Neutrino energy quantization in rotating medium

Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle moving in the presence of a constant magnetic field. Accordingly, the particle in the rotating matter has circle orbits with energy levels, analogous to the Landau levels in magnetic field. The relevant physical realization of the problem is motion of neutrino inside the rotating neutron star. The feature of such motion to form binding states leads to the prediction of the new mechanism for neutrino trapping. The solution found can be used for detailed description of relativistic and nearly massless neutrino dynamics in neutron stars. Results obtained further develop the "method of exact solutions" in application to particle interactions in presence of dense matter.Comment: 5 pages, in: "Particle Physics on the Eve of LHC" (Proc. of the 13th Lomonosov Conference on Elementary Particle Physics, Moscow, August 2007), ed. by A.Studenikin, p.176, World Scientific, Singapore, 200

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;

Neutrinos and electrons in background matter

We present a rather powerful method in investigations of different phenomena that can appear when neutrinos and electrons propagate in background matter. This method is based on the use of the modified Dirac equations for particles wave functions, in which the correspondent effective potentials accounting for the matter influence on particles are included.Comment: submitted to J.Phys.: Conference Series (Proceedings of Neutrino 2006 Conference, June 2006, Santa Fe, New Mexico

An Approximation Scheme for the Generalized Geometric Minimum Spanning Tree Problem with Grid Clustering

This paper is concerned with a special case of the Generalized Minimum Spanning Tree Problem. The Generalized Minimum Spanning Tree Problem is de¯ned on an undirected graph, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges. The problem is to ¯nd a tree of minimum cost containing exactly one vertex in each cluster. We consider a geometric case of the problem where the graph is complete, all vertices are situated in the plane, and Euclidean distance de¯nes the edge cost. We prove that the problem admits PTAS if restricted to grid clustering.operations research and management science;

Algorithms for graphs embeddable with few crossings per edge

We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximation schemes when restricted to such graphs. This extends previous results by Baker [1] and Eppstein [3] to a much broader class of graphs.operations research and management science;

Spin light in neutrino transition between different mass states

The spin light of neutrino is considered in the process of a neutrino radiative transition between two different mass states in presence of medium. By this study we investigate the influence of background matter on the initial and final neutrino states in the process of massive Dirac neutrino decay due to the non-zero transition magnetic moment. We derive corresponding corrections to the total width of the process over the matter density in most important for applications cases.Comment: 5 pages in LaTex, to appear in proceedings of the 9th Conference on Quantum Field Theory Under the Influence of External Conditions (Univ. of Oklahoma, Norman, OK USA, September 21-25, 2009), eds. Kim Milton and Michael Bordag (World Scientific, Singapore, 2010