Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem

The aim of this paper is that of investigating the asymptotic exponential cone of a single Metzler matrix, introduced in [23], and of defining and analysing the new concept of asymptotic exponential cone of a family of Metzler matrices (along a certain direction). These results will provide necessary and/or sufficient conditions for the solvability of an interesting algebraic problem that arises in the context of continuous-time positive switched systems and, specifically, in the investigation of the reachability property [21,22,25].     

Controllable synthesis and characterization of ammonium polyphosphate with crystalline form V by phosphoric acid process

Ammonium polyphosphate (APP) with crystalline form V (APP-V) was synthesized by heating a mixture of 85% food-grade phosphoric acid and melamine under dry ammonia atmosphere. Effects such as raw material ratios, charging methods, dehydration temperature, condensation temperature and condensation time were investigated. Its water solubility was tested, its XRD and FTIR were characterized and compared with those of industrial APP-I and APP-II. Results showed that the prepared APP-V was insoluble in water, its XRD spectrum was the same as APP-V in literature. The molecular structures of the prepared APP-V and APP-I/APP-II were speculated and discussed in detail.     

Effect of calcium malonate on the formation of β crystalline form in isotactic poly(propylene)

Calcium malonate (Camt) is used to induce the β crystalline form in isotactic polypropylene (iPP) for the first time. The relative content of the β crystalline form (K value) increases markedly with the addition of Camt and attains the maximum value of 73.48% at 0.40% Camt. The amounts of bright and colorful β spherulites increase and the spherulitic sizes decrease with the increase in Camt contents. The tensile strength and the Izod notched impact strength of the nucleated iPP samples increase with the addition of Camt; in particular, the latter almost doubles at 0.40% Camt compared to that of the blank iPP sample. The β nucleation mechanism of Camt is analyzed by the dimensional lattice match criterion. Copyright © 2008 John Wiley & Sons, Ltd.     

Local Heaviside‐weighted LRPIM meshless method and its application to two‐dimensional potential flows

In this paper, the local radial point interpolation meshless method (LRPIM) is used for the analysis of two‐dimensional potential flows, based on a local‐weighted residual method with the Heaviside step function as the weighting function over a local subdomain. Trial functions are constructed using radial basis functions. The present method is a truly meshless method based only on a number of randomly located nodes. Integration over the subdomains requires only a simple integration cell to obtain the solution. No element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. The novelty of the paper is the use of a local Heaviside weight function in the LRPIM, which does not need local domain integration and integrations only on the boundary of the local domains are needed. Effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated. The behavior of shape parameters of multiquadrics has been systematically studied. Two numerical tests in groundwater and fluid flows are presented and compared with closed‐form solutions and finite element method. The results show that the use of a local Heaviside weight function in the LRPIM is highly accurate and possesses no numerical difficulties. Copyright © 2008 John Wiley & Sons, Ltd.     

On locally convex hypersurfaces in Hadamard manifolds

Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces with nonpositive definite second quadratic form of rank no smaller than one is obtained. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 498–507, April, 2000.     

The last subconstituent of the Hemmeter graph

We prove that when q is any odd prime power, the distance-2 graph on the set of vertices at maximal distance D from any fixed vertex of the Hemmeter graph Hem_D(q) is isomorphic to the graph Quad_D-1(q) of quadratic forms on .     

Hermite四点插指公式

文章利用Hermite插值基函数,将求解Hermite四点插指问题转换为求解8个派生出来的多项式插值问题,证明了Hermite四点插指公式的存在唯一性,并用两种方法构造出Hermite四点插指公式,最后给出了一个算例.     

A contribution to the global formulation of the higher-order Poincaré-Cartan form

The global formulation of the higher-order Poincaré-Cartan form for Lagrangian field theories in the calculus of variations is re-examined in terms of the theory of lifts of tensor fields on a manifold to its higher-order prolongated jet bundles.Partially supported by CNPq, Brazil, Proc. MA 30.1115/79.     

Projective DNF formulae and their revision

Combinatorial and learnability results are proven for projective disjunctive normal forms, a class of DNF expressions introduced by Valiant.     

Imprimitive matrices of zeros and ones with extremal numbers of ones

In [X. Zhan, Extremal numbers of positive entries of imprimitive nonnegative matrices, Linear Algebra Appl. 424 (2007) 132–138], Zhan determined the maximum and minimum numbers of positive entries of irreducible nonnegative matrices. In this paper, we characterize the irreducible (0,1) matrices with the maximum and minimum numbers of positive entries.