A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

The Characterization of PSL(2,q) by Its Element Orders

The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥2, q≠9), then G is isomorphic toPSL(2, q), where π_e(G) denotes the set of all orders of elements in G.

On the Characterizability of the Automorphism Groups of Sporadic Simple Groups by Their Element Orders

For G a finite group,π_e(G)denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω)stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M_(12),M_(22),J_2,He,Suz,M^cL and O'N, then Aut(M)is charaeterizable by its dement orders.It is also proved that if M is isomorphic to M_(12),M_(22),He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.

The Characterization of Finite Simple Groups,L_3(3^(2m-1))(m 2),by Their Element Orders

In this paper the following theorem is proved： Every group L3（q） for q = 3^（2m-1）（m≥2） is characterized by its set of element orders.

Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.

Approximation and Superconvergence Analysis for a New Higher Order Wilson Element to Sobolev Type Equations

In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.

Finite Element Analysis for the Structure Optimization Design of the CPUE Load-Bearing Wheel of Tracked Vehicle

A new kind of material cast polyurethane elastomers (CPUE) is introduced to take the place of rubber on load bearing wheel for the first time. Based on load bearing wheel dimensions, material properties and operating conditions, the structure of wheel flange is optimized by zero order finite element method. A detailed three dimensional finite element model of flange of load bearing wheel is developed and utilized to optimize structure of wheel flange. Its service life, which is affected by flange structure parameter, is analyzed by comparing the optimization results with those of prototype of wheel. The results of optimization are presented and the stress field of load bearing wheel in optimal dimension obtained by using finite element analysis method is demonstrated. The finite element analysis and optimization results show that the CPUE load bearing wheel is feasible and suitable for the tracked vehicle and has a guiding value in practice of the weighting design of the whole tracked vehicle.

Evaluate All the Order of Every Element in the Higher Order of Group for Addition and Multiplication Composition

This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C× each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.

Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.

Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.

Conjugate natural convection of non-Newtonian hybrid nanofluid in wavy-shaped enclosure

The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid.The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder.The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM).The dependency of various factors and their interrelationships affecting the hydro-thermal behavior and heat exchange rate are delineated.The numerical experiments reveal that the best heat transfer rate is achieved for the pseudo-plastic hybrid nanoliquid with high Rayleigh number and thermal conductivity ratio and low Hartmann number.Besides,the power-law index has a major effect in deteriorating the heat convection at high Rayleigh number.

Group-Theoretic Remarks on Goldbach’s Conjecture

The famous strongly binary Goldbach’s conjecture asserts that every even number 2n ≥ 8 can always be expressible as a sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element order prime graphs of alternating groups of degrees 2n and 2n &#8722;1 to characterize this conjecture, and present its six group-theoretic versions;and further prove that this conjecture is true for p +1 and p &#8722;1 whenever p ≥ 11 is a prime number.

Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems

In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.

SPECTRAL AND SPECTRAL ELEMENT METHODS FOR HIGH ORDER PROBLEMS WITH MIXED BOUNDARY CONDITIONS

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

Classification about Non-Solvable Groups with Exactly 40 Maximal Order Elements

Let φ be a homomorphism from a group H to a group Aut（N）. Denote by Hφ× N the semidirect product of N by H with homomorphism φ. This paper proves that： Let G be a finite nonsolvable group. If G has exactly 40 maximal order elements, then G is isomorphic to one of the following groups： （1） Z4φ×A5, kerφ = Z2; （2） D8φ ×A5, kerφ = Z2 ×Z2; （3） G/N = S5, N = Z（G） = Z2; （4） G/N = S5, N = Z2 ×Z2, N∩Z（G） = Z2.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING TRANSIENT NAVIER-STOKES EQUATIONS WITH HIGH REYNOLDS NUMBER

In this paper,we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure.We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme.The scheme is proven to possess the absolute stability and the optimal error estimates.Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods,Pet ro-Galerkin finite element method and st reamline diffusion method.

CHARACTERISTICS-FINITE ELEMENT METHODS FOR SEAWATER INTRUSION NUMERICAL SIMULATION AND THEORETICAL ANALYSIS

Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a problem of the initial boundary values for a system of 3-dimensional nonlinear parabolic partial differential equations, one being the pressure flow equation and the other is the concentration convection-dispersion equation of the salt contained. For a generic case of a 3-dimensional bounded region, a backward-difference time-stepping scheme is defined. It approximates the pressure by the standard Galerkin procedure and the concentration by a Galerkin method of charederistics, where calculus of variations, theory of prior estimates and techniques are made use of Optimal order estimates in H1 norm are derived for the errors in the approximate solution.

On hp refinements of independent cover numerical manifold method——some strategies and observations

In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,which gets rid of NMM's important defect of rank deficiency when using higher-order local approximation functions.Several techniques are presented.In terms of mesh generation,a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement.As to the condition number,a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch;an overlapping width of 1%–10%can ensure a good condition number for 2nd,3rd,and 4th order local approximation functions;the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch.On numerical accuracy,local approximation using complete polynomials is necessary for the optimal convergence rate.Two issues that may damage the convergence rate should be prevented.The first is to approximate the curved boundary of a higher-order element by overly few straight lines,and the second is excessive overlapping width.Finally,several refinement strategies are verified by numerical examples.

Finite Groups Isospectral to Simple Groups

The spectrum of a finite group is the set of element orders of this group.The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum,in particular,to list all finite simple groups for which the recognition problem is solved.