second order differential operators with feller wentzell type boundary conditions in this paper we study a basic generation problem concerning the second order differential operator ad2dx2 bddx c in the space c 0 1 of complex continuous functions equipped with feller wentzell type boundary conditions which originates from the work of feller w feller the parabolic differential equations and the associated semi groups of transformations ann of math 2 55 1952 468 519 we prove successfully that the operator under suitable assumptions generates a strongly continuous cosine function on c 0 1 or on a subspace of c 0 1 by means of an operator matrix analysis combined with perturbation approximation and similarity techniques

a computational algorithm for special nth order pentadiagonal toeplitz determinants abstract in this short note we present a fast and reliable algorithm for evaluating special n th order pentadiagonal toeplitz determinants in linear time the algorithm is suited for implementation using computer algebra systems cas such as macsyma and maple two illustrative examples are given

polarized endomorphisms of complex normal varieties it is shown that a complex normal projective variety has non positive kodaira dimension if it admits a non isomorphic quasi polarized endomorphism the geometric structure of the variety is described by methods of equivariant lifting and fibrations

a center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the gurtin mccamy equation

perturbation theory for dual semigroups i the sun reflexive case soit a 0 le generateur infinitesimal d un co semigroupe d operateurs lineaires bornes to t sur un espace de banach x soit b un operateur lineaire borne sur x a 0 b engendre un co semigroupe t t sur x b agit hors de l espace x dans un espace plus grand y on donne une methode systematique pour construire un tel espace y

building blocks of polarized endomorphisms of normal projective varieties abstract an endomorphism f of a projective variety x is polarized resp quasi polarized if f h q h linear equivalence for some ample resp nef and big cartier divisor h and integer q 1 first we use cone analysis to show that a quasi polarized endomorphism is always polarized and the polarized property descends via any equivariant dominant rational map next we show that a suitable maximal rationally connected fibration mrc can be made f equivariant using a construction of n nakayama that f descends to a polarized endomorphism of the base y of this mrc and that this y is a q abelian variety quasi etale quotient of an abelian variety finally we show that we can run the minimal model program mmp f equivariantly for mildly singular x and reach either a q abelian variety or a fano variety of picard number one as a consequence the building blocks of polarized endomorphisms are those of q abelian varieties and those of fano varieties of picard number one along the way we show that f always descends to a polarized endomorphism of the albanese variety alb x of x and that the pullback of a power of f acts as a scalar multiplication on the neron severi group of x modulo torsion when x is smooth and rationally connected partial answers about x being of calabi yau type or fano type are also given with an extra primitivity assumption on f which seems necessary by an example

signal flow graph approach to efficient and forward stable dst algorithms abstract in this paper signal flow graphs are mainly addressed for the efficient and forward stable discrete sine transform dst algorithms having sparse scaled orthogonal rotational rotational reflection and butterfly matrices in electrical engineering theoretical computer science control theory system engineering etc we often use signal flow graphs as a modeling tool which interconnects the system components or represents the realization of a system as electronic devices the objective in this paper is to establish the connection between algebraic operations used in sparse and scaled orthogonal factorizations of dst i iv matrices with the signal flow graph building blocks this paper elaborates signal flow graphs for the foundational frameworks with n 8 and n 16 and use these together with the digital structures to describe the dst algorithms having a n 1 point signal flow graph for dst i and n point signal flow graphs for dst ii iv the presented dst algorithms are completely recursive and solely based on corresponding matrices dst i iv these dst algorithms have low arithmetic complexity especially the low number of multiplications and significant speed improvement factor as opposed to most existing algorithms finally this paper establishes that the presented algorithms are forward stable dst algorithms

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

complete radiation boundary conditions for the helmholtz equation i waveguides we consider the use of complete radiation boundary conditions for the solution of the helmholtz equation in waveguides a general analysis of well posedness convergence and finite element approximation is given in addition methods for the optimization of the boundary condition parameters are considered the theoretical results are illustrated by some simple numerical experiments

parabolic evolution equations in interpolation and extrapolation spaces on etudie le probleme de cauchy pour des equations d evolution lineaires a t u f t o t t de type parabolique dans un espace de banach x 0 on considere des resultats d existence d unicite et de continuite pour a t u u f t u o t t

hopf bifurcation in a size structured population dynamic model with random growth abstract this paper is devoted to the study of a size structured model with ricker type birth function as well as random fluctuation in the growth process the complete model takes the form of a reaction diffusion equation with a nonlinear and nonlocal boundary condition we study some dynamical properties of the model by using the theory of integrated semigroups it is shown that hopf bifurcation occurs at a positive steady state of the model this problem is new and is related to the center manifold theory developed recently in p magal s ruan center manifold theorem for semilinear equations with non dense domain and applications to hopf bifurcation in age structured models mem amer math soc in press for semilinear equation with non densely defined operators

building blocks of amplified endomorphisms of normal projective varieties let x be a normal projective variety a surjective endomorphism f x rightarrow x is int amplified if f l l h for some ample cartier divisors l and h this is a generalization of the so called polarized endomorphism which requires that f h sim qh for some ample cartier divisor h and q 1 we show that this generalization keeps all nice properties of the polarized case in terms of the singularity canonical divisor and equivariant minimal model program

algebraic signal processing theory 1 d space in our paper titled ldquoalgebraic signal processing theory foundation and 1 d timerdquo appearing in this issue of the ieee transactions on signal processing we presented the algebraic signal processing theory an axiomatic and general framework for linear signal processing the basic concept in this theory is the signal model defined as the triple a m phi where a is a chosen algebra of filters m an associated a module of signals and phi is a generalization of the z transform each signal model has its own associated set of basic sp concepts including filtering spectrum and fourier transform examples include infinite and finite discrete time where these notions take their well known forms in this paper we use the algebraic theory to develop infinite and finite space signal models these models are based on a symmetric space shift operator which is distinct from the standard time shift we present the space signal processing concepts of filtering or convolution ldquoz transform rdquo spectrum and fourier transform for finite length space signals we obtain 16 variants of space models which have the 16 discrete cosine and sine transforms dcts dsts as fourier transforms using this novel derivation we provide missing signal processing concepts associated with the dcts dsts establish them as precise analogs to the dft get deep insight into their origin and enable the easy derivation of many of their properties including their fast algorithms

existence of solutions for a class of multivalued functional integral equations of volterra type via the measure of nonequicontinuity on the frechet space c ω e abstract the existence of continuous not necessarily bounded solutions of nonlinear functional volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity new abstract topological fixed point results for admissible condensing operators are introduced weak compactness criterion in the space of locally integrable functions in the sense of bochner is set forth some examples illustrating the usefulness of the presented approach are also included

approximation theorems for the propagators of higher order abstract cauchy problems in this paper we present two quite general approximation theorems for the propagators of higher order in time abstract cauchy problems which extend largely the classical trotter kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions then we apply the approximation theorems to deal with the second order dynamical boundary value problems

on impulsive functional differential inclusions with hille yosida operators in banach spaces abstract we consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a banach space assuming that its linear part is a non densely defined hille yosida operator we assume that the multivalued nonlinearity of upper caratheodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness we apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results the application to an optimization problem for an impulsive feedback control system is given

resolvent positive operators resolvent positive operators on an ordered banach space with generating and normal positive cone are by definition linear possibly unbounded operators whose resolvent exists and is positive on a right half line even though these operators are defined by a simple purely algebraic condition analogues of the basic results of the theory of q semigroups can be proved for them in fact if a is resolvent positive and has a dense domain then the cauchy problem associated with a has a unique solution for every initial value in the domain of a and the solution is positive if the initial value is positive also the converse is true if we assume that a has a non empty resolvent set and d a n e is dense in moreover every positive resolvent is a laplace stieltjes transform of a so called integrated semigroup and conversely every such increasing non degenerate integrated semigroup defines a unique resolvent positive operator

an iterative shrinkage approach to total variation image restoration the problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications a particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill conditioned operator in such a situation the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties such a priori information commonly referred to as simply priors is essential for image restoration rendering it stable and robust to noise moreover using the priors makes the recovered images exhibit some plausible features of their original counterpart particularly if the original image is known to be a piecewise smooth function one of the standard priors used in this case is defined by the rudin osher fatemi model which results in total variation tv based image restoration the current arsenal of algorithms for tv based image restoration is vast in this present paper a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage aka iterated thresholding in the proposed method the tv based image restoration is performed through a recursive application of two simple procedures viz linear filtering and soft thresholding therefore the method can be identified as belonging to the group of first order algorithms which are efficient in dealing with images of relatively large sizes another valuable feature of the proposed method consists in its working directly with the tv functional rather then with its smoothed versions moreover the method provides a single solution for both isotropic and anisotropic definitions of the tv functional thereby establishing a useful connection between the two formulae finally a number of standard examples of image deblurring are demonstrated in which the proposed method can provide restoration results of superior quality as compared to the case of sparse wavelet deconvolution

α times integrated semigroups α r abstract the times integrated semigroups 0 are introduced and analyzed it is shown that suitable differential operators generate times integrated semigroups for 1 2 1

the green s function for the huckel tight binding model applications of the huckel tight binding model are ubiquitous in quantum chemistry and solid state physics the matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph which is also the laplacian matrix plus twice the identity in this paper we analytically calculate the determinant and when it exists the inverse of this matrix in connection with the green s function g of the n n huckel matrix a corollary is a closed form expression for a harmonic sum eq 12 we then extend the results to d dimensional lattices whose linear size is n the existence of the inverse becomes a question of number theory we prove a new theorem in number theory pertaining to vanishing sums of cosines and use it to prove that the inverse exists if and only if n 1 and d are odd and d is smaller than the smallest divisor of n 1 we corroborate our results by demonstrating the entry patterns of the green s function and discuss applications related to transpo

the discretew transform four different versions of the discretew transform dwt are introduced the dwt may be decomposed into the discrete cosine transform dct and the discrete sine transform dst eight versions of both dct and dst are introduced for the decomposition of the dwt the relationship among different versions of dwt and their relation with the discrete fourier transform dft are given convolution theorems represented by different versions of the dwt are derived

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

existence for neutral impulsive differential inclusions with nonlocal conditions abstract in this paper by using a fixed point theorem for condensing multi valued maps we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions as an application an example has been presented to illustrate the results obtained

an uncertainty principle for finite frames abstract we consider the notion of uncertainty for finite frames using a difference operator inspired by the gauss hermite differential equation we obtain a time frequency measure for finite frames we then find the minimizer of the measure over all equal norm parseval frames dependent on the dimension of the space and the number of elements in the frame next we show that given a frame one can find the dual frame that minimizes this time frequency measure generalizing some work of daubechies landau and landau to the finite case and extending some recent work on sobolev duals for finite frames

parallel preconditioners for large scale partial difference equation systems we propose a new preconditioner dasp discrete approximate spectral preconditioner based on the existing well known preconditioners and our computational experience parallel preconditioning strategies for large scale partial difference equation systems arising from partial differential equations are investigated numerical results are given to show the efficiency and effectiveness of the new preconditioners for both model problems and real applications in petroleum reservoir simulation

a new approach to constrained total least squares image restoration abstract recently there has been a growing interest and progress in using total least squares tls methods for solving blind deconvolution problems arising in image restoration here the true image is to be estimated using only partial information about the blurring operator or point spread function psf which is subject to error and noise in this paper we present a new iterative regularized and constrained tls image restoration algorithm neumann boundary conditions are used to reduce the boundary artifacts that normally occur in restoration processes preliminary numerical tests are reported on some simulated optical imaging problems in order to illustrate the effectiveness of the approach as well as the fast convergence of our iterative scheme

nonlinear perturbations of a class of holomorphic semigroups of growth order α by comparison theorems for volterra equations abstract this paper studies nonlinear perturbation of a holomorphic semigroup of growth order in a banach space x the generator a of a holomorphic semigroup is assumed to be almost sectorial and it is also assumed that the part a 0 in the closure x 0 of the domain d a is sectorial a nonlinear perturbing operator b is assumed to be locally continuous from a subset of a real interpolation space between x 0 and d a 0 into x existence and uniqueness of mild solutions to the associated cauchy problems are proved by using comparison theorems for integral equations of volterra type the result obtained is applied to show the global well posedness of drift diffusion systems with no flux boundary conditions in the two dimensional case

weighted inner products for gmres and gmres dr the convergence of the restarted gmres method can be significantly improved for some problems by using a weighted inner product that changes at each restart how does this weighting affect convergence and when is it useful we show that weighted inner products can help in two distinct ways when the coefficient matrix has localized eigenvectors weighting can allow restarted gmres to focus on eigenvalues that otherwise cause slow convergence for general problems weighting can break the cyclic convergence pattern into which restarted gmres often settles the eigenvectors of matrices derived from differential equations are often not localized thus limiting the impact of weighting for such problems incorporating the discrete cosine transform into the inner product can significantly improve gmres convergence giving a method we call w gmres dct integrating weighting with eigenvalue deflation via gmres dr can also give effective solutions

a class of semigroups regularized in space and time we consider times integrated c regularized semigroups which are a hybrid between semigroups regularized in space c semigroups and integrated semigroups regularized in time we study the basic properties of these objects also in absence of exponential boundedness we discuss their generators and establish an equivalence theorem between existence of integrated regularized semigroups and well posedness of certain cauchy problems we investigate the effect of smoothing regularized semigroups by fractional integration

essential growth rate for bounded linear perturbation of non densely defined cauchy problems abstract this paper is devoted to the study of the essential growth rate of some class of semigroup generated by bounded perturbation of some non densely defined problem we extend some previous results due to thieme h r thieme quasi compact semigroups via bounded perturbation in advances in mathematical population dynamics molecules cells and man houston tx 1995 in ser math biol med vol 6 world sci publishing river edge nj 1997 pp 691 711 to a class of non densely defined cauchy problems in l p in particular in the context the integrated semigroup is not operator norm locally lipschitz continuous we overcome the lack of lipschitz continuity of the integrated semigroup by deriving some weaker properties that are sufficient to give information on the essential growth rate

on the order k generalized lucas numbers in this paper we give a new generalization of the lucas numbers in matrix representation also we present a relation between the generalized order k lucas sequences and fibonacci sequences

integrated semigroups and integrated solutions to abstract cauchy problems abstract concepts which have been developed in the theory of weakly continuous semigroups on dual banach spaces are extended to integrated semigroups the relation to integrated solutions of homogeneous and inhomogeneous abstract cauchy problems is established the results are illustrated for the wave equation in l2 rm

persistence of a normally hyperbolic manifold for a system of non densely defined cauchy problems abstract we consider a system of non densely defined cauchy problems and we investigate the persistence of normally hyperbolic manifolds the notion of exponential dichotomy is used to characterize the normal hyperbolicity and a generalized lyapunov perron approach is used in order to prove our main result the result presented in this article extend the previous results on the center manifold by allowing a nonlinear dynamic in the unperturbed central part of the system we consider two examples to illustrate our results the first example is a parabolic equation coupled with an ode that can be considered as an interaction between an antimicrobial and bacteria while the second one is a ross macdonald epidemic model with age of infection in both examples we were able to reduce the infinite dimensional system to an ordinary differential equation

stationary signal processing on graphs graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets in this context it is of high importance to develop flexible models of signals defined over graphs or networks in this paper we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs we show that stationarity is expressed through the graph localization operator reminiscent of translation we prove that stationary graph signals are characterized by a well defined power spectral density that can be efficiently estimated even for large graphs we leverage this new concept to derive wiener type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression

existence results for impulsive differential inclusions with nonlocal conditions abstract in this paper we shall establish sufficient conditions for the existence of mild solutions for nonlocal impulsive differential inclusions on the basis of the fixed point theorems for multivalued maps and the technique of approximate solutions new results are obtained examples are also provided to illustrate our results

on a constant diagonals matrix in this paper we consider a constant diagonals matrix the matrix was discussed in witula and slota r witula d slota on computing the determinants and inverses of some special type of tridiagonal and constant diagonals matrices appl math comput 189 1 2007 514 527 the authors gave some results on determinant and the inverse of the matrix for some special cases we give lu factorization and then compute determinant of the matrix we determine eigenvalues of the matrix further we obtain some relationships between permanent of the matrix and terms of a certain recurrence relation

kronecker product approximations for image restoration with whole sample symmetric boundary conditions reflexive boundary conditions bcs assume that the array values outside the viewable region are given by a symmetry of the array values inside the reflection guarantees the continuity of the image in fact there are usually two choices for the symmetry symmetry around the meshpoint and symmetry around the midpoint the first is called whole sample symmetry in signal and image processing the second is half sample many researchers have developed some fast algorithms for the problems of image restoration with the half sample symmetric bcs over the years however little attention has been given to the whole sample symmetric bcs in this paper we consider the use of the whole sample symmetric boundary conditions in image restoration the blurring matrices constructed from the point spread functions psfs for the bcs have block toeplitz plus pseudohankel with toeplitz plus pseudohankel blocks structures recently regardless of symmetric properties of the psfs a technique of kronecker product approximations was successfully applied to restore images with the zero bcs half sample symmetric bcs and anti reflexive bcs respectively all these results extend quite naturally to the whole sample symmetric bcs since the resulting matrices have similar structures it is interesting to note that when the size of the true psf is small the computational complexity of the algorithm obtained for the kronecker product approximation of the resulting matrix in this paper is very small it is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices finally detailed experimental results reporting the performance of the proposed algorithm are presented

on isolated singularities with a noninvertible finite endomorphism abstract we prove that if x 0 x 0 is a finite endomorphism of an isolated singularity such that deg 2 and is etale in codimension 1 then x is q gorenstein and log canonical

the relationship of transform coefficients for differing transforms and or differing subblock sizes jiang and feng have developed a relationship between the discrete cosine transform dct coefficients of a block and those of its subblocks their derivation of this result can be significantly simplified the new derivation also generalizes to all linear invertible transforms and any separable subblock geometry

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

tight wavelet frames on multislice graphs we present a framework for the design of wavelet transforms tailored to data defined on multislice graphs i e multiplex or dynamic graphs graphs with multiple types of interactions are ubiquitous in real life motivating the extension of wavelets to these complex domains our framework generalizes the recently proposed spectral graph wavelet transform sgwt d hammond p vandergheynst and r gribonval wavelets on graphs via spectral graph theory appl comput harmon anal vol 30 pp 129 150 mar 2011 which is designed in the spectral frequency domain of an arbitrary finite weighted graph we extend the sgwt to form a tight frame which conserves energy in the wavelet domain and define the relationship between conventional and spectral graph wavelets we then propose a design for multislice graphs that is based on the higher order singular value decomposition hosvd a powerful tool from multilinear algebra in particular the multiple adjacency matrices are stacked to form a tensor and the hosvd decomposition provides information about its third order structure analogous to that provided by matrix factorizations we obtain a set of eigennetworks and from these graph wavelets which exploit the variability across the graphs we demonstrate the feasibility of our method 1 by capturing different orientations of a gray scale image and 2 by decomposing brain signals from functional magnetic resonance imaging we show its effectiveness to identify variability across graph edges and provide meaningful decompositions

distribution semigroups and abstract cauchy problems we present a new definition of distribution semigroups covering in particular non densely defined generators we show that for a closed operator a in a banach space e the following assertions are equivalent a a generates a distribution semigroup b the convolution operator i a has a fundamental solution in d l e d where d denotes the domain of a supplied with the graph norm and i denotes the inclusion d e c a generates a local integrated semigroup we also show that every generator of a distribution semigroup generates a regularized semigroup introduction distribution semigroups in banach spaces and their generators were introduced by j l lions in 16 as a generalization of c0 semigroups and their generators like the generators of c0 semigroups the generators of the distribution semigroups in 16 are densely defined it was then shown in 16 that the densely defined closed linear operators a that generate a distribution semigroup are exactly those for which the convolution operator i a where i denotes the inclusion d a e has a fundamental solution treating cauchy problems as convolution equations has turned out to be very useful see 6 12 13 and 14 but in doing so the assumption that d a is dense in e is unnecessary in most of the results on the other hand in the last years there has been an interest in dealing with operators that are not densely defined starting perhaps with 7 reasons for this interest may be that it might not be so easy to decide whether a given operator is densely defined and the difficulties that arise when passing from e to e or l e so the question how the theory of distribution semigroups introduced in 16 can be extended to cover non densely defined generators in such a way that the above characterization via fundamental solutions holds seems natural it turns out that this indeed is possible in a way that even simplifies the original definitions given in 16 moreover the local strongly continuous representations see section 4 of the distribution semigroups thus obtained are exactly the local integrated semigroups for the distribution semigroups in the sense of 16 a relation to local integrated semigroups has been obtained in 23 theorem 5 6 see also 15 theorem 7 6 or 2 theorem 7 2 so the theory presented here received by the editors october 17 1995 and in revised form february 6 1997 1991 mathematics subject classification primary 47d03 34g10 47a10 46f10 c 1999 american mathematical society

perturbation theory for dual semigroups ii time dependent perturbations in the sun reflexive case we consider time dependent perturbations of generators of strongly continuous semigroups on a banach space the perturbations map the banach space into a bigger space which is the second dual of the original space in a specific semigroup sense using the theory of dual semigroups we show that the solutions of a generalised variation of constants formuladefine an evolutionary system we investigate continuity and differentiability propertiesof this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems it is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics

competitive exclusion in a multi strain virus model with spatial diffusion and age of infection abstract in this paper a multi strain virus dynamic model with spatial diffusion age of infection and general incidence function is formulated the well posedness of the initial boundary value problem of the model in the bounded domain r n is analyzed by constructing a suitable lyapunov functional the global stability of the uninfected steady state is established if all reproduction numbers are smaller or equal to one it is shown that if r i the reproduction number corresponding to strain i is larger than one the steady state corresponding to strain i exists if r 1 1 is the maximal reproduction number the steady state e 1 corresponding strain one is globally stable that is competitive exclusion occurs and strain one eliminates all other strains

diagonalizing properties of the discrete cosine transforms since its introduction in 1974 by ahmed et al the discrete cosine transform dct has become a significant tool in many areas of digital signal processing especially in signal compression there exist eight types of discrete cosine transforms dcts we obtain the eight types of dcts as the complete orthonormal set of eigenvectors generated by a general form of matrices in the same way as the discrete fourier transform dft can be obtained as the eigenvectors of an arbitrary circulant matrix these matrices can be decomposed as the sum of a symmetric toeplitz matrix plus a hankel or close to hankel matrix scaled by some constant factors we also show that all the previously proposed generating matrices for the dcts are simply particular cases of these general matrix forms using these matrices we obtain for each dct a class of stationary processes verifying certain conditions with respect to which the corresponding dct has a good asymptotic behavior in the sense that it approaches karhunen loeve transform performance as the block size n tends to infinity as a particular result we prove that the eight types of dcts are asymptotically optimal for all finite order markov processes we finally study the decorrelating power of the dcts obtaining expressions that show the decorrelating behavior of each dct with respect to any stationary processes

approximations of laplace transforms and integrated semigroups abstract let f m m n be a sequence of functions from 0 to a banach space e we give a new and essential condition on f m which is weaker than the usual local lipschitz continuity condition ensuring that the convergence of f m is equivalent to the convergence of their laplace transforms this enables us to establish new approximation theorems for r times integrated semigroups on e for all r 0 as a consequence an open problem for the convergence of integrated semigroups on the whole space e is solved in essence moreover we present an application to nonhomogeneous cauchy problems

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

an age structured within host model for multistrain malaria infections in this paper we propose an age structured malaria within host model taking into account multistrains interaction we provide a global analysis of the model depending upon some threshold mathcal t 0 when mathcal t 0 leq1 then the disease free equilibrium is globally asymptotically stable and the parasites are cleared on the contrary if mathcal t 0 1 the model exhibits the competition exclusion principle roughly speaking only the strongest strain according to a suitable order survives while the other strains go to extinction under some additional parameter conditions we prove that the endemic equilibrium corresponding to the strongest strain is globally asymptotically stable

a characteristic number for links of surface singularities milnor and thurston mt define a characteristic number of a closed orientable 3 manifold m to be a real valued topological invariant r m such that if p m is defined and m is a k sheeted covering of m then p m is defined and equal to k p m this multiplicative property is clear for the euler characteristic but of course this is 0 for a 3 manifold if m has an appropriate riemannian metric e g hyperbolic or with all sectional curvatures 1 then the volume is a characteristic number milnor and thurston introduce several characteristic numbers one is defined for all 3 manifolds is positive on a fixed hyperbolic manifold and has the additional property that if m n is a general map of degree k then m i kk i n another characteristic number is the simplicial volume introduced by gromov g in this paper we introduce a characteristic number for each link of a complex surface singularity it is a nonnegative rational number is 0 only in wellunderstood cases is computable from any resolution dual graph plumbing diagram and has in addition the submultiplicative property above for degree k maps arising from morphisms of the singularities themselves this is the only characteristic number for links which we know of that can be computed from the graph we call this invariant p p since it is the negative of the self intersection number of a rational cycle on a complex surface a resolution of the singularity the definition arose from our work on the generalized miyaoka inequality for normal surfaces w3 this term appeared in the inequality another ingredient is the notion of zariski decomposition of a line bundle or divisor on a surface especially on a resolution of a surface singularity as in sakai s let x o be the germ of a normal complex surface singularity necessarily isolated with x contractible and ax m the link of x m is a closed connected orientable 3 manifold let x e x o be a good resolution hence the inverse image e u ei of o is the union of nonsingular curves intersecting transversally no three through a point the resolution dual graph

square smoothing regularization matrices with accurate boundary conditions this paper is concerned with the solution of large scale linear discrete ill posed problems the determination of a meaningful approximate solution of these problems requires regularization we discuss regularization by the tikhonov method and by truncated iteration the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution the present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions the regularization matrices considered have a structure that makes them easy to apply in iterative methods including methods based on the arnoldi process numerical examples illustrate the properties and effectiveness of the regularization matrices described

hopf bifurcation of an infection age structured eco epidemiological model with saturation incidence abstract a novel infection age structured eco epidemiological model with saturation incidence is constructed the model is regarded as an abstract non densely defined cauchy problem and the condition of the existence of the interior equilibrium is derived by employing the method of integrated semigroup and the hopf bifurcation theory for semilinear equations with non dense domain we obtain that the model undergoes a hopf bifurcation around the interior equilibrium which manifests that this model has a non trivial periodic orbit that bifurcates from the interior equilibrium when bifurcation parameter crosses the bifurcation critical value 0 in other words the sustained periodic oscillation phenomenon appears to support and extend our theoretically analytic results numerical simulations are performed

maximal regularity for evolution equations by interpolation and extrapolation on considere le probleme aux valeurs initiales pour l equation d evolution abstraite u t b t u t f t 0 t t ou b t est pour tout t le generateur infinitesimal d un semi groupe analytique dans un b espace e on considere le cas ou le domaine d b t de b t ne depend pas de t

column continuous transition functions abstract a column continuous transition function is by definition a standard transition function p t whose every column is continuous for t 0 in the norm topology of bounded sequence space l we will prove that it has a stable q matrix and that there exists a one to one relationship between column continuous transition functions and increasing integrated semigroups on l using the theory of integrated semigroups we give some necessary and sufficient conditions under which the minimal q function is column continuous in terms of its generator of the markov semigroup as well as its q matrix furthermore we will construct all column continuous q functions for a conservative single exit and column bounded q matrix q as applications we find that many interesting continuous time markov chains ctmcs say feller reuter riley processes monotone processes birth death processes and branching processes etc have column continuity

on the convergence and approximation of integrated semigroups abstract we extend the well known theorem on convergence and approximation of c 0 semigroups due to h f trotter and t kato to the context of integrated semigroups the result is obtained as a consequence of an integrated version of the trotter kato theorem based on the laplace transform an application to the complete second order equation is given

galois coverings and endomorphisms of projective varieties we prove that the vector bundle associated to a galois covering of projective manifolds is ample resp nef under very mild conditions this results is applied to the study of ramified endomorphisms of fano manifolds with b2 1 it is conjectured that mathbb p n is the only fano manifold admitting an endomorphism of degree d 2 and we verify this conjecture in several cases an important ingredient is a generalization of a theorem of andreatta wisniewski characterizing projective space via the existence of an ample subsheaf in the tangent bundle

convoluted c cosine functions and semigroups relations with ultradistribution and hyperfunction sines abstract convoluted c cosine functions and semigroups in a banach space setting extending the classes of fractionally integrated c cosine functions and semigroups are systematically analyzed structural properties of such operator families are obtained relations between convoluted c cosine functions and analytic convoluted c semigroups introduced and investigated in this paper are given through the convoluted version of the abstract weierstrass formula which is also proved in the paper ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups several examples of operators generating convoluted cosine functions analytic convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors as an application it is proved that the polyharmonic operator 2 n n n acting on l 2 0 with appropriate boundary conditions generates an exponentially bounded k n convoluted cosine function and consequently an exponentially bounded analytic k n 1 convoluted semigroup of angle 2 for suitable exponentially bounded kernels k n and k n 1

factorizations and representations of the backward second order linear recurrences we show the relationships between the determinants and permanents of certain tridiagonal matrices and the negatively subscripted terms of second order linear recurrences also considering how to the negatively subscripted terms of second order linear recurrences can be connected to chebyshev polynomials by determinants of these matrices we give factorizations and representations of these numbers

optimal control of fractional diffusion equation in this paper we apply the classical control theory to a fractional diffusion equation in a bounded domain the fractional time derivative is considered in a riemann liouville sense we first study the existence and the uniqueness of the solution of the fractional diffusion equation in a hilbert space then we show that the considered optimal control problem has a unique solution interpreting the euler lagrange first order optimality condition with an adjoint problem defined by means of right fractional caputo derivative we obtain an optimality system for the optimal control

hille yosida type theorems for o ω t n times integrated semigroups abstract for an arbitrary continuous increasing function t 0 c we introduce the concept and characterize the properties of n times integrated laplace transforms of o t vector valued functions based on these properties we have established hille yosida type theorems for o t n times integrated semigroups an explanation example is given

an analytical approach explicit inverses of periodic tridiagonal matrices abstract we derive an explicit formula for the inverse of a general periodic tridiagonal matrix our approach is to derive its l u factorization using backward continued fractions bcf which are an essential tool in number theory we then use these formulae to construct an algorithm for inverting a general periodic tridiagonal matrix which we implement in maple 1 finally we present the results of testing the efficiency of our new algorithm against another published implementation and against the library procedures available within maple to invert a general matrix and to compute its determinant

integrated semigroups and higher order abstract equations abstract let e be a banach space b 0 b n 1 closed linear operators on e and f 0 e this paper is devoted to the study of well posedness of the cauchy problem for higher order abstract differential equations formula using the theory of integrated semigroups we obtain some concise and useful criteria

projectors on the generalized eigenspaces for functional differential equations using integrated semigroups the aim of this article is to derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues for linear functional differential equations fde by using integrated semigroup theory the idea is to formulate the fde as a non densely defined cauchy problem and obtain an explicit formula for the integrated solutions of the non densely defined cauchy problem from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues the results are useful in studying bifurcations in some semi linear problems

normal forms for semilinear equations with non dense domain with applications to age structured models normal form theory is very important and useful in simplifying the forms of equations restricted on the center manifolds in studying nonlinear dynamical problems in this paper using the center manifold theorem associated with the integrated semigroup theory we develop a normal form theory for semilinear cauchy problems in which the linear operator is not densely defined and is not a hille yosida operator and present procedures to compute the taylor expansion and normal form of the reduced system restricted on the center manifold we then apply the main results and computation procedures to determine the direction of the hopf bifurcation and stability of the bifurcating periodic solutions in a structured evolutionary epidemiological model of influenza a drift and an age structured population model

curl constrained gradient estimation for image recovery from highly incomplete spectral data in this paper we introduce new gradient based methods for image recovery from a small collection of spectral coefficients of the fourier transform which is of particular interest for several scanning technologies such as magnetic resonance imaging since gradients of a medical image are much more sparse or compressible than the corresponding image classical ell 1 minimization methods have been used to recover these relative differences the image values can then be obtained by integration algorithms imposing boundary constraints compared with classical gradient recovery methods we propose two new techniques that improve reconstruction first we cast the gradient recovery problem as a compressed sensing problem taking into account that the curl of the gradient field should be zero second inspired by the emerging field of signal processing on graphs we formulate the gradient recovery problem as an inverse problem on graphs iteratively reweighted ell 1 recovery methods are proposed to recover these relative differences and the structure of the similarity graph once the gradient field is estimated the image is recovered from the compressed fourier measurements using least squares estimation numerical experiments show that the proposed approach outperforms the state of the art image recovery methods

positive integer powers of certain complex tridiagonal matrices in this paper we firstly present a general expression for the entries of the rth email protected n power of a certain n square complex tridiagonal matrix in terms of the chebyshev polynomials of the first kind secondly we obtain a complex factorization formula for generalized fibonacci pell numbers obeying also classical fibonacci and pell numbers

the hille yosida and trotter kato theorems for integrated semigroups abstract we completely characterize the generators of non degenerate exponentially bounded n times integrated semigroups we deduce some perturbation results we also give a proof of the trotter kato theorem inspired from the classical one

the volume of an isolated singularity we introduce a notion of volume of a normal isolated singularity that gener alizes wahl s characteristic number of surface singularities to arbitrary dimensions we prove a basic monotonicity property of this volume under finite morphisms we draw sev eral consequences regarding the existence of non invertible finite endomorphisms fixing an isolated singularity using a cone construction we deduce that the anticanonical di visor of any smooth projective variety carrying a non invertible polarized endomorphism is pseudoeffective our techniques build on shokurov s b divisors we define the notion of nef weil b divisors and of nef envelopes of b divisors we relate the latter notion to the pull back of weil divisors introduced by de fernex and hacon using the subadditivity theorem for multiplier ideals with respect to pairs recently obtained by takagi we carry over to the isolated singularity case the intersection theory of nef weil b divisors formerly developed by boucksom favre and jonsson in the smooth case

characterizations of toric varieties via polarized endomorphisms let x be a normal projective variety and f x rightarrow x a non isomorphic polarized endomorphism we give two characterizations for x to be a toric variety first we show that if x is mathbb q factorial and g almost homogeneous for some linear algebraic group g such that f is g equivariant then x is a toric variety next we give a geometric characterization if x is of fano type and smooth in codimension 2 and if there is an f 1 invariant reduced divisor d such that f x backslash d is quasi etale and k x d is mathbb q cartier then x admits a quasi etale cover widetilde x such that widetilde x is a toric variety and f lifts to widetilde x in particular if x is further assumed to be smooth then x is a toric variety

local existence and stability for some partial functional differential equations with infinite delay we study the existence regularity and stability of solutions for some partial functional dierential equations with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the hille yosida condition on a banach space x the nonlinear term takes its values in space larger than x namely the extrapolated favard class of the extrapolated semigroup corresponding to the linear part our approach is based on the theory of the extrapolation spaces

singularities of varieties admitting an endomorphism let x be a normal variety such that k x is mathbb q cartier and let f x rightarrow x be a finite surjective morphism of degree at least two we establish a close relation between the irreducible components of the locus of singularities that are not log canonical and the dynamics of the endomorphism f as a consequence we prove that if x is projective and f polarised then x has at most log canonical singularities

hopf bifurcation of an age structured compartmental pest pathogen model abstract this paper investigates an age structured compartmental pest pathogen model by using the theory of integrated semigroup we study the stability of the steady state of the model by analyzing the associated characteristic transcendental equation it is shown that hopf bifurcation occurs at a positive steady state as bifurcating parameter passes a sequence of critical values

a new texture generation method based on pseudo dct coefficients in this paper a new method for generating different texture images is presented this method involves a simple transform from a certain one dimensional 1 d signal to an expected two dimensional 2 d image unlike traditional methods the input signal is generated by a simple 1 d function in our work instead of a sample texture we first transform the 1 d input signal into frequency domain using fast fourier transform based on the sufficient analysis in 2 d discrete cosine transform dct domain where each of the coefficients expresses a texture feature in a certain direction the 2 d pseudo dct coefficients are then constructed by appropriately rearranging the fourier coefficients in terms of their frequency components finally the corresponding texture image can be produced by 2 d inverse dct algorithm we applied the proposed method to generate several stochastic textures i e cloud illumination and sand and several structural texture images experimental results indicate the good performance of the proposed method

on solutions of neutral nonlocal evolution equations with nondense domain in this paper with sadovskii s and banach s fixed point theorems applied we establish some results on the existence of integral solutions strong solutions and strict solutions for a class of nondensely defined neutral evolution equations with nonlocal conditions also an example is given in the end to show the applications of the obtained results

the discrete cosine transform each discrete cosine transform dct uses n real basis vectors whose components are cosines in the dct 4 for example the j th component of boldv k is cos j frac 1 2 k frac 1 2 frac pi n these basis vectors are orthogonal and the transform is extremely useful in image processing if the vector boldx gives the intensities along a row of pixels its cosine series sum c k boldv k has the coefficients c k boldx boldv k n they are quickly computed from a fast fourier transform but a direct proof of orthogonality by calculating inner products does not reveal how natural these cosine vectors are we prove orthogonality in a different way each dct basis contains the eigenvectors of a symmetric second difference matrix by varying the boundary conditions we get the established transforms dct 1 through dct 4 other combinations lead to four additional cosine transforms the type of boundary condition dirichlet or neumann centered at a meshpoint or a midpoint determines the applications that are appropriate for each transform the centering also determines the period n 1 or n in the established transforms n frac 1 2 or n frac 1 2 in the other four the key point is that all these eigenvectors of cosines come from simple and familiar matrices

explicit formula for the inverse of a tridiagonal matrix by backward continued fractions in this paper we consider a general tridiagonal matrix and give the explicit formula for the elements of its inverse for this purpose considering usual continued fraction we define backward continued fraction for a real number and give some basic results on backward continued fraction we give the relationships between the usual and backward continued fractions then we reobtain the lu factorization and determinant of a tridiagonal matrix furthermore we give an efficient and fast computing method to obtain the elements of the inverse of a tridiagonal matrix by backward continued fractions comparing the earlier result and our result on the elements of the inverse of a tridiagonal matrix it is seen that our method is more convenient efficient and fast