Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.     

A STABILITY RESULT ON SOLUTIONS TO CERTAIN FOURTH ORDER NON-HOMOGENEOUS DIFFERENTIAL EQUATIONS

In this paper,we study the fourth order non-homogeneous differential equations x(4) + f1()+ f2() + f3(■) + f4(x) = p(t,x,■,,x),and obtain suffcient conditions,under which the solutions to the system tend to zero as t →∞.     

A remark on the range of elementary operators

Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ _A : L(H) → L(H) by Δ _A (X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C ₁(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of Δ _A is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints operators.     

Specific heat and phase transition of (Li1−xKx)2SO4 single crystals

A specific heat study of (Li_1–xK_x)₂SO₄ — LKS — mixed crystals has been made in a wide concentration rangex covering the temperature range 300–800 K. The phase diagram was determined. It is shown that a variation of the Li⁺:K⁺ concentration changes the critical behaviour of the specific heat. The results are discussed in terms of scattering mechanisms of energy carriers.

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Zusammenfassung Bei Temperaturen zwischen 300 und 800 K wurde für einen breiten Konzentrationsbereich für x die spezifische Wärme von (Li_1–xK_x)₂SO₄-Mischkristallen untersucht und das entsprechende Phasendiagramm erstellt. Es wurde gezeigt, daß eine Änderung des Verhältnisses Li⁺:K⁺ auch das kritische Verhalten der spezifischen Wärme verändert. Die Ergebnisse werden hinsichtlich von Sreuungsmechanismen der Energieträger diskutiert.

     

Banach空间上有界线性算子的Drazin逆的扰动分析

设X为一复域C上的Banach空间,设T:X→X为一有界线性算子,其指标为k且R(T^k)闭.记T的Drazin逆为T^D.设T=T+δT,则在一定条件下,T^D有简明分解式T^D=T^D(I+δTT^D)^-1=(I+T^DδT)^-1T^D,从而导出了相对误差‖T^D-T^D<     

Entanglement and quantum teleportation via decohered tripartite entangled states

The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleported state by controlling on Bell measurements, analyzer angle and channel’s strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the decay rate of entanglement and the fidelity of the teleported states are smaller than those depicted for GHZ state.     

EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION

By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained.     

Thermal shock problem in a homogeneous isotropic hollow cylinder with energy dissipation

In this work, we constructed the equations of generalized thermoelasticity of a homogeneous isotropic hollow cylinder. The formulation is applied in the context of the Green and Naghdi theory of types II and III. The material of the cylinder is assumed to be homogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite-element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. Comparisons are made with the results predicted by the types II and III. The results obtained in this paper can be used to design various homogeneous thermoelastic elements under thermal load to meet special engineering requirements.