In floorplan design it is useful to allow users to specify some placement constraints in the final packing. Clustering constraint is a popular type of placement constraint in which a given set of modules are restricted to be placed adjacent to one another. The wiring cost can be reduced by placing modules with a lot of interconnections closely together. Designers may also need this type of cons...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

Let $R$ be a commutative Noetherian ring with non-zero identity, $fa$ an ideal of $R$, and $X$ an $R$--module. Here, for fixed integers $s, t$ and a finite $fa$--torsion $R$--module $N$, we first study the membership of $Ext^{s+t}_{R}(N, X)$ and $Ext^{s}_{R}(N, H^{t}_{fa}(X))$ in the Serre subcategories of the category of $R$--modules. Then, we present some conditions which ensure the exi...

For a simplicial complex on {1, 2, . . . , n} we define enriched homology and cohomology modules. They are graded modules over k[x1, . . . , xn] whose ranks are equal to the dimensions of the reduced homology and cohomology groups. We characterize Cohen-Macaulay, l-Cohen-Macaulay, Buchsbaum, and Gorenstein∗ complexes , and also orientable homology manifolds in terms of the enriched modules. We ...

This article introduces a biologically inspired modular swimming robot. Due to defi ned interfaces in mass, energy, and information fl ux, the robot’s swimming behavior is changeable: an undulant, successive called anguilliform as well as a thunniform swimming mode is adjustable. Unlike the current state of the art, the robot comes with specifi c designed mechanics for the reduction of the comp...

The purpose of this paper is to outline a new approach to the classii-cation of nitely generated indecomposable modules over certain kinds of pullback rings. If R is the pullback of two hereditary noetherian serial rings over a common semi{simple artinian ring, then this classiication can be divided into the classiica-tion of indecomposable artinian modules and those modules over the coordinate...

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

Let R be a commutative ring and M be an R-module. We say that M is fully primary, if every proper submodule of M is primary. In this paper, we state some characterizations of fully primary modules. We also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. Furthermore, we will introduce some ...

Solar sailing is a proposed means of space propulsion in which a reflective surface collects momentum from solar photons to accelerate a vehicle. The current trend within the solar sailing community is to increase sail size as solar sailing technologies advance, allowing for larger payloads and higher accelerations. However, with the miniaturization of modern payloads, sail sizes can be dramati...

This paper investigates a class of Lagrangian control systems with n degrees-offreedom (DOF) and n − 1 actuators, assuming that n − 1 virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which ...