homological dimensions over non commutative semi local rings abstract an associative ring r is called semi local if r j is artinian semisimple where j is the radical of r in this paper we discuss homological dimensions over non commutative semi local rings the results obtained here will generalize the corresponding ones over commutative semi local rings and commutative coherent local rings

numerical analysis of the cahn hilliard equation with a logarithmic free energy a fully discrete finite element method for the cahn hilliard equation with a logarithmic free energy based on the backward euler method is analysed existence and uniqueness of the numerical solution and its convergence to the solution of the continuous problem are proved two iterative schemes to solve the resulting algebraic problem are proposed and some numerical results in one space dimension are presented

some mixed finite element methods for biharmonic equation abstract some perturbed mixed finite element methods related to the reduced integration technique are considered for solving the biharmonic equation problem on a rectangular mesh a similar scheme was proposed in malkus and hughes comput methods appl mech eng 15 1978 63 81 and its convergence was analyzed in johnson and pitkaranta math comp 38 1982 375 400 here we modify the scheme proposed in malkus and hughes 1978 and prove the optimal order error estimate without the extra smoothness assumption on the solution made in johnson and pitkaranta 1982 on a triangular mesh an analogous scheme is studied and an order error estimate is proved some numerical results are given to show the convergence behavior of the numerical solutions

on the auslander reiten conjecture for algebras abstract a recent result of araya asserts that if the auslander reiten conjecture holds in codimension one for a commutative gorenstein ring r then it holds for r this note extends this result to left gorenstein r algebras whenever r is a commutative gorenstein ring this in particular implies that any finitely generated self orthogonal gorenstein projective module is projective provided is an isolated singularity and dim r 2 also some examples of bound quiver algebras satisfying the auslander reiten conjecture are presented

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

symplectic coarse grained classical and semclassical evolution of subsystems new theoretical approach we study the classical and semiclassical time evolutions of subsystems of a hamiltonian system this is done using a generalization of heller s thawed gaussian approximation introduced by littlejohn the key tool in our study is an extension of gromov s principle of the symplectic camel obtained in collaboration with dias de gosson and prata arxiv 1911 03763v1 math sg 2019 this extension says that the orthogonal projection of a symplectic phase space ball on a phase space with a smaller dimension also contains a symplectic ball with the same radius in the quantum case the radii of these symplectic balls are taken equal to and represent the ellipsoids of minimum uncertainty which we called quantum blobs in previous work

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

a second order splitting method for the cahn hilliard equation a semi discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary fourth order in space cahn hilliard equation optimal order error bounds are derived in various norms for an implementation which uses mass lumping the continuous problem has an energy based lyapunov functional it is proved that this property holds for the discrete problem

whitehead test modules a right r module n is said to be a whitehead test module for projectivity shortly a p test module provided for each module m extr m n 0 implies m is projective dually i test modules are defined for example z is a p test abelian group iff each whitehead group is free our first main result says that if r is a right hereditary non right perfect ring then the existence of p test modules is independent of zfc gch on the other hand for any ring r there is a proper class of i test modules dually there is a proper class of p test modules over any right perfect ring a non semisimple ring r is said to be fully saturated saturated provided that all non projective generated non projective modules are i test we show that classification of saturated rings can be reduced to the indecomposable ones indecomposable 1 saturated rings fall into two classes type i where all simple modules are isomorphic and type ii the others our second main result gives a complete characterization of rings of type ii as certain generalized upper triangular matrix rings gt 1 n p s t the four parameters involved here are skew fields s and t and natural numbers n p for rings of type i we have several partial results e g using a generalization of bongartz lemma we show that it is consistent that each fully saturated ring of type i is a full matrix ring over a local quasi frobenius ring in several recent papers our results have been applied to tilting theory and to the theory of modules in modern algebra the structure of rings r is studied by means of properties of corresponding module categories mod r in most cases it is not possible to characterize mod r fully nevertheless there are important subclasses of mod r that can be treated in detail and that shed light on the whole of mod r among the prominent ones are the classes of all projective and all injective modules recall that a module m is said to be projective injective provided that the functorhomr m homr m preserves short exact sequences there is also a universal algebraic aspect each module is a factor module of a projective module and a submodule of an injective module so a possible strategy to investigate modr consists in describing all injective modules and for each injective module i all its submodules the first step is usually relatively easy but the second may be quite hard for example using this strategy for abelian groups one meets serious difficulties already for i q q see e g e theorem 2 received by the editors march 17 1995 1991 mathematics subject classification primary 16e30 secondary 03e35 20k35

convergence of frozen gaussian approximation for high frequency wave propagation the frozen gaussian approximation provides a highly efficient computational method for high frequency wave propagation the derivation of the method is based on asymptotic analysis in this paper for general linear strictly hyperbolic systems we establish the rigorous convergence result for frozen gaussian approximation as a byproduct higher order frozen gaussian approximation is developed 2011 wiley periodicals inc

quantum harmonic analysis on phase space relative to an irreducible representation of the canonical commutation relations convolutions between quantum mechanical operators and between functions and operators are defined for which the usual weyl transform acts as a fourier transform basic properties of these operations are developed in close analogy to harmonic analysis on r2n using the quantum version of wiener s approximation theorem a natural one to one correspondence between the closed phase space translation invariant subspaces of classical and quantum observables is established

level set methods for the simulation of epitaxial phenomena we introduce a model for epitaxial phenomena based on the motion of island boundaries which is described by the level set method our model treats the growing film as a continuum in the lateral direction but retains atomistic discreteness in the growth direction an example of such an island dynamics model using the level set method is presented and compared with the corresponding rate equation description extensions of our methodology to more general settings are then discussed s1063 651x 98 50212 7

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

analysis of a sequential regularization method for the unsteady navier stokes equations the incompressibility constraint makes navier stokes equations difficult a reformulation to a better posed problem is needed before solving it numerically the sequential regularization method srm is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods in the paper we study the existence and uniqueness for the solution of the srm and provide a simple proof of the convergence of the solution of the srm to the solution of the navier stokes equations we also give error estimates for the time discretized srm formulation

on mixed finite element methods for the reissner mindlin plate model in this paper we analyze the convergence of mixed finite element approximations to the solution of the reissner mindlin plate problem we show that several known elements fall into our analysis thus providing a unified approach we also introduce a low order triangular element which is optimalorder convergent uniformly in the plate thickness

continuity statements and counterintuitive examples in connection with weyl quantization we use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart q f to derive continuity properties of the weyl transform from classes of distributions to classes of quadratic forms we also give examples of pathological behavior of the weyl transform with respect to other topologies e g bounded functions leading to unbounded operators

almost split sequences in subcategories let r be a commutative artin ring and let i be an r algebra which is a finitely generated r module in 5 auslander and reiten introduced the notion of an almost split sequence in mod a the category of finitely generated modules over a and the existence and uniqueness of such short exact sequences were established there the theory of almost split sequences developed further and similar results for certain subcategories of mod i were proved by bautista and martinez 8 and roggenkamp 9 the main purpose of this paper is to develop a more general theory for subcategories of mod i having almost split sequences which has the previous examples as special cases notions closely related to that of almost split sequences are those of minimal left and right almost split morphisms these notions were introduced in 61 for mod i and further developed in 7 for subcategories of mod ii this paper is based upon 7 and we therefore use the same notations and conventions as used there we now give some definitions and then proceed to describe the content of the paper section by section let c be a subcategory of mod ii then a morphism g b c in c is said to be a right almost split morphism in c if i g is not a splittable epimorphism and ii whenever there is a nonsplittable epimorphism h c c in c there exists an h c b such that gh h dually a morphismfi a f b in c is said to be left almost split if i f is not a splittable monomorphism and ii whenever there is a nonsplittable monomorphism h a a there exists an h b a such that h f h we say that c has right almost split morphisms if for all indecomposable objects

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

error analysis of a mixed finite element method for the cahn hilliard equation we propose and analyze a semi discrete and a fully discrete mixed finite element method for the cahn hilliard equation ut u 1f u 0 where 0 is a small parameter error estimates which are quasi optimal order in time and optimal order in space are shown for the proposed methods under minimum regularity assumptions on the initial data and the domain in particular it is shown that all error bounds depend on only in some lower polynomial order for small the cruxes of our analysis are to establish stability estimates for the discrete solutions to use a spectrum estimate result of alikakos and fusco 2 and chen 15 to prove a discrete counterpart of it for a linearized cahn hilliard operator to handle the nonlinear term on a stretched time grid the ideas and techniques developed in this paper also enable us to prove convergence of the fully discrete finite element solution to the solution of the hele shaw mullins sekerka problem as 0 in 29

stability analysis of large time stepping methods for epitaxial growth models numerical methods for solving the continuum model of the dynamics of the molecular beam epitaxy mbe require very large time simulation and therefore large time steps become necessary the main purpose of this work is to construct and analyze highly stable time discretizations which allow much larger time steps than those of a standard implicit explicit approach to this end an extra term which is consistent with the order of the time discretization is added to stabilize the numerical schemes then the stability properties of the resulting schemes are established rigorously numerical experiments are carried out to support the theoretical claims the proposed methods are also applied to simulate the mbe models with large solution times the power laws for the coarsening process are obtained and are compared with previously published results

a dyson like expansion for solutions to the quantum liouville equation given a hamiltonian of the form h h v the convergence of a dyson like expansion in is constructed and shown for the wigner distribution function that solves the quantum liouville equation that corresponds to h here h is a quadratic polynomial in p q its coefficients may depend continuously on time the potential v is a function of p and t as well as q roughly speaking it is the fourier transform of a time dependent measure

upper bound on the coarsening rate for an epitaxial growth model we study a specific example of energy driven coarsening in two space dimensions the energy is u 2 1 u 2 2 the evolution is the fourth order pde representing steepest descent this equation has been proposed as a model of epitaxial growth for systems with slope selection numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t1 3 and the energy per unit area decays like t 1 3 we prove a weak one sided version of the latter statement the time averaged energy per unit area decays no faster than t 1 3 our argument follows a strategy introduced by kohn and otto in the context of phase separation combining i a dissipation relation ii an isoperimetric inequality and iii an ode lemma the interpolation inequality is new and rather subtle our proof is by contradiction relying on recent compactness results for the aviles giga energy 2003 wiley periodicals inc

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

error analysis of a mixed finite element method for the molecular beam epitaxy model this paper investigates the error analysis of a mixed finite element method with crank nicolson time stepping for simulating the molecular beam epitaxy mbe model the fourth order differential equation of the mbe model is replaced by a system of equations consisting of one nonlinear parabolic equation and an elliptic equation then a mixed finite element method requiring only continuous elements is proposed to approximate the resulting system it is proved that the semidiscrete and fully discrete versions of the numerical schemes satisfy the nonlinearity energy stability property which is important in the numerical implementation moreover detailed analysis is provided to obtain the convergence rate numerical experiments are carried out to validate the theoretical results

optimal rate convergence analysis of a second order scheme for a thin film model with slope selection abstract in this paper an energy stable second order mixed finite element scheme is proposed and analyzed for the thin film epitaxial growth model with slope selection we employ second order backward differentiation formula bdf scheme with a second order stabilized term which guarantees the long time energy stability to approximate the continuous model in terms of the convergence analysis the key difficulty to derive an optimal rate spatial estimate is associated with the appearance of the gradient operator in the nonlinear terms which may lead to a loss of optimal accuracy order to overcome this well known difficulty we make use of some auxiliary techniques over triangular elements and obtain an optimal convergence rate o h q 1 t 2 in comparison with o h q t 2 rate from a standard projection estimate furthermore we use an efficient preconditioned steepest descent psd solver for the numerical implementation a few numerical examples are presented to validate the stability and convergence

features of moyal trajectories we study the moyal evolution of the canonical position and momentum variables we compare it with the classical evolution and show that contrary to what is commonly found in the literature the two dynamics do not coincide we prove that this divergence is quite general by studying hamiltonians of the form p2 2m v q several alternative formulations of moyal dynamics are then suggested we introduce the concept of star function and use it to reformulate the moyal equations in terms of a system of ordinary differential equations on the noncommutative moyal plane we then use this formulation to study the semiclassical expansion of moyal trajectories which is cast in terms of a order by order in recursive hierarchy of i first order partial differential equations as well as ii systems of first order ordinary differential equations the latter formulation is derived independently for analytic hamiltonians as well as for the more general case of locally integrable ones we present various examples i

a fourth order parabolic equation modeling epitaxial thin film growth abstract we study the continuum model for epitaxial thin film growth from phys d 132 1999 520 542 which is known to simulate experimentally observed dynamics very well we show existence uniqueness and regularity of solutions in an appropriate function space and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain in an investigation of asymptotical behavior we give a weak assumption under which the limit set of the dynamical system consists only of steady states in the one dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element the article closes with some illustrative numerical examples

a nonconforming finite element method for the two dimensional cahn hilliard equation the cahn hilliard equation is a nonlinear evolutionary equation that is fourth order in space in this paper a continuous in time finite element galerkin approximation is considered we use the nonconforming morley element and derive optimal order error bounds in l 2

irreversibility from staircases in symplectic embeddings abstract we present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of hamiltonian systems of many degrees of freedom we use recent flexibility and rigidity results of symplectic embeddings quantified via the stabilized fibonacci and pell staircases to encode the underlying breadth of the possible initial conditions which alongside the multitude of degrees of freedom of the underlying system give rise to time irreversibility

a mixed finite element method for thin film epitaxy we present a mixed finite element method for the thin film epitaxy problem comparing to the primal formulation which requires c 2 elements in the discretization the mixed formulation only needs to use c 1 elements by introducing proper dual variables the dual variable in our method is defined naturally from the nonlinear term in the equation and its accurate approximation will be essential for understanding the long time effect of the nonlinear term for time discretization we use a backward euler semi implicit scheme which involves a convex concave decomposition of the nonlinear term the scheme is proved to be unconditionally stable and its convergence rate is analyzed

the problem of moments in the phase space formulation of quantum mechanics long ago moyal proc cambridge philos soc 45 99 1949 formulated a moment problem in the context of the wigner weyl phase space formulation of quantum mechanics the problem amounts to giving necessary and sufficient conditions for a sequence of numbers to be moments of a wigner function in this paper that problem is solved and so is a truncated version of it

numerical analysis of a continuum model of phase transition a method for solution of the cahn hilliard equation is presented unlike previous work the discrete equations for the new method possess a lyapunov function this makes it possible to prove convergence of the approximate solutions without assumptions beyond those necessary for existence and uniqueness of the differential equation several consequences are explored

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

numerical approximation of mindlin reissner plates we consider a finite element approximation of the so called mindlin reissner formulation for moderately thick elastic plates we show that stability and optimal error bounds hold independently of the value of the thickness 1 introduction the so called mindlin reissner model for moderately thin plates is often used by engineers in connection with plate and shell problems it is well known that many numerical schemes for this model are satisfactory only when the thickness parameter t is not too small for a very small t some bad behavior such as the locking phenomenon might occur here we present a method which is uniformly good as t goes to zero and we prove optimal error estimates for transversal displacement rotations and shear stresses with constants independent of t

when are torsionless modules projective abstract in this paper we study the problem when a finitely generated torsionless module is projective let be an artinian local algebra with radical square zero then a finitely generated torsionless module m is projective if ext 1 m m 0 for a commutative artinian ring a finitely generated torsionless module m is projective if the following conditions are satisfied 1 ext i m 0 for i 1 2 3 and 2 ext i m m 0 for i 1 2 as a consequence of this result we have that for a commutative artinian ring a finitely generated gorenstein projective module is projective if and only if it is selforthogonal

mixed states with positive wigner functions the wigner distribution function of a pure quantum state is everywhere positive if and only if the state is coherent according to a result of hudson the characterization of mixed states with a positive wigner function is a special case of the problem of determining functions satisfying a twisted positive definiteness condition for a prescribed set of twisting parameters i e functions with given wigner spectrum in the sense of narcowich if a state is a convex combination of coherent states it has the property that the wigner spectrum contains the unit interval which in turn implies that the wigner function is positive it is shown by explicit examples that the converses of both implications are false the examples are taken from a low dimensional section of the state space in which all wigner spectra can be computed in this set counterexamples to a conjecture by narcowich concerning the wigner spectrum of products are also found as well as a state whose wigner spectrum is a convergent sequence of discrete points

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

distributions of ℏ positive type and applications states in classical mechanics are probability measures and their fourier transforms are continuous functions of positive type states in the phase space formulation of quantum mechanics are wigner distribution functions and their symplectic fourier transforms have been characterized by kastler commun math phys 1 14 1965 and loupias and miracle sole commun math phys 2 31 1966 ann insto h poincare 6 39 1967 as being continuous functions of positive type in this paper schwartz distributions of positive type are defined and studied it is shown that if such distributions are bounded on a certain sequence of test functions then they are symplectic fourier transforms of wigner distribution functions these results are applied to a variety of problems ranging from ones involving the quantum liouville equation to a problem in signal analysis

derivation and application of extended parabolic wave theories i the factorized helmholtz equation the reduced scalar helmholtz equation for a transversely inhomogeneous half space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial value plane defines a direct acoustic propagation model this elliptic formulation admits a factorization and is subsequently equivalent to a first order weyl pseudodifferential equation which is recognized as an extended parabolic propagation model perturbation treatments of the appropriate weyl composition equation result in a systematic development of approximate wave theories which extend the narrow angle weak inhomogeneity and weak gradient ordinary parabolic schrodinger approximation the analysis further provides for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic and seismic studies the wave theories foreshadow computational algorithms the inclusion of range dependent effects and the extension to 1 the vector formulation appropriate for elas

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem