SUPERBOOLEAN ALGEBRAS

In this paper we define a new algebraic structure called super boolean algebras and characterizethem.Definition 1 A super boolean algebra V is a nonempty set with two binary operations+and.satisfying the following postulates.(i)V is closed with respect to+and.i.e.,a+b∈V and a·b∈V for all a,b∈V.(ii)a+b=b+a and a·b=b·a for all a,b∈V.(iii)(a+b)+c=a+(b+c)and a(bc)=(ab)c for all a,b,c∈V.(iv)(a+b)(a+c)(a+d)=a+bc(a+d)+cd(a+b)+db(a+c)for all a,b,c,d∈V.ab+ac+ad=a(b+c+ad)(c+d+ab) (b+d+ac)for all a,b,c,d∈V.     

JAK3 mediatesc-myc gene expression induced by interleukin-2

C myc gene expression can be rapidly induced by IL 2 through intracellular signal transduction which is triggered by the interaction between IL 2 and its receptor (IL 2R). JAK3 which associates to the intracellular domain of IL_2R γ may play a critical role in this process. To reveal the action of JAK3 in c myc induction, a chimeric receptor gene IL_2R α/γ/Δ NJAK3 is constructed which consists of extracellular domain derived from IL 2R α subunit (IL_2R α), the transmembrane sequence derived from IL_2R γ and the cytoplasmic domain derived from the catalytic domain of JAK3 (Δ NJAK3), and then transfected this chimeric gene into mouse fibroblast cell line L929 β which had been transfected with IL_2R β gene and stably expressed IL_2R β in high level. In the transfectants coexpressing IL_2R β and α/γ/Δ NJAK3, the stimulation of IL_2 could intensively induce c myc gene expression. Because the whole cytoplasmic domain of IL_2R γ which could recruit signaling molecules was replaced by JAK3 and the c myc could be still induced by IL_2 in this situation, the results here gave the direct evidence demonstrating that JAK3 plays an important role in c myc gene expression induced by IL_2.     

Comment on shear-rotation mechanism for martensitic transformations

The "shear-rotation mechanism" for f.c.c.→b.c.c.(b.c.t.) martensitic transformation is further discussed in this paper. Although "shear-rotation mechanism" involves some valuable ideas which is based on the Nishiyama's model, the concept of "rotation" in "shear-rotation mechanism" may not be consistent with the general definition in crystallography. In addition, the mathematical expression of this mechanism is questionable. Furthermore, a detailed mathematical analysis given in the present paper indicates that the nature of "shear-rotation mechanism" is equivalent to the first two steps of Nishiyama's model, I.e. It is an invariant line strain (ILS) rather than an invariant plane strain (IPS). In other words, it is difficult to obtain the IPS based on the "shear-rotation mechanism" even though the isotropic contraction is involved. Therefore, a new method should be developed to explain the IPS based on Nishiyama's model.     

An improvement to the data processing course of electrochemical impedance technique

For some electrochemical systems the traditional data processing methods can not be met, so it is necessary to develop a new method to deal with these problems. When processing the electrochemical AC impedance data of titanium alloy TAl2 in 3% NaCl solution (at free corrosion potential, room temperature) a new method is developed which can detach the information of the interface resistance demonstrably from the interface capacitance. The results show that the interface resistance and capacitance are all functions of frequency. And the AC impedance of the resistance and capacitance obey the following relations:C(f)=104.01982 f-0.9292,R(f)=104.80011 (f+0.008)-0.90897, which is completely different from the traditional conception that the interface resistance and capacitance are constants. And this phenomenon is ubiquitous in titanium alloys according to the study. So perhaps it is an innate characteristic of interface.     

Influence of multi-stage heat treatment on the microstructure and mechanical properties of TC21 titanium alloy

Duplex-structured TC21 alloy samples were first solution-treated at a higher temperature in the α + β region(940°C) with furnace cooling(FC), air cooling(AC), and water cooling(WC), followed by a second-stage solution treatment at a lower temperature in the α + β region(900°C), and then finally aged at 590°C. The effects of the morphology and quantity of α phases on the structure and properties of the TC21 alloy after the different heat treatments were analyzed. The in-situ tensile deformation process and crack propagation behavior were observed using scanning electron microscopy(SEM). The quantity of equiaxed α phases as well as the thickness of lamellar α phases reduced, the tensile strength increased firstly and then decreased, the elongation decreased with the increasing cooling rate after the first-stage solution treatment. The amount and size of lamellar α phases increased after the second-stage solution treatment because of sufficient diffusion of the alloying elements, thereby leading to increased tensile strength. The amount of dispersed α phases increased after the third-stage aging treatment owing to the increase in the nucleation rate, resulting in a noteworthy strengthening effect. After the third-stage aging treatment, the first-stage FC sample exhibited better mechanical properties because it contained more equiaxed α and βtrans phases than the first-stage AC and WC samples.     

Dispersion relation and energy allotment of eigenmode of layer-by-layer photonic crystal

The photonic crystal of layer-by-layer(LBL) structure is discussed in this paper.The structure of LBL photonic crystal is body-centered tetragonal (b.c.t)rather than face-centered tetragonal(f.c.t.)For the LBL photonic crystal of f.e.c or b.c.c lattice,to obtain the fulll information on its Brillouin zone,the calculation of three restricted volumes is needed and our calculation result agrees well with the experiment.The allotments of optical fields of eigenmodes in a dielectric material are also calculated.In the dielectric material,for the eigenmode at the bottom of the forbidden gap,electric field takes a larger fraction of the whole energy than magnetic field,while for the eigenmode at the top of the forbidden gap,allotment of energy is just the other way round.     

ON THE SOLUTION OF THE SINGULAR INTEGRAL EQUATIONS WITH BOTH CAUCHY AND CONVOLUTION KERNEL

The following equations are basic forms of C-K equation (which is simplified in the following as singu-lar integral equations with convolution, that is C-K equations):where a,b,a_j,b_j are known constants or known functions, and find its solution f L_P(R), {0} or {α,β}.There were rather complete investigations on the method of solution for equations of Cauchy type aswell as integral equations of convolution type. But there is not investigation to the C-K equations, nodoubt, such that is important.     

锥巴拿赫空间上(α,β)-导子的稳定性（英文）

运用不动点法和直接法,研究了从单位环R到R-双模M的(α,β)-导子关于下列方程f ((a+b) c)=f (a)α(c)+β(a) f (c)+f (b)α(c)+β(b) f (c)的Hyers-Ulam稳定性.M关于锥范数||?||_P是一个锥巴拿赫空间,其中P是实巴拿赫空间E中的一个正规锥.     

Boltzmann Equations with Quantum Effects (1):Long Time Behavior of Spatial Decay Solutions

IntroductionIn the absence of external force fields,the modifiedBoltzmann equations governing Bose- Einsteinparticles and Fermi- Dirac particles can be unifiedto the following form[13 ] ,f(x,v,t)t +v .xf(x,v,t) =Qα(f) (x,v,t) ,(x,v,t)∈ R3× R3× R+ ,　 (BQE)whereα is proportional to h3 (h is Planck' scostant) and R+ =[0 ,∞ ) .The solution f=f(x,v,t) is the particle number density for the gasparticles possessing quantum effects at time t andposition x with velocity v.In a dilute g…     

Exact n-width on the class of analytic functions in the space of continuous functions

Let ω ( · ) be a given concave modulus of continuity and ω (g, · ) be the modulus of continuity of a function g ∈ C,where C is the space of 2π-periodic, continuous functions on (R) with norm ‖ f ‖ C := max | f( t ) |,(h) ∞,β r,ω( r= 0,1,2,… ) denotes those 2π-periodic, real-valued functions f on R that are analytic in the strip Sβ:= { z ∈ C: |Imz | ＜ β|, β ＞ 0, and satisfy the restriction condition: ω(f(r), ·)≤ω(·). In this paper, the exact n-width of the class of functions(h) ∞,β r,ωin the space C is determined.     

多级热处理对TC21钛合金组织和力学性能的影响

Duplex-structured TC21 alloy samples were first solution-treated at a higher temperature in the α + β region (940°C) with furnace cooling (FC), air cooling (AC), and water cooling (WC), followed by a second-stage solution treatment at a lower temperature in the α + β region (900°C), and then finally aged at 590°C. The effects of the morphology and quantity of α phases on the structure and properties of the TC21 alloy after the different heat treatments were analyzed. The in-situ tensile deformation process and crack propagation behavior were observed using scanning electron microscopy (SEM). The quantity of equiaxed α phases as well as the thickness of lamellar α phases reduced, the tensile strength increased firstly and then decreased, the elongation decreased with the increasing cooling rate after the first-stage solution treatment. The amount and size of lamellar α phases increased after the second-stage solution treatment because of sufficient diffusion of the alloying elements, thereby leading to increased tensile strength. The amount of dispersed α phases increased after the third-stage aging treatment owing to the increase in the nucleation rate, resulting in a noteworthy strengthening effect. After the third-stage aging treatment, the first-stage FC sample exhibited better mechanical properties because it contained more equiaxed α and β_trans phases than the first-stage AC and WC samples.     

亚纯函数f(az+b)与f(az+c)分担3CM的定理

主要针对非常数亚纯函数f(az+b)与f(az+c)分担3CM的情况进行研究讨论,得到了f(az+b)≡f(az+c)或f(az+b)≡f(az+2c-b),其中a≠0,b≠c.特别地,当a=1,b=0时, f(z)是以c或2c为周期的周期函数.     

关于洪福猜想(英文)

In[1],R.Huff introduced the concept of nearly uniformly convex Banach space.A Banach space X is said to be nearly uniformly convex(NUC) if for any ε>0,there exists δ<1,such that whenever {X_n}??X,||X_n||≤1,sep(X_n)=inf{||x_n-x_m||·m≠n}>ε,then there exist a_i≥0,i=1,…,n,sum for i=1 to n (a_i=1),and ||sum for i=1 to n (a_ix_i)||≤δ. R.Huff conjectured that NUC Banach space has the Banach Saks property(A Banach space X has the Bana ch-Sakseproperty(BSP) whenever every bounded sequence in X has a subsequence whose arithmetic means converge in norm.In this note,we give a negative answer to this conjecture. First we give a sufficient condition of NUC space.     

Superconvergence for triangular cubic elements

A new structure of superconvergence for the cubic triangular finite element approximation u/2 to a second-order elliptic problem Au = f is studied based on some orthogonal expansions in an interval. Suppose that Ω \s a convex polygonal domain with boundary Γ, its triangulation is uniform and Th is a set of vertexes and side midpoints of all elements. Then uh itself has no superconvergence points in Ω, while in any interior subdomain Ω0 the average gradient Duh has superconvergence D(dh - u) = O(hm+1 lnh) at z ∈ Th∩Ω0(no other superconvergence points). Furthermore, prescribe u = 0 on Γ1. Then the superconvergence near Γ1 will surely disappear; if α vu + bu = 0 on Γ3, where v is the conormal direction, the numercal experiments show superconvergence up to Γ3 (the case of A =-Δ and b = 0 has already been proved).     

Moderate deviations for a test of symmetry based on deconvolution kernel density estimators

Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X + ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n ( x )to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R | f n ( x ) f n( x) |are given by Gine and Guillou’s exponential inequality.     

Moderate Deviations for a Test of Symmetry Based on Deconvolution Kernel Density Estimators

Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X + ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n ( x )to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R | f n ( x ) f n( x) |are given by Gine and Guillou’s exponential inequality.     

Boltzmann Equations with Quantum Effects (2): Entropy Identity, Existence and Uniqueness of Spatial Decay Solutions

IntroductionAs in Zhang and Lu[1] ,we can write the modifiedBoltzmann equation for particles with quantumeffects in the absence of external force fields asfollows[2 5] :f(x,v,t)t +v .xf(x,v,t) =Qα(f) (x,v,t) ,(x,v,t)∈ R3 × R3 × R+ ,　 (BQE)whereα is proportional to h3 (h is Planck' sconstant) and R+ =[0 ,∞ ) .Let f =f (x,v,t)denote the particle number density for the gasparticles with quantum effects at time t andposition x with velocity v.The collision integralQα(f) in the BQ…     

Investigation of an energy nonadditivity for nonextensive systems

We investigate the energy nonadditivity relationship E(AαB) = E(A) + E(B) + αE(A)E(B) which is often considered in the development of the statistical physics of nonextensive systems. It was recently found that α in this equation was not constant for a given system in a given situation and could not characterize nonextensivity for that system. In this work, we select several typical nonextensive systems and compute the behavior of α when a system changes its size or is divided into subsystems in different fashions. Three kinds of interactions are considered. It is found by a thought experiment that α depends on the system size and the interaction as expected and on the way we divide the system. However, one of the major results of this work is that, for given system, α has a minimum with respect to division position. Around this position, there is a zone in which α is more or less constant, a situation where the sizes of the subsystems are comparable. The width of this zone depends on the interaction and on the system size. We conclude that if α is considered approximately constant in this zone, the two mathematical difficulties raised in previous studies are solved, meaning that the nonadditive relationship can characterize the nonadditivity of the system as an approximation. In all the cases, α tends to zero in the thermodynamic limit (N→∞) as expected.     

Large Time Behavior of Solutions to the Generalized Hall-Magnetohydrodynamics System

In this paper, we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD) system in the spaces χ~s(R~3).We obtain that the temporal decay rate is ■ with 1/2≤α, β≤1 for the small global solution by using Fourier splitting method. The parameters α and β are the fractional dissipations corresponding to the velocity and magnetic field, respectively.     

Microstructural evolution in the surface of Ti-10V-2Fe-3Al alloy by solution treatments

By solution treatments in vacuum and in air,the surface region of Ti-10V-2Fe-3Al exhibits different microstructures from the interior region of the alloy.When solution treated in vacuum,the microstructure of the specimen is composed of dominant β phase and a few of α " martensite in surface region,with a large amount of α" martensite and a little of β phase in interior.When solution treated in air,the specimen is characterized by dominant surficial a phase and interior β phase.In addition,the lattice parameter evolutions of a and β phases were observed in the surface region of the specimens by solution treatment in air.The mechanism for the surface effects is discussed in light of the structural stability and phase evolution in Ti-10V-2Fe-3Al alloy with solution treatments.