The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age

The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal, and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years.     

《概率论与数理统计》教学改革研究

针对概率论与数理统计课程的特点,以经济管理类专业的学生为对象,提出了概率论与数理统计课程教学改革的几点建议．     

The Generalized Clifford-Gegenbauer Polynomials Revisited

By applying a method introduced by De Bie and Sommen in Clifford superanalysis, the orthogonality relations of the generalized Clifford–Gegenbauer polynomials of wavelet analysis are extended. Moreover, this new approach allows for proving new important properties of these polynomials, such as an annihilation equation, a differential equation and an expression in terms of the Jacobi polynomials on the real line. This paper is dedicated to the memory of our friend and colleague Jarolim Bureš     

运筹学教学与数学建模

根据从事《运筹学》教学的体会 ,论述了运筹学教学与数学建模教育的关系 ,并介绍了教学的一些做法     

数理统计在支架形貌分析中的应用

采用一种简易的手段,利用数理统计的方法表征支架的形貌结构特点,并与直观的电镜图相比较,两者结果基本相一致.该方法对于支架形貌表征确立数据的、直观的结果具有一定的指导价值.     

The geometry of Kato Grassmannians

We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.     

The minimizing of the Nielsen root classes

Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M ₂)−χ(M ₁0/(1−χ(M ₂)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M ₂)−χ(M ₂)/(1−χ(M ₂)). Also we construct, for each integer n≥3, an example of a map f: K _n →N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time.     

The basic component of the mean curvature of Riemannian foliations

For a Riemannian foliation % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] on a compact manifold M with a bundle-like metric, the de Rham complex of M is C-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacciGae8NUdS% 2aaSbaaSqaaiaadkgaaeqaaaaa!38B9!\[\kappa _b \] of the mean curvature form of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is closed and defines a class (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) in the basic cohomology that is invariant under any change of the bundle-like metric. Moreover, any element in (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) can be realized as the basic component of the mean curvature of some bundle-like metric.It is also proved that (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\]) vanishes iff there exists some bundle-like metric on M for which the leaves are minimal submanifolds. As a consequence, this tautness property is verified in any of the following cases: (a) when the Ricci curvature of the transverse Riemannian structure is positive, or (b) when % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFXeIraaa!4094!\[\mathcal{F}\] is of codimension one. In particular, a compact manifold with a Riemannian foliation of codimension one has infinite fundamental group.     

Existence theory and Q-matrix characterization for the generalized linear complementarity problem: Revisited

We provide conditions under which a vertical block matrix is a Q-matrix if one or all representative sub-matrices are Q-matrices and vice versa. It is also shown, by means of counterexamples, that Eq. (3) of [A.A. Ebiefung, Existence theory and Q-matrix characterization for the generalized linear complementarity problem, Linear Algebra Appl. 223/224 (1995) 155-169] is incorrect.     

The Discrete-Time GI/Geo/1 Queue with Multiple Vacations

We study a discrete-time GI/Geo/1 queue with server vacations. In this queueing system, the server takes vacations when the system does not have any waiting customers at a service completion instant or a vacation completion instant. This type of discrete-time queueing model has potential applications in computer or telecommunication network systems. Using matrix-geometric method, we obtain the explicit expressions for the stationary distributions of queue length and waiting time and demonstrate the conditional stochastic decomposition property of the queue length and waiting time in this system.     

The dimension of leaf closures of K-contact flows

For K-contact flows on (2n+1)-dimensional compact manifolds, we show that the dimension of any leaf closure is at most the smaller of (n+1) and 2n+1) minus the rank of the vector space of harmonic vector fields.     

红富士干周增长规律的数学模型

程述汉等．红富士干周增长规律的数学模型．在对鲁西平原上１～１４年生红富士苹果树干周大量调查的基础上,研究了红富士苹果树干周增长规律及负荷量对干周增长的影响;建立了干周增长规律的数学模型     

The prime and maximal spectra and the reticulation of BL-algebras

In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T ₀ topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.     

公务员最优录用分配方案的数学模型

本文通过建立0-1规划模型,设计了一种公务员招聘中的最优录用分配方案,并运用L INGO软件求得了一个实际问题的最优解.     

The classification of transversal multiplicity-free group actions

Multiplicity-free Hamiltonian group actions are the symplectic analogs of multiplicity-free representations, that is, representations in which each irreducible appears at most once. The most well-known examples are toric varieties. The purpose of this paper is to show that under certain assumptions multiplicity-free actions whose moment maps are transversal to a Cartan subalgebra are in one-to-one correspondence with a certain collection of convex polytopes. This result generalizes a theorem of Delzant concerning torus actions.Supported by an ONR Graduate Fellowship.     

L-fuzzy群理论的数理逻辑基础

Zadeh在文[1]中引入Fuzzy集概念之后，这一概念被Goguen[2]推广，真值域由单位闭区间被更一般的格所代替。Rosenfeld[3]将Zadeh的思想引入到群论中，提出Fuzzy群概念，真值域为格的Fuzzy群被称为L—fuzzy群[4]。本文的目的是用数理逻辑的语言陈述L—fuzzy群理论，构造L—fuzzy群的形式数学系统，从而建立L—fuzzy群理论的数理逻辑基础。     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

The closure diagram for nilpotent orbits of the split real form of E8

Let and be adjoint nilpotent orbits in a real semisimple Lie algebra. Write ≥ if is contained in the closure of . This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split real form of the simple complex Lie algebra, E ₈. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries and of the intersections .     

微波传输路由的数学模型

在微波通讯中，电波射束和障碍物之间应留有足够的余隙，以保证能量的有效传输．本文考虑地球表面自然凸特征，建立在此意义下的余隙的数学模型，从而获得微波传输路由的数学模型．利用此模型的解与海拔制高点的余隙进行比较，便可获得工程建设中的最佳余隙值及相联系的有效的经济的路由设计．     

The heat flow for subharmonic orbits

LetV: M be a smooth (potential) function on a compact Riemannian manifold. This gives rise to a second order Hamiltonian system. Assuming that the corresponding action functional is a Morse function, we will prove that the heat flow for subharmonics exists globally and converges to a critical point of the energy. As a Corollary, this shows the convergence of the geodesic heat flow (to a geodesic) without any curvature assumptions onM.