The de Rham Bundle on a Compactification of Moduli Space of Abelian Varieties

In this paper, we show that the Chern classes c _k of the de Rham bundle defined on any good toroidal compactification of the moduli space of Abelian varieties of dimension g are zero in the rational Chow ring of , for g=4, 5 and k>0.     

Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.     

Robustness and nondegenerateness for linear complementarity problems

In this paper the main focus is on a stability concept for solutions of a linear complementarity problem. A solution of such a problem is robust if it is stable against slight perturbations of the data of the problem. Relations are investigated between the robustness, the nondegenerateness and the isolatedness of solutions. It turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated. Since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set, attention is paid to Garcia's classG _n of linear complementarity problems. The nondegenerate problems inG _n form an open set.     

Rank 2 Ample Vector Bundles on Some Smooth Rational Surfaces

Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with _c2 less than seven on Hirzebruch surfaces, and with _c2 less than four on Del Pezzo surfaces.     

Single-commodity robust network design problem: Complexity,instances and heuristic solutions

We study a single-commodity Robust Network Design problem (RND) in which an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. In each scenario, a subset of the nodes is exchanging flow. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. Previously conducted computational investigations on the problem motivated the study of the complexity of some special cases and we present complexity results on them, including hypercubes. In turn, these results lead to the definition of new instances (random graphs with {−1, 0, 1} balances) that are computationally hard for the natural flow formulation. These instances are then solved by means of a new heuristic algorithm for RND, which consists of three phases. In the first phase the graph representing the network is reduced by heuristically deleting a subset of the arcs, and a feasible solution is built. The second phase consists of a neighborhood search on the reduced graph based on a Mixed-Integer (Linear) Programming (MIP) flow model. Finally, the third phase applies a proximity search approach to further improve the solution, taking into account the original graph. The heuristic is tested on the new instances, and the comparison with the solutions obtained by Cplex on a natural flow formulation shows the effectiveness of the proposed method.     

Scheduling jobs with release dates on parallel batch processing machines

In this paper we consider the problem of scheduling jobs with release dates on parallel unbounded batch processing machines to minimize the maximum lateness. We show that the case where the jobs have deadlines is strongly NP-hard. We develop a polynomial-time approximation scheme for the problem to minimize the maximum delivery completion time, which is equivalent to minimizing the maximum lateness from the optimization viewpoint.     

The Coding Complexity of Lévy Processes

We introduce a new coding scheme for general real-valued Lévy processes and control its performance with respect to L _p [0,1]-norm distortion under different complexity constraints. We also establish lower bounds that prove the optimality of our coding scheme in many cases.      

Chern Classes of Gauss–Manin Bundles of Weight 1 Vanish

We show that the Chern character of a variation of polarized Hodge structures of weight one with nilpotent residues at dies up to torsion in the Chow ring, except in codimension 0.     

A NEW FAMILY OF BINARY SEQUENCES WITH OPTIMAL AUTOCORRELATION VALUES AND NICE PSEUDO-RANDOM PROPERTIES

In this paper we present a series of binary sequences which is a generalization of GMW sequences constructed by Scholtz and Welch. Our sequences have optimal autocorrelation values as m -sequences, and nice pseudo-random property. The number of such sequences is counted and the linear span of such sequences is evaluated.     

关于群类的Sylow性质

群类理论是在有限可解群研究工作的基础上发展起来的,但近年来对有限群论的许多方面都起到越来越大的作用.在考察群类性质时,注意到一个Fitting类(?)在可解群G中的(?)内射子具有Sylow子群所具有的某些性质,并且关于Sylow定理中(Sy13),证明了对于群的本原子群,成立更强的结论.