Analytical Descriptions of Magnetic Properties and Magnetoresistance in n-Type HgCr_2Se_4

We present a detailed investigation of magnetic properties of colossal magnetoresistance material HgCr2Se4. While spontaneous magnetization and zero-field magnetic susceptibility are found to follow asymptotic scaling laws for a narrow range of temperatures near the critical point, two methods with connections to the renormalization group theory provide analytical descriptions of the magnetic properties for much wider temperature ranges. Based on this, an analytical formula is obtained for the temperature dependence of the low field magnetoresistance in the paramagnetic phase.

Mechanical properties of lattice grid composites

An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid com- posite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.

VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON THE COMPLEX BALL AND THE ANALYTIC RADON-NIKODYM PROPERTY

The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.

A Class of Complex Quasi-Orlicz Spaces and Their Analytic RN Property

Let X be a complex quasi Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0 , lim t→∞Φ(t)=∞ and Φ∈Δ 2 . Then L * Φ(X) is a quasi Banach space with continuous quasi norm and L * Φ(X) has the ARNP if and only if X does.

THE ANALYTIC KREIN-MILMAN PROPERTY IN BANACH SPACES

In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property.

Extraction of fish body oil from Sardinella longiceps by employing direct steaming method and its quantitative and qualitative assessment

Objective:To analyze the quantitative and qualitative properties of the extracted fish oil from Sardinella longiceps(S.longiceps).Methods:Four size groups of S.longiceps were examined for the extraction of fish oil based on length.The size groups included Group I(size range of 7.1-10.0 cm),Group II(size range of 10.1-13.0 cm),Group III(size range of 13.1-16.0 cm)and Group IV(size range of 16.1-19.0 cm).Fish oil was extracted from the tissues of S.longiceps by direct steaming method.The oil was then subjected to the determination of specific gravity,refractive index,moisture content,free fatty acids,iodine value,peroxide value,saponification value and observation of colour.Results:The four groups showed different yield of fish oil that Group IV recorded the highest values of(165.00±1.00)mL/kg followed by Group III[(145.66±1.15)mL/kg]and Group II[(129.33±0.58)mL/kg],whereas Group I recorded the lowest values of(78.33±0.58)mL/kg in monsoon season,and the average yield was(180.0±4.9)mL/kg fish tissues.These analytical values of the crude oil were well within the acceptable standard values for both fresh and stocked samples.Conclusions:The information generated in the present study pertaining to the quantitative and qualitative analysis of fish oil will serve as a reference baseline for entrepreneurs and industrialists in future for the successful commercial production of fish oil by employing oil sardines.

Spectrum transformation and conservation laws of lattice potential KdV equation

Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In this paper, we derive infinitely many conserved quantities for the lattice potential Korteweg-de Vries equation whose solutions have nonzero backgrounds. The derivation is based on the fact that the scattering data a（z） is independent of discrete space and time and the analytic property of Jost solutions of the discrete Schr5dinger spectral problem. The obtained conserved densities are asymptotic to zero when ｜n｜ （or ｜m｜） tends to infinity. To obtain these results, we reconstruct a discrete Riccati equation by using a conformal map which transforms the upper complex plane to the inside of unit circle. Series solution to the Riccati equation is constructed based on the analytic and asymptotic properties of Jost solutions.

A COUNTER-EXAMPLE CONCERNING THE ANALYTIC RADON-NIKODYM PROPERTY

It is shown that there exists a J-convex subset C of a complex Hilbert space X, such that the J-convex hull of the set of all Jensen boundary points of C is different from C..

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a complex Banach space without the analytic Radon-Nikodym property. The author shows that G = {f∈H∞(D,X) there exists∈＞ 0, such that for almost allθ∈[0, 2], lim sup f(reiθ) - f(seiθ)≥∈ } is a dense open subset of H∞(D, X). It is also shown that for every open subset B of T, there exists F∈H∞ (D, X), such that F has boundary values everywhere on Bc and F has radial limits nowhere on B. When A is a measurable subset of T with positive measure, there exists f∈H∞ (D, X), such that f has nontangential limits almost everywhere on Ac and f has radial limits almost nowhere on A.