computation of steady and unsteady vortex dominated flows with shock waves the unsteady euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference the resulting equations are solved by using a central difference finite volume scheme with four state runge kutta time stepping for steady flow applications local time stepping is used and for unsteady applications the minimum global time stepping is used a three dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings the capability of the three dimensional program has been demonstrated for a rigid sharp edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow

the structure of rings of quotients abstract for an arbitrary ring r we completely characterize when q r the maximal right ring of quotients of r is a direct product of indecomposable rings and when q r is a direct product of prime rings in terms of conditions on ideals of r our work generalizes decomposition results of goodearl for a von neumann regular right self injective ring and of jain lam and leroy for q r when r is right nonsingular to develop our results we define a useful dimension on bimodules and characterize the subset of ideals of r which are dense in ring direct summands of q r a structure theorem for r b q r the subring of q r generated by r e r r and e b q r is provided for a semiprime ring r our methods allow us to properly generalize rowen s theorem for semiprime pi rings we also apply our results to functional analysis to obtain a direct product decomposition of the local multiplier algebra m loc a of a c algebra a as a byproduct we obtain a complete description of a c algebra whose extended centroid is c as a consequence we show that a c algebra with only finitely many minimal prime ideals and satisfying a polynomial identity is finite dimensional

fractional kinetic equations and universal decoupling of a memory function in mesoscale region it is proved that kinetic equations containing non integer integrals and derivatives appear in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region in other words it means that after a proper statistical average the microscopic dynamics is converted into a collective motion in the mesoscopic regime a fractal medium containing weakly and strongly correlated relaxation units has been considered it is shown that in most cases the original of the memory function recovers the riemann liouville integral for a strongly correlated fractal medium a generalization of the riemann liouville integral is obtained for the fractal branched processes one can derive the stretched exponential law of relaxation that is widely used for description of relaxation phenomena in disordered media it is shown that the generalized stretched exponential function describes the averaged collective motion in the fractal branched complex systems it is confirmed that the generalized stretched exponential law can be definitely applicable for description of a set of spontaneous evoked postsynaptic signals in the living matter the application of these fractional kinetic equations for the description of the dielectric relaxation phenomena is also discussed these kinetic equations and their generalizations can be applicable for the description of different relaxation or diffusion processes in the intermediate mesoscale region

hulls of semiprime rings with applications to c algebras abstract for a ring r we investigate and determine minimal right essential overrings right ring hulls belonging to certain classes which are generated by r and subsets of the central idempotents of q r where q r is the maximal right ring of quotients of r we show the existence of and characterize a quasi baer hull and a right fi extending hull for every semiprime ring our results include i r b q r i e the subring of q r generated by r e r r and e b q r where b q r is the set of all central idempotents of q r is the smallest quasi baer and the smallest right fi extending right ring of quotients of a semiprime ring r with unity in this case various overrings of r b q r including all right essential overrings of r containing b q r are also quasi baer and right fi extending ii lying over going up and incomparability of prime ideals various regularity conditions and classical krull dimension transfer between r and r b q r and iii the existence of a boundedly centrally closed hull for every c algebra and a complete characterization for an intermediate c algebra between a c algebra a and its local multiplier c algebra m loc a to be boundedly centrally closed

fdtd dispersive modeling of human tissues based on quadratic complex rational function we propose a dispersive finite difference time domain fdtd suitable for the electromagnetic analysis of human tissues the dispersion relation of biological tissues is characterized by a quadratic complex rational function qcrf that leads to an accurate fdtd algorithm in 400 mhz 3 ghz qcrf coefficients are extracted by applying the complex curve fitting technique without initial guess numerical examples are used to illustrate the computational accuracy and stability of qcrf based fdtd

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

application of subival in solving initial value problems with fractional derivatives abstract the application of a numerical method for the approximation of the fractional derivative in riemann liouville and caputo definitions in initial value problems is discussed the method previously known as the subinterval based method is now referred to by its acronym subival for simpler future references it is dependent on subinterval partitions performed according to a proposed algorithm interpolations using selected time axis nodes i e nodes where solutions have been computed and analytical monomial integrodifferentiation formulae two exemplary circuit problems have been introduced as a test for the method these problems have analytical solutions available in literature the evaluations of these solutions have been compared with results obtained through an adaptive step size predictor corrector scheme where the core computations relied on the proposed numerical method subival has been implemented into an activex dynamic link library dll the paper contains instructions on how the predictor corrector algorithm can be implemented into a computer algebra system where the subival library is applied for the fractional derivative approximation examples of this are given in the form of scripts in matlab and mathematica these scripts generally allow to solve systems of fractional order state equations to which the introduced circuit examples can be brought to

skew polynomial rings of formal triangular matrix rings abstract let r s be rings with unity and m be a unital r s bimodule in this paper we give a description of homomorphisms and skew derivations of the formal triangular matrix ring t r m 0 s and apply it to provide a triangular representation of the skew polynomial ring t z d also we introduce some special mappings on modules which are generalization of ring homomorphisms and skew derivations we characterize the ring endomorphisms of t when t z d has a triangular representation these results are applied to introduce the notion of skew polynomial modules and present some results and examples concerning this notion

z transform theory and the fdtd method in implementing the finite difference time domain fdtd method on materials which are dispersive or nonlinear the relationship between the flux density and the electric field can be the most complicated part of the problem because the fdtd method is a sampled time domain method this relationship can be can be looked upon as a digital filtering problem the z transform is typically used in digital filtering and signal processing problems the paper illustrates the use of the z transform in implementing the fdtd method where complicated dispersive or nonlinear materials are involved

computation of vortex dominated flow for a delta wing undergoing pitching oscillation the conservative unsteady euler equations for the flow relative to a moving frame of reference are used to solve for the three dimensional steady and unsteady flows around a sharp edged delta wing the resulting equations are solved by using an implicit approximately factored finite volume scheme implicit second order and explicit second and fourth order dissipations are added to the scheme the boundary conditions are explicitly satisfied the grid is generated by locally using a modified joukowski transformation in crossflow planes at the grid chord stations the computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack the steady results are compared with the experimental data and the unsteady results are compared with results of a flux difference splitting scheme

perfectly matched layer for the time domain finite element method a new perfectly matched layer pml formulation for the time domain finite element method is described and tested for maxwell s equations in particular we focus on the time integration scheme which is based on galerkin s method with a temporally piecewise linear expansion of the electric field the time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form which reduces to the well known newmark scheme in the case without pml extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities for a circular cylinder the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2 root mean square error in the bistatic radar cross section rcs for resolutions with more than 10 points per wavelength an ogival cylinder which has sharp corners supporting field singularities shows similar accuracy in the monostatic rcs

direct sums of rickart modules abstract the notion of rickart modules was defined recently it has been shown that a direct sum of rickart modules is not a rickart module in general in this paper we investigate the question when are the direct sums of rickart modules also rickart we show that if m i is m j injective for all i j i 1 2 n then i 1 n m i is a rickart module if and only if m i is m j rickart for all i j i as a consequence we obtain that for a nonsingular extending module m e m m is always a rickart module other characterizations for direct sums to be rickart under certain assumptions are provided we also investigate when certain classes of free modules over a ring r are rickart it is shown that every finitely generated free r module is rickart precisely when r is a right semihereditary ring as an application we show that a commutative domain r is prufer if and only if the free r module r 2 is rickart we exhibit an example of a module m for which m 2 is rickart but m 3 is not so further von neumann regular rings are characterized in terms of rickart modules it is shown that the class of rings r for which every finitely cogenerated right r module is rickart is precisely that of right v rings examples which delineate the concepts and the results are provided

differential forms galerkin duality and sparse inverse approximations in finite element solutions of maxwell equations we identify primal and dual formulations in the finite element method fem solution of the vector wave equation using a geometric discretization based on differential forms these two formulations entail a mathematical duality denoted as galerkin duality galerkin dual fem formulations yield identical nonzero dynamical eigenvalues up to machine precision but have static zero eigenvalue solution spaces of different dimensions algebraic relationships among the degrees of freedom of primal and dual formulations are explained using a deep rooted connection between the hodge helmholtz decomposition of differential forms and descartes euler polyhedral formula and verified numerically in order to tackle the fullness of dual formulation algebraic and topological thresholdings are proposed to approximate inverse mass matrices by sparse matrices

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

influence of numerical dissipation on computational euler equations for vortex dominated flows etude d ecoulements supersoniques tourbillonnaires pour des ailes delta a aretes vives ou arrondies on developpe un schema de volumes finis

locally implicit total variation diminishing schemes on mixed quadrilateral triangular meshes locally implicit total variation diminishing schemes on mixed quadrilateral triangular static dynamic meshes have been developed to study steady and unsteady flows respectively in a cartesian coordinate system the euler equations are solved by using a cell centered finite volume algorithm for steady inviscid flows the efficiency and accuracy of the present approach are confirmed by investigating the oblique shock reflection at a wall and transonic flow around an nag a 0012 airfoil to treat unsteady flow problems with moving boundaries a new dynamic mesh algorithm which saves memory is efficient and maintains quality is presented in this paper for analyzing the unsteady transonic flow around an naca 0012 airfoil that pitches harmonically about the quarter chord a quadrilateral triangular dynamic mesh system is used the calculated instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with related numerical and experimental data

fractional calculus based fdtd algorithm for ultrawideband electromagnetic characterization of arbitrary dispersive dielectric materials a novel finite difference time domain algorithm for modeling ultrawideband electromagnetic pulse propagation in arbitrary multirelaxed dispersive media is presented the proposed scheme is based on a general yet computationally efficient series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time marching scheme moreover a total field scattered field formulation is adopted in order to analyze the material response under plane wave excitation compared with alternative numerical methodologies available in the scientific literature the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher order dispersive dielectrics such as the ones typically encountered in geoscience and bioengineering applications

log periodic corrections to the cole cole expression in dielectric relaxation abstract a model of the self similar process of relaxation is given and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested the derived kinetic equations contain integro differential operators having non integer order they lead to the cole cole expression for the complex dielectric permittivity it is shown rigorously that the power law exponent in the cole cole expression coincides with the dimension of the mixed space temporal fractal ensemble if the discrete scale invariance for the temporal space structure of the dielectric medium considered becomes important then the expression for the complex dielectric permittivity contains log periodic corrections oscillations and hence it generalizes the conventional cole cole expression the corrections obtained in this model suggest another way of interpretation and analysis of dielectric spectra for different complex materials

total pressure loss in vortical solutions of the conical euler equations a technique for the solution of the conically self similar form of the euler equations is described solutions for the flow past a flat plate delta wing at angle of attack are presented these solutions show strong leading edge vortices with large total pressure losses in the cores a study of the effects of various computational parameters on the total pressure loss is made an explanation for the cause of the total pressure loss is presented it is shown to be consistent with the results for both a quasi one dimensional model problem and the conically self similar flow past the flat plate delta wing

euler and navier stokes solutions for flow over a conical delta wing the simulation of vortical flow about a conical delta wing 14 1 elliptic cone by the euler equations is studied navier stokes solutions are generated for comparison with the inviscid results at the flight condition considered the viscous solutions reveal a large primary leading edge separation vortex and a smaller secondary vortex the viscous solutions are shown to be grid resolved on a coarse grid the euler solutions result in a primary separation vortex but no secondary vortex a comparison of pressure coefficient with the viscous solution shows surprising agreement the agreement is unfortunately fortuitous when the euler equations are solved on the fine viscous grid the large separation vortex is eliminated instead a cross flow shock appears shock curvature introduces sufficient vorticity to produce a small vortex downstream of the shock this inviscid result fundamentally different from the viscous case is a valid solution to the euler equations the coarse grid euler solution is characterized by the production of spurious vorticity and entropy due to numerical error at the leading edge it is neither a valid solution to the euler equations nor a reliable approximation to the real viscous flow the use of a kutta condition is investigated for both the fineand coarse grid euler solutions it is shown that the kutta condition fails to produce a grid independent simulation of the actual viscous flow

efficient real gas upwinded navier stokes computations of high speed flows an efficient method to account for the chemically frozen thermodynamic and transport properties of air in three dimensional navier stokes calculations has been demonstrated this approach uses an explicitly specified equation of state eos so that the fluid pressure temperature and transport properties are directly related to the flow variables the method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code the flexibility of the eos approach is shown by its implementation into a high order total variation diminishing upwinding scheme as well as a standard central differencing scheme the eos approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central differencing schemes he capability to efficiently compute chemically frozen single stream flows using an explicitly specified equation of state eos has been added to a three dimensional navier stokes solver this flow solver is based upon the parc codes whose origin can be traced to the air2d 3d solvers by pul liam and steger 1 which used the block alternating direction implicit adi algorithm presented by beam and warming 2 to increase the computational efficiency and to reduce storage requirements pulliam3 diagonalized the block implicit opera tors of the original beam warming adi algorithm resulting in the arc2d 3d codes cooper4 further modified the arc codes to be used in a production environment for solving the propulsion oriented applications at the arnold engineering development center resulting in the parc codes coirier5 replaced the implicit operator with the lu sgs lower upper symmetric gauss seidel algorithm and demonstrated this scheme for hypersonic corner and gap seal problems this scheme is based on an lu decomposition method proposed by jameson and turkel6 and demonstrated by jameson and yoon7 for the euler equations in addition shuen and yoon8 and yu et al 9 with the rplus series of codes have shown the efficiency and robustness of this algorithm for solving the navier stokes equations fully coupled to the chemical trans port equations for computing finite rate chemically reacting flowfields for flows where the dissociation and recombination rates are much slower than the fluid residence time i e in the limit as the damkohler number approaches zero the fluid can be modeled as a mixture of inert chemically frozen gases when the converse is true i e the damkohler number approaches infinity the fluid can be modeled as if it were in chemical equilibrium if either of these limitations holds for the flow field to be considered great simplifications can be made and the resulting computational work reduced the present re search demonstrates the capability to efficiently model gen eral nonmixing chemically frozen flows using a method based on a generalized equation of state an eos for chemi cally frozen air is generated and its ease in implementation is shown for both a high order total variation diminishing tvd upwinding scheme based upon flux differencing10 and van leer s flux vector splitting11 as well as a standard central differencing scheme with added first and third difference dissi pation the upwinding scheme is then compared favorably to experimental data for the hypersonic flow through the corner region of two mutually perpendicular flat plates corner flow to demonstrate the eos a similar corner flowfield is com puted at a higher freestream stagnation enthalpy and detailed comparisons between the central difference and upwinding schemes are made for both 7 const and the chemically frozen air eos

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

ring hulls and applications our goal is to develop methods that enable one to select a class k of rings and then to describe all right essential overrings or all right rings of quotients of a given ring r which lie in k our major method of attack is to determine the existence and or uniqueness of right ring hulls of r in k and to use these to characterize the right essential overrings of r which are in k some applications are 1 a characterization of the right rings of quotients of the 2 by 2 upper triangular matrix ring over a pid which are either baer or right extending 2 a characterization of a continuous ring hull for a commutative ring whose singular ideal has finite uniform dimension 3 a characterization of the right extending rings which have the 2 by 2 matrix ring over a given division ring for their maximal right ring of quotients 4 a characterization of the intermediate right extending rings between the 2 by 2 upper triangular matrix ring and the 2 by 2 matrix ring over a large class of local right finitely extending rings 5 a characterization of the classical right ring of quotients as a ring hull from a certain class of rings

role of artificial viscosity in euler and navier stokes solvers a method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the navier stokes equations the stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity the eigenvalues were determined for a small time dependent perturbation about a steady inviscid flow over a naca 0012 airfoil at a mach number of 0 8 and angle of attack of 0 deg the method has been applied to inviscid flows here but as discussed is also applicable to viscous flows the movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied the stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time marching scheme are also presented the eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity but also for the effects of different forms of artificial viscosity nomenclature a speed of sound e total energy per unit volume 7 identity matrix jacobian of transformation m mach number p pressure re reynolds number p v c fi t nondimensional physical time u v cartesian velocity components x y physical cartesian coordinates a angle of attack 6 finite difference operator eef e coefficients of artificial viscosity x eigenvalues ijl viscosity coefficient r transformed coordinates p density t transformed time

a nonlinear hybrid vortex method for wings at large angle of attack a steady and unsteady nonlinear hybrid vortex nhv method is developed for low aspect ratio wings at large angles of attack the method uses vortex panels with linear vorticity distribution equivalent to a quadratic doublet distribution to calculate the induced velocity in the near field using closed form expressions in the far field the distributed vorticity is reduced to concentrated vortex lines and the simpler biot savart law is employed the method is applied to rectangular wings in steady and unsteady flows the numerical results show that the method accurately predicts the distributed aerodynamic loads and that it is of acceptable computational efficiency n recent years the development of numerical methods for predicting the steady and unsteady aerodynamic characteristics of lifting surfaces exhibiting leading and or side edge separations has received considerable attention for the steady flow problems several numerical techniques have been developed these include the nonlinear discrete vortex1 6 ndv methods higher order doublet panel methods 7 9 and nonlinear hybrid vortex nhv methods 10 11 for the unsteady flow problems the literature shows fewer numerical techniques which include the ndv methods12 15 and constant doublet panel methods 16 17 the literature lacks high order panel methods for the unsteady flow problems for this reason we are presenting in this paper an efficient and accurate method for the steady and unsteady flow problems of lifting surfaces at large angles of attack in this method vortex panels with linear vorticity distribution are used in the near field calculations in the farfield calculations the distributed vorticity over each far field panel is lumped into equivalent concentrated vortex lines in this way accuracy is satisfied in the near field while computational efficiency is maintained in the far field the coupling of a continuous vortex sheet representation and a concentrated vortex line representation for solving the nonlinear lifting surface problem is called the nonlinear hybrid vortex nhv method

mur nedelec finite element schemes for maxwell s equations we study mapped mass lumped edge elements for approximating a three dimensional scattering problem the elements are mapped mur nedelec second kind elements and the scheme is designed to handle anisotropic inhomogeneous scatterers with moderately complicated geometry a novel aspect of the scheme is the use of an unusual choice of the magnetic field finite element that results in a very efficient discrete curl operator using a non standard dispersion analysis we show that the phase accuracy of the cubic edge element does not deteriorate disastrously when the mesh is deformed our numerical experiments in two dimensions confirm that the scheme performs well on a distorted mesh and that it is efficient compared to the standard yee scheme

anomalous diffusion with under and overshooting subordination a competition between the very large jumps in physical and operational times in this paper we present an approach to anomalous diffusion based on subordination of stochastic processes application of such a methodology to analysis of the diffusion processes helps better understanding of physical mechanisms underlying the nonexponential relaxation phenomena in the subordination framework we analyze a coupling between the very large jumps in physical and two different operational times modeled by under and overshooting subordinators respectively we show that the resulting diffusion processes display features by means of which all experimentally observed two power law dielectric relaxation patterns can be explained we also derive the corresponding fractional equations governing the spatiotemporal evolution of the diffusion front of an excitation mode undergoing diffusion in the system under consideration the commonly known type of subdiffusion corresponding to the mittag leffler or cole cole relaxation appears as a special case of the studied anomalous diffusion processes

an efficient vector finite element method for nonlinear electromagnetic modeling we have developed a mixed vector finite element method vfem for maxwell s equations with a nonlinear polarization term the method allows for discretization of complicated geometries with arbitrary order representations of the b and e fields in this paper we will describe the method and a series of optimizations that significantly reduce the computational cost additionally a series of test simulations will be presented to validate the method finally a nonlinear waveguide mode mixing example is presented and discussed

unsteady transonic airfoil computation using implicit euler scheme on body fixed grid the unsteady euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil the resulting equations preserve the conservation form the grid is generated once by an elliptic solver without any need for dynamic grid computation an implicit approximately factored finite volume scheme has been developed and implemented through a fully vectorized computer program the scheme is based on the spatial approximate factorization of beam and warming implicit second order and explicit second and fourth order dissipations are added to the scheme the boundary conditions are explicitly satisfied the scheme is applied to steady and unsteady transonic rigid airfoil flows for forced harmonic airfoil motions periodic solutions are achieved within the third cycle of oscillation the results are in good agreement with the experimental data sonic flows past a naca 0015 airfoil at a constant pitch rate 18 the latter case is the same application considered in ref 16 the numerical solution has been obtained by using the flux vector splitting and the flux difference splitting meth ods extended for dynamic meshes 19 in ref 18 it is noted that different turbulence models give different normal force and pitching moment coefficients numerical solutions of the unsteady euler equations are less expensive than those of the unsteady navier stokes equations for the unsteady transonic flow the unsteady euler equations adequately model most of the real flow features with the exception of viscous effects whenever they are substantial the euler equations model shock waves and their motion entropy increase across shocks and entropy gradient and vorticity production and convection behind shocks as can be seen from crocco s theorem and the inviscid vorticity transport equa tion recently successful time accurate solutions of the un steady euler equations have been presented for pitching air foils19 and wings in transonic flows 20 and for the rolling oscillation of delta wings a vortex dominated flow problem in a locally conical supersonic flows 21 to the best of bur knowledge ref 21 is the first work done for unsteady vortex dominated flows with shock waves which is directly applica ble to maneuvering delta wings in this paper we present an implicit approximately factored finite volume scheme for the time accurate numerical solution of the unsteady euler equations of the flow relative motion with respect to an airfoil fixed frame of reference the scheme is applied to steady and unsteady transonic flows around a naca 0012 airfoil for the unsteady flows the airfoil is in pitching oscillation about a small and moderate mean angle of attack at a large amplitude the computational results are compared with the experimental data

triangular matrix representations in this paper we develop the theory of generalized triangular matrix representation in an abstract setting this is accomplished by introducing the concept of a set of left triangulating idempotents these idempotents determine a generalized triangular matrix representation for an algebra the existence of a set of left triangulating idempotents does not depend on any specific conditions on the algebras however if the algebra satisfies a mild finiteness condition then such a set can be refined to a complete set of left triangulating idempotents in which each diagonal subalgebra has no nontrivial generalized triangular matrix representation we then apply our theory to obtain new results on generalized triangular matrix representations including extensions of several well known results

triangular matrix representations of ring extensions in this paper we investigate the class of piecewise prime pwp rings which properly includes all piecewise domains hence all right hereditary rings which are semiprimary or right noetherian for a pwp ring we determine a large class of ring extensions which have a generalized triangular matrix representation for which the diagonal rings are prime

transonic vortex flows past delta wings integral equation approach the steady full potential equation is written in the form of poisson s equation and the solution of the velocity field is expressed in terms of an integral equation the solution consists of a surface integral of vorticity distribution on the wing and its free vortex sheets and a volume integral of source distribution within a volume around the wing and its free vortex sheets the solution is obtained through successive iteration cycles the density gradient in the source distribution is computed by using a type differencing scheme the method is applied to delta wings and the numerical examples show that a curved shock is captured on the suction side of the wing it is attached to the lower surface of the leading edge vortex but does not necessarily reach the wing surface the present solution does not suffer from the numerical diffusion problem usually encountered with the finite difference solutions of euler equations

unsteady navier stokes computations past oscillating delta wing at high incidence the unsteady compressible thin layer navier stokes equations written in the moving frame of reference for the flow relative motion are solved for the unsteady supersonic flow around a round edged delta wing for supersonic flow a local conical flow solution has been obtained from the three dimensional equations pseudotime stepping is used for the steady flow problem while time accurate stepping is used for the unsteady flow problem the computational scheme is an implicit approximately factored finite volume scheme which uses implicit and explicit dissipation terms the scheme is verified for the steady flow solution the scheme is then applied to a delta wing undergoing rolling oscillation at a reduced frequency of 1 337 with 15 deg maximum amplitude about a mean angle of attack of 10 deg for a mach number of 2 and a reynolds number of 0 5 x 10 6

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

polycyclic group rings whose principal ideals are projective abstract let k g be a prime group algebra with g a polycyclic by finite group in this paper we prove that k g is a cs ring or a pp ring if and only if either g is torsion free or g d and char k 2 the proof requires group theoretic as well as group ring arguments

propagation in linear dispersive media finite difference time domain methodologies finite difference time domain fdtd methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media an nth order lorentz and an mth order debye medium the temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first order differential equations from this the final equations are temporally advanced using the classical leapfrog method one dimensional scattering from a dielectric slab is chosen for a test case provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space as shown in the error analysis the agreement between the computed and exact solutions will be excellent the attached data which are associated with the four pole lorentz dielectric and the five pole debye medium verify this assertion