growth of rounding errors and repetitivity of large eddy simulations this paper studies the propagation of rounding errors in large eddy simulation and shows that instantaneous flowfields produced by large eddy simulation are partially controlled by these rounding errors and depend on multiple parameters number of processors used for parallel simulation even in an explicit code changes in initial conditions even of the order of machine accuracy machine precision simple double or quadruple etc using a laminar poiseuille pipe flow a fully developed turbulent channel flow and a complex burner geometry as test cases results show that only turbulent flows exhibit a high sensitivity to these parameters these results confirm that large eddy simulation reflects the true nature of turbulence insofar as it may exponentially amplify infinitely small perturbations on initial conditions in time however they highlight an often overlooked limitation of large eddy simulation in terms of validation and prediction of unsteady phenomena

conditionally solvable path integral problems ii natanzon potentials new classes of exactly solvable potentials are discussed within the path integral formalism they are constructed from the hypergeometric and confluent natanzon potentials respectively it is found that they allow incorporation of four free parameters which give rise to fractional power behaviour long range and strongly anharmonic terms we find six different classes of such potentials

deformed shape invariance and exactly solvable hamiltonians with position dependent effective mass known shape invariant potentials for the constant mass schrodinger equation are taken as effective potentials in a position dependent effective mass pdem one the corresponding shape invariance condition turns out to be deformed its solvability imposes the form of both the deformed superpotential and the pdem a lot of new exactly solvable potentials associated with a pdem background are generated in this way a novel and important condition restricting the existence of bound states whenever the pdem vanishes at an end point of the interval is identified in some cases the bound state spectrum results from a smooth deformation of that of the conventional shape invariant potential used in the construction in others one observes a generation or suppression of bound states depending on the mass parameter values the corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials

algebraic shape invariant potentials in two steps the simplified algebraic structure of the shape invariance condition in two steps is developed by imposing an extra relation on the two superpotentials of the corresponding two step potentials this simplified version of potential algebra is found to be similar to that of the shape invariance condition in one step the solvable potentials of shape invariance in two steps with a translation change of parameters a1 a0 are shown to possess such a simplified version of potential algebra the condition under which the potential algebra of shape invariance in more than two steps becomes simplified is also discussed

a fully discrete stable and conservative summation by parts formulation for deforming interfaces we introduce an interface coupling procedure for hyperbolic problems posed on time dependent curved multi domains first we transform the problem from cartesian to boundary conforming curvilinear coordinates and apply the energy method to derive well posed and conservative interface conditions next we discretize the problem in space and time by employing finite difference operators that satisfy a summation by parts rule the interface condition is imposed weakly using a penalty formulation we show how to formulate the penalty operators such that the coupling procedure is automatically adjusted to the movements and deformations of the interface while both stability and conservation conditions are respected the developed techniques are illustrated by performing numerical experiments on the linearized euler equations and the maxwell equations the results corroborate the stability and accuracy of the fully discrete approximations

on solvable potentials related to so 2 2 ii natanzon potentials general natanzon potentials related to the so 2 2 group are studied the s matrices for systems under consideration are related to intertwining operators between weyl equivalent most degenerate principal series representations of so 2 2

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

algebraic solution for the natanzon hypergeometric potentials an algebraic method based on a strategy that makes use of a realization of the algebra so 2 1 in terms of differential operators is used to solve the bound state problem for the most general natanzon potentials for which the schrodinger equation can be reduced to hypergeometric form hence hypergeometric potentials

an algebraic approach to shape invariance with reflections we consider a realization of supersymmetric shape invariant quantum systems where generalized ladder operators are constructed through the association of the supersymmetric partner operators the parameter potential translation operator and the reflection operator the basic algebraic relations as well as the system eigenstates and energy eigenvalues are obtained as an illustration we apply the generalized formalism for two important shape invariant potential systems the scarf hyperbolic and the morse potentials

generalized coherent states for associated hypergeometric type functions we introduce a right inverse for the annihilation operator which appears in the factorization of associated hypergeometric type operators this makes possible the definition of generalized coherent states for the associated eigenfunctions these generalized coherent states satisfy the relevant properties i e label continuity overcompleteness temporal stability and action identity required to establish a close connection between the quantum and classical formulations of a given physical system

neighborhood exploring detector an em based signal detector for multiple antenna systems we introduce a computationally efficient detector of the space time uncoded symbols for multiple antenna systems in a high data rate communication system reliable real time detection algorithm with low complexity is highly attractive however the space time signal detection problem is mathematically equivalent to the combinatorial optimization problem which is known to be np hard essentially most of the existing algorithms incorporate one or more of the following strategies 1 sequential detection of signals in a lower dimensional space 2 a posteriori probability density approximation or 3 reduction of the signal searching space the proposed detector explicitly incorporates all of these three strategies the principal concept of the proposed detector is the exploration of the neighborhood for each transmitted symbol by using a signal decoupling technique and the expectation maximization em algorithm the proposed detector provides a good balance between the computational complexity and the performance simulation results show that the symbol detection error rate of the proposed detector is close to the maximum likelihood detector with reasonably low complexity

on scattering systems related to the so 2 1 group ii we study a class of solvable hamiltonians h which have strongly broken potential group structure however the scattering matrices of the systems under consideration are also related to the intertwining operator of so 2 1

fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains a time dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered by applying the energy method well posed boundary conditions for the continuous problem are derived summation by parts sbp operators for the space and time discretization together with a weak imposition of boundary and initial conditions using simultaneously approximation terms sats lead to a provable fully discrete energy stable conservative finite difference scheme we show how to construct a time dependent sat formulation that automatically imposes boundary conditions when and where they are required we also prove that a uniform flow field is preserved i e the numerical geometric conservation law ngcl holds automatically by using sbp sat in time and space the developed technique is illustrated by considering an application using the linearized euler equations the sound generated by moving boundaries numerical calculations corroborate the stability and accuracy of the new fully discrete approximations

supersymmetry operator transformations and exactly solvable potentials a large class of potentials can be solved algebraically by using supersymmetry and shape invariance the authors apply operator transformations f transformations to these algebraically solvable problems to obtain a larger class of solvable potentials the natanzon class of potentials which are not shape invariant the important condition which is independent of supersymmetry for finding new potentials from old ones using operator transformations is that the resulting schrodinger equation has a potential which does not depend on the state as a special case of the f transformation they rederive the previously known connection between the 3d harmonic oscillator the hydrogen atom and the morse potential they also discuss the lack of commutivity of susy and the f transformations

convergence of the compact finite difference method for second order elliptic equations abstract in this paper we give a fourth order compact finite difference scheme for the general forms of two point boundary value problems and two dimensional elliptic partial differential equations pde s by decomposing the coefficient matrix into a sum of several matrixes after we discretize the original problems we can obtain a lower bound for the smallest eigenvalue of the coefficient matrix thus we prove the compact finite difference scheme converges with the fourth order of accuracy to solve the discretized block tri diagonal matrix equations of the two dimensional elliptic pde s we develop an efficient iterative method full multigrid method in our numerical experiments we compare the compact finite difference method with the finite element method and crank nicolson finite difference method the results show that the compact finite difference scheme is a highly efficient and accurate method

estimation of co channel signals with linear complexity to increase wireless system capacity using co channel signals and multiple receiver antennas we develop the partitioned viterbi algorithm pva the pva estimation complexity increases linearly with each additional co channel signal rather than exponentially as it does with joint maximum likelihood sequence estimation mlse the estimation problem involves multiple signals simultaneously transmitted and observed through slow fading frequency selective channels although transmission is assumed to be in bursts according to a time division multiple access scheme more than one signal can occupy the same time and frequency slot these signals are referred to as co channel signals separation and estimation of the symbol bursts is accomplished by exploiting channel differences pva estimation consists of a set of viterbi detectors one per signal that operate in parallel with cross coupling to allow approximate interference cancellation by means of tentative decisions the forward filter of a decision feedback equalizer dfe is used to prefilter received signals prior to pva estimation prefiltering delays the energy of interfering signals so that tentative decisions become reliable enough to use simulation results show pva performance remains near optimal with respect to the performance of joint mlse

from semidiscrete to fully discrete stability of runge kutta schemes by the energy method the integration of semidiscrete approximations for time dependent problems is encountered in a variety of applications the runge kutta rk methods are widely used to integrate the ode systems which arise in this context resulting in large ode systems called methods of lines these methods of lines are governed by possibly ill conditioned systems with a growing dimension consequently the naive spectral stability analysis based on scalar eigenvalues arguments may be misleading instead we present here a stability analysis of rk methods for well posed semidiscrete approximations based on a general energy method we review the stability question for such rk approximations and highlight its intricate dependence on the growing dimension of the problem in particular we prove the strong stability of general fully discrete rk methods governed by coercive approximations we conclude with two nontrivial examples which demonstrate the versatility of our approach in the context of general systems of convection diffusion equations with variable coefficients a straightforward implementation of our results verify the strong stability of rk methods for local finite difference schemes as well as global spectral approximations since our approach is based on the energy method which is carried in the physical space and since it avoids the von neumann analysis which is carried in the dual fourier space we are able to easily adapt additional extensions due to nonperiodic boundary conditions general geometries etc

path integral treatment for the one dimensional natanzon potentials the green s function relative to the one dimensional natanzon potentials is exactly calculated by the path integral approach the energy spectrum the wave functions and the scattering function s are deduced

a class of energy stable high order finite difference interface schemes suitable for adaptive mesh refinement of hyperbolic problems we present a class of energy stable high order finite difference interface closures for grids with step resolution changes these grids are commonly used in adaptive mesh refinement of hyperbolic problems the interface closures are such that the global accuracy of the numerical method is that of the interior stencil the summation by parts property is built into the stencil construction and implies asymptotic stability by the energy method while being non dissipative we present one dimensional closures for fourth order explicit and compact pade type finite differences tests on the scalar one and two dimensional wave equations the one dimensional navier stokes solution of a shock and two dimensional inviscid compressible vortex verify the accuracy and stability of this class of methods

connection between type a and e factorizations and construction of satellite algebras recently we introduced a new class of symmetry algebras called satellite algebras which connect with one another wavefunctions belonging to different potentials of a given family and corresponding to different energy eigenvalues here the role of the factorization method in the construction of such algebras is investigated a general procedure for determining an so 2 2 or so 2 1 satellite algebra for all the hamiltonians that admit a type e factorization is proposed such a procedure is based on the known relationship between type a and e factorizations combined with an algebraization similar to that used in the construction of potential algebras it is illustrated with examples of the generalized morse potential the rosen morse potential and the kepler problem in a space of constant negative curvature and in each case the conserved quantity is identified it should be stressed that the method proposed is fairly general since the other factorization types may be considered as limiting cases of type a or e factorizations

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

on the generalized morse potential the equivalence between the generalized morse gmp and eckart potentials is shown the study of the hypergeometric natanzon potentials using so 2 1 techniques is applied to compute the eigenfunctions and eigenvalues of the eckart gmp potential the action of the group generators is studied with the result that a family of eckart potentials is obtained which is different from the one obtained in susyqm

energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition overlapping domain decomposition methods otherwise known as overset grid or chimera methods are useful for simplifying the discretization of partial differential equations in or around complex geometries though in wide use such methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used especially for higher order methods to address this shortcoming high order provably energy stable overlapping domain decomposition methods are derived for hyperbolic initial boundary value problems the overlap is treated by splitting the domain into pieces and using generalized summation by parts derivative operators and polynomial interpolation new implicit and explicit operators are derived that do not require regularization for stability in the linear limit applications to linear and nonlinear problems in one and two dimensions are presented where it is found the explicit operators are preferred to the implicit ones

highly accurate compact mixed methods for two point boundary value problems finite difference method and finite element method are widely used partly for their simplicity though these methods can obtain first order or second order of accuracy in this paper we give two highly accurate fourth order and sixth order of accuracy respectively while still quite simple schemes for two point boundary value problems we call them compact mixed methods since they can obtain numerical solutions for unknown function and its first derivative simultaneously to yield best numerical solutions we combine our compact mixed schemes with a direct solver and an iterative solver then we employ fourier method to analyze differencing errors shows that our compact mixed formulae are closer to the true wavenumber numerical experiments show compact mixed schemes are very efficient and highly accurate techniques

strict stability of high order compact implicit finite difference schemes temporal or strict stability of approximation to pdes is much more difficult to achieve than the classical lax stability in this paper we present a class of finite difference schemes for hyperbolic initial boundary value problems in one and two space dimensions that possess the property of strict stability the approximations are constructed so that all eigenvalues of corresponding differentiation matrix have a nonpositive real part boundary conditions are imposed by using penalty like terms fourth and sixth order compact implicit finite difference schemes are constructed and analyzed computational efficacy of the approach is corroborated by a series of numerical tests in 1 d and 2 d scalar problems

a cartesian based embedded geometry technique with adaptive high order finite differences for compressible flow around complex geometries an immersed boundary methodology to solve the compressible navier stokes equations around complex geometries in cartesian fluid dynamics solvers is described the objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts a standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended boundary conditions on the surface are enforced by an approach inspired by analytic continuation each fluid field is extended independently constrained only by the boundary condition associated with that field unlike most existing methods no jump conditions or explicit derivation of them from the boundary conditions are required in this approach numerical stiffness that arises when the fluid solid interface is close to grid points of the mesh is addressed by preconditioning in addition the embedded geometry technique is coupled with a stable high order adaptive discretization that is enabled around the object boundary to enhance resolution the stencils used to transition the order of accuracy of the discretization are derived using the summation by parts technique that ensures stability applications to shock reflections shock ramp interactions and supersonic and low mach number flows over two and three dimensional geometries are presented

potentials of the heun class we review different methods of generating potentials such that the one dimensional schrodinger equation odse can be transformed into the hypergeometric equation we compare our results with previous studies and complement the subject with new findings our main result is to derive new classes of potentials such that the odse can be transformed into the heun equation and its confluent cases the generalized heun equation is also considered

a dual consistent summation by parts formulation for the linearized incompressible navier stokes equations posed on deforming domains in this article well posedness and dual consistency of the linearized incompressible navier stokes equations posed on time dependent spatial domains are studied to simplify the derivation of the

on the outflow conditions for spectral solution of the viscous blunt body problem the purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic hypersonic flow over blunt bodies governed by the compressible navier stokes equations with an emphasis motivated primarily by the use of spectral methods without any filtering the subsonic supersonic composition of the outflow boundary requires a dual boundary treatment for well posedness all compatibility relations modified to undertake the hyperbolic parabolic behaviour of the governing equations are used for the supersonic part of the outflow regarding the unknown downstream information in the subsonic region different subsonic outflow conditions in the sense of the viscous blunt body problem are examined a verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer it is demonstrated that two approaches for imposing subsonic outflow conditions namely 1 extrapolating all flow variables and 2 extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high speed flows over blunt bodies using spectral collocation methods

explicit wavefunctions for shape invariant potentials by operator techniques the authors obtain explicit expressions for the wavefunctions of all the known shape invariant potentials by using the operator method

matched interface and boundary mib for the implementation of boundary conditions in high order central finite differences high order central finite difference schemes encounter great difficulties in implementing complex boundary conditions this paper introduces the matched interface and boundary mib method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high order central finite difference schemes to attain arbitrarily high order the mib method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions the proposed approach is extensively validated via boundary value problems initial boundary value problems eigenvalue problems and high order differential equations successful implementations are given to not only dirichlet neumann and robin boundary conditions but also more general ones such as multiple boundary conditions in high order differential equations and time dependent boundary conditions in evolution equations detailed stability analysis of the mib method is carried out the mib method is shown to be able to deliver high order accuracy while maintaining the same or similar stability conditions of the standard high order central difference approximations the application of the proposed mib method to the boundary treatment of other non standard high order methods is also considered

nondissipative and energy stable high order finite difference interface schemes for 2 d patch refined grids a class of finite difference interface schemes suitable for two dimensional cell centered grids with patch refinement and step changes in resolution is presented grids of this type are generated by adaptive mesh refinement methods according to resolution needs dictated by the physics of the problem being modeled for these grids coarse and fine nodes are not aligned at the mesh interfaces resulting in hanging nodes three distinct geometries are identified at the interfaces of a domain with interior patch refinement edges concave corners and convex corners asymptotic stability in time of the numerical scheme is achieved by imposing a summation by parts condition on the interface closure which is thus also nondissipative interface stencils corresponding to an explicit fourth order finite difference scheme are presented for each geometry to preserve stability a reduction in local accuracy is required at the corner geometries it is also found that no second order accurate solution exists that satisfies the summation by parts condition tests using the 2 d scalar advection equation and an inviscid compressible vortex support the stability and accuracy of these stencils for both linear and nonlinear problems

unified treatment of the coulomb and harmonic oscillator potentials in d dimensions quantum mechanical models and practical calculations often rely on some exactly solvable models like the coulomb and the harmonic oscillator potentials the d dimensional generalized coulomb potential contains these potentials as limiting cases thus it establishes a continuous link between the coulomb and harmonic oscillator potentials in various dimensions we present results which are necessary for the utilization of this potential as a model and practical reference problem for quantum mechanical calculations we define a hilbert space basis the generalized coulomb sturmian basis and calculate the green s operator on this basis and also present an su 1 1 algebra associated with it we formulate the problem for the one dimensional case too and point out that the complications arising due to the singularity of the one dimensional coulomb problem can be avoided with the use of the generalized coulomb potential

algebraic solution for the natanzon confluent potentials an algebraic method is used to solve the bound state problem for the most general natanzon potential for which the schrodinger equation can be reduced to the confluent hypergeometric form hence confluent potentials the solution is obtained straightforwardly a simple argument is given to sustain that the natanzon potential is the most general confluent potential

algebraic treatment of second poschl teller morse rosen and eckart equations the method of an earlier paper see ibid vol 20 p 4075 1987 is applied to the non compact case to solve a family of second poschl teller morse rosen and eckart equations with quantised coupling constants both discrete and continuous spectra bound state and scattering wavefunctions transmission coefficients are found from the matrix elements of group representations

a second class of solvable potentials related to the jacobi polynomials levai 1991 has used a simple method for generating solvable wave equations to construct potentials whose solutions include as factors jacobi polynomials of functions g x which solve specific differential equations application of this method to a previously unconsidered differential equation involving jacobi polynomials results in a new class of solvable potentials missing from earlier compilations an interesting property of these new potentials is that when two of their defining parameters are fixed they all possess the same energy eigenvalue spectrum independent of any change in a third parameter leading to an indefinite number of different potentials with the same energies

high order non uniform grid schemes for numerical simulation of hypersonic boundary layer stability and transition the direct numerical simulation of receptivity instability and transition of hypersonic boundary layers requires high order accurate schemes because lower order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields the main limiting factor in the application of high order schemes to practical boundary layer flow problems is the numerical instability of high order boundary closure schemes on the wall this paper presents a family of high order non uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary layer transition by using an appropriate grid stretching and clustering grid points near the boundary high order schemes with stable boundary closures can be obtained the order of the schemes ranges from first order at the lowest to the global spectral collocation method at the highest the accuracy and stability of the new high order numerical schemes is tested by numerical simulations of the linear wave equation and two dimensional incompressible flat plate boundary layer flows the high order non uniform grid schemes up to the 11th order are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge the steady and unsteady results show that the new high order schemes are stable and are able to produce high accuracy for computations of the nonlinear two dimensional navier stokes equations for the wall bounded supersonic flow

iterative receivers with bit level cancellation and detection for mimo bicm systems the multiple input multiple output mimo detection in the iterative receiver is investigated for a modulation of square constellation for computationally efficient mimo detection we employ the hard decision bit level cancellation blc to reduce the dimension of the mimo detection as it has advantages over the symbol level cancellation 1 it can provide better performance and 2 the extrinsic bit information can be directly used for the blc a set of reliably decoded bits from the channel decoder in iterations is used for hard decision blc to approximate the maximum a posteriori probability map detection under the partial map detection principle for the bits that are not canceled the nulling using projection is employed to approximate the map detection this approach is applicable for a lower order modulation for a higher order modulation the minimum mean square error mmse filtering with soft decision cancellation sc is applied to further mitigate the bits that are not canceled

on conservation and stability properties for summation by parts schemes abstract we discuss conservative and stable numerical approximations in summation by parts form for linear hyperbolic problems with variable coefficients an extended setting where the boundary or interface may or may not be included in the grid is considered we prove that conservative and stable formulations for variable coefficient problems require a boundary and interface conforming grid and exact numerical mimicking of integration by parts finally we comment on how the conclusions from the linear analysis carry over to the nonlinear setting

systematic search for symmetric potentials with real energy spectra changes of coordinates represent one of the most effective ways of deriving solvable potentials from ordinary differential equations for separate special functions here we relax the standard hermiticity requirement and find an innovative construction which leads to unusual complex potentials their energy spectrum is shown to stay real after a weakening of the hermiticity of the schr dinger equation to its mere invariance under the combined parity and time reversal symmetry this ultimately results in richer bound state spectra some of our new exactly solvable potentials generalize the current textbook models details are given for constructions based on the hypergeometric and confluent hypergeometric special functions

the convergence rate for difference approximations to general mixed initial boundary value problems the convergence rate is investigated for the solutions to difference schemes approximating the mixed initial boundary value problem for general systems of differential equations it is shown that if an energy estimate holds then the extra boundary conditions can be of one order lower accuracy without destroying the convergence rate expected from the approximation at inner points if the maximal order of the derivatives occurring in the boundary conditions is low enough then even lower accuracy can be permitted for the extra boundary conditions

solvable potentials associated with su 1 1 algebras a systematic study we consider a specific differential realization of the su 1 1 algebra and use it to explore such algebraic structures associated with shape invariant potentials our approach combines elements of various methods of solving the schrodinger equation such as supersymmetric quantum mechanics or the factorization method algebraic techniques and special function theory in fact it amounts to reformulating transformations mapping the schrodinger equation into the differential equation of orthogonal polynomials in group theoretical terms our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings the procedure presented here implicitly contains a similar treatment of the compact su 2 algebra as well possible generalizations of this approach involving different realizations of the su 1 1 algebra other algebraic structures and larger classes of potentials are also outlined

an approximate κ state solutions of the dirac equation for the generalized morse potential under spin and pseudospin symmetry by using an improved approximation scheme to deal with the centrifugal pseudo centrifugal term we solve the dirac equation for the generalized morse potential with arbitrary spin orbit quantum number in the presence of spin and pseudospin symmetry the analytic bound state energy eigenvalues and the associated upper and lower spinor components of two dirac particles are found by using the basic concepts of the nikiforov uvarov method we study the special cases when 1 l l 0 s wave the non relativistic limit and the limit when becomes zero kratzer potential model the present solutions are compared with those obtained by other methods

the potential group approach and hypergeometric differential equations this paper proposes a generalized realization of the potential groups so 2 1 and so 2 2 to describe the confluent hypergeometric and the hypergeometric equations respectively it implies that the classes of schrodinger equations with solvable potentials whose analytical solutions are related to the confluent hypergeometric and the hypergeometric functions can be realized in terms of the above group structure

factorization of sturm liouville operators solvable potentials and underlying algebraic structure in this paper a general method of factorization of sturm liouville sl operators is provided a method to solve sl eigenvalue problems is presented new classes of exactly solvable potentials are obtained the supersymmetry and shape invariance approaches are generalized to the sl operators it is shown that the sl shape invariance potentials have an underlying algebraic structure this algebra is in general infinite dimensional the condition of finite algebra is obtained

generalized morse potential symmetry and satellite potentials we study in detail the bound state spectrum of the generalized morse potential gmp which was proposed by deng and fan as a potential function for diatomic molecules by connecting the corresponding schrodinger equation with the laplace equation on the hyperboloid and the schrodinger equation for the poschl teller potential we explain the exact solvability of the problem by an symmetry algebra and obtain an explicit realization of the latter as we prove that some of the generators connect among themselves wavefunctions belonging to different gmps called satellite potentials the conserved quantity is some combination of the potential parameters instead of the level energy as for potential algebras hence belongs to a new class of symmetry algebras we also stress the usefulness of our algebraic results for simplifying the calculation of frank condon factors for electromagnetic transitions between rovibrational levels based on different electronic states

comprehensive analysis of conditionally exactly solvable models we study a quantum mechanical potential introduced previously as a conditionally exactly solvable ces model besides an analysis following its original introduction in terms of the point canonical transformation we also present an alternative supersymmetric construction of it we demonstrate that from the three roots of the implicit cubic equation defining the bound state energy eigenvalues there is always only one that leads to a meaningful physical state finally we demonstrate that the present ces interaction is in fact an exactly solvable natanzon class potential

satellite potentials for hypergeometric natanzon potentials as a result of the so 2 1 treatment of the hypergeometric natanzon potentials vn a set of potentials related to a given one is determined these are the satellite potentials and all belong to the natanzon class the set arises as the result of the action of the so 2 1 generators on the carrier space of an irreducible representation the results are compared to those obtained from supersymmetric quantum mechanics susyqm for some natanzon potentials the chains of natanzon potentials constructed using the idea of a satellite potential are in most cases different from the susyqm chains

single variable realisation of the su 1 1 spectrum generating algebra and discrete eigenvalue spectra of a class of potentials a wide range of operators can be expressed in terms of the generators of the su 1 1 algebra the spectral properties of which are well known we attempt to find a realisation of the algebra in its most general form and thus evolve a unified approach to the problem of finding the spectra of hamiltonians amenable to the technique rather than taking each case separately we extend the analysis to obtain the spectra of potentials whose coordinate dependence is implicit

the general besselian and legendrian path integrals the general besselian and legendrian path integrals based on the confluent and hypergeometric natanzon potentials are calculated these two solutions cover all other path integral representations which are related to the radial harmonic oscillator and the modified poschl teller path integral

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

high order unconditionally stable fc ad solvers for general smooth domains i basic elements we introduce a new methodology for the numerical solution of partial differential equations in general spatial domains our algorithms are based on the use of the well known alternating direction implicit adi approach in conjunction with a certain fourier continuation fc method for the resolution of the gibbs phenomenon unlike previous alternating direction methods of order higher than one which can only deliver unconditional stability for rectangular domains the present high order algorithms possess the desirable property of unconditional stability for general domains the computational time required by our algorithms to advance a solution by one time step in turn grows in an essentially linear manner with the number of spatial discretization points used in this paper we demonstrate the fc ad methodology through a variety of examples concerning the heat and laplace equations in two and three dimensional domains with smooth boundaries applications of the fc ad methodology to hyperbolic pdes together with a theoretical discussion of the method will be put forth in a subsequent contribution the numerical examples presented in this text demonstrate the unconditional stability and high order convergence of the proposed algorithms as well the very significant improvements they can provide in one of our examples we demonstrate a one thousand improvement factor over the computing times required by some of the most efficient alternative general domain solvers

dynamical potential algebras for gendenshtein and morse potentials a differential realization of so 2 1 is shown to be the potential algebra for the one dimensional systems with the morse or gendenshtein potentials this shows that two classes of gendenshtein potentials will support the same eigenvalues as the morse potential and that the three sets of eigenfunctions may be derived in a common formalism the potential algebra is then extended to a dynamical potential algebra with operators connecting states both in different potentials and with different energies giving new dynamical algebras for the gendenshtein problem the matrix elements of certain corresponding operators in the three types of system may then be given by a single formula involving so 2 1 wigner coefficients the authors also give ladder operators connecting the gendenshtein potential eigenstates

derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation in this paper simple polynomial interpolation is used to derive arbitrarily high order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative consisting of three second derivative nodes in the interior and two on the boundary on non uniform grids boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme the high order non uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non uniform grid with appropriate stretching so that more grid points are clustered near the boundary the stability and resolution properties of the high order non uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented

on the partial map detection with applications to mimo channels we investigate a multidimensional detection problem with a partial information of the a posteriori probability which is referred to as the partial maximum a posteriori probability map detection problem we show that the maximum likelihood ml detection of a higher dimension can be reduced to the ml detection of a lower dimension with cancellation under a certain condition through the formulation of the partial map detection problem using this we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output mimo channels including multiple transmit and multiple receive antenna mtmr channels and intersymbol interference isi channels it is shown that the proposed method has less error propagation effect and its performance is close to that of the full ml detection with a lower computational complexity

a lie algebraic approach to effective mass schrodinger equations we use lie algebraic techniques to obtain exact solutions of the effective mass schrodinger equation in particular we use the su 1 1 algebra both as a spectrum generating algebra and as a potential algebra to obtain exact solutions of effective mass schrodinger equations corresponding to a number of potentials we also discuss the construction of isospectral hamiltonians for which both the mass and the potential are different

a novel strategy for deriving high order stable boundary closures based on global conservation i basic formulas abstract it is well known that for initial boundary value problems one may need to decrease the order of boundary closures to ensure strict stability also called time stability of finite difference schemes for high order schemes this often reduces the global convergence rate significantly to cure this issue we derive high order accurate boundary closures that satisfy a global conservation property we show that the boundary closures cannot be both high order accurate and conservative in the l 2 inner product if the grid is equidistant therefore we derive particular sets of nonuniform solution points and quadrature weights near the domain boundaries the new schemes are high order accurate on the modified grids and conservative in the derived quadrature rules although we have no theoretical stability proof numerical eigenvalue analysis suggests that the new schemes are strictly stable up to eleventh order global accuracy for scalar linear advection equations numerical experiments with one and two dimensional linear equations corroborate the design orders of the schemes

strict stability of high order compact implicit finite difference schemes the role of boundary conditions for hyperbolic pdes ii abstract this paper deals with the problem of systems of hyperbolic pdes in one and two space dimensions using the theory of part i 7