Abelian gauge theories on homogeneous spaces

An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S ³ is calculated. A generalization of the Chern-Simons action is suggested and analyzed with the example of SU(3)/U(1) X U(1).     

Fabrication of polyaniline/ heterojunction structure using plasma enhanced polymerization technique

The work reports on the fabrication of a p–n heterojunction structure comprised of polyaniline (PANI) and TiO₂ nanoparticles. PANI was deposited by plasma enhanced polymerization on TiO₂ thin film substrates. The structural and the crystalline properties demonstrated the coherence and the substantive interaction of the plasma polymerized PANI molecules with the TiO₂ nanoparticle thin film. The UV–Vis studies of PANI/TiO₂ thin film supported the internalization of PANI with TiO₂ nanoparticles due to π–π^* transition of the phenyl rings with the lone pair electrons () of the nitrogen atom present in the PANI molecules. The I–V characteristics of the PANI/TiO₂ heterojunction structure were obtained in the forward and the reverse biased at applied voltage ranging from −1 V to +1 V with a scan rate of 2 mV/s. The proficient current in the PANI/TiO₂ heterojunction structure was attributed to the well penetration of PANI molecules into the pores of the TiO₂ nanoparticle thin film. The I–V characteristics ensured an efficient charge movement at the junction of PANI/TiO₂ interface and thus, behaved as a typical ohmic system.     

Fuzzy measures and discreteness

The main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the σ-algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics.     

Fractional integrals on compact Riemannian symmetric spaces of rank one

In this paper we study mixed norm boundedness for fractional integrals related to Laplace–Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is the analysis of weighted inequalities for fractional integral operators associated to trigonometric Jacobi polynomials expansions. In particular, we find a novel sharp estimate for the Jacobi fractional integral kernel with explicit dependence on the type parameters.     

Parameters Related to Tree‐Width,Zero Forcing,and Maximum Nullity of a Graph

Tree‐width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters, including several Colin de Verdière type parameters, and introduce numerous variations, including the minor monotone floors and ceilings of some of these parameters. This leads to new graph parameters and to new characterizations of existing graph parameters. In particular, tree‐width, largeur d'arborescence, path‐width, and proper path‐width are each characterized in terms of a minor monotone floor of a certain zero forcing parameter defined by a color change rule.     

Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators

Strong solvability in Sobolev spaces is proved for a unilateral boundary value problem for nonlinear parabolic operators. The operator is assumed to be of Carathéodory type and to satisfy a suitable ellipticity condition; only measurability with respect to the independent variable X is required. The main tools of the proof are an estimate for the second derivatives of functions which satisfy the unilateral boundary conditions and the monotonicity of the operator − u _t with respect to Δu for the same functions.     

A simple GAP-canceling algorithm for the generalized maximum flow problem

We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs). We use ideas of Wallacher (A generalization of the minimum-mean cycle selection rule in cycle canceling algorithms, 1991) to find GAPs that have a good trade-off between the gain of the GAP and the residual capacity of its arcs; our algorithm may be viewed as a special case of Wayne’s algorithm for the generalized minimum-cost circulation problem (Wayne in Math Oper Res 27:445–459, 2002). Most previous algorithms for the generalized maximum flow problem are dual-based; the few previous primal algorithms (including Wayne in Math Oper Res 27:445–459, 2002) require subroutines to test the feasibility of linear programs with two variables per inequality (TVPIs). We give an O(mn) time algorithm for finding negative-cost GAPs which can be used in place of the TVPI tester. This yields an algorithm with O(m log(mB/ε)) iterations of O(mn) time to compute an ε-optimal flow, or O(m ² log (mB)) iterations to compute an optimal flow, for an overall running time of O(m ³ nlog(mB)). The fastest known running time for this problem is , and is due to Radzik (Theor Comput Sci 312:75–97, 2004), building on earlier work of Goldfarb et al. (Math Oper Res 22:793–802, 1997). David P. Williamson is supported in part by an IBM Faculty Partnership Award and NSF grant CCF-0514628.     

Radial solutions of a class of iterated partial differential equations

We give some expansion formulas and the Kelvin principle for solutions of a class of iterated equations of elliptic type