F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.     

环F2+uF2+vF2上自对偶码的两种构造方法

本文研究环R=F2+uF2+vF2上的自对偶码问题.利用Rn到F3n2的Gray映射及R上的自对偶码C的Gray像为F2上自对偶码,获得了R上任何偶长度的自对偶码存在性的结论.最后,给出了R上两种构造自对偶码的方法.     

A joint SSPDF–CMC method for simulating turbulent methane–air jet combustion

A joint single scalar probability density function and conditional moment closure (SSPDF–CMC) method is proposed for modeling a turbulent methane–air jet flame. In general, the probability density function (PDF) of passive scalar (such as mixture fraction) is non-Gaussian and not fully determined by the advecting velocity field, therefore the presumed shape of PDF of mixture fraction assumed as clipped Gaussian distribution or beta function in normal conditional moment closure (CMC) method is incorrect. In SSPDF–CMC method, the PDF of mixture fraction is obtained using a Monte-Carlo method to solve a PDF transport equation. An assumption that the averaged scalar advection is approximately equal to the averaged scalar dissipation in the wake of a grid-generated turbulence flow is adopted to model the averaged scalar dissipation. The predictions using the proposed method are compared with those using the conventional CMC method and the experimental data. It is seen that the predicted Favre conditional averaged statistics and Favre unconditional averaged statistics using the proposed method are in better agreement with the measurement data than those using the conventional CMC method. The predicted conditional or unconditional mean NO even using the SSPDF model is only in fair agreement with the experiments. It shows that the first-order closure for the conditional reaction rate of NO should be improved.     

A 3-local characterization of U6(2) and Fi22

The unitary group U₆(2), often referred to as Fi₂₁, and the sporadic simple group Fi₂₂, discovered by Fischer [B. Fischer, Finite groups generated by 3-transpositions. I, Invent. Math. 13 (1971) 232–246 [6]], are characterized by specifying partial information about the structure of the normalizer of a non-trivial 3-central cyclic subgroup.     

Asymptotic zero distribution of a class of 3F2 hypergeometric functions

We study the asymptotic behavior of the zeros of certain families of ₃F₂ functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial In addition, families of ₃F₂ functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form and are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica.     

Cyclic codes over the rings Z 2?+ uZ 2 and Z 2?+ uZ 2?+ u 2 Z 2

In this paper, we study cyclic codes over the rings Z ₂ + uZ ₂ and Z ₂ + uZ ₂ + u ² Z ₂ . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as well. Examples of cyclic codes of various lengths are also studied.      

The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

环F3+vF3上的循环码与常循环码

本文研究了环F₃+vF₃上的循环码与常循环码.通过环F₃+vF₃与域F₃上的循环码之间关系,证明了环F₃+vF₃上循环码是由一个多项式生成的.最后,用类似的方法,得到了环F₃+vF₃上v-常循环码也是由一个多项式生成的.     

When isf(x1, x2, ..., xn) =u1(x1) +u2(x2) + ... +un(xn)?

We discuss subsetsS of ℝⁿ such that every real valued functionf onS is of the formf(x₁, x₂, ..., x_n) =u ₁(x₁) +u ₂(x₂) +...+u _n(x_n), and the related concepts and situations in analysis.     

Three-dimensional modelling of NOx and particulate traps using CFD: A porous medium approach

Lean burn after-treatment systems are the current focus for reducing emissions from diesel exhaust. The trend is for commercial CFD packages to use a single channel modelling approach. Due to computational demands, this necessitates specification of representative channels for modelling, implying prior knowledge of the flow field. This paper investigates a methodology for applying the porous medium approach to lean burn after-treatment systems. This approach has proved successful for three-way catalysis modelling and has the advantage that the flow field is predicted. Chemical kinetic rates for NO_x trapping and regeneration in the model are based on information available in the open literature. Similarly, filtration information based on mass accumulation and soot combustion kinetics are also readily available. Modification of the source terms in a commercial CFD package enables prediction of trapping and release of NO_x. This is an effective way to model a NO_x trap after-treatment system and provides simultaneous 3D modelling of the flow field. With diesel, particulate filtration is required. In the case of particulate traps, however, because of channel geometry, some assumptions are necessary for use of the porous medium approach and these are discussed in this paper. Both models produce qualitatively correct output and have parameters that can be tuned to conform to experimental data. Data to validate the NO_x trap model is to be measured. The particulate trap model, on the other hand, is a feasibility study for modelling the complete diesel after-treatment system using the porous medium approach.     

A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

Best simultaneous L1 approximations

Three possible definitions are proposed for best simultaneous L₁ approximation to n continuous real-valued functions, and the relation between best simultaneous approximations and best L₁ approximations to the arithmetic mean of the n functions is discussed.     

On the sum ∑k=13 | 2πk − αk |, αk algebraic numbers

If α₁, α₂, α₃ are algebraic numbers satisfying (i) the height of α₁, α₂, α₃ do not exceed H (ii) the degree of the field generated by α₁, α₂, α₃ over the field of rational numbers do not exceed D, then a positive lower bound for

$\text{∑}\text{k=1}\text{3}\text{|2π}{}^{\mathrm{k}}\text{?αk|}$

is determined explicitly (except for an absolute constant) in terms of D and H.     

Groups with T1 primitive ideal spaces

We give a simple necessary and sufficient condition for the group C¹-algebra of a connected locally compact group to have a T₁ primitive ideal space, i.e., to have the property that all primitive ideals are maximal. A companion result settles the same question almost entirely for almost connected groups. As a by-product of the method used, we show that every point in the primitive ideal space of the group C¹-algebra of a connected locally compact group is at least locally closed. Finally, we obtain an analog of these results for discrete finitely generated groups; in particular the primitive ideal space of the group C¹-algebra of a discrete finitely generated solvable group is T₁ if and only if the group is a finite extension of a nilpotent group.     

K2 and K3 of the circle

Let k be $\text{Z}\text{[}\text{1}\text{2}\text{]}$, $\text{Q}$ or $\text{R}$, and set $\text{A =}\text{k[x,y]}\text{(x}{}^2\text{+ y}{}^2\text{? 1)}$. We compute K₂(A) and K₃(A). Our method is to construct a map $\text{? : K}{}_1\text{(k[i])→K}{}_{\mathrm{1\; +\; 1}}\text{(A)}$ and compare this to a localization sequence.We give three applications. We show that ? accounts for the primitive elements in K₂(A), and compare our results to computations of Bloch [1] for group schemes. Secondly, we consider the problem of basepoint independence, and indicate the interplay of geometry upon the K-theory of affine schemes obtained by glueing points of Spec(A). Third, we can iterate the construction to compute the K-theory of the torus ring A ?_kA.     

Effect of Mg and C contents in MgCNi3, and structure and superconductivity of MgCNi3- x -Co x

The effect of Mg and C contents on T_C in MgCN₃, and structure and superconductivity of MgCNi_3-x Co _x were studied. It is found that the excess of Mg and C in initial material mixture is favorable to improvement inT _c and helps to obtain single-phase samples. For preparing MgCNi₃ superconductor, the optimum composition of starting materials is MgC_1.45Ni₃ with excess of Mg (20 wt.%) of the stoichiometric composition. In gCNi_3-x Co _x system, a continuous solid solution is formed, lattice parameter decreases slightly andT _c decreases obviously with increasingx. A suppression of superconductivity is observed due to the substitution of Co (Mn) for Ni. The suppression effect is smaller for the substitution of Co than that of Mn     

Universal embeddings for theD4(2) hexagon andJ2near-octagon

The universal embeddings overF₂ of the generalized hexagon for³D₄(2)and the near-octagon forJ₂are determined to be the 28-dimensional adjoint modules: for typeD₄in the first case, and in the second from the 14-dimensional adjointF₄-module forG₂(4)containingJ₂.     

一类Z_2对称五次微分系统的中心条件和极限环分支

本文研究了一类Z2对称五次微分系统的中心条件和小振幅极限环分支.通过前6阶焦点量的计算,获得了原点为中心的充要条件,并证明系统从原点分支出的小振幅极限环的个数至多为6.最后通过构造后继函数,给出系统具有6个围绕原点的小振幅极限环的实例.     

Superpositions for nonlinear operators II. Generalized affine operators

From a previously given type of operators having strong superpositions, the C_f1,f2 classes, a generalization of affine transformations is obtained. The resulting operators have invariant quasilinear means. In addition, the operators have strong superpositions which are abelian semigroup operations with an idempotent property. It is natural, in this case, to define scalar operations on pairs of scalars and pairs of vectors on the domain and range spaces. Properties of this algebraic structure and its similarity to the superposition rules for color sensations are shown.     

Some group actions on K(x 1 , x 2 , x 3 )

LetK be any field which may not be algebraically closed,K(x ₁ ,x ₂ ,x ₃ ) be the rational function field of three variables overK, and σ:K(x ₁ ,x ₂ ,x ₃ ) → K(x ₁ ,x ₂ ,x ₃ ) be aK-automorphism defined by wherea _i ,b _i ,c _i ,d _i ∈K anda _i d _i −b _i c _i ≠0. Let ,f _i (T)=T ² −(a _i +d _i )T+(a _i d _i −b _i c _i )∈K[T] be the “characteristic polynomial” of σ _i . Theorem:Assume that charK≠2.Then the fixed field K(x ₁ ,x ₂ ,x ₃ ) ^<σ> is not rational (=purely transcendental) over K if and only if (i) for each 1≤i≤3, f _i (T) is irreducible; (ii) the Galois group of f ₁ (T)f ₂ (T)f ₃ (T) over K is of order 8; and (iii) for each 1≤i≤3,ord (σ _[itn] )is an even integer.