Set of involutions arising from an egglike inversive plane

To every egglike inversive plane there is associated a family of involutions of the point set of such that circles of are the fixed point sets of the involutions in . Korchmaros and Olanda characterized a family of involutions on a set of size n² + 1to be for an egglike inversive plane of order n by four conditions. In this paper, we give an alternative proof where the Galois space PG(3,n) in which is embedded is built up directly by using concepts and results on finite linear spaces.     

On the graph labellings arising from phylogenetics

We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.     

On the products arising from the Kummer conjecture

Let q be a sufficiently large integer and χ be a Dirichlet character modulo q.In this paper,we extend the product ∏χ(-1)=-1L(1,χ) with prime q,arising from the Kummer conjecture,to the products of some general Dirichlet series,and give some meaningful estimates for them.     

On a linearized system arising in the study of viscous surface flow down an inclined plane

We consider the linearized problem describing motion of a viscous incompressible fluid flow down an inclined plane under the effect of gravity. We formulate the problem for downward periodic disturbances from the laminar steady flow as an evolution equation in the product of Sobolev spaces \(H^{\frac{3}{2}}_0({\mathbb {T}}) \times {\mathbb {P}}^0H^0(\Omega ) \) . It is crucial to study qualitative behavior of solutions that the operator arising in the linearized problem has compact resolvent operators and generates an analytic semigroup in \(H^{\frac{3}{2}}_0({\mathbb {T}}) \times {\mathbb {P}}^0H^0(\Omega ) \) .     

Numerical solution for degenerate scale problem arising from multiple rigid lines in plane elasticity

This paper studies the degenerate scale problem arising from multiple rigid lines in plane elasticity. In the first step, the problem should be formulated on a degenerate scale by distribution of body force densities along rigid lines. The condition of vanishing displacement along lines is also assumed. The coordinate transform with a reduced factor “h” is performed in the next step. The new obtained BIE is a particular non-homogenous BIE defined in the transformed coordinates with normal scale. In the normal scale, the integral operator is invertible. By using two fundamental solutions that are formulated in the normal scale, the new obtained BIE can be reduced to an equation for finding the factor “h”. Finally, the degenerate scale is obtained. It is proved from computed results that the degenerate scale only depends on the configuration of rigid lines, and does not depend on the initial normal scale used. In addition, the degenerate scale is invariant with respect to the rotation of rigid lines. Many examples are carried out.     

On the noncommutative Donaldson-Thomas invariants arising from brane tilings

Given a brane tiling, that is a bipartite graph on a torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson-Thomas type invariants of the moduli space of framed cyclic modules over the corresponding quiver potential algebra. We relate this formula with the counting of perfect matchings of the periodic plane tiling corresponding to the brane tiling. We prove that the same consistency conditions imply that the quiver potential algebra is a 3-Calabi-Yau algebra. We also formulate a rationality conjecture for the generating functions of the Donaldson-Thomas type invariants.     

On the smoothness of orthonormal wavelets arising from HDAFs

In this paper, we give an estimation for the smoothness of a new family of symmetric orthonormal wavelets arising from Hermite Distributed Approximating Functionals (HDAFs). Their corresponding associated low pass filters are symmetric with respect to the origin.     

On character groups arising from dimension groups

Character groups associated with certain dimension groups are considered. It is shown how these character groups can be used to construct an AF groupoid whose dimension group is isomorphic to the original dimension group.

     

On toric ideals arising from signed graphs

Journal of Algebraic Combinatorics - A signed graph is a pair $$(G,\tau )$$ of a graph G and its sign $$\tau $$ , where a sign $$\tau $$ is a function from $$\{ (e,v)\mid e\in E(G),v\in V(G), v\in...     

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

On the semilinear reaction diffusion system arising from nuclear reactors

In this work, the initial-boundary value problem for a class of semilinear reaction-diffusion systems is considered. By an abstract fixed point theorem on positive cone together with an accurate a priori estimate, we establish the coexistence of the positive stationary solutions and the uniqueness of ordered positive stationary solutions. Next, we study the global existence and blowup of positive solutions and obtain a threshold result. Finally, we give the blowup rate estimate of positive blowup solutions.     

On a phase-change problem arising from inductive heating

In this paper we study a phase-change problem arising from induction heating. The mathematical model consists of time-harmonic Maxwell’s system in a quasi-stationary field coupled with nonlinear heat conduction. The enthalpy form is used to characterize the phase-change in the material. It is shown that the problem has a global solution. Moreover, it is shown that the solution is unique and regular in one-space dimension even with an unbounded resistivity. This work is supported in part by a NSF grant: DMS-0102261