℤ, respectively. Our method is based on the intrinsic branching structure within the (L, 1)-RWRE formulated in Hong and Wang

 

 

201319

Code: 201319

Regularity of Solutions to Nonlinear Time Fractional Differential Equation

Mirjana Stojanovic

 

Abstracts

We find an upper viscosity solution and give a proof of the existence-uniqueness in the space <img height="31" border="0" style="vertical-align:bottom" width="408" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601186-si1.gif">$C^{\infty }\left(t\in \left(0,\infty \right);H_2^{s+2}\left({\text{R}}^n\right)\right)\cap C^0\left(t\in [0,\infty \right);H^s\left(R^n\right)),\hspace{0.17em}s\hspace{0.17em}\in R,$ to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions

equation(0.1)

<img height="54" border="0" style="vertical-align:bottom" width="304" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601186-si2.gif">$\begin{array}{l}{\int }_0^{2}p\left(\beta \right)D_{*}^{\beta }\hspace{0.17em}u\left(x,t\right)d\beta ={\Delta }_{x}u\left(x,t\right)+f(t,u(t,\hspace{0.17em}x)),\\ t\ge 0,x\in {\text{R}}^n,u\left(o,x\right)=u_t(0,x)=\psi (x),\end{array}$

where Δ_x is the spatial Laplace operator, <img height="22" border="0" style="vertical-align:bottom" width="24" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601186-si3.gif">$D_{*}^{\beta }$ is the operator of fractional differentiation in the Caputo sense and the force term F satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval <img height="27" border="0" style="vertical-align:bottom" width="502" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601186-si4.gif">$(0,2)\hspace{0.17em}i.e.,\hspace{0.17em}p(\beta )=\sum _{k=1}^m{b}_k\hspace{0.17em}\delta \left(\beta -{\beta }_k\right),\hspace{0.17em}0\hspace{0.17em}<{\beta }_k<2,\hspace{0.17em}{b}_k>0,\hspace{0.17em}k=1,2,\mathrm{\dots },m.$ The regularity of the solution is established in the framework of the space C^∞(t∈(0,∞); C^∞(Rn))∩Co(t∈[0,∞);C^∞(Rn))$C^{\infty }\left(t\in \left(0,\infty \right);\hspace{0.17em}{C}^{\infty }\left(R^n\right)\right)\cap C^o(t\in [0,\infty );C^{\infty }(R^n))$ when the initial data belong to the Sobolev space

 

201318

Code: 201318

Some Geometric Properties of a New Difference Sequence Space Involving Lacunary Sequences

Murat Karakash, Mikail Et, Vatan Karakaya

 

Abstracts

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property (β) for this space and also show that it is not rotund where p = (p_r) is a bounded sequence of positive real numbers with p_r ≥ 1 for all r ∈ ℕ.

 

201317

Code: 201317

Self-Dual Permutation Codes Over Formal Power Series Rings and Finite Principal Ideal Rings  

Guanghui Zhang, Hongwei Liu

 

Abstracts

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings

 

201316

Code: 201316

Properties of the Convolution with Prestarlike Functions 

Jacek Dziok

 

Abstracts

In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interesting applications involving the well-known classes of functions defined by linear operators are also considered

 

201315

Code: 201315

Szegö Type Factorization Theorem for Noncommutative Hardy-Lorentz Spaces 

Jingjing Shao, Yazhou Han

 

Abstracts

We introduce noncommutative Hardy-Lorentz spaces and give the Szegö and inner-outer type factorizations of these spaces

 

201314

Code: 201314

Some Normality Criteria of Meromorphic Functions

Chunlin Lei, Mingliang Fang, Cuiping Zeng

 

Abstracts

Let ℱ be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ ℱ, all of whose zeros have multiplicity at least k + 1, and f + a(f^(k))ⁿ ≠ b in D, then ℱ is normal in D

 

 

201313

Code: 201313

Lelong-Demailly Numbers in Terms of Capacity and Weak Convergence for Closed Positive Currents

Fredj Elkhadhra

 

Abstracts

In this paper we give a new definition of the Lelong-Demailly number in terms of the C_T-capacity, where T is a closed positive current and C_T is the capacity associated to T. This derived from some esimate on the growth of the C_T-capacity of the sublevel sets of a weighted plurisubharmonic (psh for short) function. These estimates enable us to give another proof of the Demailly's comparaison theorem as well as a generalization of some results due to Xing concerning the characterization of bounded psh functions. Another problem that we consider here is related to the existence of a psh function v that satisfies the equality C_T (K) = ∫_K T ∧ (dd^cv)^p, where K is a compact subset. Finally, we give some conditions on the capacity C_T that guarantees the weak convergence u_kT_k → uT, for positive closed currents T, T_k and psh functions u_k u

 

201312

Code: 201312

Expected Present Value of Total Dividends in the Compound Binomial Model with Delayed Claims and Random Income

Jieming Zhou, Xiaoyun Mo, Hui Ou, Xiangqun Yang

 

Abstracts

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer's arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends

 

 

201311

Code: 201311

Modified Roper-Suffridge Operator for Some Subclasses of Starlike Mappings on Reinhardt Domains

Jianfei Wang

 

Abstracts

In this note, the author introduces some new subclasses of starlike mappings

<img height="67" border="0" style="vertical-align:bottom" width="519" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601101-si1.gif">$\begin{array}{l}S*\Omega n,p_2\mathrm{\dots }{P}_n(\beta ,A,B)\\ =\{f\in H(\Omega ):|i\hspace{0.17em}tan\hspace{0.17em}\beta +(1-i\hspace{0.17em}tan\hspace{0.17em}\beta \frac{2}{\rho (z)}\frac{\partial \rho }{\partial z}(z)J_f^{-1}(z)f(z)-\frac{1-AB}{1-B^2}|<\frac{B-A}{1-B^2}\},\end{array}$

on Reinhardt domains <img height="47" border="0" style="vertical-align:bottom" width="316" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601101-si2.gif">${\Omega }_{n,p_2\mathrm{\dots }{p}_n}=\{z\in {ℂ}^n:|z_1{|}^2+{\sum _{j=2}^n\left|z_j\right|}^{p_j}<\hspace{0.17em}1\hspace{0.17em}\}$ where –1 ≤ A < B < 1, q = min{p₂,…, p_n} ≥ 1, l = max{p₂,…, p_n} ≥ 2 and β ∈ ( <img height="27" border="0" style="vertical-align:bottom" width="42" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601101-si3.gif">$-\frac{\pi }{2},\hspace{0.17em}\frac{\pi }{2}$) Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator

<img height="43" border="0" style="vertical-align:bottom" width="286" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601101-si4.gif">$F\left(z\right)={\left(f\left(z_1\right)+f^{\prime }\left(z_1\right)P_m\left(z_0\right),{\left(f^{\prime }\left(z_1\right)\right)}^{\frac{1}{m}}{z}_0\right)}^{\prime },$

where f is a normalized biholomorphic function on the unit disc D, z = (z₁, z₀) ∈ Ω_{n,p2,…, pn}, z₀ = (z₂,…, z_n) ∈ ℂⁿ⁻¹. Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type β and order α. These results generalize the modified Roper-Suffridge extension operator from the unit ball to Reinhardt domains. Notice that when p₂ = p₃ = … = p_n = 2, our results reduce to the recent results of Feng and Yu

201310

Code: 201310

Reconstruction of the Attenuated Radon Transform in π-Scheme Short-Scan Spect

Tingting Shi, Jinping Wang

 

Abstracts

In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography (SPECT) with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov's inversion operator into three parts bounded in the L² sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to ℒ(L²(<img height="10" border="0" style="vertical-align:bottom" width="9" alt="" title="" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0252960213601095-fx1.jpg">)). Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method

20139

Code: 20139

A Solution of a General Equilibrium Problem

H. R. Sahebi, A. Razani

 

Abstracts

Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper

20138

Code: 20138

Toeplitz Operators on Heisenberg Group

Peizhu Xie, Guangfu Cao

 

Abstracts

Denote by Ω the Siegel domain in ℂⁿ, n >1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H² (∂Ω). In addition, the characteristic equation of analytic Toeplitz operators is obtained

20137

Code: 20137

Vertex-Fault-Tolerant Cycles Embedding on Enhanced Hypercube Networks

Yanjuan Zhang, Hongmei Liu, Min Liu

 

Abstracts

In this paper, we study the enhanced hypercube, an attractive variant of the hypercube and obtained by adding some complementary edges from a hypercube, and focus on cycles embedding on the enhanced hypercube with faulty vertices. Let F_v be the set of faulty vertices in the n-dimensional enhanced hypercube Q_n,k (n ≥ 3, 1 ≤ k ≤ n − 1). When |F_v| = 2, we showed that Q_n,k − F_v contains a fault-free cycle of every even length from 4 to 2ⁿ – 4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2ⁿ − 4, simultaneously, contains a cycle of every odd length from n − k + 2 to 2ⁿ − 3 where n (≥ 3) and k have the different parity. Furthermore, when |F_v| = f_v ≤ n − 2, we prove that there exists the longest fault-free cycle, which is of even length 2ⁿ − 2f_v whether n (n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2ⁿ − 2f_v + 1 in Q_n,k − F_v where n (≥ 3) and k have the different parity

20136

Code: 20136

A Class of Entire Dirichlet Series as an FK-Space and a Frechet Space

Niraj Kumar, Garima Manocha

 

Abstracts

In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra and prove it to be a complex FK-space and a Frechet space

20135

Code: 20135

An Estimate for the Mean Curvature of Submanifolds Contained in a Horoball

Hongbing Qiu

 

Abstracts

We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies some decay condition, which generalizes our previous results in [17]. Using this generalized maximum principle, we give an estimate on the mean curvature of properly immersed submanifolds in ℍⁿ × ℝ^l with the image under the projection on ℍⁿ contained in a horoball and the corresponding situation in hyperbolic space. We also give other applications of the generalized maximum principle

20134

Code: 20134

Doubling Measures on Generalized Cantor Sets

Peng sun, Xiaohua Wang

 

Abstracts

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed

20133

Code: 20133

Nonlinear Stability of Planar Shock Profiles for the Generalized KdV-Burgers Equation in Several Dimensions

Zhengzheng Chen, Quinghua Xiao

 

Abstracts

This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation

20132

Code: 20132

On a Class of Inhomogeneous, Energy-Critical, Focusing, Nonlinear Schrödinger Equations

Zhaoxia Liu

 

Abstracts

In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrödinger equation: $\text{i}{\partial }_{t}u=-\Delta u-k\left(x\right)|u{|}^{\frac{4}{N-2}}u,\hspace{0.17em}N\ge 3$. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in the nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, Invent. Math. 166, 645-675 (2006)], where only the radial case is considered in dimensions 3, 4, 5.

20131

Code: 20131

Fractional 2D-Stochastic Currents

Ciprian A. Tudor,  Maria Tudor

 

Abstracts

Using multiple stochastic integrals and the stochastic calculus for the fractional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents