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151.
Given a field F and integer n≥3, we introduce an invariant sn (F) which is defined by examining the vanishing of subspaces of alternating bilinear forms on 2-dimensional subspaces of vector spaces. This invariant arises when we calculate the largest dimension of a subspace of n?×?n skew-symmetric matrices over F which contains no elements of rank 2. We show how to calculate sn (F) for various families of field F, including finite fields. We also prove the existence of large subgroups of the commutator subgroup of certain p-groups of class 2 which contain no non-identity commutators.  相似文献   
152.
Let V be a vector space of dimension n over any field F. Extreme values for the possible dimension of a linear subspace of EndF(V) with a particular property are considered in two specific cases. It is shown that if E1 is a subspace of EndF(V) and there exists an endomorphism g of V, not in E1, such that for every hyperplane H of V some element of E1 agrees with g on H, then E1 has dimension at least . This answers a question that was posed by Szechtman in 2003. It is also shown that a linear subspace of Mn(F) in which no element possesses a non-zero eigenvalue in F may have dimension at most . The connection between these two properties, which arises from duality considerations, is discussed.  相似文献   
153.
In this paper we assume dynamical systems are represented by linear differential-algebraic equations (DAEs) of order possibly higher than one. We consider a structured system of DAEs for both the to-be-controlled plant and the controller. We model the structure of the plant and the controller as an undirected and bipartite graph and formulate necessary and sufficient conditions on this graph for the structured controller to generically achieve arbitrary pole placement. A special case of this problem also gives new equivalent conditions for structural controllability of a plant. Use of results in matching theory, and in particular, ‘admissibility’ of edges and ‘elementary bipartite graphs’, make the problem and the solution very intuitive. Further, our approach requires standard graph algorithms to check the required conditions for generic arbitrary pole placement, thus helping in easily obtaining running time estimates for checking this. When applied to the state space case, for which the literature has running time estimates, our algorithm is faster for sparse state space systems and comparable for general state space systems.  相似文献   
154.
We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be recovered from m?slog4(N) random samples that are chosen independently according to the Chebyshev probability measure dν(x)=π?1(1?x2)?1/2dx. As an efficient recovery method, ?1-minimization can be used. We establish these results by verifying the restricted isometry property of a preconditioned random Legendre matrix. We then extend these results to a large class of orthogonal polynomial systems, including the Jacobi polynomials, of which the Legendre polynomials are a special case. Finally, we transpose these results into the setting of approximate recovery for functions in certain infinite-dimensional function spaces.  相似文献   
155.
Let R = (r1,…, rm) and S = (s1,…, sn) be nonnegative integral vectors, and let U(R, S) denote the class of all m × n matrices of 0's and 1's having row sum vector R and column sum vector S. An invariant position of U(R, S) is a position whose entry is the same for all matrices in U(R, S). The interchange graph G(R, S) is the graph where the vertices are the matrices in U(R, S) and where two matrices are joined by an edge provided they differ by an interchange. We prove that when 1 ≤ rin ? 1 (i = 1,…, m) and 1 ≤ sjm ? 1 (j = 1,…, n), G(R, S) is prime if and only if U(R, S) has no invariant positions.  相似文献   
156.
This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.  相似文献   
157.
The structure of strontium niobium dioxygen nitride, SrNbO2N, has been solved by powder neutron diffraction at room temperature and 1.5 K. SrNbO2N crystallizes in the tetragonal space group I4/mcm, with a = 5.7056 (4) and c = 8.1002 (9) Å at room temperature, and a = 5.6938 (4) and c = 8.0974 (8) Å at 1.5 K. The crystal structure is derived from the cubic perovskite archetype by a slight rotation of the Nb(O,N)6 octahedra with respect to the tetragonal axis. A partially ordered distribution of oxygen and nitrogen on the anionic sites was found.  相似文献   
158.
159.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 456–466, March, 1994.  相似文献   
160.
We report direct evidence for the control of the oscillator strength of the exciton state in a single quantum dot by the application of a vertical electric field. This is achieved through the study of the radiative lifetime of a single InGaN-GaN quantum dot in a p-i-n diode structure. Our results are in good quantitative agreement with theoretical predictions from an atomistic tight-binding model. Furthermore, the increase of the overlap between the electron and hole wave functions due to the applied field is shown experimentally to increase the attractive Coulomb interaction leading to a change in the sign of the biexcitonic binding energy.  相似文献   
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