the existence of countably many positive solutions for singular multipoint boundary value problems abstract in this paper we study the existence of countably many positive solutions for a singular multipoint boundary value problem by using fixed point index theory and the leggett williams fixed point theorem sufficient conditions for the existence of countably many positive solutions are established

singular values of fractional integral operators a unification of theorems of hille tamarkin and chang abstract we obtain upper bounds on the singular values of fractional integral operators of the form l 0 x x y x 1 dy under the constraint 0 these bounds are employed to extend various results obtained over the last half century on the rate of decrease of eigenvalues and singular values of much more general integral operators apart from one relatively difficult theorem of hardy and littlewood math z 27 1928 565 606 the devices used are quite simple they involve no complex variable arguments

high quality image resizing using oblique projection operators the standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate however one can obtain more accurate results if one applies a filter prior to sampling a fact well known from sampling theory the optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space unfortunately the optimal projection prefilter is difficult to implement when sine or high order spline functions are used we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster simpler and more general algorithms we show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space the main advantage is that it becomes perfectly feasible to use higher order models e g splines of degree n spl ges 3 we develop the theoretical background and present a simple and practical implementation procedure using b splines our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure least squares solution with considerably fewer computations the method works for arbitrary scaling factors and is applicable to both image enlargement and reduction

generalized sampling expansions with multiple sampling rates for lowpass and bandpass signals in the fractional fourier transform domain the objective of generalized sampling expansion gse is the reconstruction of an unknown continuously defined function f left t right from samples of the responses from m linear time invariant lti systems that are each sampled using the 1 m th nyquist rate in this paper we investigate the gse for lowpass and bandpass signals with multiple sampling rates in the fractional fourier transform frft domain first we propose an improvement of papoulis gse which has multiple sampling rates in the frft domain based on the proposed gse we derive the periodic nonuniform sampling scheme and the derivative interpolation method by designing different fractional filters and selecting specific sampling rates in addition the papoulis gse and the previous gse associated with frft are shown to be special instances of our results second we address the problem of the gse of fractional bandpass signals a new gse for fractional bandpass signals with equal sampling rates is derived we show that the restriction of an even number of channels in the gse for fractional bandpass signals is unnecessary and perfect signal reconstruction is possible for any arbitrary number of channels further we develop the gse for a fractional bandpass signal with multiple sampling rates lastly we discuss the application of the proposed method in the context of single image super resolution reconstruction based on gse illustrations and simulations are presented to verify the validity and effectiveness of the proposed results

an m point boundary value problem of neumann type for a p laplacian like operator abstract let and be two odd increasing homeomorphism from r onto r with 0 0 0 0 and let f 0 1 r r r be a function satisfying caratheodory s conditions let a i r i 0 1 i 1 2 m 2 0 1 2 m 2 be given we are interested in the problem of existence of solutions for the m point boundary value problem x f t x x t 0 1 x 0 0 x 1 i 1 m 2 a i x i we note that this non linear m point boundary value problem is always at resonance since the associated m point boundary value problem x 0 t 0 1 x 0 0 x 1 i 1 m 2 a i x i has non trivial solutions x t r an arbitrary constant our results are obtained by a suitable homotopy leray schauder degree properties and a priori bounds

multiple results of p laplacian dynamic equations on time scales in this paper a new fixed point theorem introduced by avery and peterson and another fixed point theorem are applied to boundary value problems for p laplacian dynamic equations on time scales by imposing some growth conditions on the nonlinearity f we establish the existence results of at least three positive solutions as an application some examples are included to illustrate the main results

on the approximation power of convolution based least squares versus interpolation there are many signal processing tasks for which convolution based continuous signal representations such as splines and wavelets provide an interesting and practical alternative to the more traditional sine based methods the coefficients of the corresponding signal approximations are typically obtained by direct sampling interpolation or quasi interpolation or by using least squares techniques that apply a prefilter prior to sampling we compare the performance of these approaches and provide quantitative error estimates that can be used for the appropriate selection of the sampling step h specifically we review several results in approximation theory with a special emphasis on the strang fix 1971 conditions which relate the general o h sup l behavior of the error to the ability of the representation to reproduce polynomials of degree n l 1 we use this theory to derive pointwise error estimates for the various algorithms and to obtain the asymptotic limit of the l sub 2 error as h tends to zero we also propose a new improved l sub 2 error bound for the least squares case in the process we provide all the relevant bound constants for polynomial splines some of our results suggest the existence of an intermediate range of sampling steps where the least squares method is roughly equivalent to an interpolator with twice the order we present experimental examples that illustrate the theory and confirm the adequacy of our various bound and limit determinations

positive solutions for three point boundary value problems with dependence on the first order derivative abstract a new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three point boundary value problem x f t x x 0 0 x 0 0 x 1 x where f is a nonnegative continuous function 0 0 1

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

on multiple fixed sign solutions of a discrete system with hermite boundary conditions abstract we consider the discrete system m u i k p i k u 1 k u 2 k u n k k 0 1 n 1 i n together with hermite boundary conditions j u i k 0 j 0 m 1 1 r 1 i n where r 2 m 1 for 1 r 1rm m and k s are integers such that 0 k1

asymptotic behavior of the singular values of a generalization of the operator fractional integration abstract in this paper we find the first term in the asymptotics of singular values of the generalized fractional integration operator

multiple fixed sign solutions for a system of difference equations with sturm liouville conditions we consider the following system of difference equations d mu i k p i k u 1 k u 2 k u n k 0 k 0 1 n i 1 2 ntogether with sturm liouville boundary conditions d ju i 0 0 0 2 n m 1 z 0 w 0 h 0 d w z w n 1 z d h w 0 by using two different fixed point theorems we develop criteria for the existence of three solutions of the system which are of fixed signs on 0 1 n m examples are also included to illustrate the results obtained

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

linear interpolation revitalized we present a simple original method to improve piecewise linear interpolation with uniform knots we shift the sampling knots by a fixed amount while enforcing the interpolation property we determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation surprisingly enough this optimal value is nonzero and close to 1 5 we confirm our theoretical findings by performing several experiments a cumulative rotation experiment and a zoom experiment both show a significant increase of the quality of the shifted method with respect to the standard one we also observe that in these results we get a quality that is similar to that of the computationally more costly high quality cubic convolution

positive solutions for one dimensional p laplacian boundary value problems with dependence on the first order derivative abstract this paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one dimensional p laplacian differential equation p u a t f u u 0 subject to some boundary conditions we show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem

sharp bounds for singular values of fractional integral operators abstract from the results of dostanic m r dostanic asymptotic behavior of the singular values of fractional integral operators j math anal appl 175 1993 380 391 and v and gorenflo kim tuan v r gorenflo singular values of fractional and volterra integral operators in inverse problems and applications to geophysics industry medicine and technology ho chi minh city 1995 ho chi minh city math soc ho chi minh city 1995 pp 174 185 it is known that the jth singular value of the fractional integral operator of order 0 is approximately j for all large j in this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is j 1 o j 1

multiple positive solutions for some four point boundary value problems with p laplacian this paper is devoted to the existence of multiple positive solutions for some nonlinear singular four point boundary value problems with p laplacian under appropriate assumptions on the nonlinear terms by applying several known fixed point theorems sufficient conditions for the existence of at least three positive solutions are established

asymptotic behavior of the singular values of fractional integral operators in this paper we find the precise asympotic of the singular numbers of the fractional integral operator i x0 x y 1 dy in the case 0 1 2 and improve the known estimates for 1 2 1 also we obtain some results concerning the precise asympotic of the singular numbers of convolution operators similar to the fractional integral operators

spatially variant convolution with scaled b splines we present an efficient algorithm to compute multidimensional spatially variant convolutions or inner products between n dimensional signals and b splines or their derivatives of any order and arbitrary sizes the multidimensional b splines are computed as tensor products of 1 d b splines and the input signal is expressed in a b spline basis the convolution is then computed by using an adequate combination of integration and scaled finite differences as to have for moderate and large scale values a computational complexity that does not depend on the scaling factor to show in practice the benefit of using our spatially variant convolution approach we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector

the three solutions theorem for p laplacian boundary value problems abstract the three solutions theorem is established for p laplacian boundary value problems in the presence of two pairs of lower and upper solutions which are well ordered by the relationship between the lower and upper solutions and degree theory in addition an application of the three solutions theorem is given

moms maximal order interpolation of minimal support we consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly supported basis function spl phi z we first give the expression for the cases of spl phi that have minimal support for a given accuracy also known as approximation order this class of functions which we call maximal order minimal support functions moms is made of linear combinations of the b spline of the same order and of its derivatives we provide an explicit form of the moms that maximizes the approximation accuracy when the step size is small enough we compute the sampling gain obtained by using these optimal basis functions over the splines of the same order we show that it is already substantial for small orders and that it further increases with the approximation order l when l is large this sampling gain becomes linear more specifically its exact asymptotic expression is 2 spl pi e l since the optimal functions are continuous but not differentiable for even orders and even only piecewise continuous for odd orders our result implies that regularity has little to do with approximating performance these theoretical findings are corroborated by experimental evidence that involves compounded rotations of images

sharp conditions for the existence of sign changing solutions to equations involving the one dimensional p laplacian abstract we consider the boundary value problem involving the one dimensional p laplacian u p 2 u a x f u 0 0 x 1 u 0 u 1 0 where p 1 we establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f s s p 1 at infinity and zero our argument is based on the shooting method together with the qualitative theory for half linear differential equations

least squares image resizing using finite differences we present an optimal spline based algorithm for the enlargement or reduction of digital images with arbitrary noninteger scaling factors this projection based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are b splines of any degree n a noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a for a given choice of basis functions the results of our method are consistently better than those of the standard interpolation procedure the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal to noise ratio the method can be generalized to include other classes of piecewise polynomial functions expressed as linear combinations of b splines and their derivatives

three solutions for a class of quasilinear elliptic systems involving the p q laplacian abstract the existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the p q laplacian with dirichlet boundary condition our technical approach is based on the three critical points theorem obtained by b ricceri

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

variational image reconstruction from arbitrarily spaced samples a fast multiresolution spline solution we propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations we adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms 1 the sum of squared errors at the specified points and 2 a quadratic functional that penalizes the lack of smoothness we search for a solution that is a uniform spline and show how it can be determined by solving a large sparse system of linear equations we interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach using the two scale relation for b splines we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution we use this relation to develop a fast multigrid algorithm we demonstrate the effectiveness of our approach on some image reconstruction examples

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian p x t q t f t x t x t 0 t 0 1 subject to one of the following boundary conditions p x 0 p x 0 0 p x 1 p x 1 0 or x 0 g1 x 0 0 x 1 g2 x 1 0 where p s s p 2s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions the interesting point is the nonlinear term f is involved with the first order derivative explicitly

positive solutions for a fourth order p laplacian boundary value problem abstract in this paper we study the existence multiplicity and uniqueness of positive solutions for the fourth order p laplacian boundary value problem u p 1 u f t u u 2 i 0 u 2 i 1 0 i 0 1 here p 0 and f c 0 1 r r r 0 based on a priori estimates achieved by utilizing properties of concave functions we use fixed point index theory to establish our main results

construction of image reduction operators using averaging aggregation functions in this work we present an image reduction algorithm based on averaging aggregation functions we axiomatically define the concepts of image reduction operator and local reduction operator we study the construction of the latter by means of averaging functions and we propose an image reduction algorithm image reduction operator we analyze the properties of several averaging functions and their effect on the image reduction algorithm finally we present experimental results where we apply our algorithm in two different applications analyzing the best operators for each concrete application

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

calculus of variations for a boundary value problem of differential system on the half line boundary value problem of second order differential equations on the half line is investigated in this paper the method mainly depends on the calculus of variations to the classical functionals sufficient conditions are obtained for the existence of the solutions

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

three positive solutions for the one dimensional p laplacian in this paper nonlinear two point boundary value problems with p laplacian operators subject to dirichlet boundary condition and nonlinear boundary conditions are studied we show the existence of three positive solutions by the five functionals fixed point theorem

multiple positive solutions for the one dimensional singular p laplacian we consider the following boundary value problem f p y q t f y 0 p 1 t 0 1 with y 0 y 1 0 or y 0 y 1 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem an example is also included to illustrate the importance of the result obtained

existence of positive solutions for the one dimensional singular p laplacian this paper concerns the positive solutions of boundary value problems for the one dimensional singular p laplacian by the classical method of elliptic regularization we obtain some existence results which generalize some results of w zhou x wei positive solutions to bvps for a singular differential equation nonlinear anal 2006 doi 10 1016 j na 2006 06 015

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

shifting interpolation kernel toward orthogonal projection orthogonal projection offers the optimal solution for many sampling reconstruction problems in terms of the least square error in the standard interpolation setting where the sampling is assumed to be ideal however the projection is impossible unless the interpolation kernel is related to the sinc function and the input is bandlimited in this paper we propose a notion of shifting kernel toward the orthogonal projection for a given interpolation kernel we formulate optimization problems whose solutions lead to shifted interpolations that while still being interpolatory are closest to the orthogonal projection in the sense of the minimax regret the quality of interpolation is evaluated in terms of the average approximation error over input shift for the standard linear interpolation we obtain several values of optimal shift dependent on a priori information on input signals for evaluation we apply the new shifted linear interpolations to a gaussian signal an ecg signal a speech signal a two dimensional signal and three natural images significant improvements are observed over the standard and the 0 21 shifted linear interpolation proposed early

existence of three solutions for a quasilinear two point boundary value problem abstract in this paper we investigate a quasilinear second order differential equation with dirichlet boundary conditions the existence of an open interval of parameters which ensures this problem admits at least three solutions is determined by using the critical point theory

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian f p x t q t f t x t x t 0 t 0 1 subject to the following boundary value conditions x 0 i 1n a ix x i x 1 i 1n b ix x i where f p s s p 2 s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem

a map based image interpolation method via viterbi decoding of markov chains of interpolation functions a new method of image resolution up conversion image interpolation based on maximum a posteriori sequence estimation is proposed instead of making a hard decision about the value of each missing pixel we estimate the missing pixels in groups at each missing pixel of the high resolution hr image we consider an ensemble of candidate interpolation methods interpolation functions the interpolation functions are interpreted as states of a markov model in other words the proposed method undergoes state transitions from one missing pixel position to the next accordingly the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing hr pixel positions we derive a parameter free probabilistic model for this to be estimated sequence of interpolation functions then we solve the estimation problem using a trellis representation and the viterbi algorithm using directional interpolation functions and sequence estimation techniques we classify the new algorithm as an adaptive directional interpolation using soft decision estimation techniques experimental results show that the proposed algorithm yields images with higher or comparable peak signal to noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

positive solutions for a system of second order quasilinear boundary value problems abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order quasilinear boundary value problems u p 1 f t u v v q 1 g t u v u 0 u 1 0 v 0 v 1 0 where p q 1 and f g c 0 1 r 2 r r 0 based on a priori estimates achieved by utilizing jensen s inequality for nonnegative concave functions and homogeneous operators we use fixed point index theory to establish the main results

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

approximate singular values of the fractional difference and summation operators abstract we obtain sharp bounds on the singular values of the fractional difference and summation operators on r n these bounds allow us to establish that the convergence rates of the distributions of the singular values of these operators are o 1 n since the fractional difference operator of order is associated with the toeplitz matrix with fisher hartwig symbol 2 2 cos u 0 we are able to obtain similar bounds on the eigenvalues of this toeplitz matrix and a similar result on the convergence rate of the distribution of its eigenvalues

approximation power of biorthogonal wavelet expansions this paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions the strang fix conditions imply that the error for an orthogonal wavelet approximation at scale a 2 sup i globally decays as a sup n where n is the order of the transform this is why for a given number of scales higher order wavelet transforms usually result in better signal approximations we prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone we also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero these results strengthen sweldens earlier analysis and confirm that the approximation power of biorthogonal and semi orthogonal wavelet expansions is essentially the same finally we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines we also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error

twin positive solutions for the one dimensional p laplacian boundary value problems abstract in this paper we study the existence of multiple positive solutions for the equation g u e t f u 0 where g v v p 2 v p 1 subject to nonlinear boundary conditions we show the existence of at least two positive solutions by using a new three functionals fixed point theorem in cones

three periodic solutions for p hamiltonian systems abstract the existence of at least three periodic solutions is established for a class of p hamiltonian systems our technical approach is based on two general three critical points theorems obtained by ricceri and averna bonanno

existence of multiple positive solutions for one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value conditions p u 0 i 1 n 2 a i p u i u 1 i 1 n 2 b i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and a i b i satisfy a i b i 0 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem

a minimum squared error framework for generalized sampling we treat the problem of reconstructing a signal from its nonideal samples where the sampling and reconstruction spaces as well as the class of input signals can be arbitrary subspaces of a hilbert space our formulation is general and includes as special cases reconstruction from finitely many samples as well as uniform sampling of continuous time signals which are not necessarily bandlimited to obtain a good approximation of the signal in the reconstruction space from its samples we suggest two design strategies that attempt to minimize the squared norm error between the signal and its reconstruction the approaches we propose differ in their assumptions on the input signal if the signal is known to lie in an appropriately chosen subspace then we propose a method that achieves the minimal squared error on the other hand when the signal is not restricted we show that the minimal norm reconstruction cannot generally be obtained instead we suggest minimizing the worst case squared error between the reconstructed signal and the best possible but usually unattainable approximation of the signal within the reconstruction space we demonstrate both theoretically and through simulations that the suggested methods can outperform the consistent reconstruction approach previously proposed for this problem

image quality assessment based on a degradation model we model a degraded image as an original image that has been subject to linear frequency distortion and additive noise injection since the psychovisual effects of frequency distortion and noise injection are independent we decouple these two sources of degradation and measure their effect on the human visual system we develop a distortion measure dm of the effect of frequency distortion and a noise quality measure nqm of the effect of additive noise the nqm which is based on peli s 1990 contrast pyramid takes into account the following 1 variation in contrast sensitivity with distance image dimensions and spatial frequency 2 variation in the local luminance mean 3 contrast interaction between spatial frequencies 4 contrast masking effects for additive noise we demonstrate that the nonlinear nqm is a better measure of visual quality than peak signal to noise ratio psnr and linear quality measures we compute the dm in three steps first we find the frequency distortion in the degraded image second we compute the deviation of this frequency distortion from an allpass response of unity gain no distortion finally we weight the deviation by a model of the frequency response of the human visual system and integrate over the visible frequencies we demonstrate how to decouple distortion and additive noise degradation in a practical image restoration system

quantitative fourier analysis of approximation techniques i interpolators and projectors we present a general fourier based method that provides an accurate prediction of the approximation error as a function of the sampling step t our formalism applies to an extended class of convolution based signal approximation techniques which includes interpolation generalized sampling with prefiltering and the projectors encountered in wavelet theory we claim that we can predict the l sup 2 approximation error by integrating the spectrum of the function to approximate not necessarily bandlimited against a frequency kernel e spl omega that characterizes the approximation operator this prediction is easier yet more precise than was previously available our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function our error prediction is exact for stationary processes as well as for bandlimited signals we apply this method to the comparison of standard interpolation and approximation techniques our method has interesting implications for approximation theory in particular we use our results to obtain some new asymptotic expansions of the error as t spl rarr 0 as well as to derive improved upper bounds of the kind found in the strang fix 1971 theory we finally show how we can design quasi interpolators that are near optimal in the least squares sense

a multiplicity result for p lapacian boundary value problems via critical points theorem abstract in this paper we deal with the existence of at least three classical solutions for the following two point boundary value problem p u f t u 0 1 u a 2 u a 0 1 u b 2 u b 0 where p s s p 2 s p 1 is a constant is a positive parameter a b r a b our main tool is a recent three critical point theorem of ricceri our emphasis here is constructing an appropriate separable and reflexive real banach space

quantitative fourier analysis of approximation techniques ii wavelets for pt i see ibid vol 47 no 10 p 2783 95 1999 in a previous paper we proposed a general fourier method that provides an accurate prediction of the approximation error irrespective of the scaling properties of the approximating functions here we apply our results when these functions satisfy the usual two scale relation encountered in dyadic multiresolution analysis as a consequence of this additional constraint the quantities introduced in our previous paper can be computed explicitly as a function of the refinement filter this is in particular true for the asymptotic expansion of the approximation error for biorthonormal wavelets as the scale tends to zero one of the contributions of this paper is the computation of sharp asymptotically optimal upper bounds for the least squares approximation error another contribution is the application of these results to b splines and daubechies 1988 1992 scaling functions which yields explicit asymptotic developments and upper bounds thanks to these explicit expressions we can quantify the improvement that can be obtained by using b splines instead of daubechies wavelets in other words we can use a coarser spline sampling and achieve the same reconstruction accuracy as daubechies specifically we show that this sampling gain converges to spl pi as the order tends to infinity

three solutions for a navier boundary value problem involving the p biharmonic the existence of at least three weak solutions is established for a class of navier boundary value problem involving the p biharmonic our technical approach is based on the three critical points theorem obtained by b ricceri

existence of multiple positive solutions for nonlinear m point boundary value problems abstract in this paper we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m point boundary value problem for the one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i

quasilinear equations with dependence on the gradient abstract we discuss the existence of positive solutions of the problem q t u t f t u t u t for t 0 1 and u 0 u 1 0 where the nonlinearity f satisfies a superlinearity condition at 0 and a local superlinearity condition at this general quasilinear differential operator involves a weight q and a main differentiable part which is not necessarily a power due to the superlinearity of f and its dependence on the derivative a condition of the bernstein nagumo type is assumed also involving the differential operator our main result is the proof of a priori bounds for the eventual solutions the presence of the derivative in the right hand side of the equation requires a priori bounds not only on the solutions themselves but also on their derivatives which brings additional difficulties as an application we consider a quasilinear dirichlet problem in an annulus div a u u f x u u in r 1 x r 2 u x 0 on x r 1 and x r 2

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

on the existence of positive solution for a kind of multi point boundary value problem at resonance abstract this paper concerns the existence of positive solution for a class of second order m point boundary value problems under different resonant conditions by using the leggett williams norm type theorem due to o regan and zima we obtain the existence of positive solution an example is given to demonstrate the main results

existence of three positive pseudo symmetric solutions for a one dimensional p laplacian abstract we apply the five functionals fixed point theorem to verify the existence of at least three positive pseudo symmetric solutions for the three point boundary value problem g u a t f u 0 u 0 0 and u u 1 where g v v p 2 v with p 1 and 0 1

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed