Algebraic Modification of the Method of Undetermined Coefficients For Solving Nonhomogeneous Linear Difference Equations

In this paper, an algebraic modification of the method of undetermined coefficients for solving nonhomogeneous linear stationary difference equations for quasipolynomial right-hand sides is proposed. Although the classical method of undetermined coefficients is well-known in both differential equations and difference equations case, its application in the difference equations case is severely limited. For example, it is hard to apply for rather complex expressions that can arise in case of complex quasipolynomials and resonance. The novelty of the research is the proposition of an algebraic modification to the method. That modification eliminates major drawbacks of the primary method and also allows to modify the superposition principle to apply the method to the entire difference equation at once without dividing the problem into several less complicated ones. The superposition principle in matrix form is formulated

“New Nation-Building” or What?: Serbian and Kosovan laws on expatriates

Special legal provisions on preferential treatment of expatriates introduced during last decade by the kin-states are oftentimes construed by the scholars as visible sings and effective tools of new, post-territorial nation-building in Eastern Europe. However, the analysis of Serbian and Kosovan laws on citizenship and diaspora shows that the picture is more complex, whereas the situation varies across countries of the region. Despite the rising concerns with the issues of the co-ethnics since late 2000 the Serbian government for some years has been reluctant to introduce the exclusive preferential treatment for the Serbs in the realm of citizenship. Only the law passed in 2009 overtly showed that the executives and legislators of the Republic of Serbia now are on the way of creating post-territorial Serb national community. Contrariwise the political establishment of Kosovo equally pushing forward special laws on “diaspora” in 2008 and 2011 was rather concerned with forming and reasserting of as well as tightening its grip over post-territorial citizenry because of notable social and economic problems. In contrast to Easter European status laws, trans-border “ethnic relatives” of the Kosovan majority are effectively excluded by the documents from the membership in the “diaspora,” while the representatives of ethnic minorities from the territory of the country legally qualify for being Kosovo diasporans

Self-assembled nanostructuring of a-Si:H films with ultrashort light pulses

For several decades, hydrogenated amorphous silicon (a-Si:H) has been playing a significant role in the world's production of photovoltaic modules. In this work, we investigate different types of modifications induced by a femtosecond laser in a-Si:H thin films. We demonstrate that several distinctive modification regimes with peculiar optical properties can be obtained in a narrow range of the laser pulse energies

On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad