Unimodularity of zeros of self-inversive polynomials

We generalise a necessary and sufficient condition given by Cohn for all the zeros of a self-inversive polynomial to be on the unit circle. Our theorem implies some sufficient conditions found by Lakatos, Losonczi and Schinzel. We apply our result to the study of a polynomial family closely related to Ramanujan polynomials, recently introduced by Gun, Murty and Rath, and studied by Murty, Smyth and Wang as well as by Lalín and Rogers. We prove that all polynomials in this family have their zeros on the unit circle, a result conjectured by Lalín and Rogers on computational evidence.     

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在对国内外液态锂回路研究综述的基础上,重点介绍了四川大学流动液态锂回路的研究进展。为开展等离子体与流动自由液态锂表面相互作用的研究而设计了该回路,其目标是：(1)获得稳定、均匀的流动自由液态锂表面;(2)研究等离子体辐照下液态锂的蒸发、溅射以及氢、氢同位素和氦在液态锂中的滞留行为;(3)研究等离子体辐照下液态锂与结构材料的相容性。系统包括液态锂循环部分和直线高密度等离子体发生装置。     

Spacelike Surfaces in {{\mathbb L}^4} with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz?CMinkowski space ${\mathbb L^4}$ .     

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on n letters, where n is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.     

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

In this paper a finite element formulation of a reduction method for dynamic buckling analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The implementation of a single-mode dynamic buckling analysis in a general purpose finite element code is described. The effectiveness of the approach is illustrated by application to the dynamic buckling of composite cylindrical shells under axial and radial step loads. Results of the reduction method are compared with results available in the literature. The results are also compared with full model finite element explicit dynamic analysis, and a reasonable agreement is obtained.     

Lattice tolerances and congruences

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.     

Diffusive semiconductor moment equations using Fermi�CDirac statistics

Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman?CEnskog expansion. The moment equations are closed by employing a generalized Fermi?CDirac distribution function obtained from entropy maximization. The current densities allow for a drift-diffusion-type formulation or a ??symmetrized?? formulation, using dual-entropy variables from nonequilibrium thermodynamics. Furthermore, drift-diffusion and new energy-transport equations based on Fermi?CDirac statistics are obtained and their degeneracy limit is studied.     

Maximum number of colors: C-coloring and related problems

We discuss problems and results on the maximum number of colors in combinatorial structures under the assumption that no totally multicolored sets of a specified type occur.     

The Clifford-Fourier Transform {mathcal {F}_o} and Monogenic Extensions

In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.     

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??We consider probabilistic meanings for some numerical characteristics of single birth processes. Some probabilities of events, such as extinction probability, returning probability, are represented in terms of these numerical characteristics. Two examples are also presented to illustrate the value of the results.