4,292 research outputs found
Two-Dimensional Bosonization from Variable Shifts in the Path Integral
A method to perform bosonization of a fermionic theory in (1+1) dimensions in
a path integral framework is developed. The method relies exclusively on the
path integral property of allowing variable shifts, and does not depend on the
explicit form of Greens functions. Two examples, the Schwinger model and the
massless Thirring model, are worked out.Comment: 4 page
Placing regenerators in optical networks to satisfy multiple sets of requests.
The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]
The maximum number of minimal codewords in an code
Upper and lower bounds are derived for the quantity in the title, which is
tabulated for modest values of and An application to graphs with many
cycles is given.Comment: 6 pp. Submitte
On vertex coloring without monochromatic triangles
We study a certain relaxation of the classic vertex coloring problem, namely,
a coloring of vertices of undirected, simple graphs, such that there are no
monochromatic triangles. We give the first classification of the problem in
terms of classic and parametrized algorithms. Several computational complexity
results are also presented, which improve on the previous results found in the
literature. We propose the new structural parameter for undirected, simple
graphs -- the triangle-free chromatic number . We bound by
other known structural parameters. We also present two classes of graphs with
interesting coloring properties, that play pivotal role in proving useful
observation about our problem. We give/ask several conjectures/questions
throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac
Plasmas and Controlled Nuclear Fusion
Contains reports on two research projects.U. S. Atomic Energy Commission (Contract AT(11-1)-3070
Газоаналитические средства системы контроля утечек хлора на основе электрохимических сенсоров
Созданы и внедряются газоаналитические средства контроля и сигнализации утечек хлора на основе электрохимических сенсоров с улучшенными характеристиками
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