Resolvable group divisible designs with block size four and index three

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hⁿ and index three. The necessary conditions for the existence of such a design are n?4 and hn≡0. These necessary conditions are shown to be sufficient except for (h,n)∈{(2,4),(2,6)} and possibly excepting (h,n)=(2,54).     

Solutions of nonlinear evolution inclusions

In this paper, the solution of the nonlinear evolution inclusion problem of the form u^′(t)+B(t,u(t))∋f(t) is studied. In this problem, the operators are of type (M) or type (S₊), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications.     

A general two-sided matching market with discrete concave utility functions

In the theory of two-sided matching markets there are two standard models: (i) the marriage model due to Gale and Shapley and (ii) the assignment model due to Shapley and Shubik. Recently, Eriksson and Karlander introduced a hybrid model, which was further generalized by Sotomayor. In this paper, we propose a common generalization of these models by utilizing the framework of discrete convex analysis introduced by Murota, and verify the existence of a pairwise-stable outcome in our general model.     

Measurement of the F5/2 and H(2)9/2 manifold lifetime in Nd:YLiF4

We present direct measurements of the lifetime of the ⁴F_5/2 and ²H(2)_9/2 manifold in Nd³⁺:YLiF₄, using a fluorescence pump-probe technique. The technique populates the ⁴F_5/2 and ²H(2)_9/2 manifold directly with a pump pulse. Via excited state absorption from this excited manifold, the ²F(2)_5/2 manifold of Nd³⁺ is populated with a delayed probe pulse. The population in the ⁴F_5/2 and ²H(2)_9/2 manifold is monitored as a function of time by observing the change in integrated UV fluorescence from the ²F(2)_5/2 manifold for each time delay between pump and probe pulses. The pump and probe beams come from the fundamental and second harmonic wavelengths of a femtosecond Ti:sapphire regenerative amplifier. The measured lifetime agrees well with the energy gap law, based on other nonradiative lifetime measurements from the literature for Nd³⁺:YLiF₄.     

Potential energy curve of Be2 in its ground electronic state

The potential energy curve of Be₂ in its ground electronic state is constructed by morphing accurate MR-CI ab initio potentials from the literature to available experimental ro-vibrational data within the framework of the reduced potential curve (RPC) approach of Jen? and Plíva [Adv. At. Mol. Phys. 19 (1983) 265-307]. The resulting potential energy curves are in close harmony with experiment allowing thus for reliable prediction of the so-far experimentally unprobed part of the molecular potential energy function.     

Turán’s theorem inverted

In this note we complete an investigation started by Erd?s in 1963 that aims to find the strongest possible conclusion from the hypothesis of Turán’s theorem in extremal graph theory.Let be the complete r-partite graph with parts of sizes s₁≥2,s₂,…,s_r with an edge added to the first part. Letting t_r(n) be the number of edges of the r-partite Turán graph of order n, we prove that:For all r≥2 and all sufficiently small c>0, every graph of sufficiently large order n with t_r(n)+1 edges contains a .We also give a corresponding stability theorem and two supporting results of wider scope.     

Scattering matrices of regular coverings of graphs

We give a decomposition formula for the determinant on the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the determinant on the bond scattering matrix of a regular covering of G by means of its L-functions.     

Non-commutative generalisations of Urysohn's lemma and hereditary inner ideals

We establish several generalisations of Urysohn's lemma in the setting of JB^∗-triples which provide full answers to Problems 1.12 and 1.13 in Fernández-Polo and Peralta (2007) [22]. These results extend the previous generalisations obtained by C.A. Akemann, G.K. Pedersen and L.G. Brown in the setting of C^∗-algebras. A generalised Kadison's transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in JBW^∗-triples. We introduce the notion of positively open tripotent in the bidual of a JB^∗-triple as an extension of a concept which was already considered in the setting of ternary rings of operators. We investigate the connections appearing between positively open tripotents and hereditary inner ideals.     

The Rohlin property for automorphisms of the Jiang-Su algebra

For projectionless C^∗-algebras absorbing the Jiang-Su algebra tensorially, we study a kind of the Rohlin property for automorphisms. We show that the crossed products obtained by automorphisms with this Rohlin property also absorb the Jiang-Su algebra tensorially under a mild technical condition on the C^∗-algebras. In particular, for the Jiang-Su algebra we show the uniqueness up to outer conjugacy of the automorphism with this Rohlin property.     

The Dirichlet problem of higher order quasilinear elliptic equation

The paper is concerned with the Dirichlet problem of higher order quasilinear elliptic equation: