Negative Definite Functions on the Space of Infinite Hermitian Matrices

In this paper we investigate a Lévy–Khinchin type integral formula of negative definite functions defined over the Olshanski spherical pair of infinite hermitian matrices.     

Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds

Using a variational method, we prove the existence of nodal solutions to prescribed scalar Q- curvature type equations on compact Riemannian manifolds with boundary. These equations are fourth-order elliptic equations with critical Sobolev growth.     

Entropy formulation of degenerate parabolic equation with zero-flux boundary condition

We consider the general degenerate hyperbolic-parabolic equation: $$u_t + {\rm div} f(u) - \Delta \phi(u) = 0\; {\rm in} Q = (0, T) \times \Omega, \quad T > 0, \quad \Omega \subset \mathbb{R}^N;$$ with initial condition and the zero flux boundary condition. Here ${\phi}$ is a continuous non-decreasing function. Following Bürger et al. (J Math Anal Appl 326:108–120, 2007), we assume that f is compactly supported (this is the case in several applications), and we define an appropriate notion of entropy solution. Using vanishing viscosity approximation, we prove existence of entropy solution for any space dimension N ≥ 1 under a partial genuine nonlinearity assumption on f. Uniqueness is shown for the case N = 1, using the idea of Andreianov and Bouhsiss (J Evol Equ 4:273–295, 2004), nonlinear semigroup theory and a specific regularity result for one dimension.     

Correction of eigenvalues estimated by the Legendre–Gauss Tau method

It is known that the accuracy in estimating a large number of eigenvalues deteriorates when the standard numerical methods are applied, because of the sharp oscillatory behavior of the corresponding eigenfunctions. One method which has proved to be efficient in treating such problems is the Legendre–Gauss Tau method. In this paper we present an exponentially fitted version of this method and we develop practical formulae to correct the estimated eigenvalues.     

Study of the glassy magnetic behaviour and charge-ordering phase transitions in La0.75Ca0.25FeO3−δ perovskite

Abstract

In this work, La_0.75Ca_0.25FeO_3?δ perovskite sample was prepared by the coprecipitation method. The nanoparticle was found to crystallize in the orthorhombic (Pbnm) phase as confirmed by X-ray diffraction (XRD) and transmission electron microscopic (TEM). The oxygen non-stoichiometry (δ) and magnetic states of iron ions (three magnetic sextets and non-magnetic doublet) were investigated by Mössbauer spectroscopy at room temperature (RT). The shape of the magnetic hysteresis loop of the sample reveals the existence of a weak ferromagnetism at RT. The magnetization vs. temperature curves, measured in the 9 to 200 K range, showed that the sample exhibits two magnetic-phase transition temperatures at 29 K (T_g) and 120 K (T_CO). The magnetization isotherms, M (H), around these magnetic-phase transition temperatures for the sample are analyzed.     

A central limit theorem for stationary random fields

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form _Xk=g(_εk−s,s∈Z^d)$X_k=g({\epsilon }_{k-s},s\in {\mathbb{Z}}^d)$, k∈Z^d$k\in {\mathbb{Z}}^d$, where _(εi)i∈Zd${\left({\epsilon }_i\right)}_{i\in {\mathbb{Z}}^d}$ are iid random variables and g$g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.     

Synthesis and Structure of a Copper Complex of a Macrocyclic Ligand with Dissimilar HN+N(Amino)O2 and N2(Imino)O2 Inners

Abstract The copper complex [Cu(C₂₃H₂₇Br₂N₄O₂)(H₂O)(NO₃)]₂ was synthesized and characterized by X-ray diffraction. The complex crystallizes in the triclinic system with space group P-1, lattice parameters: a = 13.2293(18) (?), b = 14.184(20) (?), c = 16.522(23) (?), α = 91.923(2)°, β = 111.777(2)°, γ = 111.259(2)°, V = 2632.0(6) ?³, Z = 4, D _c = 0.88 Mg m⁻³. In the title compound [Cu(C₂₃H₂₇Br₂N₄O₂)(H₂O)(NO₃)]₂, the coordination polyhedron of the Cu atom is a square-planar environment. The structure consists of mononuclear units in which the copper(II) ions are linked in the plane by N, N′ iminato and O, O′ phenoxo atoms. In addition the crystal lattice contains one water molecule per unit. Graphical Abstract Dissymmetric ligand was efficiently synthesized and used to prepfsare a copper(II) complex which was characterized by X-ray diffraction