analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

analytic solutions for a stefan problem with gibbs thomson correction we provide existence of a unique smooth solution for a class of oneand two phase stefan problems with gibbs thomson correction in arbitrary space dimensions in addition it is shown that the moving interface depends analytically on the temporal and spatial variables of crucial importance for the analysis is the property of maximal lpregularity for the linearized problem which is fully developed in this paper as well

texture analysis using fractal descriptors estimated by the mutual interference of color channels fractal descriptors are used to describe color textures spatial structure and color distribution are analyzed without separating the image into channels the volumes of the dilated structure express the level of details at each scale based on the intensity color distribution the descriptors combine the efficiency of fractals in describing complex structures with the richness of color analysis the method outperformed other approaches whose effectiveness is widely attested in studies on texture analysis methods this work presents a method for color texture analysis based on fractal geometry the method is based on its predecessor 4 and consists of mapping each color channel onto a surface and dilating such surface by spheres with a variable radius the descriptors are obtained from the relation between the volumes of the dilated surfaces and the dilation radii the dilation process creates a mutual interference among the color channels the proposed descriptors measure the degree of such interference as well as the complexity of pixel intensity arrangements this combination provides a robust and precise texture description the efficiency of the method is assessed in a classification task of well known texture data sets and the results demonstrate that it outperforms the best approaches described in the literature

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

locally self similar phase diagram of the disordered potts model on the hierarchical lattice we study the critical behavior of the random q state potts model in the large q limit on the diamond hierarchical lattice with an effective dimensionality d eff 2 by varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points according to our renormalization group study the phase boundary in the vicinity of the multicritical point is self similar it is well represented by a logarithmic spiral we expect an infinite number of reentrances in the thermodynamic limit consequently one cannot define standard thermodynamic phases in this region

well posedness and stability results for a quasilinear periodic muskat problem abstract we study the muskat problem describing the spatially periodic motion of two fluids with equal viscosities under the effect of gravity in a vertical unbounded two dimensional geometry we first prove that the classical formulation of the problem is equivalent to a nonlocal and nonlinear evolution equation expressed in terms of singular integrals and having only the interface between the fluids as unknown secondly we show that this evolution equation has a quasilinear structure which is at a formal level not obvious and we also disclose the parabolic character of the equation exploiting these aspects we establish the local well posedness of the problem for arbitrary initial data in h s s with s 3 2 2 determine a new criterion for the global existence of solutions and uncover a parabolic smoothing property besides we prove that the zero steady state solution is exponentially stable

a novel multiresolution spatiotemporal saliency detection model and its applications in image and video compression salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on and finding these areas is the key step in object detection in computer vision many models have been proposed to simulate the behavior of eyes such as saliencytoolbox stb neuromorphic vision toolkit nvt and others but they demand high computational cost and computing useful results mostly relies on their choice of parameters although some region based approaches were proposed to reduce the computational complexity of feature maps these approaches still were not able to work in real time recently a simple and fast approach called spectral residual sr was proposed which uses the sr of the amplitude spectrum to calculate the image s saliency map however in our previous work we pointed out that it is the phase spectrum not the amplitude spectrum of an image s fourier transform that is key to calculating the location of salient areas and proposed the phase spectrum of fourier transform pft model in this paper we present a quaternion representation of an image which is composed of intensity color and motion features based on the principle of pft a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion fourier transform pqft is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation distinct from other models the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos in addition the pqft model can compute the saliency map of an image under various resolutions from coarse to fine therefore the hierarchical selectivity hs framework based on the pqft model is introduced here to construct the tree structure representation of an image with the help of hs a model called multiresolution wavelet domain foveation mwdf is proposed in this paper to improve coding efficiency in image and video compression extensive tests of videos natural images and psychological patterns show that the proposed pqft model is more effective in saliency detection and can predict eye fixations better than other state of the art models in previous literature moreover our model requires low computational cost and therefore can work in real time additional experiments on image and video compression show that the hs mwdf model can achieve higher compression rate than the traditional model

quaternion generic fourier descriptor for color object recognition by introducing quaternions fourier transforms the fundamental tool in signal and image processing were extended to treat a color image in a holistic manner on the other hand color image description has long been a major topic of pattern recognition in this work inspired by the quaternion fourier transforms we propose a quaternion generic fourier descriptor to describe color images holistically and effectively without losing any color information the theoretical framework to construct a set of invariants with respect to geometric transformation is also provided moreover several experiments are conducted on color image databases to illustrate the effectiveness of the proposed invariants the results provide supports for that the quaternion generic fourier descriptor invariants have striking robustness to geometric transformation and noise remarkable progress in accuracy robustness and efficiency of color object recognition has been made by the proposed descriptor in addition it presents superior performances on real recognition scenarios highlightswe propose an image descriptor with the quaternion algebra to describe color images a framework to develop robust invariants to geometric transformation is provided experiments are conducted to validate the performance of the proposed descriptor the proposed descriptor performs robustly to geometric transformation and noise a progress in accuracy of recognition has been made by the proposed descriptor on real recognition scenarios the proposed descriptor also performs superiorly

a center manifold analysis for the mullins sekerka model abstract the mullins sekerka model is a nonlocal evolution model for hypersurfaces which arises as a singular limit for the cahn hilliard equation we show that classical solutions exist globally and tend to spheres exponentially fast provided that they are close to a sphere initially our analysis is based on center manifold theory and on maximal regularity

a stable manifold theorem for the curve shortening equation on presente une famille de solutions homothetiques de l equation pour une courbe planaire x kn et on demontre l existence de varietes non lineaires stables et instables autour de telles solutions

a comparative analysis of algorithms for fast computation of zernike moments abstract this paper details a comparative analysis on time taken by the present and proposed methods to compute the zernike moments z pq the present method comprises of direct belkasim s prata s kintner s and coefficient methods we propose a new technique denoted as q recursive method specifically for fast computation of zernike moments it uses radial polynomials of fixed order p with a varying index q to compute zernike moments fast computation is achieved because it uses polynomials of higher index q to derive the polynomials of lower index q and it does not use any factorial terms individual order of moments can be calculated independently without employing lower or higher order moments this is especially useful in cases where only selected orders of zernike moments are needed as pattern features the performance of the present and proposed methods are experimentally analyzed by calculating zernike moments of orders 0 to p and specific order p using binary and grayscale images in both the cases the q recursive method takes the shortest time to compute zernike moments

multiphase thermomechanics with interfacial structure 2 evolution of an isothermal interface paper 1 1988 g 1 of this series began an investigation whose goal is a thermomechanics of two phase continua based on gibbs s notion of a sharp phase interface endowed with thermomechanical structure in that paper a balance law balance of capillary forces was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics the chief results are thermodynamic restrictions on constitutive equations exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems the simplest versions of these problems the mullins sekerka problems are essentially the classical stefan problem with the free boundary condition u 0 for the temperature replaced by the condition u h k where k is the curvature of the free boundary and h 0 is a material constant this dependence on curvature renders the problem difficult and apart from numerical studies involving linearization stability there are almost no supporting theoretical results

locations of multicritical points for spin glasses on regular lattices we present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices the conventional technique for determination of the location of the multicritical point was previously derived using a hypothesis emerging from duality and the replica method in the present study we propose a systematic technique by an improved technique giving more precise locations of the multicritical points on the square triangular and hexagonal lattices by carefully examining the relationship between two partition functions related with each other by the duality we can find that the multicritical points of the ifmmode pm else textpm fi j ising model are located at p c 0 890 phantom rule 0 2em 0ex 813 on the square lattice where p c means the probability of j ij j g0 at p c 0 835 phantom rule 0 2em 0ex 985 on the triangular lattice and at p c 0 932 phantom rule 0 2em 0ex 593 on the hexagonal lattice these results are in excellent agreement with recent numerical estimations

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

regularity of solutions to a free boundary problem modeling tumor growth by stokes equation in this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid like tissues the model equations include a quasi stationary diffusion equation for the nutrient concentration and a stokes equation with a source representing the proliferation density of the tumor cells subject to a boundary condition with stress tensor effected by surface tension this problem is a fully nonlinear problem involving nonlocal terms based on the employment of the functional analytic method and the theory of maximal regularity we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity

existence of analytic solutions for the classical stefan problem we prove that under mild regularity assumptions on the initial data the two phase classical stefan problem admits a unique solution that is analytic in space and time

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

duality and multicritical point of two dimensional spin glasses abstract we present a conjecture on the exact location of the multicritical point of models of spin glasses on the two dimensional square lattice using duality transformation the results not only agree very well with numerical estimates but also conform excellently to the existing knowledge on annealed systems and to the arguments using gauge symmetry

parabolic equations for curves on surfaces part i curves with p integrable curvature this is the first of a two part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so called curve shortening of flow by mean curvature problem as well as to a number of models for phase transitions in two dimensions we introduce a class of equations for which the initial value problem is solvable for initial data with p integrable curvature and we also give estimates for the rate at which the p norms of the curvature must blow up if the curve becomes singular in finite time a detailed discussion of the way in which solutions can become singular and a method for continuing the solution through a singularity will be the subject of the second part

duality relation for frustrated spin models we consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions we first analyze the ising model with frustrated plaquettes we use an algebraic approach to derive the result that an ising model with some of its plaquettes frustrated has a dual model which is an ising model with an external field i ensuremath pi 2 applied to the dual sites centered at frustrated plaquettes in the case where all plaquettes are frustrated this leads to the known result that the dual model has a uniform field i ensuremath pi 2 whose partition function can be evaluated in the thermodynamic limit for regular lattices the analysis is extended to a potts spin glass with analogous results obtained

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

quaternion bessel fourier moments and their invariant descriptors for object reconstruction and recognition in this paper the quaternion bessel fourier moments are introduced the significance of phase information in quaternion bessel fourier moments is investigated and an accurate estimation method for rotation angle is described furthermore a new set of invariant descriptors based on the magnitude and the phase information of quaternion bessel fourier moments is derived experimental results show that quaternion bessel fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion zernike moments quaternion pseudo zernike moments and quaternion orthogonal fourier mellin moments in addition the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments the proposed invariant descriptors show also better robustness to geometric and photometric transformations quaternion bessel fourier moments for color image reconstruction and recognition an accurate estimation method for rotation angle throughout quaternion moments the invariant descriptor using the moment magnitudes and phase coefficients

phase diagram and critical exponents of a potts gauge glass the two dimensional q state potts model is subjected to a z q symmetric disorder that allows for the existence of a nishimori line at q 2 this model coincides with the j random bond ising model for q 2 apart from the usual pure and zero temperature fixed points the ferro paramagnetic phase boundary is controlled by two critical fixed points a weak disorder point whose universality class is that of the ferromagnetic bond disordered potts model and a strong disorder point which generalizes the usual nishimori point we numerically study the case q 3 tracing out the phase diagram and precisely determining the critical exponents the universality class of the nishimori point is inconsistent with percolation on potts clusters

quaternion fourier mellin moments for color images the quaternion fourier mellin moments for describing color images are introduced which can be seen as the generalization of traditional fourier mellin moments for gray level images then the quaternion fourier mellin moment invariants are derived which could be a useful tool in color object recognition tasks that require the similarity invariance in addition the problem of color image registration using quaternion fourier mellin moments is discussed the registration method can match color images differing in rotation and scaling the advantage of our method is that it can process color image directly without losing color information experimental results validate the effectiveness of the method we proposed