stability in a semilinear boundary value problem via invariant conefields abstract we give a geometric proof of stability for spatially nonhomogeneous equilibria in the singular perturbation problem u t e 2 u xx f x u t r 1 u 1 with the neumann boundary conditions on x 0 1 the nonlinearity is of the form f x u 1 u 2 u c x where c x is merely continuous with a finite number of zeros the strength of the method is in dealing with non transversal zeros of c the case escaping the existing techniques of singular perturbations the approach is also used for showing existence of unstable equilibria with one transition layer

estimation of amplitude and phase parameters of multicomponent signals this paper considers the problem of estimating signals consisting of one or more components of the form a t e sup j spl phi t where the amplitude and phase functions are represented by a linear parametric model the cramer rao bound crb on the accuracy of estimating the phase and amplitude parameters is derived by analyzing the crb for the single component case if is shown that the estimation of the amplitude and the phase are decoupled numerical evaluation of the crb provides further insight into the dependence of estimation accuracy on signal to noise ratio snr and the frequency separation of the signal components a maximum likelihood algorithm for estimating the phase and amplitude parameters is also presented its performance is illustrated by monte carlo simulations and its statistical efficiency is verified

a class of nonlinear problems with perturbation both in boundary and interior points under appropriate conditions using the boundary perturbation theory and the technique of differential inequalities a class of nonlinear singularly perturbed problems with perturbation not only arising in the equation but also arising in interior points and boundary points is considered the existence of solution is proved by improving the structure of auxiliary functions in the literature the uniformly valid asymptotic expansion of the solution and its derivation for arbitrary order are obtained the conclusion in this paper richens and improves some early results

multiple internal layer solutions generated by spatially oscillatory perturbations abstract for a singularly perturbed system of reaction diffusion equations we study the bifurcation of internal layer solutions due to the addition of a spatially oscillatory term in the singular limit the existence and stability of internal layer solutions are determined by the intersection of a fast jump surface 1 and a slow switching curve c the case when the intersection is transverse was studied by x b lin construction and asymptotic stability of structurally stable internal layer solutions preprint in this paper we show that when 1 intersects with c tangentially saddle node or cusp type bifurcation may occur higher order expansions of internal layer solutions and eigenvalue eigenfunctions are also presented to find a true internal layer solution and true eigenvalue eigenfunctions we use a newton s method in functions spaces that is suitable for numerical computations

harmonics in gaussian multiplicative and additive noise cramer rao bounds the concern here is retrieval of single and multiple tone harmonics observed in white gaussian multiplicative and additive noise computable cramer rao bound crb expressions are derived on the frequency and phase estimates as well as on the sample mean or variance of the multiplicative noise processes the zero and nonzero mean multiplicative noise cases are addressed separately and are shown to yield distinct crbs on the frequency and phase estimates tight lower and upper bounds on the crbs themselves are developed which relative to the crbs are intuitively more appealing and easier to implement well established formulas on the achievable accuracy for estimates of constant amplitude harmonics turn put to be special cases of our results numerical studies support our claims

phase transition layers with boundary intersection for an inhomogeneous allen cahn equation abstract we consider the nonlinear problem of inhomogeneous allen cahn equation 2 u v y u 1 u 2 0 in u 0 on where is a bounded domain in r 2 with smooth boundary is a small positive parameter denotes the unit outward normal of v is a positive smooth function on let be a curve intersecting orthogonally with at exactly two points and dividing into two parts moreover satisfies stationary and non degenerate conditions with respect to the functional v 1 2 we can prove that there exists a solution u such that as 0 u approaches 1 in one part of while tends to 1 in the other part except a small neighborhood of

paths and trails in edge colored graphs this paper deals with the existence and search for properly edge colored paths trails between two not necessarily distinct vertices s and t in an edge colored graph from an algorithmic perspective first we show that several versions of the s t path trail problem have polynomial solutions including the shortest path trail case we give polynomial algorithms for finding a longest properly edge colored path trail between s and t for a particular class of graphs and characterize edge colored graphs without properly edge colored closed trails next we prove that deciding whether there exist k pairwise vertex edge disjoint properly edge colored s t paths trails in a c edge colored graph g c is np complete even for k 2 and c w n 2 where n denotes the number of vertices in g c moreover we prove that these problems remain np complete for c edge colored graphs containing no properly edge colored cycles and c w n we obtain some approximation results for those maximization problems together with polynomial results for some particular classes of edge colored graphs

bi criteria and approximation algorithms for restricted matchings abstract in this work we study approximation algorithms for the restricted matching problem which is defined as follows given a graph in which each edge e has a color c e and a profit p e q we want to compute a maximum cardinality or profit matching in which no more than w j z edges of color c j are present this kind of problems beside the theoretical interest on its own right emerges in multi fiber optical networking systems where we interpret each unique wavelength that can travel through the fiber as a color class and we would like to establish communication between pairs of systems we study approximation and bi criteria algorithms for this problem which are based on linear programming techniques and in particular on polyhedral characterizations of the natural linear formulation of the problem in our setting we allow violations of the bounds w j and we can model our problem as a bi criteria problem we have two objectives that we want to optimize namely a to maximize the profit maximum matching while b minimizing the violation of the color bounds we prove how we can beat the integrality gap of the natural linear programming formulation of the problem by allowing only a slight violation of the color bounds in particular our main result is constant approximation bounds for both criteria of the corresponding bi criteria optimization problem

interfaces in some elliptic nonlinear boundary value problems on riemannian manifolds necessary condition and location we show that the equal area condition is a necessary hypothesis for the existence of layered solutions to a nonlinear boundary value problem depending on a positive real parameter on a riemannian manifold with or without boundary as an application we give examples where the results can be used in order to determine in advance the location of possible limiting interface as the parameter goes to zero

on the role of diffusivity in some stable equilibria of a diffusion equation our main goal in this work is to exhibit a class of diffusivity functionswhich regardless of the shape of 0 allows for the existence of patternsfor p by considering p as a singularly perturbed problem where the dif fusivity is given by k x a small positive parameter the existence of pat terns which develop boundary transition layers and spikes was studied in n1 the case in which these patterns develop internal transition layerswas studied for a more general equation in n2 using an approach basedon 1 convergence see also n3 n4 problem p was considered in m for the case in which k is a constantfunction therein the author resorted to the shape of 0 to produce pat terns therefore the geometric structure of the patterns found here is dif ferent from the geometric structure of the ones found in m actually the technique we use here stems from the one presented in m where after finding a invariant set for the flow the monotonicity propertyof the flow as well as property s see m p 431 which is based onzorn s lemma were used our approach is different since after finding an invariant set we only usebasic results for the flow and variational techniques to show existence of alocal minimiser of the energy functional in this invariant set this localminimiser turns out to be a stable stationary solution to p the very same analysis still go through for the case in which the trivialequilibrium solutions a and b are positive i e 0 a b and the reactionterm is replaced by a spatially inhomogeneous term s x f v where s x isa positive continuous function problem p appears as a mathematical model in many distinct areasand just for the sake of illustration as well as interpreting the results froma physical point of view let us suppose that v models the time evolutionof the concentration of a diffusing substance in a medium whose diffusivityis given by k x x 0 and under the effect of a source term f when0 a b then typically as far as the existence of patterns in higher space dimen sion is concerned the diffusivity is small on a closed surface s 0 but thisis not sufficient and another condition on the behavior of k x has to beimposed in n2 n4 this condition relates the slope and concavity of k x alongthe normal to s to the gaussian and mean curvatures of s herein as longas the areas of the negative and positive bumps of f are the same theequal area condition it is only required that k x be large on two smootharbitrary sets o

a genetic based framework for solving multi criteria weighted matching problems abstract the purpose of this paper is to present a flexible genetic based framework for solving the multi criteria weighted matching problem mc wmp in the first part of this paper we design a genetic based framework for solving the ordinary weighted matching problem we present an extensive analysis of the quality of the results and introduce a methodology for tuning its parameters in the second part we develop a modified genetic based algorithm for solving the mc wmp the algorithm generates a significant and representative portion of the pareto optimal set to assess the performance of the algorithm we conduct computational experiments with two and three criteria the potential of the proposed algorithm is demonstrated by comparing to a multi objective simulated annealing algorithm

paths and trails in edge colored weighted graphs abstract let g c w be an edge colored weighted graph where g is a nontrivial connected graph c is an edge coloring of g and w is an edge weighting of g a path a trail a cycle or a closed trail of g say f is called proper under the edge coloring c if every two consecutive edges of f receive different colors in c let s and t be two specified nonadjacent vertices in g in this paper we study the problems for finding in g c w the minimum weighted proper s t path the minimum weighted proper s t trail the minimum weighted proper cycle the minimum weighted proper closed trail the maximum weighted proper s t path and the maximum weighted proper s t trail when the minimization problems are considered we assume that g c w has no negative proper cycle and when the maximization problems are considered we assume that g c w has no proper closed trail we show that all these problems are solvable in polynomial time

fully dynamic maximal matching in o log n update time we present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges our algorithm is randomized and it takes expected amortized o log n time for each edge update where n is the number of vertices in the graph while there exists a trivial o n time algorithm for each edge update the previous best known result for this problem is due to ivkovic and lloyd lecture notes in comput sci 790 springer verlag london 1994 pp 99 111 for a graph with n vertices and m edges they gave an o n m 0 7072 update time algorithm which is sublinear only for a sparse graph for the related problem of maximum matching onak and rubinfeld proceedings of stoc 10 cambridge ma 2010 pp 457 464 designed a randomized algorithm that achieves expected amortized o log 2 n time for each update for maintaining a c approximate maximum matching for some unspecified large constant c in contrast we can maintain a factor 2 approximate maximum matching in expected amortized o log n time per update as a direct corollary of the maximal matching scheme this in turn also implies a 2 approximate vertex cover maintenance scheme that takes expected amortized o log n time per update

approximating binary images from discrete x rays we study the problem of approximating binary images that are accessible only through few evaluations of their discrete x ray transform i e through their projections counted with multiplicity along some lines this inverse discrete problem belongs to a class of generalized set partitioning problems and allows natural packing and covering relaxations for these mathbb np hard optimization problems we present various approximation algorithms and provide estimates for their worst case performance further we report on computational results for various variants of these algorithms in particular the corresponding integer programs are solved with only small absolute error for instances up to 250 000 binary variables

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

a shortest path algorithm for real weighted undirected graphs we present a new scheme for computing shortest paths on real weighted undirected graphs in the fundamental comparison addition model in an efficient preprocessing phase our algorithm creates a linear size structure that facilitates single source shortest path computations in o m log alpha time where alpha alpha m n is the very slowly growing inverse ackermann function m the number of edges and n the number of vertices as special cases our algorithm implies new bounds on both the all pairs and single source shortest paths problems we solve the all pairs problem in o mn log alpha m n time and if the ratio between the maximum and minimum edge lengths is bounded by n log n o 1 we can solve the single source problem in o m n log log n time both these results are theoretical improvements over dijkstra s algorithm which was the previous best for real weighted undirected graphs our algorithm takes the hierarchy based approach invented by thorup

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

bounds for estimation of multicomponent signals with random amplitude and deterministic phase we study a class of nonstationary multicomponent signals where each component has the form a t exp j spl phi t where a t is a random amplitude function and spl phi t is a deterministic phase function the amplitude function consists of a stationary gaussian process and a time varying mean the phase and the amplitude mean are characterized by a linear parametric model while the covariance of the amplitude function is parameterized in some general manner this model encompasses signals that are commonly used in communications radar sonar and other engineering systems we derive the cramer rao bound crb for the estimates of the amplitude and phase parameters and of functions of these parameters such as the instantaneous frequencies of the signal components

solutions with transition layer and spike in an inhomogeneous phase transition model abstract we consider the following singularly perturbed elliptic problem e 2 u u a y 1 u 2 0 in u n 0 on where is a bounded domain in r 2 with smooth boundary 1 a y 1 e is a small parameter n denotes the outward normal of assume that y a y 0 is a simple closed and smooth curve contained in in such a way that separates into two disjoint components y a y 0 and y a y 0 and a 0 on where is the outer normal to we will show the existence of a solution u e with a transition layer near and a downward spike near the maximum points of a y whose profile looks like u e c 1 at a point p e u e 1 in p e u e 1 in as e 0

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

shortest paths algorithms we conduct an extensive computational study of shortest paths algorithms including some very recent algorithms we also suggest new algorithms motivated by the experimental results and prove inter

harmonics in multiplicative and additive noise performance analysis of cyclic estimators multiplicative noise causes smearing of spectral lines and thus hampers frequency estimation relying on conventional spectral analysis in contrast cyclic mean and correlation statistics have proved to be useful for harmonic retrieval in the presence of multiplicative and additive noise of arbitrary color and distribution performance analysis of cyclic estimators is carried through both for nonzero and zero mean multiplicative noises cyclic estimators are shown to be asymptotically equivalent to certain nonlinear least squares estimators and are also compared with the maximum likelihood ones large sample variance expressions of the cyclic estimators are derived and compared with the corresponding cramer rao bounds when the noises are white gaussian it is demonstrated that previously well established results on constant amplitude harmonics are special cases of the present analysis simulations not only validate the large sample performance analysis but also provide concrete examples regarding relative statistical efficiency of the cyclic estimators

algorithmic applications of baur strassen s theorem shortest cycles diameter and matchings consider a directed or an undirected graph with integral edge weights from the set w w that does not contain negative weight cycles in this article we introduce a general framework for solving problems on such graphs using matrix multiplication the framework is based on the usage of baur strassen s theorem and of strojohann s determinant algorithm it allows us to give new and simple solutions to the following problems finding shortest cycles we give a simple o wn time algorithm for finding shortest cycles in undirected and directed graphs for directed graphs and undirected graphs with nonnegative weights this matches the time bounds obtained in 2011 by roditty and williams on the other hand no algorithm working in o wn time was previously known for undirected graphs with negative weights furthermore our algorithm for a given directed or undirected graph detects whether it contains a negative weight cycle within the same running time computing diameter and radius we give a simple o wn time algorithm for computing a diameter and radius of an undirected or directed graphs to the best of our knowledge no algorithm with this running time was known for undirected graphs with negative weights finding minimum weight perfect matchings we present an o wn time algorithm for finding minimum weight perfect matchings in undirected graphs this resolves an open problem posted by sankowski 2009 who presented such an algorithm but only in the case of bipartite graphs these three problems that are solved in the full generality demonstrate the utility of this framework hence we believe that it can find applications for solving larger spectra of related problems as an illustrative example we apply it to the problem of computing a set of vertices that lie on cycles of length at most t for some given t we give a simple o wn time algorithm for this problem that improves over the o wn t time algorithm given by yuster in 2011 besides giving this flexible framework the other main contribution of this article is the development of a novel combinatorial interpretation of the dual solution for the minimum weight perfect matching problem despite the long history of the matching problem such a combinatorial interpretation was not known previously this result sheds a new light on the problem as there exist many structural theorems about unweighted matchings but almost no results that could cope with the weighted case

boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions abstract we show that for large 0 the generalized boundary value problem u u u a x 1 u in u where 1 x behaves like the special case 1 in particular we show the existence of solutions with sharp boundary layers and interior spikes and determine the location of the spikes

stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in n dimensional domains we prove existence and establish the asymptotic behavior as e 0 of stable stationary solutions to the equation ut e d x u 1 u2 u a x for t x r where rn n 2 with neumann boundary condition the function a x c0 satisfies 1 a x 1 and vanishes on some hypersurfaces the results generalize to n dimensional domains and to variable diffusivity earlier paper by angenent et al j differential equations 67 1987 212

on the convergence of stable phase transitions we consider the local behavior of critical points of the functional as e 0 here w is a double well potential and u is a regular domain in n n 2 assuming that ue e 0 is stable for n 2 and locally energy minimizing for n 3 we show that the level sets of solutions converge in an average sense to a stationary n 1 rectifiable varifold our study is based on estimates derived from the second variation formula and is entirely local 1998 john wiley sons inc

efficient implementation of graph algorithms using contraction the component merging problem is a new graph problem versions of this problem appear as bottlenecks in various graph algorithms a new data structure solves this problem efficiently and two special cases of the problem have even more efficient solutions based on other data structures the performance of the data structures is sped up by introducing a new algorithmic tool called packets the algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures specifically trees can be used simultaneously as a priority queue and a concatenable queue similarly f heaps support some kinds of split operations with no loss of efficiency an immediate application of the solution to the simplest version of the merging problem is an o t m n algorithm for finding minimum spanning trees in undirected graphs without using f heaps where t m n m log 2 log 2 log d n the graph has n vertices and m edges and d max m n 2 packets also improve the f heap minimum spanning tree algorithm giving the fastest algorithm currently known for this problem the efficient solutions to the merging problem and the new observation about f heaps lead to an o n t m n n log n algorithm for finding a maximum weighted matching in general graphs this settles an open problem posed by tarjan 15 p 123 where the weaker bound of o nm log n 2 m was conjectured

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

new algorithms for maximum weight matching and a decomposition theorem we revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights we present an algorithm that operates by decomposing the problem into w unweighted versions of the problem where w is the largest edge weight our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when w is small one of the highlights of our algorithm is that it also produces an integral optimal dual solution thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed our algorithm yields a new proof to the total dual integrality of edmonds matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs we also consider the maximum weight capacitated b matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed i

an o ev log v algorithm for finding a maximal weighted matching in general graphs we define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue we show that they can be implemented efficiently consequently each operation takes o log n time we use these generalized priority queues to construct an o ev log v algorithm for finding a maximal weighted matching in general graphs

estimating particles velocity from laser measurements maximum likelihood and cramer rao bounds we address the problem of estimating particles velocity in the vicinity of an aircraft by means of a laser doppler system when a particle passes through the region of interference fringes generated by two coherent laser beams the signal backscattered is of the form aexp 2 spl alpha sup 2 spl middot f sub d sup 2 t sup 2 cos 2 spl pi f sub d t where the doppler frequency f sub d is related to the aircraft speed this paper is concerned with the most precise estimation of the parameters a and f sub d in the model considered cramer rao bounds crbs on the accuracy of estimates of a and f sub d are derived and closed formed expressions are given approximated formulas provide quantitative insights into the influence of spl alpha and f sub d additionally a maximum likelihood estimator mle is presented numerical examples illustrate the performance of the mle and compare it with the crb the influence of the snr the sample size the optical parameter spl alpha and the frequency f sub d on the estimation performance is emphasized finally an application to real data is presented

maximum skew symmetric flows and matchings the maximum integer skew symmetric flow problem msfp generalizes both the maximum flow and maximum matching problems it was introduced by tutte 28 in terms of self conjugate flows in antisymmetrical digraphs he showed that for these objects there are natural analogs of classical theoretical results on usual network flows such as the flow decomposition augmenting path and max flow min cut theorems we give unified and shorter proofs for those theoretical results we then extend to msfp the shortest augmenting path method of edmonds and karp 7 and the blocking flow method of dinits 4 obtaining algorithms with similar time bounds in general case moreover in the cases of unit arc capacities and unit node capacities our blocking skew symmetric flow algorithm has time bounds similar to those established in 8 21 for dinits algorithm in particular this implies an algorithm for finding a maximum matching in a nonbipartite graph in time which matches the time bound for the algorithm of micali and vazirani 25 finally extending a clique compression technique of feder and motwani 9 to particular skew symmetric graphs we speed up the implied maximum matching algorithm to run in time improving the best known bound for dense nonbipartite graphs also other theoretical and algorithmic results on skew symmetric flows and their applications are presented

sinusoidal signals with random amplitude least squares estimators and their statistical analysis the asymptotic properties of constrained and unconstrained least squares estimates of the parameters of a random amplitude sinusoid are analyzed an explicit formula for the asymptotic covariance matrix of the estimation errors is derived for both the constrained and unconstrained estimators accuracy aspects are investigated with the following main results for a certain weighting matrix which is shown to be the same for the constrained and unconstrained methods the estimation errors achieve their lower bounds it is proven that in the optimal case the constrained method always outperforms the unconstrained method it is also proven that the accuracy of the optimal estimators improves as the number of least squares equations increases a formula for the sample length needed for the asymptotic theory to hold is derived and its dependence on the lowpass modulating sequence is stressed simulations provide illustrations of the difference between the constrained and unconstrained estimators as well as the difference between the optimal and basic estimates the influence of the number of least squares equations and the characteristics of the lowpass envelope on the estimation accuracy is also investigated

band ordering in lossless compression of multispectral images in this paper we consider a model of lossless image compression in which each band of a multispectral image is coded using a prediction function involving values from a previously coded band of the compression and examine how the ordering of the bands affects the achievable compression we present an efficient algorithm for computing the optimal band ordering for a multispectral image this algorithm has time complexity o n sup for an n band image while the naive algorithm takes time spl omega n a slight variant of the optimal ordering problem that is motivated by some practical concerns is shown to be np hard and hence computationally infeasible in all cases except for the most trivial possibility in addition we report on our experimental findings using the algorithms designed in this paper applied to real multispectral satellite data the results show that the techniques described here hold great promise for application to real world compression needs

incremental assignment problem in this paper we introduce the incremental assignment problem in this problem a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known and the maximum weighted matching of the extended graph is sought we propose an o v 2 algorithm for the problem

connectivity of boundaries by clustering phase transition layers of fife greenlee problem on smooth bounded domain abstract we consider the fife greenlee problem e 2 u u a y 1 u 2 0 in u 0 on where is a bounded domain in r 2 with smooth boundary e 0 is a small parameter denotes the unit outward normal of let y a y 0 be a simple smooth curve intersecting orthogonally with at exactly two points and dividing into two disjoint nonempty components we assume that 1 a y 1 on and a 0 on and also some admissibility conditions hold for a and for any fixed integer n 2 m 1 3 we will show the existence of a clustered solution u e with n transition layers near with mutual distance o e log e provided that e stays away from a discrete set of values at which resonance occurs

stable transition layers in a balanced bistable equation with degeneracy abstract in this paper we consider the semilinear elliptic problem e2uxx u x 2 u2 in 0 1 with the neumann boundary condition the function is positive and is allowed to degenerate at where takes its local minimum we construct a stable solution which has exactly one layer near the interval where degenerates

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution