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1.
Jiancai Sun 《代数通讯》2013,41(4):1647-1670
In this article, we introduce and study a common generalization of the twisted tensor product construction of nonlocal vertex algebras and their modules. We investigate some properties of this new construction; for instance, we give the relations between L-R-twisted tensor product nonlocal vertex algebras and twisted tensor product vertex algebras. Furthermore, we find the conditions for constructing an iterated L-R-twisted tensor product nonlocal vertex algebra and its module. 相似文献
2.
Positivity - We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of 0-symmetric convex bodies in Euclidean spaces. We prove... 相似文献
3.
J. Bair et J. Gwinner 《Arkiv f?r Matematik》1978,16(1):207-212
Summary In this note we generalize two theorems of Klee [9] and a result of Bair-Jongmans [7] about the true separation of two convex
cones; afterwards, we introduce the notion of true separation forn(n≧2) convex sets and we extend our three first statements forn convex cones.
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4.
Christophe Rabut 《Numerical Algorithms》2005,39(1-3):329-348
We present in this paper a family of functions which are tensor product functions in subdomains, while not having the usual drawback of functions which are tensor product functions in the whole domain. With these functions we can add more points in some region without adding points on lines parallel to the axes. These functions are linear combinations of tensor product polynomial B-splines, and the knots of different B-splines are less connected together than with usual polynomial B-splines. Approximation of functions, or data, with such functions gives satisfactory results, as shown by numerical experimentation.
AMS subject classification 41A15, 41A63, 65Dxx 相似文献
5.
We generalize Brylawski’s formula of the Tutte polynomial of a tensor product of matroids to colored connected graphs, matroids,
and disconnected graphs. Unlike the non-colored tensor product where all edges have to be replaced by the same graph, our
colored generalization of the tensor product operation allows individual edge replacement. The colored Tutte polynomials we
compute exists by the results of Bollobás and Riordan. The proof depends on finding the correct generalization of the two
components of the pointed Tutte polynomial, first studied by Brylawski and Oxley, and on careful enumeration of the connected
components in a tensor product. Our results make the calculation of certain invariants of many composite networks easier,
provided that the invariants are obtained from the colored Tutte polynomials via substitution and the composite networks are
represented as tensor products of colored graphs. In particular, our method can be used to calculate (with relative ease)
the expected number of connected components after an accident hits a composite network in which some major links are identical
subnetworks in themselves.
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6.
The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces. 相似文献
7.
It is known that if f is a multiplicative increasing function on
, then either f(n)=0 for all
or f(n)=n for some 0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we first study the multiplicative increasing functions over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopless multidigraphs. 相似文献
8.
Let Ω be a rectangular bounded domain of a plane equipped with a rectangular partition Δ. Assume a piecewise bivariate function
that is differentiable up to order (k,l) except at the knots of Δ, where it is less differentiable. In this paper, we introduce a new method for smoothing the above
function at the knots. More precisely, we describe algorithms allowing one to transform it into another function that will
be differentiable up to order (k,l) in the whole domain Ω. Then, as an application of this method, we give a recursive computation of tensor product Hermite
spline interpolants. To illustrate our results, some numerical examples are presented.
AMS subject classification (2000) 41A05, 41A15, 65D05, 65D07, 65D10 相似文献
9.
Geir Dahl Jon Magne Leinaas Jan Myrheim Eirik Ovrum 《Linear algebra and its applications》2007,420(2-3):711-725
We consider a matrix approximation problem arising in the study of entanglement in quantum physics. This notion represents a certain type of correlations between subsystems in a composite quantum system. The states of a system are described by a density matrix, which is a positive semidefinite matrix with trace one. The goal is to approximate such a given density matrix by a so-called separable density matrix, and the distance between these matrices gives information about the degree of entanglement in the system. Separability here is expressed in terms of tensor products. We discuss this approximation problem for a composite system with two subsystems and show that it can be written as a convex optimization problem with special structure. We investigate related convex sets, and suggest an algorithm for this approximation problem which exploits the tensor product structure in certain subproblems. Finally some computational results and experiences are presented. 相似文献
10.
Convergence of a transition probability tensor of a higher‐order Markov chain to the stationary probability vector 下载免费PDF全文
In this paper, first we introduce a new tensor product for a transition probability tensor originating from a higher‐order Markov chain. Subsequently, some properties of the new tensor product are explained, and its relationship with the stationary probability vector is studied. Also, similarity between results obtained by this new product and the first‐order case is shown. Furthermore, we prove the convergence of a transition probability tensor to the stationary probability vector. Finally, we show how to achieve a stationary probability vector with some numerical examples and make some comparison between the proposed method and another existing method for obtaining stationary probability vectors. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
12.
This paper addresses itself to the algorithm for minimizing the product of two nonnegative convex functions over a convex set. It is shown that the global minimum of this nonconvex problem can be obtained by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a branch-and-bound algorithm using an underestimating function. Computational results indicate that our algorithm is efficient when the objective function is the product of a linear and a quadratic functions and the constraints are linear. An extension of our algorithm for minimizing the sum of a convex function and a product of two convex functions is also discussed. 相似文献
13.
We apply results in operator space theory to the setting of multidimensional measure theory. Using the extended Haagerup tensor product of Effros and Ruan, we derive a Radon–Nikodým theorem for bimeasures and then extend the result to general Fréchet measures (scalar-valued polymeasures). We also prove a measure-theoretic Grothendieck inequality, provide a characterization of the injective tensor product of two spaces of Lebesgue integrable functions, and discuss the possibility of a bounded convergence theorem for Fréchet measures. 相似文献
14.
A new combinatorial expression is given for the dimension of the space of invariants in the tensor product of three irreducible finite dimensional sl(r + 1)-modules (we call this dimension the triple multiplicity). This expression exhibits a lot of symmetries that are not clear from the classical expression given by the Littlewood–Richardson rule. In our approach the triple multiplicity is given as the number of integral points of the section of a certain universal polyhedral convex cone by a plane determined by three highest weights. This allows us to study triple multiplicities using ideas from linear programming. As an application of this method, we prove a conjecture of B. Kostant that describes all irreducible constituents of the exterior algebra of the adjoint sl(r + 1)-module. 相似文献
15.
16.
Diego Maldonado 《Journal of Differential Equations》2018,264(2):624-678
We prove a Harnack inequality for nonnegative strong solutions to degenerate and singular elliptic PDEs modeled after certain convex functions and in the presence of unbounded drifts. Our main theorem extends the Harnack inequality for the linearized Monge–Ampère equation due to Caffarelli and Gutiérrez and it is related, although under different hypotheses, to a recent work by N.Q. Le.Since our results are shown to apply to the convex functions with and their tensor sums, the degenerate elliptic operators that we can consider include subelliptic Grushin and Grushin-like operators as well as a recent example by A. Montanari of a nondivergence-form subelliptic operator arising from the geometric theory of several complex variables. In the light of these applications, it follows that the Monge–Ampère quasi-metric structure can be regarded as an alternative to the usual Carnot–Carathéodory metric in the study of certain subelliptic PDEs. 相似文献
17.
Xiufu Zhang 《代数通讯》2013,41(9):3754-3775
We study the tensor product of a highest weight module with an intermediate series module over the Neveu–Schwarz algebra. If the highest weight module is nontrivial, the weight spaces of such a tensor product are infinite dimensional. We show that such a tensor product is indecomposable. Using a “shifting technique” developed by H. Chen, X. Guo, and K. Zhao for the Virasoro algebra case, we give necessary and sufficient conditions for such a tensor product to be irreducible. Furthermore, we give necessary and sufficient conditions for two such tensor products to be isomorphic. 相似文献
18.
19.
We introduce two classes of radicals by means of tensor product of modules and module homomorphisms and prove some properties of these radicals and their connection with attracting modules. 相似文献
20.
Ja-Yong Koo 《Journal of multivariate analysis》1998,67(2):367-384
We consider bivariate logspline density estimation for tomography data. In the usual logspline density estimation for bivariate data, the logarithm of the unknown density function is estimated by tensor product splines, the unknown parameters of which are given by maximum likelihood. In this paper we use tensor product B-splines and the projection-slice theorem to construct the logspline density estimators for tomography data. Rates of convergence are established for log-density functions assumed to belong to a Besov space. 相似文献