We consider the following problem: For a system consisting of two submodules, the behavior of one submodule is known as well as the desired behavior S of the global system. What should be the behavior of the second submodule such that the behavior of the composition of the two submodules conforms to S ? Solutions to this problem have been described in the context of various specification formal...

1. [10 points] Determine whether the following statements are true or false (you have to include proofs/counterexamples): (a) Let R be an integral domain, F – a free R-module of finite rank, and M – a torsion R-module. Then there is no injective homomorphism from F to M . Solution: True. Suppose there was an injective homomorpism φ : F → M . Then let N = φ(F ); N is a submodule of M , and there...

This paper focuses on the engineering trade-offs in designing capacitor voltage balancing schemes for modular multilevel converters (MMC) HVDC: regulation performance and switching loss. MMC is driven by the on/off switch operation of numerous submodules and the key design concern is balancing submodule capacitor voltages minimizing switching transition among submodules because it represents th...

BRST-resolution is studied for the principally graded Wakimoto module of ŝl2 recently found in [9]. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. e-mail:[email protected]

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

The cross-characteristic permutation modules for the actions of the finite classical groups on singular 1-spaces of their natural modules are studied. The composition factors and submodule lattices are determined.

Let $F$ be a non-negatively graded free module over polynomial ring $\mathbb{K}[x_1,\dots,x_n]$ generated by $m$ basis elements. $M$ submodule of elements in with degrees bounded $D$ and dim $F/M$=$r$. We prove that if is graded, the degree reduced Gr\"{o}bner for any term order $2\left[1/2((Dm)^{n-r}m+D) \right]^{2^{r-1}}$. If not bound $2\left[1/2((Dm)^{(n-r)^2}m+D) \right]^{2^{r}}$. This gen...

Altered brain morphometry has been widely acknowledged in chronic pain, and recent studies have implicated altered network dynamics, as opposed to properties of individual brain regions, in supporting persistent pain. Structural covariance analysis determines the inter-regional association in morphological metrics, such as gray matter volume, and such structural associations may be altered in c...

(1.2) PV~V where p is defined by p(s, t) = (t, s), (s, tET). We shall assume throughout that T is arcwise connected. Let 77 be an associative and anticommutative graded if-algebra with unit 1, where ii is a field. We assume throughout that 77'= 0 if i<0, and 77° = 7C-1. Let 77+ denote the submodule spanned by the elements of positive degree. 77 is a Hopf algebra over K if there is an algebra ho...