We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non-trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way. 2000 Mathematics Subject C...

We augmented an existing inertial measurement unit, IMU, with a secondary module sampling at high speeds (100Hz) an array of 1260 force sensitive resistors, FSR, embedded in a flexible, thin plastic foil. Due to legacy imposed by the existing sensor platform, we were confronted with severe bandwidth restrictions on the IC channel between the two modules. The secondary module created data at abo...

The objective of this paper is to clarify the relationships between quantum Dmodule and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper “Homological Geometry”. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohomology for the universal cover of the free loop space. First, motivated by the work o...

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...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

The Submillimeter High Angular Resolution Camera II (SHARC-II) is a 32 x 12 pixel submillimeter camera that is used with the ten-meter diameter Caltech Submillimeter Observatory (CSO) on Mauna Kea. SHARC-II can be operated at either 350 or 450 microns. We are developing an optics module that we will install at a position between the SHARC-II camera and the focus of the CSO's secondary mirror. W...