on non archimedean recurrence equations and their applications in the present paper we study stability of recurrence equations which in particular case contain dynamics of rational functions generated by contractive functions defined on an arbitrary non archimedean algebra moreover multirecurrence equations are considered we also investigate reverse recurrence equations which have application in the study of p adic gibbs measures note that our results also provide the existence of unique solutions of nonlinear functional equations we should stress that the non archimedeanity of the algebra is essentially used therefore the methods applied in the present paper are not valid in the archimedean setting

stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

p adic quantum mechanics with p adic valued functions an extension of the formalism of quantum mechanics to the case where the canonical variables and functions are valued in a field of p adic numbers is considered a new p adic integral calculus is used for the realization of the gauss representation in p adic quantum mechanics

on a class of rational p adic dynamical systems in this paper we investigate the behavior of trajectories of one class of rational p adic dynamical systems in complex p adic field cp we studied siegel disks and attractors of such dynamical systems we found the basin of the attractor of the system it is proved that such dynamical systems are not ergodic on a unit sphere with respect to the haar measure

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

an asymptotic property of the camassa holm equation abstract asymptotic densities are used to study an asymptotic property of the dispersionless camassa holm equation an asymptotic density of a global solution is a weak limit of its scaled momentum density along a sequence of time increasing to infinity for a global solution with non negative compactly supported initial momentum density we show that if the asymptotic density is unique then it is a positive combination of dirac measures supported in a bounded interval in the non negative axis with zero as the only possible accumulation point in other words if the scaled momentum density does not oscillate as time goes to infinity the solution behaves as a combination of peakons moving to the right at different speeds in contrast to many investigations on the topic our approach is not spectral theoretic and hence is independent of the structure of the isospectral problem associated with the equation

fast rcs computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique the method of moments mom in conjunction with the asymptotic waveform evaluation awe technique is applied to obtain the radar cross section rcs of an arbitrarily shaped three dimensional 3 d perfect electric conductor pec body over a frequency band the electric field integral equation efie is solved using the mom to obtain the equivalent surface current on the pec body in the awe technique the equivalent surface current is expanded in a taylor s series around a frequency in the desired frequency band the taylor series coefficients are then matched via the pade approximation to a rational function using the rational function the surface current is obtained at any frequency within the frequency range which is in turn used to calculate the rcs of the 3 d pec body a rational function approximation is also obtained using the model based parameter estimation mbpe method and compared with the pade approximation numerical results for a square plate a cube and a sphere are presented over a frequency bandwidth good agreement between the awe and the exact solution over the bandwidth is observed

well conditioned asymptotic waveform evaluation for finite elements the frequency domain finite element method fem results in matrix equations that have polynomial dependence on the frequency of excitation for a wide band fast frequency sweep technique based on a moment matching model order reduction more process researchers generally take one of two approaches the first is to linearize the polynomial dependence which will either limit the bandwidth of accuracy or require the introduction of extra degrees of freedom and then use a well conditioned krylov subspace technique the second approach is to work directly with the polynomial matrix equation and use one of the available but ill conditioned asymptotic waveform evaluation awe methods for large scale fem simulations introducing extra degrees of freedom and therefore increasing the length of the more vectors and the amount of memory required is not desirable therefore the first approach is not alluring on the other hand an ill conditioned awe process is unattractive this paper presents a novel more technique for polynomial matrix equations that circumvents these problematic issues first this novel process does not require any additional unknowns second this process is well conditioned along with the presentation of the novel algorithm which is called well conditioned awe wcawe numerical examples modeled using the fem are given to illustrate its accuracy

long time behaviour for a class of low regularity solutions of the camassa holm equation in this paper we investigate the long time behaviour for a class of low regularity solutions of the camasssa holm equation given by the superposition of infinitely many interacting traveling waves with corners at their peaks

multipeakons and the classical moment problem abstract classical results of stieltjes are used to obtain explicit formulas for the peakon antipeakon solutions of the camassa holm equation the closed form solution is expressed in terms of the orthogonal polynomials of the related classical moment problem it is shown that collisions occur only in peakon antipeakon pairs and the details of the collisions are analyzed using results from the moment problem a sharp result on the steepening of the slope at the time of collision is given asymptotic formulas are given and the scattering shifts are calculated explicitly

geometric location of periodic points of 2 ramified power series abstract in this paper we study the geometric location of periodic points of power series defined over fields of positive characteristic p we find a lower bound for the norm of all nonzero periodic points in the open unit disk of 2 ramified power series we prove that this bound is optimal for a large class of power series our main technical result is a computation of the first significant terms of p power iterates of 2 ramified power series as a by product we obtain a self contained proof of the characterization of 2 ramified power series

fredholm determinants and the camassa holm hierarchy the equation of camassa and holm 2 2 is an approximate description of long waves in shallow water

persistence properties and unique continuation of solutions of the camassa holm equation it is shown that a strong solution of the camassa holm equation initially decaying exponentially together with its spacial derivative must be identically equal to zero if it also decays exponentially at a later time in particular a strong solution of the cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution

on p adic bounded functions ii in this paper besides the definition of maximal operators over the p adic number field using the properties of section 1 we can define p adic bounded mean oscillation space and obtain its examples we prove sufficient conditions of boundedness of maximal operators over the p adic number field

poisson brackets as the adelic limit of quantum commutators we show that the adelic limit of the quantum commutator between operators gives a suitable generalization of the poisson bracket on p adic phase space

quantum mechanics on p adic numbers a quantum system with positions in and momenta in is studied displacement operators in the phase space of this system and the corresponding heisenberg weyl group are studied it is shown that such a system can be constructed from a semi infinite chain of spins which are coupled in a particular way

efficient wideband electromagnetic scattering computation for frequency dependent lossy dielectrics using wcawe this paper presents a model order reduction algorithm for the volume electric field integral equation efie formulation that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering an inhomogeneous two dimensional lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered the variation in the dielectric properties of the ceramic baxla4ti 2 xo 12 3x in the 1 ghz frequency range is investigated for various values of x in a frequency sweep analysis we apply the well conditioned asymptotic waveform evaluation wcawe method to circumvent the computational complexity associated with the numerical solution of such formulations a multipoint automatic wcawe method is also demonstrated which can produce an accurate solution over a much broader bandwidth several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods

p adic dynamics the quadratic map overp adic numbers is studied in some detail we prove that near almost all indifferent fixed points it is topologically conjugate to a quasiperiodic linear map we also establish the existence of chaotic behavior and describe it using symbolic dynamics

application of asymptotic waveform evaluation to hybrid fe bi mlfma for fast rcs computation over a frequency band the asymptotic waveform evaluation awe technique has been widely used in the method of moment mom the finite element method fem and the hybrid finite element boundary integral method fe bi for fast computation over a wide frequency band however how to apply awe to the multilevel fast multipole algorithm mlfma still remains challenge this paper proposes an efficient and robust approach to apply awe to the hybrid finite element boundary integral multilevel fast multipole algorithm fe bi mlfma the validity of the proposed approach is verified by numerical examples for scattering problems numerical experiments show that the application of awe to fe bi mlfma can greatly improve the efficiency of fe bi mlfma for computation of scattering over a wide frequency band

p adic 2 1 rational dynamical systems abstract we study the dynamics of an arbitrary 2 1 rational function f x x 2 a x b c x d on the field c p of complex p adic numbers we show that the p adic dynamical system generated by f has a very rich behavior siegel disks may either coincide or be disjoint for different fixed points of the dynamical system also we find the basin of the attractor of the system varying the parameters it is proven that there are periodic trajectories for some values of the parameters there are trajectories which go arbitrary far from fixed points

periodic p adic gibbs measures of q state potts model on cayley trees i the chaos implies the vastness of the set of p adic gibbs measures we study the set of p adic gibbs measures of the q state potts model on the cayley tree of order three we prove the vastness of the set of the periodic p adic gibbs measures for such model by showing the chaotic behavior of the corresponding potts bethe mapping over mathbb q p for the prime numbers p equiv 1 mathrm mod 3 in fact for 0 theta 1 p q p 2 1 where theta exp p j and j is a coupling constant there exists a subsystem that is isometrically conjugate to the full shift on three symbols meanwhile for 0 q p 2 le theta 1 p q p 1 there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r ge 4 however these subshifts on r symbols are all topologically conjugate to the full shift on three symbols the p adic gibbs measures of the same model for the prime numbers p 2 3 and the corresponding potts bethe mapping are also discussed on the other hand for 0 theta 1 p q p 1 we remark that the potts bethe mapping is not chaotic when p 3 and p equiv 2 mathrm mod 3 and we could not conclude the vastness of the set of the periodic p adic gibbs measures in a forthcoming paper with the same title we will treat the case 0 q p le theta 1 p 1 for all prime numbers p

on the chaotic behavior of a generalized logistic p adic dynamical system abstract in the paper we describe basin of attraction p adic dynamical system g x a x 2 x 1 moreover we also describe the siegel discs of the system since the structure of the orbits of the system is related to the geometry of the p adic siegel discs

on minimal decomposition of p adic polynomial dynamical systems abstract a polynomial of degree 2 with coefficients in the ring of p adic numbers z p is studied as a dynamical system on z p it is proved that the dynamical behavior of such a system is totally described by its minimal subsystems for an arbitrary quadratic polynomial on z 2 we exhibit all its minimal subsystems

analysis on the p adic superspace i generalized functions gaussian distribution the theory of generalized functions on the p adic superspace qn mp over the super commutative banach superalgebra 0 1 with the trivial 1 annihilator is proposed the p adic gaussian supermeasure is defined as a generalized function on the p adic superspace the connection between the p adic gaussian integration and the p adic gamma function of morita is considered

mom matrix generation based on frequency and material independent reactions fmir mom a novel and efficient method of moments mom matrix generation technique called the frequency and material independent reactions for the method of moments fmir mom technique is presented this new matrix generation algorithm efficiently calculates impedance matrices while sweeping through frequency permittivity conductivity and or permeability values for frequency sweeps it has computational and memory costs comparable to those of interpolation techniques it has the advantage over interpolation techniques in that it does not divide the frequency range into segments and allows one to dynamically update the precision the technique expands the exponential of the green s function into a taylor series this allows the problem to be formulated as a summation where each term consists of a real valued matrix depending only on the geometry discretization multiplied by a scalar dependent on the propagation constant the algorithm s efficiency is obtained by calculating the geometry dependent matrices prior to sweeping through frequency or material parameters

large time behavior for vortex evolution in the half plane in this article we study the long time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering our main result is that certain asymptotic states for half plane vortex dynamics decompose naturally into a nonlinear superposition of soliton like states our approach is to combine techniques developed in the study of vortex confinement with weak convergence tools in order to study the asymptotic behavior of a self similar rescaling of a solution of the incompressible 2d euler equations on a half plane with compactly supported nonnegative initial vorticity

p adic models of ultrametric diffusion constrained by hierarchical energy landscapes we demonstrate that the p adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes a general analytical description in terms of the p adic analysis is given for a class of models two exactly solvable examples i e the ultrametric diffusion constrained by the linear energy landscape and the ultrametric diffusion with a reaction sink are considered we show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding

p adic superanalysis i infinitely generated banach superalgebras and algebraic groups a sequence of infinitely generated p adic banach superalgebras and their locally convex projective and inductive limits were constructed their spectral properties are characterized herein and by studying the algebras of matrices constructed with these superalgebras an exponential map and its inverse can be defined some examples of superalgebra with pathological spectral properties are discussed

on p adic λ model on the cayley tree we consider a nearest neighbor p adic model with spin values 1 on the cayley tree of order k 1 we prove that a p adic gibbs measure is unique for p 3 if p 2 then we find a condition which guarantees uniqueness of p adic gibbs measure besides the results are applied to the p adic ising model

p adic commutation relations representations of the canonical and deformed commutation relations by bounded operators on p adic banach spaces are constructed functions from the mahler basis of the space of p adic continuous functions and their multiplicative analogues are shown to be the p adic counterparts of the hermite and q hermite functions the analogue of the stone von neumann uniqueness theorem fails in the p adic case

evolutions of the momentum density deformation tensor and the nonlocal term of the camassa holm equation abstract methods originally developed to study the finite time blow up problem of the regular solutions of the three dimensional incompressible euler equations are used to investigate the regular solutions of the camassa holm equation we obtain results on the relative behaviors of the momentum density the deformation tensor and the nonlocal term along the trajectories in terms of these behaviors we get new types of asymptotic properties of global solutions blow up criterion and blow up time estimate for local solutions more precisely certain ratios of the quantities are shown to be vaguely monotonic along the trajectories of global solutions finite time blow up of the accumulated momentum density is necessary and sufficient for the finite time blow up of the solution an upper estimate of the blow up time and a blow up criterion are given in terms of the initial short time trajectorial behaviors of the deformation tensor and the nonlocal term

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

genesis of solitons arising from individual flows of the camassa holm hierarchy the present work offers a detailed account of the large time development of the velocity profile run by a single individual hamiltonian flow of the camassa holm ch hierarchy the hamiltonian employed being the reciprocal of any eigenvalue of the underlying spectral problem in this simpler scenario i prove some of the conjectures raised by mckean 27 notably i confirm the ultimate shaping into solitons of the cusps that appear near blowup sites of any velocity profile emanating from an initial disposition for which breakdown of the wave in finite time is sure to happen the careful large time asymptotic analysis is carried from exact expressions describing the velocity in terms of initial data the integration involving a lagrangian scale and three theta functions the rates at which the latter reach their common values at each end of the line characterizing the region where soliton genesis is expected in fact the present method also suggests how solitons may arise from initial conditions not leading to breakdown the full ch flow is nothing but a superposition of such commuting individual actions therein lies the hope that the present account will pave the way to elucidate soliton formation for more complex flows in particular for the ch flow itself 2005 wiley periodicals inc

strict ergodicity of affine p adic dynamical systems on zp abstract let p 2 be a prime number and let z p be the ring of all p adic integers for all z z p define t z z it is shown that the dynamical system z p t is minimal if and only if 1 p r p z p and is a unit here r p 1 respectively r p 2 if p 3 respectively if p 2 and that when it is minimal it is strictly ergodic and topologically conjugate to z p t 1 1 with an analytic and isometric conjugacy more importantly when the system is not minimal we find all its strictly ergodic components as application monomial systems s n z z n on the group 1 p z p are also discussed

singular solutions of a modified two component camassa holm equation the camassa holm ch equation is a well known integrable equation describing the velocity dynamics of shallow water waves this equation exhibits spontaneous emergence of singular solutions peakons from smooth initial conditions the ch equation has been recently extended to a two component integrable system ch2 which includes both velocity and density variables in the dynamics although possessing peakon solutions in the velocity the ch2 equation does not admit singular solutions in the density profile we modify the ch2 system to allow a dependence on the average density as well as the pointwise density the modified ch2 system mch2 does admit peakon solutions in the velocity and average density we analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially confined initial data numerical results for the mch2 system are given and compared with the pure ch2 case these numerics show that the modification in the mch2 system to introduce the average density has little short time effect on the emergent dynamical properties however an analytical and numerical study of pairwise peakon interactions for the mch2 system shows a different asymptotic feature namely besides the expected soliton scattering behavior seen in overtaking and head on peakon collisions the mch2 system also allows the phase shift of the peakon collision to diverge in certain parameter regimes

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

on the isospectral problem of the dispersionless camassa holm equation abstract we discuss direct and inverse spectral theory for the isospectral problem of the dispersionless camassa holm equation where the weight is allowed to be a finite signed measure in particular we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite the results are applied to deduce several facts for the dispersionless camassa holm equation in particular we show that initial conditions with integrable momentum asymptotically split into a sum of peakons as conjectured by mckean

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

large time behavior of entropy solutions of conservation laws abstract we are concerned with the large time behavior of discontinuous entropy solutions for hyperbolic systems of conservation laws we present two analytical approaches and explore their applications to the asymptotic problems for discontinuous entropy solutions these approaches allow the solutions of arbitrarily large oscillation without a priori assumption on the ways from which the solutions come the relation between the large time behavior of entropy solutions and the uniqueness of riemann solutions leads to an extensive study of the uniqueness problem we use a direct method to show the large time behavior of large l solutions for a class of m m systems including a model in multicomponent chromatography we employ the uniqueness of riemann solutions and the convergence of self similar scaling sequence of solutions to show the asymptotic behavior of large bv solutions for the 3 3 system of euler equations in thermoelasticity these results indicate that the riemann solution is the unique attractor of large discontinuous entropy solutions whose initial data are l l 1 or bv l 1 perturbation of the riemann data for these systems these approaches also work for proving the large time behavior of approximate solutions to hyperbolic conservation laws

functional equations in a p adic context abstract recently in the complex context several results were obtained concerning functional equations of the form p f q g where p and q are polynomials of only two or three terms whose coefficients are small functions in certain cases the equation does not admit any pair of admissible solutions and in other cases it only admits pairs of solutions that are of a very particular type here we consider similar questions when the ground field is a p adic complete algebraically closed field of characteristic 0 and we derive results that are often analogous for instance if f n a 1 f n m b 1 c g n a 2 g n m b 2 with a i b j small functions with regard to f g and a 2 b 2 non identically 0 then c b 1 b 2 and f h g with h m a 1 a 2 however contrary to the complex context here results apply not only to meromorphic functions defined in the whole field but also to unbounded meromorphic functions defined inside an open disc the main tool is the p adic nevanlinna theory

on metric properties of limit sets of contractive analytic non archimedean dynamical systems abstract let k be an algebraically closed field which is complete with respect to a non trivial non archimedean absolute value we study metric properties of the limit set of a semigroup g generated by a finite set of contractive analytic functions on o z k z 1 we prove that the limit set of g is uniformly perfect if the derivative of each generating function of g does not vanish on o furthermore we show that if each coefficient of the generating functions is in the field q p of p adic numbers or the limit set satisfies the strong open set condition then has the doubling property this yields that the limit set is quasisymmetrically equivalent to the space z 2 of 2 adic integers we also give a counterexample to show that not all limit sets have the doubling property the berkovich space is introduced to study the limit set and we prove that the limit set has a positive capacity in the berkovich space which yields that there exists an equilibrium measure whose support is contained in the limit set we also show that if the semigroup is generated by a countable set of contractive analytic functions then its limit set can be non compact however if coefficients of the generating functions lie in q p then the limit set is compact

on uniqueness of gibbs measure for p adic countable state potts model on the cayley tree abstract in the present paper we consider countable state of p adic potts model on the tree under some condition on weights we establish uniqueness of gibbs measures for the model note that this condition does not depend on values of the prime p an analogous fact is not true when the number of spins is finite

multipoint galerkin asymptotic waveform evaluation for model order reduction of frequency domain fem electromagnetic radiation problems in this paper a model order reduction technique is presented this technique known as galerkin asymptotic waveform evaluation gawe or multipoint galerkin asymptotic waveform evaluation mgawe if multiple expansion points are considered simultaneously can be used to reduce matrices describing electromagnetic em phenomena generated through the finite element method fem to a smaller space while still accurately approximating the characteristics of the original responses the resulting solution procedure of using gawe or mgawe to solve fem equations allows for wideband frequency simulations with a reduction in total computation time numerical simulations using these methods are shown along with traditional methods such as using an lu decomposition at each frequency point of interest and asymptotic waveform evaluation awe comparisons in accuracy as well as computation time are also given

nonlocality as well as rejection of realism are only sufficient but non necessary conditions for violation of bell s inequality in this review we remind the viewpoint that violation of bell s inequality might be interpreted not only as an evidence of the alternative either nonlocality or death of reality under the assumption the quantum mechanics is incomplete violation of bell s type inequalities is a well known sufficient condition of probabilistic incompatibility of random variables impossibility to realize them on a single probability space thus in fact we should take into account an additional interpretation of violation of bell s inequality a few pairs of random variables two dimensional vector variables involved in the epr bohm experiment are incompatible they could not be realized on a single kolmogorov probability space thus one can choose between a completeness of quantum mechanics b nonlocality c death of reality d non kolmogorovness in any event violation of bell s inequality has a variety of possible interpretations hence it could not be used to obtain the definite conclusion on the relation between quantum and classical models

p adic probability distributions of hidden variables abstract during the last years large interest was shown in p adic quantum models especially in string theory as usual new physical models generate new mathematical methods in our case a new type of stochastics p adic stochastics was arisen inside p adic quantum physics we apply this stochastics to propose a justification of the einstein podolsky rosen theory of hidden variables which was in large contradiction with the bell type inequality our main result is the following if we consider a p adic probability distribution of hidden variables then there are no problems with bell s inequality