Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...

A (d,h)-decomposition of a graph G is an order pair (D,H) such that H subgraph where has the maximum degree at most h and D acyclic orientation G−E(H) out-degree d. (d,h)-decomposable if (d,h)-decomposition. Let be embeddable in surface nonnegative characteristic. It known (d,h)-decomposable, then h-defective d+1-choosable. In this paper, we investigate graphs prove following four results. (1) ...

We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising (semisimple or non-semisimple) Lie $\mathfrak{g}$. In this approach, we deal with explicit polynomials in the enveloping algebra of $\mathfrak{g} \oplus \mathfrak{g} \mathfrak{g}$. present examples show how these can display different behaviours and lead Abelian algebras, quadratic mo...

1 Analyzing General Properties of Network Deconvolution 3 1.1 Network deconvolution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Optimality analysis of network deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Modeling assumptions and intuitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Let G be a finite simple graph and J(G) denote its vertex cover ideal in polynomial ring over field. The k-th symbolic power of is denoted by \(J(G)^{(k)}\). In this paper, we give criterion for ideals decomposable graphs to have the property that all their powers are not componentwise linear. Also, necessary sufficient condition on so \(J(G)^{(k)}\) linear some (equivalently, all) \(k \ge 2\) ...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. Analogously, a tree is called T -decomposable for a fixed tree T if it has a spanning forest whose components are all isomorphic to T . In this paper, we use a generating functions approach to derive exact and asymptotic results on the number of k-decomposable and T -decomposable trees from a so-call...

We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one given data, and where data has been symmetrized. When parameter is positive symmetrization symmetric decreasing rearrangement, we prove that solution to symmetrized problem larger increasing convex means. equals zero (so have Neumann conditions) similarly show means.