algebras of quotients of jordan algebras abstract we define a jordan analogue of lambek and utumi s associative algebra of quotients and we construct the maximal algebra of quotients for nondegenerate jordan algebras we apply those results to other classes of algebras of quotients appearing in the literature

analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

nonlinear oblique boundary value problems for nonlinear elliptic equations on considere le probleme aux valeurs limites a derivee oblique non lineaire pour des equations uniformement elliptiques quasi lineaires et totalement non lineaires d ordre 2 les operateurs elliptiques satisfont des conditions de structure naturelle on donne des theoremes d existence pour les solutions

regularity of traveling periodic stratified water waves with vorticity abstract we prove real analyticity of all the streamlines including the free surface of a steady stratified flow of water over a flat bed in the absence of stagnation points with a holder continuous bernoulli function and a holder continuously differentiable density function furthermore we show that if the bernoulli function and the density function possess some gevrey regularity of index s then the stream function admits the same gevrey regularity throughout the fluid domain in particular if the gevrey index s equals to 1 then we obtain analyticity of the stream function the regularity results hold for three distinct physical regimes capillary capillary gravity and gravity water waves

on stratified steady periodic water waves with linear density distribution and stagnation points abstract we use bifurcation theory to construct small periodic gravity stratified water waves with density which depends linearly upon the pseudostream function as a special feature the density may also decrease with depth and the waves we obtain may posses two different critical layers with cat s eye vortices within the vortex the density of the fluid has an extremum at the stagnation point

steady periodic waves and formal stability for fixed depth rotational equatorial flows abstract in this paper we apply the bifurcation theory to study the steady two dimensional periodic equatorial water waves for the f plane approximation we consider the waves with vorticity which propagate with a specified fixed depth between the thermocline and the upper boundary of the centre layer moreover we present a functional j and its first variation corresponds to the exact equations in the transformed variables using the second variation of j we prove a formal stability result for the bifurcation inducing the laminar solution

on the pressure transfer function for solitary water waves with vorticity in this paper we analyse the role which the pressure function on the sea bed plays in determining solitary waves with vorticity we prove that the pressure function on the flat bed determines a unique real analytic solitary wave solution to the governing equations given a real analytic vorticity distribution in particular the pressure function on the flat bed prescribes a unique surface profile for the resulting solitary water wave

gevrey regularity of subelliptic monge ampere equations in the plane in this paper we establish the gevrey regularity of solutions for a class of degenerate monge ampere equations in the plane under the assumptions that one principal entry of the hessian is strictly positive and the coefficient of the equation is degenerate with appropriately finite type degeneracy we prove that the solution of the degenerate monge ampere equation will be smooth in gevrey classes

local orders in jordan algebras abstract making use of results on general algebras of quotients of jordan algebras we study a notion of local order based on the version for linear jordan algebras of the ideas of fountain and gould 14 as adapted to the jordan context by fernandez lopez and garcia rus in 7 in particular we characterize the set of lesieur croisot elements of a nondegenerate jordan algebra as those elements of the jordan algebra lying in the socle of its maximal algebra of quotients and apply this relationship to extend to quadratic jordan algebras the results of fernandez lopez and garcia rus on local orders in nondegenerate jordan algebras satisfying the descending chain condition on principal inner ideals and not containing ideals which are nonartinian quadratic factors

multiple eigenvalue bifurcation for fredholm operators on fait le point sur les resultats de bifurcation locale et globale et on considere la stabilite des branches de bifurcation

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

on the existence of extreme waves and the stokes conjecture with vorticity this is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity we show that for a certain class of vorticity functions a sequence of regular waves converges to an extreme wave with stagnation points at its crests we also show that for any vorticity function the profile of an extreme wave must have either a corner of 120 or a horizontal tangent at any stagnation point about which it is supposed symmetric moreover the profile necessarily has a corner of 120 if the vorticity is nonnegative near the free surface

particle trajectories beneath small amplitude shallow water waves in constant vorticity flows abstract we investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water s free surface within the framework of small amplitude waves we find the solutions of the nonlinear differential equations system which describes the particle motion in the considered case and we describe the possible particle trajectories depending on the relation between the initial data and the constant vorticity some particle trajectories are undulating curves to the right or to the left others are loops with forward drift or with backward drift others can follow some peculiar shapes

bernoulli free boundary problems in strip like domains and a property of permanent waves on water of finite depth we study weak solutions for a class of free boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth we show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions we also prove that in very general situations the free boundary is necessarily the graph of a function

unique determination of stratified steady water waves from pressure abstract consider a two dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed in this work we study how such a wave can be recovered from data consisting of the wave speed upstream and downstream density and velocity profile and the trace of the pressure on the bed in particular we prove that this data uniquely determines the wave both in the real analytic and sobolev regimes

exact solitary water waves with vorticity the solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field the main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity each solution has a supercritical parameter value and decays exponentially at infinity the proof is based on a generalized implicit function theorem of the nash moser type the first approximation to the surface profile is given by the kdv equation with a supercritical value of the surface tension coefficient a family of small amplitude solitary waves of depression with subcritical parameter values is constructed for an arbitrary vorticity

an algorithm for computing minimal bidirectional linear recurrence relations we consider the problem of computing a linear recurrence relation or equivalently a linear feedback shift register of minimum order for a finite sequence over a field with the additional requirement that not only the highest but also the lowest coefficient of the recurrence is nonzero such a recurrence relation can then be used to generate the sequence in both directions increasing or decreasing order of indices so we call it bidirectional if the field is finite a sequence is periodic if and only if it admits a bidirectional linear recurrence relation for solving the above problem we propose an algorithm similar to the berlekamp massey algorithm and prove its correctness we describe the set of all solutions to this problem and show that if a sequence admits more than one linear recurrence relation then it admits a bidirectional one we also prove some properties regarding the bidirectionality of the recurrences of the prefixes of the sequence

local well posedness and stability of peakons for a generalized dullin gottwald holm equation abstract we establish the local well posedness for a generalized dullin gottwald holm equation by using kato s theory furthermore the orbital stability of the peaked solitary waves is also proved

the second variation of the stream function energy of water waves with vorticity abstract we compute the second variation of the stream function energy of two dimensional steady free surface gravity water waves with vorticity in the stream function formulation we prove that for nonpositive vorticity the second variation of the stream function energy at extreme waves with stokes corner asymptotics cannot be nonnegative in any small neighbourhood of a given isolated stagnation point the particular form of our second variation suggests however the possibility that certain singularities in the case of nonzero vorticity might be constructible as minimizers of the stream function energy

the maximal symmetric ring of quotients abstract the maximal symmetric ring of quotients q r as defined by utumi is a symmetric version of the maximal ring of quotients of r for the most part we study this ring when r k g is a group algebra for example we show that if g is a free product of groups and if r k g is a domain then q r is usually equal to r on the other hand there are certainly groups for which q r is properly larger than r and we construct a number of such examples

a new formulation of the water wave problem for stokes waves of constant vorticity we consider steady symmetric gravity water waves on finite depth with constant vorticity and a monotone surface profile between crests and troughs the problem is transformed into one concerning the vertical velocity a representation formula for the stream function in terms of the surface and the vorticity is presented and we show that the surface can be determined from the vertical velocity

rings of quotients of incidence algebras and path algebras we compute the maximal right left symmetric rings of quotients of finite dimensional incidence and graph algebras we show that these rings of quotients are morita equivalent to incidence algebras and path algebras respectively with respect to simpler well determined partially ordered sets and finite quivers respectively

modulational instability in the whitham equation with surface tension and vorticity abstract we study modulational stability and instability in the whitham equation combining the dispersion relation of water waves and a nonlinearity of the shallow water equations and modified to permit the effects of surface tension and constant vorticity when the surface tension coefficient is large we show that a periodic traveling wave of sufficiently small amplitude is unstable to long wavelength perturbations if the wave number is greater than a critical value and stable otherwise similarly to the benjamin feir instability of gravity waves in the case of weak surface tension we find intervals of stable and unstable wave numbers whose boundaries are associated with the extremum of the group velocity the resonance between the first and second harmonics the resonance between long and short waves and a resonance between dispersion and the nonlinearity for each constant vorticity we show that a periodic traveling wave of sufficiently small amplitude is unstable if the wave number is greater than a critical value and stable otherwise moreover it can be made stable for a sufficiently large vorticity the results agree with those based upon numerical computations or formal multiple scale expansions to the physical problem

computing the symmetric ring of quotients abstract we discuss and compute the symmetric martindale ring of quotients for various classes of prime rings in particular we consider free algebras and group algebras

associative systems of left quotients abstract in this paper we construct the maximal left quotient system of every pair of modules in some generalized matrix rings these rings can be seen as 3 graded algebras or as superalgebras we show the relation among the three different notions of left quotients

algebras of quotients of nonsingular jordan algebras abstract we define a jordan analogue of johnson s associative algebra of quotients and study it under a suitable condition of nonsingularity of the jordan algebra which we call strong nonsingularity in particular we prove the existence and describe the maximal algebras of quotients of prime strongly nonsingular jordan algebras

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

upper bound on the slope of steady water waves with small adverse vorticity abstract we consider the angle of inclination with respect to the horizontal of the profile of a steady 2d inviscid symmetric periodic or solitary water wave subject to gravity there is an upper bound of 31 15 in the irrotational case 1 and an upper bound of 45 in the case of favorable vorticity 13 on the other hand if the vorticity is adverse the profile can become vertical we prove here that if the adverse vorticity is sufficiently small then the angle still has an upper bound which is slightly larger than 45

exact steady periodic water waves with vorticity we consider the classical water wave problem described by the euler equations with a free surface under the influence of gravity over a flat bottom we construct two dimensional inviscid periodic traveling waves with vorticity they are symmetric waves whose profiles are monotone between each crest and trough we use bifurcation and degree theory to construct a global connected set of such solutions c 2004 wiley periodicals inc

minimal polynomial algorithms for finite sequences in this paper we show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of an algorithm in a recent paper of a salagean