a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

a partial regularity result for an anisotropic smoothing functional for image restoration in bv space abstract here we examine the partial regularity of minimizers of a functional used for image restoration in bv space this functional is a combination of a regularized p laplacian for the part of the image with small gradient and a total variation functional for the part with large gradient this model was originally introduced in chambolle and lions using the laplacian due to the singular nature of the p laplacian we study a regularized p laplacian we show that where the gradient is small the regularized p laplacian smooths the image u in the sense that u c 1 for some 0 1 this functional thus anisotropically smooths the image where the gradient is small and preserves edges via total variation where the gradient is large

variable exponent bounded variation spaces in the riesz sense abstract in this paper we introduce variable exponent bounded variation spaces in the riesz sense prove some embedding results and finally we show that a type of riesz representation lemma is valid in the newly introduced spaces

equivalence groupoids and group classification of multidimensional nonlinear schrodinger equations abstract we study admissible and equivalence point transformations between generalized multidimensional nonlinear schrodinger equations and classify lie symmetries of such equations we begin with a wide superclass of schrodinger type equations which includes all the other classes considered in the paper showing that this superclass is not normalized we partition it into two disjoint normalized subclasses which are not related by point transformations further constraining the arbitrary elements of the superclass we construct a hierarchy of normalized classes of schrodinger type equations this gives us an appropriate normalized superclass for the non normalized class of multidimensional nonlinear schrodinger equations with potentials and modular nonlinearities and allows us to partition the latter class into three families of normalized subclasses after a preliminary study of lie symmetries of nonlinear schrodinger equations with potentials and modular nonlinearities for an arbitrary space dimension we exhaustively solve the group classification problem for such equations in space dimension two

the painleve property lax pair auto backlund transformation and recursion operator of a perturbed korteweg de vries equation using painlevt property analysis we obtained the lax pair auto backlund transformation and recursion operator of a perturbed korteweg de vries equation u 6uu u f f u 0 the exact form off f for which the system is completely integrable is reported in this letter

nonisospectral integrable nonlinear equations with external potentials and their gbdt solutions auxiliary systems for matrix nonisospectral equations including coupled nls with external potential and kdv with variable coefficients were introduced explicit up to the inversion of finite matrices solutions of nonisospectral equations were constructed using the gbdt version of the backlund darboux transformation

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

total variation time flow with quantile regression for image restoration abstract we analyze the time flow of a modification of the standard rudin osher fatemi rof model for image restoration using the bounded variation semi norm the solution of the minimization problem is a restored image in the space of bounded variation bv recovered from a corrupted one and the functional may include a more general term s x u rather than the l 2 penalty term as used in the original rof model these new models were introduced in osher and scherzer 2004 31 in particular we will examine the non differentiable quantile regression penalty we will define an appropriate weak solution of the time flow and in particular prove the existence in l 0 b v and l stability

harmonic maps backlund darboux transformations and line solution analogues harmonic maps from or one connected domain into and u m are treated the gbdt version of the b cklund darboux transformation is applied to the case of the harmonic maps and a new and simple algebraic procedure to construct new harmonic maps from the initial ones is given using some methods from system theory a new general formula on the gbdt transformations of the sym tafel immersions is derived a new class of the unitary harmonic maps with asymptotics along one line essentially different from the asymptotics in all other directions similar in certain ways to line solutions is obtained explicitly and studied

variable exponent bergman spaces abstract in this article we define variable exponent bergman spaces and show that polynomials are dense in the spaces we also show that the bergman projection and the berezin transform are bounded in these spaces

moment modification multipeakons and nonisospectral generalizations abstract firstly a formal correspondence is established between the camassa holm ch equation and a two component modified ch or called sqq equation according to the method of moment modification for multipeakon formulae secondly based on the generalized nonisospectral ch equation in chang et al 2014 14 and the interlacing multipeakons of the two component modified ch equation in chang et al 2016 15 we propose a new generalized two component modified ch equation with two parameters which possesses a nonisospectral lax pair the proposed equation still admits multipeakon solutions of explicit and closed form sufficient conditions for global existence of solutions are given and two concrete examples with certain interesting phenomenon are presented last of all as a by product a generalized nonisospectral modified ch equation is deduced together with its lax pair

on the strong norlund summability of conjugate fourier series in continuation of a recent work by mittal m l mittal on strong norlund summability of fourier series j math anal appl 314 2006 75 84 the present authors obtain a sufficient condition for the summability n p n 1 2 of the conjugate fourier series in conjunction with the known tauberian theorem on the strong norlund summability which was also considered earlier by mittal m l mittal a tauberian theorem on strong norlund summability j indian math soc n s 44 1980 369 377 our result gives a sufficient condition for the summability c 1 2 of the conjugate fourier series our main theorem generalizes the results given earlier by prasad g prasad on norlund summability of fourier series ph d thesis university of roorkee roorkee 1967 and singh u n singh on the strong summability of a fourier series and its conjugate series proc nat inst sci india part a 13 1947 319 325

nonautonomous integrable nonlinear schrodinger equations with generalized external potentials inhomogeneous nonlinear schrodinger equations are constructed systematically using the covariance with respect to the darboux transformation the darboux invariants and the spectral parameter are functions of time and space which result in equations describing nonautonomous solitons moving in generalized external potentials all the known inhomogeneous nonlinear schrodinger equations as well as new ones of a more generalized form can be derived from the constructed equation one and two soliton solutions are explicitly constructed using the darboux transformation

interpolation on variable morrey spaces defined on quasi metric measure spaces abstract in this paper we show the validity of a riesz thorin type interpolation theorem for linear operators acting from variable exponent lebesgue spaces into variable exponent morrey space in the framework of quasi metric measure spaces

similarity reductions for variable coefficient coupled nonlinear schrodinger equations the authors categorize classes of coupled nonlinear schrodinger equations which allow generalized similarity solutions using the approach of clarkson and kruskal 1989 in all cases the resulting pair of ordinary differential equations belongs to a single class certain cases allowing solution in terms of familiar functions are identified an alternative approach shows that only two conditions need be placed on the four real and two complex coefficients in the governing equations in order that solutions generated by an arbitrary solution of the integrable nls equation exist applications to some standard coupled systems arising from fibre optics are given

non hermitian matrix schrodinger equation backlund darboux transformation weyl functions and script pscript t symmetry the non hermitian matrix schrodinger equation obtained by the backlund darboux transformation bdt is treated the potentials fundamental solutions and weyl functions are constructed explicitly a symmetric reduction of the bdt is introduced and this case is studied in greater detail including potentials fundamental solutions bound states the reality of the discrete spectrum and spontaneous break of the symmetry the sign indefinite scalar product and examples

from arzela ascoli to riesz kolmogorov abstract in this paper we study totally bounded sets in banach function spaces bfs from which we characterize compact sets via hausdorff criterion in some non standard function spaces which fall under the umbrella of bfs we obtain a riesz kolmogorov compactness theorem for the grand variable exponent lebesgue spaces

a modified kdv equation with self consistent sources in non uniform media and soliton dynamics two non isospectral modified kdv equations with self consistent sources are derived which correspond to the time dependent spectral parameter satisfying t and t 3 respectively gauge transformation between the first non isospectral equation corresponding to t and its isospectral counterpart is given from which exact solutions and conservation laws for the non isospectral one are easily listed besides solutions to the two nonisospectral modified kdv equations with self consistent sources are derived by means of the hirota method and the wronskian technique respectively nonisospectral dynamics and source effects including one soliton characteristics in non uniform media two solitons scattering and special behaviours related to sources for example the ghost solitons in the degenerate two soliton case are investigated analytically

soliton solutions to the 3rd nonisospectral akns system abstract bilinear form of the nonisospectral akns equation is given the n soliton solutions and double wronskian solution are obtained through hirota s direct method and wronskian technique respectively the nonisospectral mkdv equation and its multi soliton solutions are presented by reducing

a note on strong norlund summability abstract different authors have used different definitions of strong norlund summability n p n q in this paper after discussing these definitions we have obtained a theorem which gives an equivalence between the definitions of borwein and cass and srivastava under certain conditions on p n we have also proved several other necessary and sufficient conditions for strong norlund summability

on strong norlund summability of fourier series abstract in this note a sufficient condition for summability n p n 1 2 of fourier series has been obtained which in conjunction with the author s tauberian theorem m l mittal a tauberian theorem on strong norlund summability j indian math soc 44 1980 369 377 on strong norlund summability gives a sufficient condition for summability c 1 2 of a fourier series this generalizes results due to prasad g prasad on strong norlund summability of fourier series univ roorkee res j 9 1966 1967 1 10 and varshney o p varshney note on h 2 summability of fourier series boll un mat ital 16 1961 383 385

multicomponent integrable wave equations i darboux dressing transformation the darboux dressing transformations are applied to the lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions the general formalism is set up and the relevant equations are explicitly solved several instances of multicomponent wave equations of applicative interest such as vector nonlinear schrodinger type equations and three resonant wave equations are considered

commutation methods for jacobi operators abstract we offer two methods of inserting eigenvalues into spectral gaps of a given background jacobi operator the single commutation method which introduces eigenvalues into the lowest spectral gap of a given semi bounded background jacobi operator and the double commutation method which inserts eigenvalues into arbitrary spectral gaps moreover we prove unitary equivalence of the commuted operators restricted to the orthogonal complement of the eigenspace corresponding to the newly inserted eigenvalues with the original background operator in addition we compute the matrix valued weyl m functions of the commuted operator in terms of the background weyl m functions finally we show how to iterate the above methods and give explicit formulas for various quantities such as eigenfunctions and spectra of the iterated operators in terms of the corresponding background quantities and scattering matrix concrete applications include an explicit realization of the isospectral torus for algebro geometric finite gap jacobi operators and the n soliton solutions of the toda and kac van moerbeke lattice equations with respect to arbitrary background solutions

on time flows of minimizers of general convex functionals of linear growth with variable exponent in bv space and stability of pseudosolutions here we examine a method of selective smoothing in image restoration in bv space using a variable exponent functional of linear growth variable exponent growth was suggested in p blomgren et al 1997 6 and in y chen et al 2006 8 the notion of a pseudosolution of the minimization problem is discussed as well as the proof of existence and uniqueness of the solution of the time flow for the associated time dependent pde here we prove stability for pseudosolutions while also discussing the case for more general convex functionals of linear growth and variable exponent for use as an approximation for the time flow other than that which is used in y chen et al 2006 8