Border bases and kernels of homomorphisms and of derivations

Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.     

Extension and Lifting of Operators and Polynomials

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of ${\mathcal{L}_1}$ and ${\mathcal{L}_\infty}$ -spaces that includes and extends those of Lindenstrauss-Rosenthal [32] using compact operators and González-Gutiérrez [23] using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented.     

On some results of Strichartz and of Rallis and Schiffman

Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is ($\text{i ? j, H}\text{}\text{?}\text{bo}{}_2\text{K, E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha F}}$) an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from $\text{H}\text{}\text{?}\text{bo}{}_2\text{K}$ into $\text{E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha }}\text{F}$. Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=L^p(X,$\text{X}$,λ) for some σ-finite measure λ ? 0 then $\text{(i?j, H}\text{?}{}_2\text{K,L}{}^{\mathrm{p}}$(X,$\text{X}$,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L¹(X,$\text{X}$,λ)).     

Shellability and homology of q-complexes and q-matroids

Journal of Algebraic Combinatorics - We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that...     

Crossings and nestings of matchings and partitions

We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block elements, the crossing number and the nesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of , as well as over all matchings on . As a corollary, the number of -noncrossing partitions is equal to the number of -nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no -crossing (or with no -nesting).

     

Closedness and Adjoints of Products of Operators, and Compressions

We reprove and slightly improve theorems of Nudelman and Stenger about compressions of maximal dissipative and self-adjoint operators to subspaces of finite codimension and discuss related results concerning the closedness and the adjoint of a product of two operators on a Hilbert space.     

ERP与ISO的结合与集成实施

ERP和ISO9000的一体化结合是一个值得重视的研究课题.文中首先分析了ERP和ISO9000的对应点,指出两者可以相互支撑.最后,探讨了两者的集成实施问题.     

麻疹防治中免疫接种和有效治疗效果比较的建模分析

探讨了H.E.Soper所提出的麻疹模型的解的局部稳定性和全局稳定性,并解释了其生物意义.基于麻疹周期性爆发的特征及其防治方法,作者分别提出了具有免疫接种和有效治疗两种情况下的新模型,并分别对模型进行了分析.比较了两种防控措施的模型分析结果,得到在麻疹的防治工作中有效治疗能够有效控制大规模爆发的结论.     

钢管订购与运输问题三的数学模型与灵敏度分析

本文针对 2 0 0 0年全国大学生数学建模竞赛 B题——钢管订购与运输问题的问题 ( 3) ,建立了数学模型 ,给出了该数学模型的精确求解 .然后对问题 ( 1 )与问题 ( 3)给出了灵敏度分析 .     

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

Cremona transformations and the conundrum of dimensionality and signature of macro-spacetime

The issue of dimensionality and signature of the observed universe is analysed. Neither of the two properties follows from first principles of physics, save for a remarkably fruitful Cantorian fractal spacetime approach pursued by El Naschie, Nottale and Ord. In the present paper, the author's theory of pencil-generated spacetime(s) is invoked to provide a clue. This theory identifies spatial coordinates with pencils of lines and the time dimension with a specific pencil of conics. Already its primitive form, where all pencils lie in one and the same projective plane, implies an intricate connection between the observed multiplicity of spatial coordinates and the (very) existence of the arrow of time. A qualitatively new insight into the matter is acquired, if these pencils are not constrained to be coplanar and are identified with the pencils of fundamental elements of a Cremona transformation in a projective space. The correct dimensionality of space (3) and time (1) is found to be uniquely tied to the so-called quadro-cubic Cremona transformations – the simplest non-trivial, non-symmetrical Cremona transformations in a projective space of three dimensions. Moreover, these transformations also uniquely specify the type of a pencil of fundamental conics, i.e. the global structure of the time dimension. Some physical and psychological implications of these findings are mentioned, and a relationship with the Cantorian model is briefly discussed.     

OD-Characterization of alternating and symmetric groups of degrees 16 and 22

Let G be a finite group and π(G) be the set of all prime divisors of its order. The prime graph GK(G) of G is a simple graph with vertex set π(G), and two distinct primes p, q ∈ π(G) are adjacent by an edge if and only if G has an element of order pq. For a vertex p ∈ π(G), the degree of p is denoted by deg(p) and as usual is the number of distinct vertices joined to p. If π(G) = {p ₁, p ₂,...,p _k }, where p ₁ < p ₂ < ... < p _k , then the degree pattern of G is defined by D(G) = (deg(p ₁), deg(p ₂),...,deg(p _k )). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions |H| = |G| and D(H) = D(G). In addition, a 1-fold OD-characterizable group is simply called OD-characterizable. In the present article, we show that the alternating group A ₂₂ is OD-characterizable. We also show that the automorphism groups of the alternating groups A ₁₆ and A ₂₂, i.e., the symmetric groups S ₁₆ and S ₂₂ are 3-fold OD-characterizable. It is worth mentioning that the prime graph associated to all these groups are connected.