existence of solutions and boundary asymptotic behavior of p r laplacian equation multi point boundary value problems abstract this paper investigates the problem p r u r f r u 0 r 0 r u 0 i 1 m i u i e 0 u r as r r where p r u u p r 2 u is called the p r laplacian r is a singular coefficient the existence and nonexistence of solutions are discussed and the exact boundary blow up rate of solutions is given

on the profile of solutions with two sharp layers to a singularly perturbed semilinear dirichlet problem we discuss the existence of positive solutions of some singularity perturbed elliptic equations on convex domains with nonlinearity changing sign in particular we obtain solutions with both a boundary layer and a sharp interior peak

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

effects of a degeneracy in the competition model part i classical and generalized steady state solutions abstract we study the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of we show that there exists a critical number such that if then the model behaves similarly to the well studied classical competition model where all the coefficient functions are positive constants but when new phenomena occur our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative but can be qualitative as well in part i here we mainly study two kinds of steady state solutions which determine the dynamics of the model one consists of finite functions while the other consists of generalized functions which satisfy u v 0 on the part of the domain that b x vanishes but are positive and finite on the rest of the domain and are determined by certain boundary blow up systems the research is continued in part ii where these two kinds of steady state solutions will be used to determine the dynamics of the model

existence nonexistence and asymptotic behavior of boundary blow up solutions to p x laplacian problems with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u d i v u p x 2 u is called the p x laplacian and x is a singular coefficient the existence and nonexistence of boundary blow up solutions is discussed and the asymptotic behavior of boundary blow up solutions is given in particular we do not assume radial symmetric conditions and the pointwise different exact blow up rate of solutions has been discussed

singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series we distinguish between two dimensions of a dynamical system given by experimental time series statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe tje attractor up to the accuracy of the data taking into account sampling and noise problems the dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data singular spectrum analysis ssa provides estimates of the statistical dimension ssa also describes the main physical phenomena reflected by the data it gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data we apply ssa to four paleoclimatic records the principal climatic oscillations and the regime changes in their amplitude are detected about 10 degrees of freedom are statistically significant in the data large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension

exact multiplicity of positive solutions for a class of semilinear problem ii we consider the positive solutions to the semilinear problem u f u 0 in b n u 0 on b n where bn is the unit ball in rn n 1 and is a positive parameter it is well known that if is a smooth function then any positive solution to the equation is radially symmetric and all solutions can be parameterized by their maximum values we develop a unified approach to obtain the exact multiplicity of the positive solutions for a wide class of nonlinear functions u and the precise shape of the global bifurcation diagrams are rigorously proved our technique combines the bifurcation analysis stability analysis and topological methods we show that the shape of the bifurcation curve depends on the shape of the graph of function u u as well as the growth rale of

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

realization of prescribed patterns in the competition model we demonstrate that for any prescribed set of finitely many disjoint closed subdomains d1 dm of a given spatial domain in rn if d1 d2 a1 a2 c d e are positive continuous functions on and b x is identically zero on d d1 dm and positive in the rest of then for suitable choices of the parameters and all small e 0 the competition model ut x t d1 x u x t a1 x u e 1b x 1 u2 c x uv vt x t d2 x v x t a2 x v e x v2 e 1d x uv x t 0 under natural boundary conditions on possesses an asymptotically stable positive steady state solution ue ve that has pattern d that is roughly speaking as e 0 ue converges to a positive function over d while it converges to 0 over the rest of on the other hand ve converges to 0 over d but converges to some positive function in the rest of in other words the two competing species ue and ve become spatially segregated as e 0 with ue concentrating on d and ve concentrating on d

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

identification of linear time varying mdof dynamic systems from forced excitation using hilbert transform and emd method an algorithm is developed for the identification of linear time varying ltv multiple degrees of freedom systems it is based on the hilbert transform and the empirical mode decomposition with forced vibration response data the proposed identification algorithm is applied to single degree of freedom and multi degrees of freedom dynamic systems three ideal cases of ltv systems with smoothly varying abruptly varying and periodically varying stiffness and damping are studied to illustrate the capability of the algorithm to track the variations of the system simulation results demonstrate the effectiveness and the robustness of the proposed identification algorithm and the lack of complete orthogonality for any two intrinsic mode functions is one of the sources of error in the identification

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

study of boundary conditions in the iterative filtering method for the decomposition of nonstationary signals abstract nonstationary and non linear signals are ubiquitous in real life their decomposition and analysis is an important research topic of signal processing recently a new technique called iterative filtering has been developed with the goal of decomposing such signals into simple oscillatory components several papers have been devoted to the investigation of this technique from a mathematical point of view all these works start with the assumption that each compactly supported signal is extended periodically outside the boundaries in this work we tackle the problem of studying the influence of different boundary conditions on the decompositions produced by the iterative filtering method in particular the choice of boundary conditions gives rise to different types of structured matrices thus we describe their spectral properties and the convergence properties of iterative filtering algorithm when such matrices are involved numerical results on artificial and real life signals provide interesting insight on important aspects such as accuracy and error propagation of the proposed technique and pave the way for further promising developments

notes on the interpolation of discrete periodic signals using sinc function related approaches considering the sinc interpolation of discrete periodic signals this correspondence establishes the equivalence of two recently published methods furthermore the interpolation methods are equivalent to a fractional delay filter designed using the frequency sampling technique a numerically stable and computationally attractive form of the equivalent methods is presented

exact multiplicity for boundary blow up solutions abstract the singularly perturbed boundary blow up problem e 2 u u u a 1 u u 0 in b u on b is studied in the unit ball b r n n 2 a 1 2 1 is a constant it is shown that for e 0 sufficiently small there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions

on fourier interpolation error for band limited signals fourier interpolation is a useful tool to reconstruct continuous signals from discrete samples this correspondence derives fourier interpolation expression from fourier series for periodic signals and investigates its error expression and upper bound for general band limited signals two numerical examples are given to interpret the meaning of the formulas

sinc interpolation of discrete periodic signals the paper introduces a method for the sinc interpolation of discrete periodic signals the convolution of the sinc kernel with the infinite sequence of a periodic function is rewritten as a finite summation the method is equivalent to trigonometrical interpolation by fourier series expansion

the boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption in the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation u g x u 0 in a smooth domain n for a general class of positive nonlinearities this class includes every space independent monotone increasing g which satisfies the keller osserman condition as well as degenerate nonlinearities g q of the form g q x u d x u q 1u with 2 and q 1 the boundary trace is given by a positive regular borel measure which may blow up on compact sets in the second part we concentrate on the family of nonlinearities g q determine the critical value of the exponent q for fixed 2 and discuss a positive solutions with an isolated singularity for subcritical nonlinearities and b the boundary value problem for u g q x u 0 with boundary data given by a positive regular borel measure possibly unbounded we show that in the subcritical case the problem possesses a unique solution for every such measure 2003 wiley periodicals inc

a sampling theorem for non bandlimited signals using generalized sinc functions a ladder shaped filter of two real parameters a 1 a 2 1 1 is introduced in this note the impulse response of the corresponding linear time invariant lti system is a generalized sinc function of two parameters consequently a generalized shannon type sampling theorem is established for a class of non bandlimited signals with special spectrum properties associated with a ladder shaped filter of two parameters finally a mathematical characterization for the class of non bandlimited signals satisfying the generalized sampling theorem is offered these signals are restrictions to the real line of certain analytic functions in stripped domains symmetric about the real axis in the complex plane for these signals their spectra in higher frequency bands are measured by the spectrum of their base bands

structure of boundary blow up solutions for quasi linear elliptic problems ii small and intermediate solutions the structure of positive boundary blow up solutions to quasi linear elliptic problems of the form pu f u u on 1 0 in z1 z2 large small and intermediate solutions are obtained for sufficiently large it is known from part i see structure of boundary blow up solutions for quasilinear elliptic problems part i large and small solutions preprint that the large solution is the unique large solution to the problem we will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions our results are new even for the case p 2

exact multiplicity of positive solutions for a class of semilinear problems we establish an exact multiplicity result of positive solutions of u f u 0inbn u 0on bn wherebnis the unit ball fsatisfiesf changes sign only once and asymptotically sublinear or linear the nonlinearities which we are concerned with here includef u u u b c u for 0 2b candf u up uqfor 1 p q precise global bifurcation diagrams are obtained

unique prime factorization and bicentralizer problem for a class of type iii factors abstract we show that whenever m 1 and m 1 m m are nonamenable factors in a large class of von neumann algebras that we call c ao and which contains all free araki woods factors the tensor product factor m 1 m m retains the integer m and each factor m i up to stable isomorphism after permutation of the indices our approach unifies the unique prime factorization upf results from 33 25 and moreover provides new upf results in the case when m 1 m m are free araki woods factors in order to obtain the aforementioned upf results we show that connes s bicentralizer problem has a positive solution for all type i i i 1 factors in the class c ao

boundary blow up solutions with a spike layer abstract we prove that for large 0 the boundary blow up problem u u u a 1 u in u has a solution with a spike located near the most centered part of our proof is based on the reduction method and uses a cut off technique to avoid the difficulties for the estimates near the boundary of

arbitrary order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders in this paper we present an extended version of hilbert huang transform namely arbitrary order hilbert spectral analysis to characterize the scale invariant properties of a time series directly in an amplitude frequency space we first show numerically that due to a nonlinear distortion traditional methods require high order harmonic components to represent nonlinear processes except for the hilbert based method this will lead to an artificial energy flux from the low frequency large scale to the high frequency small scale part thus the power law if it exists is contaminated we then compare the hilbert method with structure functions sf detrended fluctuation analysis dfa and wavelet leader wl by analyzing fractional brownian motion and synthesized multifractal time series for the former simulation we find that all methods provide comparable results for the latter simulation we perform simulations with an intermittent parameter 0 15 we find that the sf underestimates scaling exponent when q 3 the hilbert method provides a slight underestimation when q 5 however both dfa and wl overestimate the scaling exponents when q 5 it seems that hilbert and dfa methods provide better singularity spectra than sf and wl we finally apply all methods to a passive scalar temperature data obtained from a jet experiment with a taylor s microscale reynolds number re 250 due to the presence of strong ramp cliff structures the sf fails to detect the power law behavior for the traditional method the ramp cliff structure causes a serious artificial energy flux from the low frequency large scale to the high frequency small scale part thus dfa and wl underestimate the scaling exponents however the hilbert method provides scaling exponents q quite close to the one for longitudinal velocity indicating a less intermittent passive scalar field than what was believed before 2011 american physical society

l 2 betti numbers of locally compact groups and their cross section equivalence relations we prove that the l betti numbers of a unimodular locally compact group g coincide up to a natural scaling constant with the l betti numbers of the countable equivalence relation induced on a cross section of any essentially free ergodic probability measure preserving action of g as a consequence we obtain that the reduced and un reduced l betti numbers of g agree and that the l betti numbers of a lattice in g equal those of g up to scaling by the covolume of in g we also deduce several vanishing results including the vanishing of the reduced l cohomology for amenable locally compact groups

rigidity for von neumann algebras given by locally compact groups and their crossed products we prove the first rigidity and classification theorems for crossed product von neumann algebras given by actions of non discrete locally compact groups we prove that for arbitrary free probability measure preserving actions of connected simple lie groups of real rank one the crossed product has a unique cartan subalgebra up to unitary conjugacy we then deduce a w strong rigidity theorem for irreducible actions of products of such groups more generally our results hold for products of locally compact groups that are nonamenable weakly amenable and that belong to ozawa s class mathcal s

detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition abstract in this paper we apply the empirical mode decomposition emd method to the recurrence plot rp and recurrence quantification analysis rqa to evaluate the frequency and time evolving dynamics of the traffic flow based on the cumulative intrinsic mode functions extracted by the emd the frequency evolving rp regarding different oscillation of modes suggests that apparent dynamics of the data considered are mainly dominated by its components of medium and low frequencies while severely affected by fast oscillated noises contained in the signal noises are then eliminated to analyze the intrinsic dynamics and consequently the denoised time evolving rqa diversely characterizes the properties of the signal and marks crucial points more accurately where white bands in the rp occur whereas a strongly qualitative agreement exists between all the non denoised rqa measures generally the emd combining with the recurrence analysis sheds more reliable abundant and inherent lights into the traffic flow which is meaningful to the empirical analysis of complex systems

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

exact multiplicity of boundary blow up solutions for a bistable problem we prove the exact multiplicity of positive boundary blow up solutions to a semilinear elliptic equation with bistable nonlinearity for the one dimensional case we use time mapping techniques to determine the exact shape of the bifurcation diagram

comments on sinc interpolation of discrete periodic signals in a recent paper by t schanze see ibid vol 43 p 1502 3 1995 the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation the expression obtained however is not numerically stable when evaluated at or near integer values of time this correspondence presents a numerically stable formulation that is equivalent to the results reported in the above cited paper and that when sampled is also shown to be equivalent to the inverse discrete fourier transform idft

a hybrid detrending method for fractional gaussian noise abstract determining trend and implementing detrending operations are important steps in data analysis yet there is neither precise definition of trend nor any logical algorithm for extracting it in this paper we propose a hybrid detrending method hdm which is based on the empirical mode decomposition emd and the detrended fluctuation analysis dfa our method can remove the polynomial and sinusoidal trends from the fractional gaussian noise fgn background we illustrate the method by selected examples from artificial time series and climate data in comparison with existing frequency domain based detrending methods our method is a posteriori the trend defined by our method is only derived from the data further our method also preserves the scaling behavior of the original signals

asymptotic behavior of large solution for boundary blowup problems with non linear gradient terms let email protected r n n 3 be a bounded domain with smooth boundary we show the asymptotic behavior of boundary blowup solutions to non linear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 f is c varying at our analysis is based on the karamata regular variation theory combined with the method of lower and supper solution

on the boundary blow up solutions of p x laplacian equations with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian x is a singular coefficient the existence and nonexistence of boundary blow up solutions are discussed and the singularity of the boundary blow up solution is given