Stationary queuing systems with dependencies

The fundamental results relating to queuing systems with dependencies are presented in condensed form in the present survey. Particular attention is paid to the extension of the results obtained earlier for classical systems to systems with dependencies, and certain early classical results in queuing theory are discussed.     

Tuberculosis model with relapse via fractional conformable derivative with power law

The present study explores the tuberculosis dynamics with relapse with a nonlocal conformable derivative in the Caputo sense. The real data of tuberculosis cases since 2002 to 2017 are used to the set the parameters. The numerical results with the realistic parameters are chosen and present the graphical results. Further, we assign different values to the fractional parameters α and β and discuss its effect on the system variables. The use of these two fractional operators on the model simultaneously with realistic data gives reliable results.     

与过程相联系的σ-代数流

讨化了σ-代数流的结构,并给出其一般性的结果;归纳出各σ-代数流的相互关系;最后介绍其两个简单应用.     

Nonautonomous Lotka-Volterra Systems with Delays

The paper studies the general nonautonomous Lotka-Volterra multispecies systems with finite delays. The ultimate boundedness, permanence, global attractivity, and existence and uniqueness of strictly positive solutions, positive periodic solutions, and almost periodic solutions are obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra multispecies systems without delay to systems with delay.     

Interval Ostrowski-type methods with guaranteed convergence

In this paper, interval extensions of the classic Ostrowski and its modified method are introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the schemes. The results of proposed methods are compared with the results of the interval Newton method.     

On general balance laws with boundary

This paper is devoted to general balance laws (with a possibly non-local source term) with a non-characteristic boundary. Basic well posedness results are obtained. New uniqueness results for the solutions to conservation and/or balance laws with boundary are also provided.     

Multidimensional Hardy-type inequalities with general kernels

Some new multidimensional Hardy-type inequalities involving arithmetic mean operators with general positive kernels are derived. Our approach is mainly to use a convexity argument and the results obtained improve some known results in the literature and, in particular, some recent results in [S. Kaijser, L. Nikolova, L.-E. Persson, A. Wedestig, Hardy-type inequalities via convexity, Math. Inequal. Appl. 8 (3) (2005) 403-417] are generalized and complemented.     

Numerical differentiation with noisy signal

The aim of this paper is to present a new numerical method, which ables one to filter and compute numerical derivatives of a function whose values are known in some points from experimental measurements, inducing noisy data. We use a piecewise cubic spline interpolation to generate a function whose Fourier coefficients give an approximation of the numerical derivatives we are looking for. Error and stability analysis of this numerical algorithm are provided. Numerical results are presented for data smoothing and for the first and second derivatives computed from noisy data. They show that this method gives good numerical results. Comparison with other methods is done.     

Integral operators with operator-valued kernels

Under fairly mild measurability and integrability conditions on operator-valued kernels, boundedness results for integral operators on Bochner spaces L_p(X) are given. In particular, these results are applied to convolutions operators.     

Variational inequalities with nonmonotone operators

In this paper, existence results on variational inequalities and generalized variational inequalities for some nonmonotone operators over closed convex subsets of a real reflexive Banach space are proved. In particular, some surjectivity results and applications to complementarity and generalized complementarity problems are given.This work was partially supported by the National Science Council of the Republic of China under Contracts NSC 81-0208-M-007-34 and NSC 82-0208-M-110-023.     

Abundant semigroups with a quasi-ideal quasi-adequate transversal

Characterization theorems for abundant sernigroups having a quasi-ideal quasi-adequate transversal are obtained. Our results generalize and amplify the related results of Satio on regular semigroup obtained in 1985 and Kong obtained in 2007 respectively. Some recent results on this topic given by Guo-Shum are strengthened. In particular, the structure of such an abundant semigroup is described.     

高阶变系数函数方程的振动性

建立了一类高阶非线性变系数函数方程一切解振动的几个充分条件,并且给出了在差分方程中的若干应用.结果全面推广了某些文献的结果.     

Micro-swimmers with hydrodynamic interactions

The low-Reynolds-number motions of Purcell’s three-link swimmer, and of a closely related two-paddle swimmer, are investigated and compared using slender-body theory and resistive-force theory. The results are compared (in the case of the three-link swimmer) with the resistive-force calculations of Becker, Koehler and Stone (BKS). In particular, we examine the effect of hydrodynamic interaction and slenderness on the displacement and efficiency of the swimmers. The BKS analysis is, for the most part, confirmed and extended. However, deviations of up to 43% are found in cases where the swimmer propels itself with large stroke angles. Finally, we discuss recent experimental data in light of our numerical results.     

Compressed sensing with structured sparsity and structured acquisition

Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually incompatible with the physics of acquisition. To reflect the physical constraints of the imaging device, we introduce the notion of blocks of measurements: the sensing scheme is not a set of isolated measurements anymore, but a set of groups of measurements which may represent any arbitrary shape (parallel or radial lines for instance). Structured acquisition with blocks of measurements are easy to implement, and provide good reconstruction results in practice. However, very few results exist on the theoretical guarantees of CS reconstructions in this setting. In this paper, we derive new CS results for structured acquisitions and signals satisfying a prior structured sparsity. The obtained results provide a recovery probability of sparse vectors that explicitly depends on their support. Our results are thus support-dependent and offer the possibility for flexible assumptions on the sparsity structure. Moreover, the results are drawing-dependent, since we highlight an explicit dependency between the probability of reconstructing a sparse vector and the way of choosing the blocks of measurements. Numerical simulations show that the proposed theory is faithful to experimental observations.     

Multiple solutions for nonlinear systems with gyroscopic terms

In this paper, we investigate the existence of multiple solutions to some nonlinear systems with gyroscopic terms via variational methods. Some new results are obtained and some results from the literature are improved.     

Codes with given distances

One of the main results says that ifC is a binary linear code of length 4t and of dimension greater than 2t, thenC contains a word of weight 2t and this bound is best possible. Several results of similar flavor are established both for linear and non-linear codes. For the proof a lemma introducing the binormal forms of binary matrices is needed. The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.     

具无限时滞的非自治捕食者-食饵系统的持久性

本文采用新的方法研究了具无限时滞的非自治、非卷积的捕食者－食饵系统的持久性问题，得到了新的、有趣的结果。本文的结果包含已知的结果作为特例．     

A note on single-machine scheduling with nonlinear deterioration

Some results in a recent paper (Wang and Wang in Optim Lett doi:) are incorrect because job processing times are variable due to nonlinear deterioration. In this note, we show by a counter-example that the results are incorrect.     

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors. Sufficient conditions for attaining consistent estimators for model parameters are presented. Asymptotic distributions for the line regression estimators are derived. Applications to the elliptical class of distributions with two error assumptions are presented. The model generalizes previous results aimed at univariate scenarios.     

分离变量非线性系统的全局稳定性

借助Lyapunov函数方法 ,讨论了一类分离变量系统的全局稳定性和全局指数稳定性 ,得到了由系统自身特点所给出的几个显示代数判据 ,这些充分性结论为实际应用提供方便 ,推广了有关文献中的一些结果 .