Tensor product surfaces of euclidean plane curves

Recently B.Y. CHEN initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold [3]. In [6] the particular case of tensor product of two Euclidean plane curves was studied. The minimal one were classified, and necessary and sufficient conditions for such a tensor product to be totally real or complex or slant were established. In the present paper we study for tensor product of Euclidean plane curves the problem of B.Y. CHEN: to what extent do the properties of the tensor product immersion f ? h of two immersions f, h determines the immersions f, h ? [3]     

Tensor invariants of natural mechanical systems on compact surfaces and the corresponding integrals

The classification problem for tensor invariants of geodesic flows on compact surfaces is considered. Such invariants include first integrals, multivalued integrals, and symmetry fields. The problem is solved for tensor invariants of arbitrary degrees. It is shown that the invariants under consideration can vanish at some point only in the presence of two-valued symmetry fields and multivalued integrals. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 417–430, September, 1999.     

Tensor products on quiver representations

The aim of this article is to translate the well-known tensor product of representations of a group given by diagonal action to the case of representations of a quiver. We provide three different approaches and exhibit their close relationship to the point-wise tensor product, which is considered in [M. Herschend, Solution to the Clebsch-Gordan problem for Kronecker representations. U.U.D.M Project Report 2003:P1, Uppsala University, 2003; M. Herschend, Solution to the Clebsch-Gordan problem for representations of quivers of type , J. Algebra Appl. 4 (5) (2005) 481-488; M. Herschend, On the Clebsch-Gordan problem for quiver representations. U.U.D.M Report 2005:43, Uppsala University, 2005].     

Tensor Functional Topology on Woronowicz Categories

Functional topology is concerned with developing topological concepts in a category endowed with certain axiomatically defined classes of morphisms (Clementino et al. 2004). In this paper, we extend functional topology to a monoidal framework, replacing categorical pullbacks by pullbacks relative to the monoidal structure (which itself replaces the product) or more generally relative to a relation on the category (Janelidze, Appl. Categ. Structures, 17(4),351–371, 2009). Our main application is to the opposite Woronowicz category of C ^?-algebras. In this category a natural class of proper morphisms yields the unital algebras as compact objects. When restricted to the commutative C ^?-algebras, we recover exactly the morphisms induced by proper continuous maps of locally compact Hausdorff spaces. We further endow this category with a factorization system and investigate the precise relation with the proper maps, building on an approach which we previously developed with the eye on the category of schemes (Lowen and Mestdagh, J. Pure Appl. Algebra 217(11), 2180–2197, 2013). We also show how our results for C ^?-algebras can naturally be adapted to the opposite Woronowicz category of nondegenerate algebras over a commutative ring.     

Tensor structures on a differentiable manifold

Summary A tensor structure is a class of equivalent G-structures and it is defined by a special tensor field. Such fields are characterized by the existence of a linear connection relative to which they have covariant derivative zero. Two tensor structures may admit a common subordinate structure. Exaples of such subordinate stuctures are given and some cases, when one stucture is a Riemannian metric, are considered. To Enrico Bompiani on his scientific Jubilee     

Local Tensor Valuations

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.     

R-n模张量积与张量函子

文[1]引进了左R-n模范畴_RM_n~L,本文是在_RM_n中,建立相应的张量积,证明了它的存在性与唯一性,并讨论了张量函子与Hom函子的伴随性。 文中沿用[1]的记号。     

Tensor spline approximation

The cyclic-shift tensor-factorization interpolation method recently described by de Boor can be used in particular for least-squares fitting of multivariate data on a rectangular grid and for evaluation of the resulting tensor-product splines, taking advantage of existing linear algebra and univariate spline software. We discuss the computational details of this method, pointing out variants and suggesting techniques for dealing with ill-conditioned least-squares problems.     

Contact Tensor Calculus

Summary It is shown that a Tensor Calculus in which the group of transformations is the group of contact transformations can be developed by making a systematic use of existing theories of non-holonomic spaces. The generalizations of Riemannian Geometry are then considered in relation to the new Calculus.     

Geodesics of Sasakian Metrics on Tensor Bundles

On the basis of the phase completion the notion of vertical and horizontal lifts of vector fields is defined in the tensor bundles over a Riemannian manifold. Such a tensor bundle is made into a manifold with a Riemannian structure of special type by endowing it with Sasakian metric. The components of the Levi-Civita and other metric connections with respect to Sasakian metrics on tensor bundles with respect to the adapted frame are presented. This having been done, it is shown that it is possible to study geodesics of Sasakian metrics dealing with geodesics of the base manifolds. Dedicated to the memory of Vladimir Vishnevskii (1929-2007)     

L—fuzzy模范畴的张量积与张量函子

本文在Ｌ—ｆｕｚｚｙ模范畴中，建立了相应的张量积，给出了它的结构性、存在性与唯一性定理，并讨论了张量函子与Ｈｏｍ函子的伴随性。所得结果为通常张量积的“良好推广”（ｇｏｏｄｅｘｔｅｎｓｉｏｎ）。     

半模的张量积

本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．     

Tensor eigenvalue complementarity problems

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial optimization. When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity. When no tensor is strictly copositive, we formulate the tensor eigenvalue complementarity problem equivalently as polynomial optimization by a randomization process. The complementarity eigenvalues can be computed sequentially. The formulated polynomial optimization can be solved by Lasserre’s hierarchy of semidefinite relaxations. We show that it has finite convergence for generic tensors. Numerical experiments are presented to show the efficiency of proposed methods.     

Tensor products of orthoalgebras

We define a tensor product via a universal mapping property on the class oforthoalgebras, which are both partial algebras and orthocomplemented posets. We show how to construct such a tensor product forunital orthoalgebras, and use the Fano plane to show that tensor products do not always exist.