A kinetic model for polytropic gases with internal energy

We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function f_i(t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on , and its evolution is governed by a Boltzmann-type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L¹ space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L² framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2^n-（n-k） DESIGNS

Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions（2fi＇s）in 2^n-（n-k）designs of resolution Ⅲ and Ⅳ by constructing 2^n-（n-k）designs.But the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-（n-k） designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2].     

On construction ofT m -type PBIB designs

Summary Recently Saha and Das [10] constructed partially balanced incomplete block (PBIB) designs of two and more associate classes by using confounded designs for 2 ⁿ factorials. Several new designs of two associate classes were obtained through those methods. This paper generalizes one of the earlier methods of construction to obtain several series ofT _m -type (m≧2) PBIB designs, i.e., the designs havingm-dimensional triangular association schemes. Some more new designs of two associate classes (i.e.,T ₂-type) are obtained through the generalized methods of construction.     

On sequences of maps into <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript> with equibounded <Emphasis Type="Italic">W</Emphasis><Superscript>1/2</Superscript> energies

In the last years there has been some interest in studying mappings in the fractional Sobolev space W^1/2(, S¹), see e.g., [4] [3] [15] [12] and the paper [5]. Motivated by these papers, we characterize here in the framework of Cartesian currents, see [9], the class of weak limits of sequences of smooth mappings with values into S¹ with equibounded W^1/2 energies.     

Hardy-Littlewood Maximal Operator,Singular Integral Operators and the Riesz Potentials on Generalized Morrey Spaces

Any continuous linear operator T: L^p → L^q has a natural vector-valued extension T: L^p(l) → L^q(l) which is automatically continuous. Relations between the norms of these operators in the cases of p = q and r = 2 were considered by Marcinkiewicz -Zygmund [28], Herz [14] and Krivine [19] - [21]. In this paper we study systematically these relations and given some applications. It turns out that some known results can be proved in a simple way as a consequence of these developments.     

A construction of balanced arrays of strengtht and some related incomplete block designs

Summary Saha [6] has shown the equivalence between a ‘tactical system’ (or at-design) and a 2-symbol balanced array (BA) of strengtht. The implicit method of construction of BA in that paper has been generalized herein to that of ans-symbol BA of strengtht. Some BIB and PBIB designs are also constructed from these arrays. Majindar [2], Vanstone [8] and Saha [6] have all shown that the existence of a symmetrical BIBD forv treatments implies the existence of six more BIBD's forv treatments in (v/2) blocks. An analogue of this result has been obtained for a large class of PBIB designs in this paper.     

The classification of flag-transitive Steiner 4-designs

Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple group classification, for Steiner t-designs with parameters t > 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273], but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs. 2000 Mathematics Subject Classification. Primary 51E10 . Secondary 05B05 . 20B25     

On the optimality of a class of designs with three concurrences

In the present paper we consider a class of unequally replicated designs having concurrence range 2 and spectrum of the form μ₁(μ₂)^v−3μ₃. Now, Jacroux’s [Some sufficient conditions for the type I optimality of block designs, J. Statist. Plann. Inference 11 (1985) 385-396] Proposition 2.4 says that a design with spectrum of the above form, if satisfies some further conditions, is type 1 optimal. Unfortunately, this proposition does not apply to our designs since they have a poor status regarding E-optimality. Yet we are able to prove the A-optimality (in the general class) of these designs using majorisation technique. A method of construction of an infinite series of our A-optimal designs has also been given.The first and only known infinite series of examples of designs satisfying Jacroux’s conditions appears to be the first one in Section 4.1 of Morgan and Srivastav [On the Type-1 optimality of nearly balanced incomplete block designs with small concurrence range, Statist. Sinica 10 (2000) 1091-1116] - hitherto referred to as [MS]. In this paper, we use majorisation technique to prove stronger optimality properties of the above mentioned designs of [MS] as well as to present simpler proof of another optimality result in [MS].     

A note on Schatten‐class membership of Hankel operators with antiholomorphic symbols on generalized Fock‐spaces

In this paper we investigate Hankel operators with anti‐holomorphic L²‐symbols on generalized Fock spaces A_m² in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator with anti‐holomorphic L²‐symbol is in the Schatten‐class S_p if and only if the symbol is a polynomial with degree N satisfying 2N < m and p > . The result has been proved independently before in the recent work [2], which also considers the case of several complex variables. However, in addition to providing a different proof for the result the present work shows that the methodology developed in [4] and [3] can be adopted in order to work to characterize Schatten‐class membership. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

C*-Nuclearity implies CPAP

In this paper we show: A C^*-algebra A with identity e is C^*-nuclear (i.e. “nuclear” in the sense of LANCE [3, p. 159] or “property T” in the sense of TAKESAKI [6] if and only if the identity operator id_A on A can be approximated in the strong operator topology by completely positive linear operators V from A into A of finite rank with norm one and V(e)=e. From which follows that every C^*-nuclear C^*-algebra (possible without identity) possesses the CPAP of LANCE [3, def. 3.5.]. This answers questions of LANCE [3, p. 173] and SAKAI [5, p. 64].     

Optimale Differentiations- und Integrationsformeln in Co [a,b]

Summary LetC _o [a, b] be the Banach space of all real valued continuous functions defined on the interval [a, b], endowed with the supremum norm. In this paper we construct optimal formulas for the numerical differentiation and integration forC _o [a, b].In particular, the questions of Meinguet [2] and Salzer [5] on the existence of such formulas are answered.     

Niveau hermitien de Certaines algèbres de quaternions

Let D [d] =(a,b/F) a quaternion divisior algebra over a field F of characteristic ? 2. Denote 1, i, j , k the basis of D, such that i²[d] n, j²[d] b, ij [d] -ji [d] k and A :D → D the involution given by i [d] -i, j [d] j (and k [d] k). In [LE] D. LEWIS asks the following question :Does there exist a quadratic Pfister form [S p. 721 [d] such that the hermitian form [d] [d] D is isotropic over (D, [d]) but not hyperbolic &; In this note, we show that the answer of this question is negative, so that the hermitien level [§I], when it is finite, of (D, A) is a power of two. This result holds for quaternion algebras with standard involution [LE].     

[a,b]-factorization of a graph

Let a and b be integers such that 0 ? a ? b. Then a graph G is called an [a, b]-graph if a ? d_G(x) ? b for every x ? V(G), and an [a, b]-factor of a graph is defined to be its spanning subgraph F such that a ? d_F(x) ? b for every vertex x, where d_G(x) and d_F(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]-factors then we say that the graph is [2a, 2a]-factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)-factorable if and only if G is a [2am,2bm]-graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]-graph is [1,2]-factorable.     

Strong approximation of Fourier series and embedding theorems

Summary In this paper, embedding results are considered which arise in the strong approximation by Fourier series. We prove several theorems on the interrelation between the classes W^r H_β^ω and H (λ,p,r,ω), the latter being defined by L. Leindler. Previous related results in Leindler’s book [2] and paper [5] are particular cases of our results.     

Some Generic Results on Nonattaining Functionals

We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the nonsupport functionals are a dense G subset of the polar set, and (b) any nonsemicoercive proper convex lsc [weak^*-lsc] function in a [dual] Banach space has a generic [dense G ] set of L -perturbations which do not attain their infimum. We also characterize the proper convex functions that have inf-nonattaining L -perturbations. This results also in a criterion for reflexivity.     

A note on weighing designs

Summary Banerjee [1], [2] has shown that the arrangements afforded by a Balanced Incomplete Block Design can be used as an efficient spring balance design. Such designs suffer from one drawback viz., there are only a few or no degrees of freedom left for the estimation of error-variance,σ ². To overcome this difficulty, it has been suggested that the whole design may be repeated a certain number of times to get an estimate of the error variance. In the present note an attempt has been made to give an alternative design where there is no necessity of such repetition. It has been also shown that these designs give a lesser variance of the estimated weights than the repeated design. Institute of Agricultural Research Statistics     

Poisson structures on Hilbert schemes of points¶of a surface and integrable systems

In this paper we prove that if S is a Poisson surface, i.e., a smooth algebraic surface with a Poisson structure, the Hilbert scheme of points of S has a natural Poisson structure, induced by the one of S. This generalizes previous results obtained by A. Beauville [B1] and S. Mukai [M2] in the symplectic case, i.e., when S is an abelian or K3 surface. Finally we apply our results to give some examples of integrable Hamiltonian systems naturally defined on these Hilbert schemes. In the simple case S=ℙ² we obtain by this construction a large class of integrable systems, which includes the ones studied by P. Vanhaecke in [V1] and, more generally, in [V2]. Received: 9 March 1998 / Revised version: 19 June 1998