On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case II

The main theme of this paper is the discussion of a family of extremal solutions of a finite moment problem for rational matrix functions in the nondegenerate case. We will point out that each member of this family is extremal in several directions. Thereby, the investigations below continue the studies in Fritzsche et al. (in press) [1]. In doing so, an application of the theory of orthogonal rational matrix functions with respect to a nonnegative Hermitian matrix Borel measure on the unit circle is used to get some insights into the structure of the extremal solutions in question. In particular, we explain characterizations of these solutions in the whole solution set in terms of orthogonal rational matrix functions. We will also show that the associated Riesz-Herglotz transform of such a particular solution admits specific representations, where orthogonal rational matrix functions are involved.     

Real-variables characterization of generalized Stieltjes functions

We obtain a characterization of generalized Stieltjes functions of any order λ>0$\lambda >0$ in terms of inequalities for their derivatives on (0,∞)$(0,\infty )$. When λ=1$\lambda =1$, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.     

The path partition problem and related problems in bipartite graphs

We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k. Finally, we propose some approximation and inapproximation results for several related problems.     

A note on blow-up of solution for a class of semilinear pseudo-parabolic equations

In this short note, we revisit the blow-up of solution for the initial boundary value problem of semilinear pseudo-parabolic equations with low/critical initial energy stated in Xu and Su (2013) [4], and amend the proofs of the original paper.     

A variational formulation of anisotropic geometric evolution equations in higher dimensions

We present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in , d ≥ 2. This new formulation leads to an unconditionally stable, fully discrete, parametric finite element approximation in the case d = 2 or 3. The resulting scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments for d = 3, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion.     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Methods of integral geometry and recovering a function with compact support from its projections in unknown directions

A method for recovering a function with compact support on a plane from its Radon transform is suggested. In particular, from the given projections of a function in unknown directions, these directions may be recovered (up to a rotation or a reflection), if there are 7 of them. This result may be applied in tomography.     

Sn Mössbauer spectroscopy of Gd0.8L0.2Mn6Sn6 and Tb0.8L0.2Mn6Sn6 compounds (L=Sc,Y, Lu)

The HfFe₆Ge₆-type compounds Gd_0.8L_0.2Mn₆Sn₆ and Tb_0.8L_0.2Mn₆Sn₆ (L = Sc, Y, Lu) have been studied by ¹¹⁹Sn Mössbauer spectroscopy. The values of the apparent quadrupolar splitting clearly evidence the easy plane magnetization of the gadolinium compounds and the easy axis one in the terbium compounds. The three tin sites behave differently with the nature and size of the substituting L element. For a given series, the hyperfine field of the Sn_2d site is almost unchanged whatever the size of the L element. The hyperfine field of the Sn_2e site strongly varies with the L size in relation with atomic displacements. The hyperfine field of the Sn_2c site exhibits a more complicated behavior. The field difference in the easy plane and easy axis compounds confirms the angle-dependent anisotropic contribution of the Mn moment to the hyperfine field. The analysis of the results also suggests the play of angle-dependent contributions arising from the rare earth moment.     

Pb(Zr,Sn,Ti)O3反铁电陶瓷的低温相变扩散与极化弛豫

用弱场介电温谱、热释电流谱、强场电滞回线和变温X射线衍射谱研究了微量La掺杂Pb(Zr ,Sn ,Ti)O3(PZST)反铁电 (AFEt)陶瓷在 - 10 0— 180℃温区内的结构与电学特性 .弱场介电温谱显示 ,AFEt陶瓷在低温段(- 10 0— 5 0℃ )呈现介电频率弥散 (0 1— 10 0kHz)和扩散型相变的特征 ,而变温X射线衍射谱却表明材料在这一温区内保持四方相结构 ;低温下经强场作用后 ,AFEt被诱导为亚稳三方铁电态 ,介电频率弥散消失 .基于多元复杂化合物的组分起伏理论 ,讨论了PZSTAFEt陶瓷的相变扩散与极化弛豫新现象 .     

Finding numerical solution of linear partial differential equations of first order with real coefficients

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order