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91.
Robert Hochberg 《Combinatorica》2006,26(1):47-64
We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and
gives a better bound on the discrepancy. 相似文献
92.
A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum,
the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without
the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in
the square. Our results differ from previous ones because we require that the entries in the square all be different from
each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from
set systems to rational linear forms.
Dedicated to the memory of Claudia Zaslavsky, 1917–2006
Received August 10, 2005 相似文献
93.
Here we present a theoretical analysis of the effect of inelastic electron scattering on spin-dependent transport characteristics (conductance, current–voltage dependence, magnetoresistance, shot noise spectrum, Fano factor) for magnetic nanojunction. Such device is composed of molecular quantum dot (with discrete energy levels) connected to ferromagnetic electrodes (treated within the wide-band approximation), where molecular vibrations are modeled as dispersionless phonons. Non-perturbative computational scheme, used in this work, is based on the Green's function theory within the framework of mapping technique (GFT–MT), which transforms the many-body electron–phonon interaction problem into a single-electron multi-channel scattering problem. The consequence of the localized electron–phonon coupling is polaron formation. It is shown that polaron shift and additional peaks in the transmission function completely change the shape of considered transport characteristics. 相似文献
94.
Scanning electron microscopy (SEM), Fourier transform infrared (FTIR) transmission, and Hall effect measurements were performed to investigate the structural, optical, and electrical properties of as-grown and in situ-annealed Hg0.7Cd0.3Te epilayers grown on CdTe buffer layers by using molecular beam epitaxy. After the Hg0.7Cd0.3Te epilayers had been annealed in a Hg-cell flux atmosphere, the SEM images showed that the surface morphologies of the Hg0.7Cd0.3Te thin films were mirror-like with no indication of pinholes or defects, and the FTIR spectra showed that the transmission intensities had increased in comparison to that of the as-grown Hg0.7Cd0.3Te epilayer. Hall-effect measurements showed that n-Hg0.7Cd0.3Te epilayers were converted to p-Hg0.7Cd0.3Te epilayers. These results indicate that the surface, optical, and electrical properties of the Hg1 − xCdxTe epilayers are improved by annealing and that as-grown n-Hg1 − xCdxTe epilayers can be converted to p-Hg1 − xCdxTe epilayers by in situ annealing. 相似文献
95.
96.
97.
Changbing Hu 《Journal of Differential Equations》2007,236(1):133-163
In this article we study the 3D Navier-Stokes equations with Navier friction boundary condition in thin domains. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. We generalize the techniques developed to study the 3D Navier-Stokes equations in thin domains, see [G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993) 503-568; G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains II: Global regularity of spatially periodic conditions, in: Nonlinear Partial Differential Equations and Their Application, College de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 205-247; R. Temam, M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996) 499-546; R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, in: Optimization Methods in Partial Differential Equations, in: Contemp. Math., vol. 209, Amer. Math. Soc., Providence, RI, 1996, pp. 281-314], to the Navier friction boundary condition by introducing a new average operator Mε in the thin direction according to the spectral decomposition of the Stokes operator Aε. Our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the Stokes operator Aε with Navier friction boundary condition. 相似文献
98.
The paper is concerned with a two-delay singular differential system with a twin parameter. Applying fixed-point index theory, we show the relationship between the asymptotic behaviors of nonlinearities (at zero and infinity) and the open regions (eigenvalue regions) of parameters, which are correlated with delays, such that the system has zero, one and two positive solution(s). 相似文献
99.
In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model. 相似文献
100.
Abdo Y. Alfakih 《Discrete Applied Mathematics》2007,155(10):1244-1253
Let V={1,2,…,n}. A mapping p:V→Rr, where p1,…,pn are not contained in a proper hyper-plane is called an r-configuration. Let G=(V,E) be a simple connected graph on n vertices. Then an r-configuration p together with graph G, where adjacent vertices of G are constrained to stay the same distance apart, is called a bar-and-joint framework (or a framework) in Rr, and is denoted by G(p). In this paper we introduce the notion of dimensional rigidity of frameworks, and we study the problem of determining whether or not a given G(p) is dimensionally rigid. A given framework G(p) in Rr is said to be dimensionally rigid iff there does not exist a framework G(q) in Rs for s?r+1, such that ∥qi-qj∥2=∥pi-pj∥2 for all (i,j)∈E. We present necessary and sufficient conditions for G(p) to be dimensionally rigid, and we formulate the problem of checking the validity of these conditions as a semidefinite programming (SDP) problem. The case where the points p1,…,pn of the given r-configuration are in general position, is also investigated. 相似文献