existence and blow up for a degenerate parabolic equation with nonlocal source in this paper we investigate the positive solution of nonlinear degenerate equation ut up u au uq dx with dirichlet boundary condition conditions on the existence of global and blow up solution are given furthermore it is proved that there exist two positive constants c1 c2 such that c1 t t 1 p q maxx u x t c2 t t 1 p q

blow up and global existence for a nonlocal degenerate parabolic system abstract this paper investigates the blow up and global existence of nonnegative solutions of the system u t u m a v p v t v n b u q x t 0 t with homogeneous dirichlet boundary data where r n is a bounded domain with smooth boundary m n 1 1 p q a b 0 and dx it is proved that if pq mn there exist both global and blow up nonnegative solutions when pq mn we show that if the domain is sufficiently small every nonnegative solution is global while if the domain is large enough that is if it contains a sufficiently large ball there exists no global solution in particular when p n q m we show that every positive solution exists globally iff x dx 1 ab where x is the unique positive solution of the linear elliptic problem x 1 x x 0 x

global existence and blow up of solutions to a nonlocal quasilinear degenerate parabolic system abstract this paper investigates the properties of nonnegative solutions of a quasilinear degenerate parabolic system u t div u p 2 u a v x t d x v t div v q 2 v b u x t d x with zero dirichlet boundary conditions in a smooth bounded domain r n n 1 where p q 2 1 and a b 0 are positive constants under appropriate hypotheses we first establish the local existence and uniqueness of solutions then we show that whether or not the solution blows up in finite time depends on the initial data and the relations between and p 1 q 1 in the special case of q 1 and p 1 we conclude that the solution exists globally if p 1 d x q 1 d x 1 a b while if p 1 d x q 1 d x 1 a b then the solution blows up in finite time here x and x denote the unique solution of the following elliptic problem div p 2 1 in x 0 and div q 2 1 in x 0 respectively

the error amended sharp edge ease scheme for image zooming this paper proposes a new interpolation method called the error amended sharp edge ease scheme which is a modified bilinear method in order to remove reduce interpolation artifacts such as image blur and the checkerboard effect ringing ease tries to amend the interpolation error by employing the classical interpolation error theorem in an edge adaptive fashion ease is applied for image zooming by both integer and noninteger magnification factors the new interpolation scheme has proved to result in high resolution images having clearer and sharper edges than linear interpolation methods for all synthetic and natural images we have tested ease can be implemented with ease it turns out to be similarly efficient as cubic interpolation schemes

regularity preserving image interpolation assumptions about image continuity lead to oversmoothed edges in common image interpolation algorithms a wavelet based interpolation method that imposes no continuity constraints is introduced the algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and preserves the underlying regularity by extrapolating a new subband to be used in image resynthesis the algorithm produces visibly sharper edges than traditional techniques and exhibits an average peak signal to noise ratio psnr improvement of 2 5 db over bilinear and bicubic techniques

a numerical study of some radial basis function based solution methods for elliptic pdes abstract during the last decade three main variations have been proposed for solving elliptic pdes by means of collocation with radial basis functions rbfs in this study we have implemented them for infinitely smooth rbfs and then compared them across the full range of values for the shape parameter of the rbfs this was made possible by a recently discovered numerical procedure that bypasses the ill conditioning which has previously limited the range that could be used for this parameter we find that the best values for it often fall outside the range that was previously available we have also looked at piecewise smooth versus infinitely smooth rbfs and found that for pde applications with smooth solutions the infinitely smooth rbfs are preferable mainly because they lead to higher accuracy in a comparison of rbf based methods against two standard techniques a second order finite difference method and a pseudospectral method the former gave a much superior accuracy

composition operators induced by smooth self maps of the unit ball in cn we study the composition operator c induced by an analytic self map of the unit ball bn in cn that extends to be smooth on b n when is of class c3 on b n we extend to weighted bergman spaces w r wogen s characterization of when c is bounded on hp bn next when is of class c4 on b n we show that if 0 and c a p bn a 1 4 p bn then c is bounded on a p bn the discrete jump of size 1 4 in the exponent of the weight is sharp examples are given that show the assumption is smooth is essential in these theorems

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

nonexistence of positive solutions to a semilinear elliptic system and blow up estimates for a reaction diffusion system abstract we get simple conditions under which the elliptic system u u p 1 v q 1 v u p 2 v q 2 in r n n 3 with p i q i 1 i 1 2 has no positive radially symmetric solutions then by using this nonexistence result we establish blow up estimates for reaction diffusion system of fujita type u t u u p 1 v q 1 v t v u p 2 v q 2 with the homogeneous dirichlet boundary value condition

bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities in this paper we establish the lower and upper bounds for the blow up time of the solution to a system of parabolic equations u t u u r x t v s x t d x in 0 t v t v v q x t u p x t d x in 0 t subject to u x t v x t 0 on 0 t and nonnegative initial data under certain assumptions here r n is a smooth bounded open domain and n 3

blowing up of solution for a nonlocal reaction diffusion problem in combustion theory abstract in a nonlocal reaction diffusion model in combustion theory the reaction function involves a physical parameter which is a measure of the strength of the reaction mechanism the purpose of this paper is to show the existence of a critical value such that for a unique global time dependent solution exists and converges to a steady state solution as t and for the solution blows up in finite time a characterization as well as upper and lower bounds of are given

blow up for a degenerate parabolic equation with a nonlocal source abstract in this paper existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained for the degenerate parabolic problem x q u t u xx 0 a u m x t d x ku n x t in 0 a 0 t where 0 t a 0 m n 1 k 0 are constants

the blow up rate for a degenerate parabolic equation with a non local source abstract in this paper we establish the local existence of the solution and the finite time blow up result for the equation v v m xx a l l v q dx x l l 0 moreover it is proved that the solution has global blow up and there exist constants c 1 c 2 such that c 1 t 1 1 q 1 max x l l v x c 2 t 1 1 q 1 where t 1 is the blow up time

global existence and asymptotic behavior of solutions to a nonlocal fisher kpp type problem abstract in this work we consider a nonlocal fisher kpp reaction diffusion problem with neumann boundary condition and nonnegative initial data in a bounded domain in r n n 1 with reaction term u 1 m t where m t is the total mass at time t with the help of poho aev s identity the non existence of nontrivial stationary solutions with dirichlet boundary conditions is being shown when 1 and the initial mass is greater than or equal to one the problem has nonnegative classical solutions while if the initial mass is less than one then the problem admits global solutions for n 1 2 with any 1 2 or n 3 with any 1 1 2 n moreover the asymptotic convergence to the solution of the heat equation is proved

global existence and blow up solutions for doubly degenerate parabolic system with nonlocal source abstract this paper deals with the following nonlocal doubly degenerate parabolic system u t div u m p 2 u m a u 1 x t v 1 x t d x v t div v n q 2 v n b u 2 x t v 2 x t d x with null dirichlet boundary conditions in a smooth bounded domain r n where m n 1 p q 2 i i 0 i 1 2 and a b 0 are positive constants we first get the non existence result for a related elliptic systems of non increasing positive solutions secondly by using this non existence result blow up estimates for above non newton polytropic filtration systems with the homogeneous dirichlet boundary value conditions are obtained then under appropriate hypotheses we establish local theory of the solutions and prove that the solution either exists globally or blows up in finite time in the special case 1 n q 1 2 2 m p 1 1 we also give a criterion for the solution to exist globally or blow up in finite time which depends on a b and x x as defined in the main results

segment adaptive gradient angle interpolation we introduce a new edge directed interpolator based on locally defined straight line approximations of image isophotes spatial derivatives of image intensity are used to describe the principal behavior of pixel intersecting isophotes in terms of their slopes the slopes are determined by inverting a tridiagonal matrix and are forced to vary linearly from pixel to pixel within segments image resizing is performed by interpolating along the approximated isophotes the proposed method can accommodate arbitrary scaling factors provides state of the art results in terms of psnr as well as other quantitative visual quality metrics and has the advantage of reduced computational complexity that is directly proportional to the number of pixels

new general solutions to linear fredholm integro differential equations and their applications on solving the boundary value problems abstract this paper introduces the n general solution to linear fredholm integro differential equations and sets its properties the conditions for existence of classical general solution and solvability criteria for the equation are provided necessary and sufficient conditions for solvability of linear boundary value problems are established algorithms for construction of the n general solutions are obtained this paper also proposes approximate and numerical methods to solve the boundary value problems

blowup estimates for a semilinear reaction diffusion system this paper deals with the blowup estimates of positive solutions for a semilinear reaction diffusion system ut u u vp vt v uqv with null dirichlet boundary conditions the upper and lower bounds of blowup rates are obtained

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

on global attractor for m laplacian parabolic equation with local and nonlocal nonlinearity abstract in this paper we study the long time behavior of solutions for m laplacian parabolic equation u t m u a x u u f 0 u k y u y t d y g x in 0 with the initial data u x 0 u 0 x l q q 1 and zero boundary condition in two cases for a x a 0 0 and a x 0 are considered we obtain the existence and l p estimate of global attractor a in l p for any p max 1 q the attractor a is in fact a bounded set in w 0 1 m l if a x a 0 0 in and a is bounded in w 0 1 m l p if a x 0 in

blow up estimate in a reaction diffusion equation with nonlinear nonlocal flux and source abstract this paper deals with a reaction diffusion equation with nonlocal inner source and nonlocal boundary flux besides the influence of exponents we find out that the weighted functions and the measure of the domain could lead to the existence of global solutions for any initial data larger weighted functions require smaller initial data in guaranteeing the existence of global solutions to the problem blow up rates are obtained under different dominations of nonlinearities in one dimensional space the upper and lower bounds of blow up time are determined for all spatial dimensions respectively moreover the solutions blow up only on the boundary when the nonlocal flux dominates the blow up

properties of non simultaneous blow up solutions in nonlocal parabolic equations abstract this paper deals with blow up solutions in parabolic equations coupled via nonlocal nonlinearities subject to homogeneous dirichlet conditions firstly some criteria on non simultaneous and simultaneous blow up are given including four kinds of phenomena i the existence of non simultaneous blow up ii the coexistence of non simultaneous and simultaneous blow up iii any blow up must be simultaneous iv any blow up must be non simultaneous next total versus single point blow up are classified completely moreover blow up rates are obtained for both non simultaneous and simultaneous blow up solutions

on compactness of the difference of composition operators abstract let and be analytic self maps of the unit disc and denote by c and c the induced composition operators the compactness and weak compactness of the difference t c c are studied on h p spaces of the unit disc and l p spaces of the unit circle it is shown that the compactness of t on h p is independent of p 1 the compactness of t on l 1 and m the space of complex measures is characterized and examples of and are constructed such that t is compact on h 1 but non compact on l 1 other given results deal with l weakly compact counterparts of the previous results and a conjecture of j e shapiro

uniform blow up rate for a nonlocal degenerate parabolic equations abstract in this paper we introduce a new method for investigating the rate of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms in some cases we prove that the solutions have global blow up and the rate of blow up is uniform in all compact subsets of the domain in each case the blow up rate of u t is precisely determined

an application of atomic decomposition in bergman spaces to the study of differences of composition operators abstract in this paper we characterize bounded differences of composition operators from standard weighted bergman spaces a p into lebesgue spaces l q when 1 and p q in the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in saukko 2011 18 by combining the results of this paper with those of saukko 2011 18 we obtain a complete characterization of bounded and compact differences between standard weighted bergman spaces

a quasilinear reaction diffusion system coupled via nonlocal sources in this paper we establish the critical exponent and the blow up rate for a quasilinear reaction diffusion system with nonlocal nonlinear sources and inner absorptions subject to homogeneous dirichlet conditions and nonnegative initial data it is found that the critical exponent is determined by the interaction among all the six nonlinear exponents from all the three kinds of the nonlinearities while the blow up rate is independent of the nonlinear diffusion exponents due to the effects of the coupled nonlocal sources two kinds of characteristic algebraic systems are introduced to get simple descriptions for the critical exponent and the blow up rate respectively we prove moreover that the blow up could be global due to the nonlocality of the nonlinear sources

blow up properties for a degenerate parabolic system with nonlinear localized sources abstract this paper deals with blow up properties for a degenerate parabolic system with nonlinear localized sources subject to the homogeneous dirichlet boundary conditions the main aim of this paper is to study the blow up rate estimate and the uniform blow up profile of the blow up solution our conclusions extend the results of l l du blow up for a degenerate reaction diffusion system with nonlinear localized sources j math anal appl 324 2006 304 320 at the end the blow up set and blow up rate with respect to the radial variable is considered when the domain is a ball

image interpolation by adaptive 2 d autoregressive modeling and soft decision estimation the challenge of image interpolation is to preserve spatial details we propose a soft decision interpolation technique that estimates missing pixels in groups rather than one at a time the new technique learns and adapts to varying scene structures using a 2 d piecewise autoregressive model the model parameters are estimated in a moving window in the input low resolution image the pixel structure dictated by the learnt model is enforced by the soft decision estimation process onto a block of pixels including both observed and estimated the result is equivalent to that of a high order adaptive nonseparable 2 d interpolation filter this new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods and it produces the best results so far over a wide range of scenes in both psnr measure and subjective visual quality edges and textures are well preserved and common interpolation artifacts blurring ringing jaggies zippering etc are greatly reduced

fast and efficient second order method for training radial basis function networks this paper proposes an improved second order iso algorithm for training radial basis function rbf networks besides the traditional parameters including centers widths and output weights the input weights on the connections between input layer and hidden layer are also adjusted during the training process more accurate results can be obtained by increasing variable dimensions initial centers are chosen from training patterns and other parameters are generated randomly in limited range taking the advantages of fast convergence and powerful search ability of second order algorithms the proposed iso algorithm can normally reach smaller training testing error with much less number of rbf units during the computation process quasi hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors respectively only one jacobian row is stored and used for multiplication instead of the entire jacobian matrix storage and multiplication memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns several practical discrete and continuous classification problems are applied to test the properties of the proposed iso training algorithm

blow up for a degenerate reaction diffusion system with nonlinear nonlocal sources this paper investigates the global existence and blow up of nonnegative solution of the systemu email protected m u p email protected wv q 1dx v email protected n v p email protected wu q 2dx x t email protected 0 t with homogeneous dirichlet boundary conditions where email protected r n is a bounded domain with smooth boundary email protected m n 1 p 1 p 2 q 1 q 2 0 the results depend crucially on the number p i q i m n the domain w and the initial data u 0 x v 0 x moreover we obtain the blow up rate of the blow up solution under some appropriate hypotheses

blow up behavior of positive solutions for a chemical fuel ignition device model blow up behavior of positive solutions of a semi linear parabolic system arising from thermal explosion which subject to the homogenous dirichlet boundary conditions is investigated in particular sufficient conditions for the solutions to blow up are obtained

blow up rate and profile for a degenerate parabolic system coupled via nonlocal sources this paper deals with a degenerate parabolic system with nonlocal nonlinear sources subject to homogeneous dirichlet condition we establish the critical exponent as well as the blow up rate and profile for the system it is interesting to observe that the blow up exponent is determined by the interaction between the nonlinear diffusion and the nonlinear reaction while the blow up rate is independent of the nonlinear diffusion the effects from the nonlocality of the sources are substatial

the utilization of total mass to determine the switching points in the symmetric boundary control problem with a linear reaction term abstract the authors study the problem u t u x x u 0 x 1 t 0 u x 0 0 and u 0 t u 1 t t where t u 0 for t 2 k t t 2 k 1 and t 0 for t 2 k 1 t t 2 k 2 k 0 1 2 with t 0 0 and the sequence t k is determined by the equations 0 1 u x t k d x m for k 1 3 5 and 0 1 u x t k d x m for k 2 4 6 and where 0 m m note that the switching points t k k 1 2 3 are unknown existence and uniqueness are demonstrated theoretical estimates of the t k and t k 1 t k are obtained and numerical verifications of the estimates are presented the case of u x 0 t u x 1 t t is also considered and analyzed

compact linear combinations of composition operators induced by linear fractional maps it has been known that the difference of two composition operators induced by linear fractional self maps of a ball cannot be nontrivially compact on either the hardy space or any standard weighted bergman space in this paper we extend this result in two significant directions the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

the role of non linear diffusion in non simultaneous blow up we study a parabolic system of two non linear reaction diffusion equations completely coupled through source terms and with power like diffusivity under adequate hypotheses on the initial data we prove that non simultaneous blow up is sometimes possible i e one of the components blows up while the other remains bounded the conditions for non simultaneous blow up rely strongly on the diffusivity parameters and significant differences appear between the fast diffusion and the porous medium case surprisingly flat homogeneous in space solutions are not always a good guide to determine whether non simultaneous blow up is possible

linear relations in the calkin algebra for composition operators we consider this and related questions when is a finite linear combination of composition operators acting on the hardy space or the standard weighted bergman spaces on the unit disk a compact operator

on a degenerate nonlocal parabolic equation with variable source abstract we study the dirichlet problem for the degenerate nonlocal parabolic equation u t div a u l 2 2 u b u l 2 2 u q x t 2 u f in q t where q t 0 t t 0 r n n 2 is a bounded domain with a sufficiently smooth boundary a b are real valued functions defined on r and q x t is a measurable function in q t with values in an interval q q 1 we show that under appropriate conditions on a b q the problem has a global in time solution and find conditions of uniqueness sufficient conditions for extinction in finite time or strict positivity of u t l 2 for all t 0 are found in the case f 0 the decay rates for u t l 2 are derived

nonlinear image upsampling method based on radial basis function interpolation in this paper we present a novel edge directed upsampling method based on radial basis function rbf interpolation in order to remove artifacts such as blurred edges or blocking effects we suggest a nonlinear method capable of taking edge information into account the resampling evaluation is determined according to the edge orientation the proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods the algorithm is compared with some well known linear schemes as well as recently developed nonlinear schemes the resulting images demonstrate the new algorithm s ability to magnify an image while preserving the edge features

a class of non linear non classical parabolic equations abstract in this paper we deal with a class of non classical parabolic equations which arise from some practical problems such as the identification of unknown parameters free boundary problems etc one of the characteristics of this kind of equation is that the maximum principle is no longer valid we will first study the local solvability for a general equation of this kind via an auxiliary problem and the schauder fixed point principle then some a priori estimates are derived to establish the global existence of the solution moreover uniqueness and continuous dependence of the solution are proved finally some examples are given to illustrate the applications of the theory

uniform blow up profile for a degenerate parabolic system with nonlocal source in this paper we establish the local existence of the solution and the finite time blow up result for the following system ut ur1 u a updx forx ohm t 0 ut ur2 u b uqdx forx ohm t 0 where p q 1 and 0 r1 r2 1 moreover it is proved that the solution has global blow up and limt t t t p 1 r2 yu x t 1 r1 11 r1 a a y p 1 r2 y q 1 r1 py xa p 1 r2 b1 r2 y limt t t t q 1 r1 yu x t 1 r2 11 r2 b a y q 1 r1 y p 1 r2 qy xb q 1 r1 a1 r1 y uniformly on compact subsets of where pq 1 r1 1 r2 and t is the blow up time

estimates for the blowup time of a combustion model with nonlocal heat sources abstract in this paper we establish the lower and upper bounds for the blowup time of the solution to a system of parabolic equations with nonlocal nonlinearities which appears in a model of combustion different techniques are applied to deal with the problems in different space dimensions we also discuss non simultaneous blowup phenomenon of the solution

blow up rate estimates for semilinear parabolic systems abstract this paper deals with the blow up rate estimates of positive solutions for semilinear parabolic systems with null dirichlet boundary conditions the upper and lower bounds of blow up rate were obtained

image zooming method using edge directed moving least squares interpolation based on exponential polynomials this paper presents a nonlinear image interpolation algorithm the suggested method is based on the moving least squares mls projection technique but introduces a fundamental modification the algebraic polynomial based mls methods provide very satisfactory results however the associated approximation space is shift and scale invariant so that it cannot be adjusted according to the characteristic of a given data as a result when upsampling images it has a limitation in producing sharp edges such that edges are often blurred in the magnified images to recover sharper edges we need to reduce smoothing parameter or adapt a new parameter sharpening the edges motivated by this observations we propose a novel mls method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data moreover for a better match to the local structures around the edges the suggested algorithm uses weights which consider the edge orientation numerical results are presented and compared visually and by using some quantitative fidelity measures psnr epsnr ssim and fsim to the bicubic spline interpolation and other recently developed nonlinear methods the results demonstrate the new algorithm s ability to magnify an image while preserving edge features

markov random field model based edge directed image interpolation this paper presents an edge directed image interpolation algorithm in the proposed algorithm the edge directions are implicitly estimated with a statistical based approach in opposite to explicit edge directions the local edge directions are indicated by length 16 weighting vectors implicitly the weighting vectors are used to formulate geometric regularity gr constraint smoothness along edges and sharpness across edges and the gr constraint is imposed on the interpolated image through the markov random field mrf model furthermore under the maximum a posteriori mrf framework the desired interpolated image corresponds to the minimal energy state of a 2 d random field given the low resolution image simulated annealing methods are used to search for the minimal energy state from the state space to lower the computational complexity of mrf a single pass implementation is designed which performs nearly as well as the iterative optimization simulation results show that the proposed mrf model based edge directed interpolation method produces edges with strong geometric regularity compared to traditional methods and other edge directed interpolation methods the proposed method improves the subjective quality of the interpolated edges while maintaining a high psnr level

asymptotic behaviour of nonlocal reaction diffusion equations abstract the existence of a global attractor in l 2 is established for a reaction diffusion equation on a bounded domain in r d with dirichlet boundary conditions where the reaction term contains an operator f l 2 l 2 which is nonlocal and possibly nonlinear existence of weak solutions is established but uniqueness is not required compactness of the multivalued flow is obtained via estimates obtained from limits of galerkin approximations in contrast with the usual situation these limits apply for all and not just for almost all time instants

joint carleson measure and the difference of composition operators on aαp bn we introduce a concept of joint carleson measure and characterize when the difference of two composition operators on a p bn the weighted bergman space over the unit ball bn in cn is bounded or compact we apply this joint carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n 2 this is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p 0 moreover the compact difference on the weighted bergman spaces over the unit disc is known to be independent of p 0 and the compact difference on a p bn is known to be independent of p 0 if each composition operator is bounded on a p bn for some 1 2

a mathematical analysis of blowup for thermal reactions the spatially nonhomogeneous case the equations describing the induction period process for a super critical high activation energy thermal explosion in a bounded domain are studied a formal proof based on comparison techniques is used to show that the temperature perturbation becomes unbounded as t to t b leqq infty for values of the frank kamenetski parameter delta greater than the critical value upper and lower bound estimates for t b are found by using specified comparison equations a comparison of these bounds with values of t b obtained from numerical solutions of the basic equations shows that the estimates provide an excellent prediction of the escape time when delta is greater than 2 3 times the critical value for smaller values of delta where heat loss is more significant a better comparison equation is required

difference of composition operators between standard weighted bergman spaces we obtain estimates for the norm and essential norm of the difference of two composition operators between certain bergman spaces in particular a necessary and sufficient condition for boundedness and compactness of the operator is established finally we give a sufficient condition for boundedness and compactness of the difference operator between hardy spaces

roles of weight functions in a nonlinear nonlocal parabolic system abstract this paper deals with a semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal dirichlet boundary conditions we establish the conditions for global and non global solutions it is interesting to observe that the weight functions for the nonlocal dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or non global but also whether for the non global solutions the blowing up occurs for any positive initial data or just for large ones

time weighted blow up profiles in a nonlinear parabolic system with fujita exponent abstract in this paper we deal with a time weighted parabolic system coupled via nonlocal sources firstly we give the critical fujita exponent of solutions secondly we propose the time weighted blow up profiles of solutions thirdly the simultaneous and non simultaneous blow up of solutions are discussed under some conditions on the initial data fourthly besides blow up rates we classify total blow up and single point blow up of solutions at last upper and lower bounds of blow up time are studied according to precise blow up phenomena

on the connected component of compact composition operators on the hardy space we show that there exist non compact composition operators in the connected component of the compact ones on the classical hardy space h2 this answers a question posed by shapiro and sundberg in 1990 we also establish an improved version of a theorem of maccluer giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols as a main tool we use aleksandrov clark measures

compact double differences of composition operators on the bergman spaces abstract as is well known on the weighted bergman spaces over the unit disk compactness of differences of two composition operators is characterized by certain cancellation property of the inducing maps at every bad boundary point which makes each composition operator in the difference fail to be compact recently the second and third authors obtained a result implying that double difference cancellation is not possible for linear combinations of three composition operators in this paper we obtain a complete characterization for compact double differences formed by four composition operators applying our characterization we easily recover known results on linear combinations of two or three composition operators as another application we also show that double difference cancellation is possible for linear combinations of four composition operators by constructing an explicit example of a compact double difference formed by two noncompact differences in spite of such an example our characterization also shows that double difference cancellation may occur in the global sense only and that genuine double difference cancellation is not possible in a certain local sense

a new orientation adaptive interpolation method we propose an isophote oriented orientation adaptive interpolation method the proposed method employs an interpolation kernel that adapts to the local orientation of isophotes and the pixel values are obtained through an oriented bilinear interpolation we show that by doing so the curvature of the interpolated isophotes is reduced and thus zigzagging artifacts are largely suppressed analysis and experiments show that images interpolated using the proposed method are visually pleasing and almost artifact free

an edge guided image interpolation algorithm via directional filtering and data fusion preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high resolution image from a low resolution counterpart we propose a new edge guided nonlinear interpolation technique through directional filtering and data fusion for a pixel to be interpolated two observation sets are defined in two orthogonal directions and each set produces an estimate of the pixel value these directional estimates modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square error estimation lmmse technique into a more robust estimate using the statistics of the two observation sets we also present a simplified version of the lmmse based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

global existence and blow up for a nonlinear reaction diffusion system abstract we consider the nonlinear reaction diffusion system u t u u m 1 v n 1 v t v u m 2 v n 2 subject to dirichlet boundary conditions andm2 m1 1 n1 n2 1 we prove that ifm1 1 n2 1 andm2n1 1 m1 1 n2 all nonnegative solutions are global while ifm1 1 orn2 1 orm2n1 1 m1 1 n2 both global existence and finite time blow up coexist

warped distance for space variant linear image interpolation the problem of image interpolation using linear techniques is dealt with in this paper conventional space invariant methods are revisited and changed into space variant ones by introducing the concept of the warped distance among the pixels of an image a better perceptual rendition of the image details is obtained in this way this effect is proved both via the evaluation of the response to an idealized sigmoidal edge model and with experiments on real world images the computational costs of the proposed approach are very small when compared to those of state of the art nonlinear interpolation operators

cancellation properties of composition operators on bergman spaces abstract the compact difference of two composition operators on the bergman spaces over the unit disc is characterized in 11 in terms of certain cancellation property of the inducing maps at every bad boundary points which make each single composition operator not to be compact in this paper we completely characterize the compactness of a linear combination of three composition operators on the bergman space as one consequence of this characterization we show that there is no cancellation property for the compactness of double difference of composition operators more precisely we show that if i are distinct and none of c i is compact then c 1 c 2 c 3 c 1 is compact if and only if both c 1 c 2 and c 3 c 1 are compact

interpolation revisited medical images application based on the theory of approximation this paper presents a unified analysis of interpolation and resampling techniques an important issue is the choice of adequate basis functions the authors show that contrary to the common belief those that perform best are not interpolating by opposition to traditional interpolation the authors call their use generalized interpolation they involve a prefiltering step when correctly applied the authors explain why the approximation order inherent in any basis function is important to limit interpolation artifacts the decomposition theorem states that any basis function endowed with approximation order ran be expressed as the convolution of a b spline of the same order with another function that has none this motivates the use of splines and spline based functions as a tunable way to keep artifacts in check without any significant cost penalty the authors discuss implementation and performance issues and they provide experimental evidence to support their claims

further spectral properties of uniformly elliptic operators that include a non local term in this paper we consider the eigenvalues of a class of non local differential operators the real eigenvalues of certain examples of these operators have previously been plotted as functions of a fundamental parameter in the operator using appropriate computer software here we show how the complex eigenvalues of such operators may also be plotted we use the plots of both the real and the complex eigenvalues to motivate a number of new theoretical results regarding the structure of the spectrum which we subsequently prove under suitable hypotheses