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In this paper, we give a description of differential operators on tensor products A ⊗ 핂 B {A\otimes_{\mathbb{K}}B} , where A and B are finitely generated 핂 {\mathbb{K}} -algebras. We prove that any differential operator on A ⊗ 핂 B {A\otimes_{\mathbb{K}}B} can be written as a finite sum of D 1 ⊗ D 2 {D_{1}\otimes D_{2}} , where D 1 {D_{1}} and D 2 {D_{2}} are differential operators on A and B, respectively. Moreover, we introduce a series of new invariants, the ( k , s ) {(k,s)} -th Tjurina algebra A ( k , s ) ⁢ ( V ) {A_{(k,s)}(V)} for an isolated hypersurface singularity ( V , ퟎ ) = ( V ⁢ ( f ) , ퟎ ) ⊆ ( ℂ r , ퟎ ) {(V,\boldsymbol{0})=(V(f),\boldsymbol{0})\subseteq(\mathbb{C}^{r},\boldsymbol{% 0})} . We formulate a sharp upper estimate for the dimension of the ℂ {\mathbb{C}} -vector space of differential operators on A ( k , s ) ⁢ ( V ) {A_{(k,s)}(V)} of order at most 1, and we give lower and upper bounds for the dimension of the ℂ {\mathbb{C}} -vector space of differential operators on A ( k , s ) ⁢ ( V ) {A_{(k,s)}(V)} of order at most n. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we discuss Lie nilpotency and Lie solvability of non-abelian tensor product of multiplicative Lie algebras. As our main results, we provide upper bounds on the Lie nilpotency class and Lie solvability length of quotient of tensor product of multiplicative Lie algebras. [ABSTRACT FROM AUTHOR]

In graph theory, graph labeling is an essential area of study because labeled graphs offer useful mathematical models for coding theory, cryptography, astronomy, radar, database administration and communication networks. Consider a bijection for a graph G of order n, f : V (G) → {1, 2, ..., n}. The weight of a vertex z of G, expressed as w(z), is defined as the sum of labels assigned to all vertices adjacent to vertex z in G. If the weights are distinct for every unique pair of vertices y, z in V (G), then the labeling f is referred to as distance antimagic. A distance antimagic graph is any graph G that accepts such a labeling. Distance antimagic labeling on various basic graph products are discussed in this paper. We explore results on (a, d)-distance antimagic labeling for the lexicographic product G * H and distance antimagic labeling for the cartesian product G * H, tensor product G x H and strong product G x H in this work, where the graphs G and H are cycle related graphs, paths or complete graphs. Also, computer-aided algorithms are designed to verify that vertex weights are distinct. [ABSTRACT FROM AUTHOR]

In this paper we study the modular structure of the Foulkes module H (2 m) of the symmetric group S 2 m acting on set partitions of a set of size 2m into m sets each of size 2, defined over a field of positive characteristic p. We aim to understand the decomposition of the tensor powers of H (2 m) . In particular, we study the asymptotics of the non-projective part of tensor powers of these modules by computing the gamma invariant as defined by Dave Benson and Peter Symonds. [ABSTRACT FROM AUTHOR]

In this paper, we prove that there exists an almost resolvable k-cycle decomposition of (Ku × Kg)(λ), (where × represents tensor product of graphs) for all even integers k ≥ 8 with some possible exceptions. [ABSTRACT FROM AUTHOR]

Kobayashi–Pevzner discovered in [Differential symmetry breaking operators: II. Rankin–Cohen operators for symmetric pairs, Selecta Math. (N.S.) 22(2) (2016) 847–911, MR 3477337] that the failure of the multiplicity-one property in the fusion rule of Verma modules of 2 occurs exactly when the Rankin–Cohen brackets vanish, and classified all the corresponding parameters. In this paper, we provide yet another characterization for these parameters, and give a precise description of indecomposable components of the tensor product. Furthermore, we discuss when the tensor products of two Verma modules are isomorphic to each other for semisimple Lie algebras . [ABSTRACT FROM AUTHOR]

Numerous works have been dedicated to the topic of m -isometries, including [2–6,14,18–20,27,47,48]. In this article, we introduce the concept of (m , N A) -isometry, where A is a non-zero operator and m is a positive integer, as an extension of the m -isometry class created by J. Alger and M. Stankus in the 1980s. We present some algebraic and spectral characteristics of (m , N A) -isometries. Additionally, we investigate the product of an (m , N A) -isometry by an (n , N B) -isometry, which enhances and broadens the previous work of Gu et al. on m -isometries [40]. Finally, we apply our main findings to elementary operators defined on the Hilbert-Schmidt class, which can be identified with a tensor product. This provides a new, less complicated, and non-combinatorial proof of Theorem 2.10 of [30]. [ABSTRACT FROM AUTHOR]

In this paper, we focus on studying two classes of finite dimensional -associative algebras, which are extensions of a family of -dimensional Kac-Paljutkin type semi-simple Hopf algebras . All their indecomposable modules are classified. Furthermore, their representation rings are described by generators with suitable relations. [ABSTRACT FROM AUTHOR]

For a positive integer k , a proper k -coloring of a graph G is a mapping f : V (G) → { 1 , 2 , ... , k } such that f (u) ≠ f (v) for each edge u v of G. The smallest integer k for which there is a proper k -coloring of G is called the chromatic number of G , denoted by χ (G). A locally identifying coloring (for short, lid-coloring) of a graph G is a proper k -coloring of G such that every pair of adjacent vertices with distinct closed neighborhoods has distinct set of colors in their closed neighborhoods. The smallest integer k such that G has a lid-coloring with k colors is called locally identifying chromatic number (for short, lid-chromatic number) of G , denoted by χ l i d (G). This paper studies the lid-coloring of the Cartesian product and tensor product of two graphs. We prove that if G and H are two connected graphs having at least two vertices, then (a) χ l i d (G □ H) ≤ χ (G) χ (H) − 1 and (b) χ l i d (G × H) ≤ χ (G) χ (H). Here G □ H and G × H denote the Cartesian and tensor products of G and H , respectively. We determine the lid-chromatic numbers of C m □ P n , C m □ C n , P m × P n , C m × P n and C m × C n , where C m and P n denote a cycle and a path on m and n vertices, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 and the ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connection under certain conditions. [ABSTRACT FROM AUTHOR]

This paper is committed in characterizing the preserving maps for the class of separable matrices and a subclass of infinitely divisible matrices which are also separable. For this, an association between the classes of separable matrices and infinitely divisible matrices is established. Also, several properties and attributes of the above mentioned classes are stated and proved. [ABSTRACT FROM AUTHOR]

We address the problem of when the tensor product of two finitely generated modules over a Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular in the original sense from the 80's. As applications, besides freeness criteria for modules, characterizations of complete intersections, and an Ulrich-based approach to the long-standing Berger's conjecture, we give simple proofs that two celebrated homological conjectures, namely the Huneke-Wiegand and the Auslander-Reiten problems, are true for the class of Ulrich modules. [ABSTRACT FROM AUTHOR]

In this paper, we present a new analytical scheme to generate atomic solutions of partial differential equations. The theory of tensor product in Banach spaces coupled with some features of atomics operators are utilized to attain our results. Some demonstrative examples are given for completeness. [ABSTRACT FROM AUTHOR]

Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded maps may be used to show that the commutative Grothendieck inequality follows from the little commutative inequality, and that this passage may be given a geometric form as a relation between a pair of compact convex sets of positive matrices, which, in turn, characterizes the little constant k G C . [ABSTRACT FROM AUTHOR]

The notion of Cauchy dual for left-invertible covariant representations was studied by Trivedi and Veerabathiran. Using the Moore-Penrose inverse, we extend this notion for the covariant representations having closed range and explore several useful properties. We obtain a Wold-type decomposition for regular completely bounded covariant representation whose Moore-Penrose inverse is regular. Also, we discuss an example related to the non-commutative bilateral weighted shift. We prove that the Cauchy dual of the concave covariant representation (σ , V) modulo N (V ~) is hyponormal modulo N (V ~) . [ABSTRACT FROM AUTHOR]

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low‐rank patterns in multidimensional and higher‐order data. A well‐known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large‐scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS‐based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR‐cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We show that if Auslander's depth formula holds for non-zero Tor-independent modules over Cohen-Macaulay local rings of dimension 1, then it holds for such modules over any Cohen-Macaulay local ring. More generally, we show that the depth formula for non-zero Tor-independent modules that have finite Cohen-Macaulay dimension over depth 1 local rings implies the depth formula for such modules over any positive depth local ring. [ABSTRACT FROM AUTHOR]

We study projective and injective tensor products of Banach L 0 -modules over a σ -finite measure space. En route, we extend to Banach L 0 -modules several technical tools of independent interest, such as quotient operators, summable families, and Schauder bases. [ABSTRACT FROM AUTHOR]

The geometric Satake correspondence can be regarded as a geometric construction of rational representations of a complex connected reductive group G. In their study of this correspondence, Mirkovi'c and Vilonen introduced algebraic cycles that provide a linear basis in each irreducible representation. Generalizing this construction, Goncharov and Shen define a linear basis in each tensor product of irreducible representations. We investigate these bases and show that they share many properties with the dual canonical bases of Lusztig. [ABSTRACT FROM AUTHOR]

In this paper, we obtain necessary and sufficient conditions for decomposing tensor product of complete graphs into some connected unicyclic bipartite graphs with eight edges. [ABSTRACT FROM AUTHOR]

We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the (m + 1) -uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We introduce some connectivity optimization problem into the hypergraph, and solve them with the algebraic connectivity. We introduce the Laplacian eigenmap algorithm to the hypergraph under our tensor product. [ABSTRACT FROM AUTHOR]

We study the category Osh of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by the representation theory of the Borel subalgebra of a quantum affine algebra and by the relevance of quantum integrable systems in this context, we prove that tensor products of prefundamental modules with irreducible modules are either cyclic or cocyclic. This implies the existence and uniqueness of morphisms, the R-matrices, for such tensor products. We prove the R-matrices are polynomial in the spectral parameter, and we establish functional relations for the R-matrices. As applications, we prove the Jordan-Holder property in the category Osh. We also obtain a proof, uniform for any finite type, that any irreducible module factorizes through a truncated shifted Yangian. [ABSTRACT FROM AUTHOR]

This paper is an extension of the research on (cartesian) product of c-spaces. This paper demonstrates that the finite (tensor)product of quotients of c-spaces can be represented as a quotient of its (tensor) product. Some properties of the tensor product of c-spaces have been investigated in this context. Properties of the space of c-continuous functions have been probed and the relevance of the standard c-structure on it has been established. [ABSTRACT FROM AUTHOR]

In this work, we introduce the concept of *-operator frame, which is a generalization of *-frames in Hilbert pro-C*-modules, and we establish some results. We also study the tensor product of *-operator frame for Hilbert pro-C*-modules. [ABSTRACT FROM AUTHOR]

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is benchmarked against state-of-the-art techniques, showing a remarkable acceleration. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of tensor product between intuitionistic fuzzy submodules. We establish a formal framework for the tensor product operation, examining its properties and applications within the context of intuitionistic fuzzy modules. We then establish a relationship between the Hom functor and the tensor product in the category of intuitionistic fuzzy modules. The connection between tensor products and hom-functors in some algebraic structures, such as modules, is made possible via a natural isomorphism known as the Hom- Tensor adjunction and it establishes a relationship between HomCR-IFM(B⊗A,C) and HomCR-IFM(A,HomCR-IFM(B,C)). An application of tensor product of intuitionistic fuzzy modules can be used in decision-making processes by embracing ambiguity and vagueness, making it a valuable tool when exact data is lacking. [ABSTRACT FROM AUTHOR]

This paper proposed an efficient spectral-Galerkin approximation and error estimation for the fourth-order Steklov resource problem. Firstly, an appropriate Sobolev space was introduced and the weak form of the original problem, along with its corresponding discrete formulation, was derived. Secondly, the existence and uniqueness of the weak solution and the approximation solution were proven based on the Lax-Milgram lemma. Furthermore, error estimates for the approximation solution were demonstrated by using the approximation properties of the orthogonal projection operators. Additionally, a set of appropriate basis functions in the approximation space was constructed and the matrix form of the discrete scheme based on tensor product was derived. Finally, some numerical examples were given to show the effectiveness of the algorithm and the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

As is well known, a class of 2 n 2 -dimensional Kac-Paljutkin Hopf algebras H 2 n 2 was introduced by Pansera. It is the generalization of the 8-dimensional Kac-Paljutkin Hopf algebra H8. In this paper, the classification of Yetter-Drinfeld modules over H 2 n 2 is given by Radford's method of constructing Yetter-Drinfeld modules for a Hopf algebra. Furthermore, the tensor product of Yetter-Drinfeld modules over H 2 n 2 is established, and the Grothendieck ring r ( H 2 n 2 H 2 n 2 Y D) is described explicitly by generators and relations. Communicated by Julia Plavnik [ABSTRACT FROM AUTHOR]

Let A be a unital C⁎-algebra equipped with its natural order. As usual the effect algebra of A is the interval { a ∈ A : 0 ≤ a ≤ I A } , where I A denotes the unit of A. In this paper, we give a complete description of order isomorphisms between effect algebras of C⁎-algebras of type C (X) ⊗ B (H) , where C (X) stands for the algebra of all continuous complex valued functions on a (non pathological) Hausdorff compact space X and B (H) denotes the algebra of all bounded linear operators on a complex Hilbert space H. Our results generalize some works by L. Molnár and P. Šemrl. [ABSTRACT FROM AUTHOR]

Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the |$\ell _1$| norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey's empirical method to tensor products of Banach spaces. The estimator provides a near-optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications. [ABSTRACT FROM AUTHOR]

The study of algebraic structures endowed with the concept of symmetry is made possible by the link between Lie algebras and symmetric monoidal categories. This relationship between Lie algebras and symmetric monoidal categories is useful and has resulted in many areas, including algebraic topology, representation theory, and quantum physics. In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing literature, have been adapted to establish a direct correspondence between these algebraic structures and Lie algebras. We show that a 2-truncation of the crossed differential graded Lie algebra, obtained from our adapted definitions, gives rise to a braided crossed module of Lie algebras. We also construct a functor to simplicial Lie algebras, enabling a systematic mapping between different Lie algebraic categories, which supports the validity of our adapted definitions and establishes their compatibility with established categories. [ABSTRACT FROM AUTHOR]

This paper investigates the tensor product of a finite dimensional nilpotent evolution algebra. Some properties that translate from tensor products to factors and vice versa have been investigated, including the index of nilpotency and annihilator. The index of nilpotency of the tensor product of two nilpotent evolution algebras with different indexes of nilpotency is determined. Moreover, we investigate the tensorially decomposable of the 4-dimensional nilpotent evolution algebra. In addition, the decomposable nilpotent evolution algebra with the maximal index of nilpotency has been carried out. [ABSTRACT FROM AUTHOR]

A cubic fuzzy graph is a fuzzy graph that simultaneously supports fuzzy membership and interval-valued fuzzy membership. This simultaneity leads to a better flexibility in modeling problems regarding uncertain variables. The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and graph structures, shows better capabilities in solving complex problems, especially where there are multiple relationships. Since many problems are a combination of different relationships, as well, applying some operations on them creates new problems; therefore, in this article, some of the most important product operations on cubic fuzzy graph structure have been investigated and some of their properties have been described. Studies have shown that the product of two strong cubic fuzzy graph structures is not always strong and sometimes special conditions are needed to be met. By calculating the vertex degree in each of the products, a clear image of the comparison between the vertex degrees in the products has been obtained. Also, the relationships between the products have been examined and the investigations have shown that the combination of some product operations with each other leads to other products. At the end, the cubic fuzzy graph structure application in the diagnosis of brain lesions is presented. [ABSTRACT FROM AUTHOR]

In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over the 2 -rank Taft algebra A ¯ are construted and classified by Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class ring of the category of Yetter-Drinfeld modules over A ¯ is described explicitly by generators and relations. [ABSTRACT FROM AUTHOR]

In this paper, we characterize when, for any infinite cardinal α , the Fremlin tensor product of two Archimedean Riesz spaces (see Fremlin in Am J Math 94:777–798, 1972) is Dedekind α -complete. We also provide an example of an ideal I in an Archimedean Riesz space E such that the Fremlin tensor product of I with itself is not an ideal in the Fremlin tensor product of E with itself. [ABSTRACT FROM AUTHOR]

We show that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin's Archimedean Riesz space tensor product of their respective Carathéodory spaces of place functions. We provide a solution to Fremlin's problem 315Y(f) [ Measure Theory , Torres Fremlin, Colchester, 2004] concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carathéodory spaces of place functions. [ABSTRACT FROM AUTHOR]

Tootkaboni and Vahed introduced the notion of some large sets near idempotent along with some combinatorial properties. We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. We then study the abundance of some large sets near idempotent. We also investigate the effect of tensor product near zero. Finally, as an application we provide a characterization of members of polynomials (with constant term 0) evaluated at idempotents in a near zero semigroup. [ABSTRACT FROM AUTHOR]

We give a necessary and sufficient condition for a pair of parabolic subgroups P and Q of G = G L n (R) such that the tensor product of any two unitarily induced representations from P and Q are tempered. We also give an L p -estimate of matrix coefficients of the regular representations on L 2 (G / L) when L is a Levi subgroup of G. [ABSTRACT FROM AUTHOR]

The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalizes separability while retaining its major advantages. Our approach is based on the expansion of the covariance into a series of separable terms. The expansion is valid for any covariance over a two-dimensional domain. Leveraging the key notion of the partial inner product, we generalize the power iteration method to general Hilbert spaces, and show how the aforementioned expansion can be efficiently constructed in practice at the level of the surface observations. Truncation of the expansion and retention of the leading terms automatically induces a nonparametric estimator of the covariance, whose parsimony is dictated by the truncation level. The resulting estimator can be calculated, stored and manipulated with little computational overhead relative to separability. Consistency and rates of convergence are derived under mild regularity assumptions, illustrating the trade-off between bias and variance regulated by the truncation level. The merits and practical performance of the proposed methodology are demonstrated in a comprehensive simulation study. [ABSTRACT FROM AUTHOR]

A $C^{*}$ -algebra A is said to detect nuclearity if, whenever a $C^{*}$ -algebra B satisfies $A\otimes _{\mathrm{min}} B = A\otimes _{\mathrm{max}} B,$ it follows that B is nuclear. In this note, we survey the main results associated with this topic and present the background and tools necessary for proving the main results. In particular, we show that the $C^{*}$ -algebra $A = C^{*}(\mathbb {F}_{\infty })\otimes _{\mathrm{min}} B(\ell ^{2})/K(\ell ^{2})$ detects nuclearity. This result is known to experts, but has never appeared in the literature. [ABSTRACT FROM AUTHOR]

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity, together with various kinds of positive maps between matrix algebras like entanglement breaking maps, k -superpositive maps, completely positive maps, k -positive maps. We will begin with concrete examples of elementary positive maps given by x ↦ s ⁎ x s , and use Choi matrices and duality to explain all the notions mentioned above. We also show that the Choi matrix can be defined free from coordinates. The above notions of positive maps give rise to mapping cones, whose dual cones are characterized in terms of compositions or tensor products of linear maps. Through the discussion, we exhibit an identity which connects tensor products and compositions of linear maps between matrix algebras through the Choi matrices. Using this identity, we show that the description of the dual cone with tensor products is possible only when the involving cones are mapping cones, and recover various known criteria with ampliation for the notions mentioned above. As another applications of the identity, we construct various mapping cones arising from ampliation and factorization, and provide several equivalent statements to PPT (positive partial transpose) square conjecture in terms of tensor products. [ABSTRACT FROM AUTHOR]

A nonstandard low‐cost spline approximation method for approximating bivariate functions is constructed. It is applied for Digital Elevation approximation and then its accuracy in the downscaling process is studied. [ABSTRACT FROM AUTHOR]

This paper presents a polytopic linear parameter varying (LPV) controller design methodology for nonlinear anti-vibration suspension based on stochastic road identification. As the main nonlinear component in semi-active suspension, the continuous damping control (CDC) damper value is mapped by damping velocity and control current through a bench experiment. linear parameter varying gain-scheduled method is applied for dealing with the nonlinear deterministic model. As the uncertainties caused by road stochastic excitation to suspension cannot be ignored, it is essential to identify the excitation signal as a measurable variable parameter. Empirical-mode-decomposition (EMD) and support vector machine (SVM) are utilized to identify and classify the road stochastic signal input into standard level, so polytopic LPV controller can be designed with CDC damper velocity, control current, and road level as variable parameters. Meanwhile the exponential increase of high-order plant elements in multi-parameter LPV model makes it too complicated for real-time computing. Hence the tensor product model transformation is utilized to identify the orthogonal basis of system plant so that low-rank approximation of it can be implemented by truncated high-order singular value decomposition (T−HOSVD) method. Real-time simulation shows the performance and feasibility of controller, which can efficaciously identify the road stochastic excitation as measurable variable parameters for nonlinear suspension polytopic LPV control. [ABSTRACT FROM AUTHOR]

Recent developments in commutative algebra, linear algebra, and graph theory allow us to approach various issues in several fields. Circulant graphs now have a wider range of practical uses, including as the foundation for optical networks, discrete cellular neural networks, small-world networks, models of chemical reactions, supercomputing and multiprocessor systems. Herein, we are concerned with the decompositions of the bipartite circulant graphs. We propose the Cartesian and tensor product approaches as helping tools for the decompositions. The proposed approaches enable us to decompose the bipartite circulant graphs into many categories of graphs. We consider the use cases of applying the described theory of bipartite circulant graph decomposition to the problems of finding new topologies and deadlock-free routing in them when building supercomputers and networks-on-chip. [ABSTRACT FROM AUTHOR]

Let A be any topological algebra over R or C. We show that the property of a topological left (right or two-sided) A-module to have a jointly continuous action of A is inherited by submodules, quotient modules, completion, direct products, direct sums, projective limits and injective limits. In the case of commutative topological A-bimodules, the same property is inherited by topological tensor products. [ABSTRACT FROM AUTHOR]

In this paper we present a class of Riemannian equilateral triangles Δ A B C of the Cartan-Hadamard Riemannian manifold of N × N positive definite matrices of determinant 1 whose Karcher mean of vertices is of the form Λ (A , B , C) = A + B + C det ⁡ (A + B + C) N . The obtained class of triples (A , B , C) forms an analytic manifold with an analytic parameterization over SL (N , C) ± × R. The determinantal identity det ⁡ (A + B + C) = det ⁡ (A − 1 + B − 1 + C − 1) and an extended arithmetic-Karcher-harmonic mean inequalities is derived for such triples. [ABSTRACT FROM AUTHOR]

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A1 by taking the tensor product of irreducible U(h)-free modules of rank 1 with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type A1, and give sufficient and necessary conditions for these induced modules to be reducible. [ABSTRACT FROM AUTHOR]

We study the behaviour of contact brackets on the tensor product of two algebras, in particular, address the question of Martínez and Zelmanov about extension of a contact bracket on the tensor product from the brackets on the factors. [ABSTRACT FROM AUTHOR]

Let n>1 be a positive integer, {H1, ..., Hn} be a finite collection of complex Hilbert spaces with dim ⁡ (H k) ≥ 2 , and P1(Hk) be the set of all rank-1 self-adjoint projections on Hk, k = 1, ..., n. Set D P 1 ⨂ k = 1 n H k = { A 1 ⊗ ⋯ ⊗ A n : A k ∈ P 1 (H k) , k = 1 , ... , n }. We characterize the maps ϕ from D (P 1 (⨂ k = 1 n H k)) to P 1 (⨂ k = 1 n H k) preserving transition probability, i.e. t r (A B) = t r (ϕ (A) ϕ (B)) , f o r a l l A , B ∈ D P 1 ⨂ k = 1 n H k . A particular case corresponding to n = 1 is well known as (non-surjective version) Wigner's theorem. Our result may be considered as a generalization of Wigner's theorem. [ABSTRACT FROM AUTHOR]