Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations

Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.

A Note on Finitely Generated Modules over a <i>PID</i>

In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.

Generalized Regular Ring

Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.

Geometric Origin of Staggered Fermion：Direct Product K—Cycle

Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. We prove the correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated Abelian groups where a lattice appears as a special case.

Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter

In this article, we introduce the discrete subgroup in ℝn as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝn and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.

Optimization of combined endoreversible Carnot heat engines with different objectives

Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

NUMERICAL MODELING OF THE INITIAL STAGE OF THE GENERATION OF UNSTEADY VORTICES FROM SHARP CORNER IN PLANE COMPRESSIBLE FLOW

The impingement of a plane shock wave in air on a rectangular or triangularobstacle is simulated numerically with high resolution TVD (total variationdiminishing) scheme in finite volume fomulation with Schwarz transformation in meshgeneration. The mesh lines are quite adaptive to the physical features of the unsieadyflow fietd and concentrate locally near the corners. At the initial stage the flow field iscomplex. and the scale of viscous diffusion is very small and the viscosity of fluid incomputation may be neglected. The unsteady generation of concerntrated vorticesdownstream of the sharp corner as the result of the nonnuiformity of both temperatureand entropy fields in plane inviscid compressible fluid, induced by bow shock wave, isshown clearly and in accordance with optical measurements, performed by our request.

THREE-DIMENSIONAL FINITE ELEMENT DELAUNAY MESH GENERATION BY A PERFECTED NODE CONNECTION METHOD

How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node creation and elements generation in traditional node connection method. Therefore, Ihe the difficulty about how to automatically create nodes in the traditional method is overcome.

SAW diffraction field generated by source with finite aperture piezoelectric crystal surfaces

So far, the diffracted SAW field generated by an IDT with finite aperture on piezoelectric crystal surfaces is usually analyzed phenomenologically with the angular spectrum theory. A major approximation of this theory is to ignore the vector nature of the field by assuming that the wave field can be represented by a scalar as in optics. In this paper, a rigorous vector field theory of the surface excitation of elastic wave field in piezoelectric crystal developed by the authors is used to evaluate the SAW diffraction field adepately and precisely. As an example, numerical results for YZ-LiNbO3 are presented and compared with those obtained form the angular spectrum theory.

ON THE FUNDAMENTAL GROUP OF OPEN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.

The Weakly Potency of Certain HNN Extensions of Nilpotent Groups

In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.

The Whitehead Groups of Semigroups

Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K1S of S is defined to be K0Ω（S）, where Ω（S）is the Loop category of（S）,and the structure of K1S is given.

Finite Generation of Lie Derived Powers of Skew Lie Algebras

Let A be a finitely generated associative algebra over a field of characteristic different from 2.Herstein asked when the Lie algebra[A,A]is finitely generated.Recently,it was shown that for a finitely generated nil algebra A all derived powers of A are finitely generated Lie algebras.Let K be the Lie algebra of skew-symmetric elements of an associative algebra with involution.We consider all derived powers of the Lie algebra K and prove that for any finitely generated associative nil algebra with an involution,all derived powers of K are finitely generated Lie algebras.

A New Approach to Fully Automatic Mesh Generation

Automatic mesh generation is one of the most important parts in CIMS (Computer Integrated Manufacturing System). A method based on mesh grad-ing propagation which automatically produces a triangular mesh in a multiply connected planar region is presented in this paper. The method decomposes the planar region into convex subregions, using algorithms which run in linear time. For every subregion, an algorithm is used to generate shrinking polygons according to boundary gradings and form Delaunay triangulation between two adjacent shrinking polygons, both in linear time. It automatically propagates boundary gradings into the interior of the region and produces satisfactory quasi-uniform mesh.

Higher Genus FJRW Theory for Fermat Cubic Singularity

In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory.Via general LG-LG mirror theorem,our results also hold for the Saito-Givental theory of the Fermat cubic singularity.

Automatic Construction of Finite Algebras

This paper deals with model genemtion for equational theories, i.e, auto-matically generating (finite) models of a given set of (logical) equations. Ourmethod of finite model generation and a tool for automatic construction of finitealgebras is described. Some examples are given to show the applications of ourprogram. We argue that, the combination of model generators and theoremprovers enables us to get a better understanding of logical theories. A briefcomparison between our tool and other similar tools is also presented.