On the Optimality of Kounias-Sotirakglou Bounds

Bonferroni inequalities are significant in application for optimal allocation in tradable emission and other scary resources. Kounias and Sotirakglou improved Bonferroni inequalities, they give the lower and upper bounds for Bonferroni inequalities in the form of P( n∪i=1 Ai ), but they did not discuss the optimal of lower and upper bounds for P(n∪i=1Ai). In this paper, we give the method to obtain the optimum lower and upper bounds for Bonferroni inequalities in the form of mΣi=1(-1)i 1aiSi for P(n∪i=1 Ai) under the condition that Q (r) ≥ (≤) 0. The optimality of Kounias-Sotirakglou bounds is also studied.     

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.     

Population-size-dependent branching processes in Markovian random environments

A branching model {Z n} n≥0is considered where the offspring distribution of the population's evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.     

EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev's sense, a;(x),i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u(x) is unknown vector, z = (x_1,x_2,…,x_n) Ω R~z,m≥1,|S_1|issuperficial measure of the unit sphere of R~Z, |i|=i_1+ i_2 +… + i., △~m=△(△~(m-1)). ,(Ω), ,(Ω), … denote the classes of vectors or matrices whose elements belong to L,(Ω),W,(Ω),…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele-     

Oscillating chemiluminescence in rhodamine B-induced Belousov-Zhabotinsky reaction catalyzed by Ce(Ⅳ)

It was found that rhodamine B could induce oscillating chemiluminescence (OCL) from the Ce4+-cata-lyzed Belousov-Zhabotinsky reaction. This new OCL system, i.e., rhodamine B-malonic acid-bromate-Ce(Ⅳ)-sulfuric acid, exhibited two clearly distinguished emission peaks in each oscillation period. The initial concentrations of the reactants strongly influenced the oscillation pattern. For the study of the CL mechanism, a platform for a versatile and simultaneous potential and CL measurement was estab-lished to ...     

An Experimental Research of Fluid PistonOscillation in Square Moonpool under the Wave-Flow Combined Conditions

The article studies the oscillation features of the water in the square moon pool under the circumstances of wave-flow combined conditions. Comparing with the results of experiments of the square moon pool, a series of studies reveal that the water piston oscillation phenomenon is quite similar to that of the circular one. Two types of oscillation are exhibited under different incoming wave periods, i.e. self-excited oscillation and forced oscillation. The difference between the circular and square moon pool is that the attack angle makes greater influences on the square one. "Beating phenomenon" is also found in the square moon pool which is not mentioned of the circular one.     

of multiply from i=1 to n (ai+bi) ≥{n~1/[ multiply from i=1 to n (ai)] +n~1/[multiply from i=1 to n (bi)]}~n的证明推广及应用

本文给出了of multiply from i=1 to n (ai+bi) ≥{n~1/[ multiply from i=1 to n (ai)] +n~1/[multiply from i=1 to n (bi)]}~n的证明,并介绍了此结论在证明一些不等式中的应用。     

MULTIVARIATE NONLINEAR INTEGRAL INEQUALITIES AND ITS APPLICATION

0 IntroductionIn this paper, we establish new generalization of the Bihari-Wendroff type multivariate integral in-equalities and show their application to some partial differential equation.We consider the following integral inequalities;where, (x)=(x_1,…,x_n)∈R_n~+= [0,-∞)k;(x_i,s_i)=(x_1,…,x_i-1,s_i.,x_(i+1),…,x_0).We suppose that u(x)≥0, c(x)≥c_0>0, α;(x)≥0 (i=1,…,n), and they belong to C(R_n~+);c(x) and α_1(x) (i=1, …,n) are nondecreasing in (R_n~+); g_i(t)=g_i(c_0)>0 (i=1,…,n), and they are     

Weak response of the Atlantic thermohaline circulation to an increase of atmospheric carbon dioxide in IAP／LASG Climate System Model

Response of the Atlantic thermohaline circulation (THC) to global warming is examined by using the climate system model developed at IAP/LASG. The evidence indicates that the gradually warming climate associated with the increased atmospheric carbon dioxide leads to a warmer and fresher sea surface water at the high latitudes of the North Atlantic Ocean, which prevents the down-welling of the surface water. The succedent reduction of the pole-toequator meridional potential density gradient finally results in the decrease of the THC in intensity. When the atmospheric carbon dioxide is doubled, the maximum value of the Atlantic THC decreases approximately by 8%. The associated poleward oceanic heat transport also becomes weaker. This kind of THC weakening centralizes mainly in the northern part of the North Atlantic basin, indicating briefly a local scale adjustment rather than a loop oscillation with the whole Atlantic “conveyor belt” decelerating.     

THE SARD BEST APPROXIMATION OF LINEAR FUNCTIONAL

In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a_1(x)f~(1)(x)dx+ sum from f=0 to i_1(b_1f~(1)(x_1))]) by a simpler linear functional Lf=sum from i=1 to m(a_1f(x_1)) In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.     

Nonstandard Numerical Schemes for a Linear Stochastic Oscillator with Additive Noise

In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.     

关于一个不等式的加强及多种证法

从一个古老的不等式multiply from i=1 to n a_i~(a_i)≥(multiply from i=1 to n a_n)_n~1 multiply from i=1 to n c_i的多种证明出发,将其加强为multiply from i=1 to n a_i~(a_i)≥(1/n multiply from i=1 to n a_i)~(multiply from i=1 to n a_i)。并用凸函数的工具给出一个简短的新证明。     

Exact number of chord diagrams and an estimation of the number of spine diagrams of ordern

The main results are as follows: ( i ) For the number of chord diagrams of order n, an exact formula is given. ( ii ) For the number of spine diagrams of order n, the upper and lower bounds are obtained. These bounds show that the estimation is asymptotically the best. As a byproduct, an upper bound is obtained, for the dimension of Vassiliev knot invariants of order n, that is, 1/2 ( n -1)! for any n≥3, and 1/2( n - 1)! - 1/2( n - 2)! for bigger n . Our upper bound is based on the work of Chmutov and Duzhin and is an improvement of their bound ( n - 1)! . For n = 3, and 4,1/2( n - 1)! is already the best.     

Macromolecules Mimicking Backbones of Nucleic and Teichoic Acids.Synthesis,Some Properties and Applications

1 Results Several methods have been elaborated in this laboratory allowing preparation of macromolecules with phosphodiester bonds,and having sequence of atoms similar as in the chains of biomacromolecules - nucleic or teichoic acids (TA),namely:-(C)n-O-PO-,where n=2 (for teichoic acids) or 3.These methods,to be discussed in the lecture,are based on the ring-opening polymerization,transesterification,and recently elaborated direct addition of phosphoric acid to diepoxides.For the first time an attempt has been made to directly reacting phosphoric acid with diols in the presence and absence of catalysts.The major side reaction,preventing high molar mass polymers formation,results from dealkylation,i.e.nucleophilic attack of the OH groups on the C atom,instead attack on the P atom.The other two methods allowed reaching high molar mass macromolecules,with Mn up to 105.Following these studies phosphorylation of polymers with side groups containing -OH groups were studied and a series of diblock copolymers with ionic and nonionic blocks were prepared.     

Oscillating chemiluminescence in rhodamine B-induced Belousov-Zhabotinsky reaction catalyzed by Ce（IV）

It was found that rhodamine B could induce oscillating chemiluminescence （OCL） from the Ce4＋-catalyzed Belousov-Zhabotinsky reaction. This new OCL system, i.e., rhodamine B-malonic acid-bromate- Ce（IV）-sulfuric acid, exhibited two clearly distinguished emission peaks in each oscillation period. The initial concentrations of the reactants strongly influenced the oscillation pattern. For the study of the CL mechanism, a platform for a versatile and simultaneous potential and CL measurement was estab- lished to compare the potential oscillation with the CL oscillation behavior of this system. The CL spectra, UV-visible absorption spectra and time-resolved fluorescence spectra of this OCL system were studied. A possible, simplified mechanism for the OCL is proposed. It is suggested that the generation of the two CL peaks is likely due to the oxidation of the intermediate of rhodamine B by Ce（IV） and Br2, respectively. This work provided a new method and platform to research the complex chemical oscilla- tions.     

Epitaxial growth of Fe/Ag single crystal superlattices and their magnetic properties

Single crystal Fe/Ag(001) superlattices with various periodicities were fabricated using ultrahigh vacuum evaporation deposition. It was found that single crystal bcc Fe layers and single crystal fcc Ag layers can epitaxially grow on a single crystal Ag buffer layer alternately, which was deposited on NaCl single crystal chips by ion beam assisted deposition. The magnetic measurements of the superlattices reveal an oscillation coupling between ferromagnetism and antiferromagnetism as a function of the Ag layer thickness. The oscillation period, which is 1 nm (5 Ag layers), is in good agreement with the calculated values when the Ag thickness is greater than 1.5 nm. While the thickness of the Ag spacer layer decreases to 1 nm, the oscillation coupling varies from calculations, which can be attributed to the intermixing of the interlayers according to the annealing results.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

Wide Diameter for Two Families of Interconnection Networks

Wide diameter is an important parameter for measuring the reliability and efficiency of interconnection networks. Diameter with width k of a graph G, k-diameter, is defined as the minimum integer d for which there exist at least k internally disjoint paths of length at most d between any two distinct vertices in G. In this paper, we will discuss the wide diameter of two families of interconnection networks and present the bounds of wide diameter of G (G0,G1,...,Gr-1,L,) , where L=∪r-1 i=1 Mi,i+1,Mi,i+1 is an arbitrary perfect matching between V(Gi) and V(Gi+1), and G(G0,G1, F), where {(ui,vi)︱1≤i≤n}U 1{(uivi+1)︱1≤i≤ n} , ui∈V(G0), vi ∈V( G1). And they are used in practical applications, especially in the distributed and parallel computer networks.     

Evaluation of Ca3(Co,M)2O6 (M=Co, Fe, Mn, Ni) as new cathode materials for solid-oxide fuel cells

Series compounds Ca_3(Co_(0.9)M_(0.1))_2O_6(M = Co,Fe,Mn,Ni) with hexagonal crystal structure were prepared by sol-gel route as the cathode materials for solid oxide fuel cells(SOFCs).Effects of the varied atomic compositions on the structure,electrical conductivity,thermal expansion and electrochemical performance were systematically evaluated.Experimental results showed that the lattice parameters of Ca_3(Co_(0.9)Fe_(0.1))_2O_6and Ca_3(Co_(0.9)Mn_(0.1))_2O_6 were both expanded to certain degree.Electron-doping and hole-doping effects were expected in Ca_3(Co_(0.9)Mn_(0.1))_2O_6and Ca_3(Co_(0.9)Ni_(0.1))_2O_6 respectively according to the chemical states of constituent elements and thermal-activated behavior of electrical conductivity.Thermal expansion coefficients(TEC) of Ca_3(Co_(0.9)M_(0.1))_2O_6 were measured to be distributed around 16×10~(-6)K~(-1) and compositional elements of Fe,Mn,and Ni were especially beneficial for alleviation of the thermal expansion problem of cathode materials.By using Ca_3(Co_(0.9)M_(0.1))_2O_6 as the cathodes operated at 800 ℃,the interfacial area-specific resistance varied in the order of M = Co M = Fe M = Ni M = Mn,and the over-potential increased in the order of M = Fe ≈ M = Co M = Mn M = Ni.Among all of these compounds,Ca_3(Co_(0.9)Fe_(0.1))_2O_6 showed the best electrochemical performance and the power density as high as ca.500 mW cm~(-2) at800 ℃ achieved in the single cell with La_(0.8)Sr_(0.2)Ga_(0.83)Mg_(0.17)O_(2.815) as electrolyte and Ni-Ce_(0.8)Sm_(0.2)O_(1.9) as anode.Ca_3(Co_(0.9)M_(0.1))_2O_6(M = Co,Fe,Mn,Ni) can be used as the cost-effective cathode materials for SOFCs.