Abstract: In this paper, we present a necessary and sufficient condition that the perturbed monomial mapping is ergodic on a sphere \(S_{p^{-1}}(1)\) , which is in a combination with Anashin’s earlier results about the perturbed monomial ergodic mappings on a sphere \(S_{p^{-r}}(1)\) ; r > 1, com-pletely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere. PubDate: 2019-03-01

Abstract: For the Hardy space H E 2 (R) over a at unitary vector bundle E on a finitely connected domain R, let TE be the bundle shift as [3]. If \(\mathcal{B}\) is a reductive algebra containing every operator ψ(TE) for any rational function ψ with poles outside of R, then \(\mathcal{B}\) is self adjoint. PubDate: 2019-03-01

Abstract: Mather gave the necessary and sufficient conditions for the finite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals finitely is defined. The containment relationships of function germs still satisfy finite k-determinacy under sufficiently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented. PubDate: 2019-03-01

Abstract: This paper studies online scheduling of jobs with kind release times on a single machine. Here “kind release time” means that in online setting, no jobs can be released when the machine is busy. Each job J has a kind release time r(J) ≥ 0, a processing time p(J) > 0 and a deadline d(J) > 0. The goal is to determine a schedule which maximizes total processing time (Σp(J)E(J)) or total number (ΣE(J)) of the accepted jobs. For the first objective function Σp(J)E(J), we first present a lower bound \(\sqrt 2 \) , and then provide an online algorithm LEJ with a competitive ratio of 3. This is the first deterministic algorithm for the problem with a constant competitive ratio. When p(J) ∈ {1, k}, k > 1 is a real number, we first present a lower bound min{(1+k)/k, 2k/(1+k)}, and then we show that LEJ has a competitive ratio of 1+⌈k⌉/k. In particular, when all the k length jobs have tight deadlines, we first present a lower bound max{4/(2 + k), 1} (for Σp(J)E(J)) and 4/3 (for ΣE(J)). Then we prove that LEJ is ⌈k⌉/k-competitive for Σp(J)E(J) and we provide an online algorithm H with a competitive ratio of 2⌈k⌉/(⌈k⌉ + 1) for the second objective function ΣE(J). PubDate: 2019-03-01

Abstract: Multi-objective optimization has many important applications and becomes a challenging issue in applied science. In typical multi-objective optimization algorithms, such as Indicator-based Evolutionary Algorithm (IBEA), all of parents and offspring need to be evaluated in every generation, and then the better solutions of them are selected as the next generation candidates. This leads to a large amount of calculation and slows down convergence rate for IBEA related applications. Our discovery is that the evaluation of evolutionary algorithm is a binary classification in nature and a meaningful preselection method will accelerate the convergence rate. Therefore this paper presents a novel preselection approach to improve the performance of the IBEA, in which a SVM (Support Vector Machine) classifier is adopted to sort the promising solutions from unpromising solutions and then the newly generated solutions are conversely added as train sample to increase the accuracy of the classifier. Firstly, we proposed an online and asynchronous training method for SVM model with empirical kernel. The initial population is randomly generated among population size, which is used as initial training. In the process of training, SVM classifier is modified and perfected to adapt to the evolutionary algorithm sample. Secondly, the classifier divides all the new generated solutions from the whole solution spaces into promising solutions and unpromising ones. And only the promising ones are forwarded for evaluation. In this way, the evaluation time can be greatly reduced and the solution quality can be obviously improved. Thirdly, the promising and unpromising solutions are labeled as new train samples in next generation to refine classifier model. A number of experiments on benchmark functions validates the proposed approach. The results show that IBEA-SVM can significantly outperform previous works. PubDate: 2019-03-01

Abstract: Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obtain some Pfaffian orientations and enumerating their Pfaffians. PubDate: 2019-03-01

Abstract: For any given positive integer m, let Xi, 1 ≤ i ≤ m be m independent random variables with distributions Fi, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio \(\frac{{P(\sum\nolimits_{i = 1}^m {{X_i}} > x})}{{\sum\nolimits_{i = 1}^m {{{\overline F }_i}(x)} }}\) equals 1 as x → ∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented. PubDate: 2019-03-01

Abstract: Let G be a simple graph with n vertices and m edges. In this paper, we present some new upper bounds for the adjacency and the signless Laplacian spectral radius of graphs in which every pair of adjacent vertices has at least one common adjacent vertex. Our results improve some known upper bounds. The main tool we use here is the Lagrange identity. PubDate: 2019-03-01

Abstract: In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved. PubDate: 2019-03-01

Abstract: In this paper, we show that a positive recurrent fluid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a fluid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period. PubDate: 2019-03-01

Abstract: Given a digraph D = (V, A), the competition graph G of D, denoted by C(D), has the same set of vertices as D and an edge between vertices x and y if and only if ND+(x)∩ND+(y) 6≠0. In this paper, we investigate the competition graphs of round digraphs and give a necessary and suffcient condition for these graphs to be hamiltonian. PubDate: 2018-12-01

Abstract: In this paper, we construct asymptotic periodic solutions of some generalized Burgers equations using a perturbative approach. These large time asymptotics (constructed) are compared with relevant numerical solutions obtained by a finite difference scheme. PubDate: 2018-12-01

Abstract: In this paper, we study the differentiability of solutions on the boundary for equations of type \({L_\lambda }u = \frac{{{\partial ^2}u}}{{\partial {x^2}}} + {\left x \right ^{2\lambda }}\frac{{{\partial ^2}u}}{{\partial {y^2}}} = f\left( {x,y} \right)\) , where λ is an arbitrary positive number. By introducing a proper metric that is related to the elliptic operator Lλ, we prove the differentiability on the boundary when some well-posed boundary conditions are satisfied. The main diffculty is the construction of new barrier functions in this article. PubDate: 2018-12-01

Abstract: Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms. PubDate: 2018-12-01

Abstract: This paper studies a stochastically forced chemostat model with feedback control in which two organisms compete for a single growth-limiting substrate. In the deterministic counterpart, previous researches show that the coexistence of two competing organisms may be achieved as a stable positive equilibrium or a stable positive periodic solution by different feedback schedules. In the stochastic case, based on the stochastic sensitivity function technique, we construct the confidence domains for different feedback schedules which allow us to find the configurational arrangements of the stochastic attractors and analyze the dispersion of the random states of the stochastic model. PubDate: 2018-12-01

Abstract: Spiral curves are free from singularities and curvature extrema. These are used in path smoothing applications to overcome the abrupt change in curvature and super-elevation of moving object that occurs between tangent and circular curve. Line to circle spiral transition is made of straight line segment and curvature continuous spiral curve. It is extendible to other important types of transitions like line to line and circle to circle. Although the problem of line to circle transition has been addressed by many researchers, there is no comprehensive literature review available. This paper presents state-of-the-art of line to circle spiral transition, applications in different fields, limitations of existing approaches, and recommendations to meet the challenges of compatibility with today’s CAD/CAM soft wares, satisfaction of Hermite end conditions, approximation of discrete data for image processing, 3D path smoothness for an unmanned aerial vehicle (UAV), and arc-length parametrization. Whole discussion is concluded with future research directions in various areas of applications. PubDate: 2018-12-01

Abstract: Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥ 1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained. PubDate: 2018-12-01

Abstract: This paper proposes and makes a study of a new model (called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests. The results show that the models are capable of fitting the market price while generating positive volatility skew. PubDate: 2018-09-01

Abstract: In this paper, the notion of L-R crossed coproduct is introduced as a unified approach for smash coproducts, crossed coproducts and L-R smash coproducts of Hopf algebras. A duality theorem for L-R crossed coproduct is proved. PubDate: 2018-09-01

Abstract: This paper deals with estimation and test procedures for restricted linear errors-invariables (EV) models with nonignorable missing covariates. We develop a restricted weighted corrected least squares (WCLS) estimator based on the propensity score, which is fitted by an exponentially tilted likelihood method. The limiting distributions of the proposed estimators are discussed when tilted parameter is known or unknown. To test the validity of the constraints, we construct two test procedures based on corrected residual sum of squares and empirical likelihood method and derive their asymptotic properties. Numerical studies are conducted to examine the finite sample performance of our proposed methods. PubDate: 2018-09-01