In a recent paper, E. G. Puckett proposed a stochastic particle method for the nonlinear diffusion-reaction PDE in [0, T]xR (the so-called "KPP" (Kolmogorov-Petrovskii-Piskunov) equation): %=Au = Au + f(u), u(0, •) = «(,(•), where 1 Mr, is the cumulative function, supposed to be smooth enough, of a probability distribution, and / is a function describing the reaction. His justification of the m...

An injective function f : V pGq Ñ t0, 1, 2, . . . , qu is an odd sum labeling if the induced edge labeling f defined by f puvq fpuq fpvq, for all uv P EpGq, is bijective and f pEpGqq t1, 3, 5, . . . , 2q 1u. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper we study the odd sum property of graphs obtained by duplicating any edge of some graphs.

Software systems evolve during their development. Even carefully designed systems change their internal structure over time, making it increasingly hard to add or change functionality. An important scaling aspect of software systems is the internal dependency structure. A good architect may have a concrete mental vision of a system and might be able to map this vision to dependencies, and vice ...

Chromium is essential in organism e.g., for the correct metabolism of glucose (an ingredient of the glucose tolerance factor ñ GTF), but it is also a toxic metal. Toxicity of chromium depends closely on its valence and is connected substantially with its oxidative properties. Cr(VI) is classified by IARC as carcinogenous for people (1, 2). Scutellaria baicalensis is a Chinese plant rich in flav...

Let (N, g) be a closed Riemannian manifold of dimension 2m − 1 and let 0→ Ñ → N be a Galois covering of N . We assume that 0 is of polynomial growth with respect to a word metric and that 1Ñ is L 2-invertible in degree m. By employing spectral sections with a symmetry property with respect to the ?-Hodge operator, we define the higher eta invariant associated with the signature operator on Ñ , ...

Abstract. Self-similarity of random trees is related to the operation of pruning. Pruning R cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex v and its parental edge is defined as the minimal number of prunings necessary to eliminate the subtree rooted at v. A branch is a group of neighboring ver...

Let 2S4 denote the double cover of S4 corresponding to the element in H(S4,Z/2Z) where transpositions lift to elements of order 2 and the product of two disjoint transpositions to elements of order 4. Given an elliptic curve E, let E[2] denote its 2-torsion points. Under some conditions on E elements in H(GalQ, E[2])\{0} correspond to Galois extensions N of Q with Galois group (isomorphic to) S...