equilibria of two sided matching games with common preferences problems of matching have long been studied in the operations research literature assignment problem secretary problem stable marriage problem all of these consider a centralized mechanism whereby a single decision maker chooses a complete matching which optimizes some criterion this paper analyzes a more realistic scenario in which members of the two groups buyers sellers employers workers males females randomly meet each other in pairs interviews dates over time and form couples if there is mutual agreement to do so we assume members of each group have common preferences over members of the other group generalizing an earlier model of alpern and reyniers alpern s reyniers d j 2005 strategic mating with common preferences j theor biol 237 337 354 we assume that one group called males is r times larger than the other r 1 thus all females but only 1 r of the males end up matched unmatched males have negative utility c we analyze equilibria of this matching game depending on the parameters r and c in a region of r c space with multiple equilibria we compare these and analyze their efficiency in several respects this analysis should prove useful for designers of matching mechanisms who have some control over the sex ratio e g by capping numbers of males at a singles event or by having ladies free nights or the nonmating cost c e g tax benefits to married couples

global well posedness and scattering for the defocusing l 2 critical nonlinear schrodinger equation when d 2 in this article we prove that the defocusing cubic nonlinear schrodinger initial value problem is globally well posed and scattering for u0 l2 r2 the proof uses the bilinear estimates of planchon and vega and a frequency localized interaction morawetz estimate similar to the high frequency estimate of colliander keel staffilani takaoka and tao and especially the low frequency estimate of dodson

the sharp hardy uncertainty principle for schrodinger evolutions we give a new proof of hardy s uncertainty principle up to the end point case which is only based on calculus the method allows us to ex tend hardy s uncertainty principle to schrodinger equations with non constant coefficients we also deduce optimal gaussian decay bounds for solutions to these schrodinger equations

on uniqueness properties of solutions of the k generalized kdv equations in this paper we study uniqueness properties of solutions of the so called k generalized korteweg de vries equations our goal is to obtain sufficient conditions on the behavior of the difference u1 u2 of two solutions u1 u2 of 1 1 at two different times t0 0 and t1 1 which guarantee that u1 u2

uniqueness properties of solutions of schrodinger equations under suitable assumptions on the potentials v and a we prove that if u c 0 1 h1 is a solution of the linear schrodinger equation i t x u vu a xu on rd 0 1 and if u 0 in x r 0 1 for some r 0 then u 0 in rd 0 1 as a consequence we obtain uniqueness properties of solutions of nonlinear schrodinger equations of the form i t x u g x t u u xu xu on rd 0 1 where g is a suitable nonlinear term the main ingredient in our proof is a carleman inequality of the form e x1 v lx2lt2 e x1 xv bx 2lt2 c e x1 i t x v bx1 2lt2 for any v c r h1 with v t 0 for t 0 1 in this inequality bx 2 and bx1 2 are banach spaces of functions on rd and e x1 is a suitable weight

penrose demosaicking the penrose pixel layout an aperiodic pixel layout in rhombus penrose tiling has been shown to substantially outperform the existing square pixel layout in super resolution however it was tested only on grayscale images to study its performance on color images we have to reconstruct regular color images from penrose raw images i e images with only one color component at each penrose pixel resulting in the problem of demosaicking from penrose pixels penrose demosaicking is more difficult than regular demosaicking because none of the color components of the reconstructed regular color images are available therefore most of the traditional demosaicking methods do not apply we develop a sparse representation based method for penrose demosaicking extensive experiments show that penrose pixel layout outperforms regular pixel layouts in terms of both perceptual evaluation and s cielab the penrose pixel layout is unique among all irregular layouts because it is uniformly three colorable and it has only two pixel shapes thick and thin rhombi making its manufacturing relatively easy

dispersive estimates for principally normal pseudodifferential operators the aim of these notes is to describe some recent re sults concerning dispersive estimates for principally normal pseu dodifferential operators the main motivation for this comes from unique continuation problems such estimates can be used to prove l q carleman inequalities which in turn yield unique continuation results for various partial differential operators with rough poten tials dispersive estimates are l q estimates for nonelliptic partial differ ential operators which are a consequence of the decay properties of their fundamental solutions these decay properties follow from spa tial spreading of the singularities of the solutions since solutions prop agate in directions conormal to the characteristic set of the operator this spreading can be related to nonzero curvatures of the characteristic set dispersive estimates for constant coefficient operators are closely related to the restriction theorem in harmonic analysis various types of dispersive estimates are known to be true for op erators such as the wave operator the schrodinger operator and the linear kdv see ginibre velo 4 keel tao 11 they have proved to be useful in the study of nonlinear problems as well as of problems with unbounded potentials more recently similar estimates have been obtained for wave op erators with variable coefficients beginning with the smooth case in kapitanskii 10 mockenhaupt seeger and sogge 14 up to operators with c 2 coefficients in smith 15 and tataru 21 23 similar results were obtained for the schrodinger equation in staffilani tataru 19 c 2 coefficients and in burq gerard tzvetkov 1 smooth coeffic ients in the variable coefficient elliptic case one should also mention sogge s l q

on unique continuation for the generalized schrodinger equations abstract in this paper we study the unique continuation properties of solutions of the generalized schrodinger equations we prove the carleman inequalities as well as the exponential decay weighted estimates as a consequence we obtain sufficient conditions on the behavior of the solution u at two different times t 0 0 and t 1 1 which guarantee that u 0 is the unique solution

some remarks on strichartz estimates for homogeneous wave equation abstract we give several remarks on strichartz estimates for homogeneous wave equation with special attention to the cases of l x estimates radial solutions and initial data from the inhomogeneous sobolev spaces in particular we give the failure of the endpoint estimate l t 4 l x for n 2

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

unique continuation for some evolution equations this work is concerned with unique continuation results for some evolution equations essentially of parabolic type to be more precise let l be an evolution operator acting on functions defined on some connected open set b of r r x r l is said to have the unique continuation property if every solution u of lu 0 which vanishes one some nonempty open set u i of fl vanishes in the horizontal component of o in 0 i e in x t e 0 3x x t e co the first general result of this type was established by mizohata 6 in the case where l is a second order parabolic operator with smooth coefficients however mizohata s proof is somewhat delicate it is based in particular on an extended class of calderon zygmund operators and does not lead obviously to a weakening of the smoothness of the coefficients on the other hand it is important for the applications to deal with nonsmooth coefficients since l is often obtained as the linearization of some nonlinear operator at a nonnecessarily smooth solution we refer to lions 4 and kernevez and lions 3 for applications to control theory and to 1 l for applications to transversality techniques let us now describe the content of this work in the first section we prove a unique continuation theorem when l is a second order parabolic equation our proof is simple and based on the derivation of a carleman estimate which is reminiscent of the classical carleman estimates for second order elliptic operators see 121 this carleman inequality allows the weakening of the 118 0022 0396187 3 00

unique continuation properties of the higher order nonlinear schrodinger equations in one dimension abstract in this paper we study the unique continuation properties of the higher order nonlinear schrodinger equations in one dimension and show exponential decay weighted estimates as well as a l p type carleman estimate based on the littlewood paley theory as a consequence we obtain that if u is a solution of the schrodinger equation such that there exists x 0 with supp u 0 supp u 1 x 0 or x 0 then u 0 in r 0 1

universal demosaicking of color filter arrays a large number of color filter arrays cfas periodic or aperiodic have been proposed to reconstruct images from all different cfas and compare their imaging quality a universal demosaicking method is needed this paper proposes a new universal demosaicking method based on inter pixel chrominance capture and optimal demosaicking transformation it skips the commonly used step to estimate the luminance component at each pixel and thus avoids the associated estimation error instead we directly use the acquired cfa color intensity at each pixel as an input component two independent chrominance components are estimated at each pixel based on the inter pixel chrominance in the window which is captured with the difference of cfa color values between the pixel of interest and its neighbors two mechanisms are employed for the accurate estimation distance related and edge sensing weighting to reflect the confidence levels of the inter pixel chrominance components and pseudoinverse based estimation from the components in a window then from the acquired cfa color component and two estimated chrominance components the three primary colors are reconstructed by a linear color transform which is optimized for the least transform error our experiments show that the proposed method is much better than other published universal demosaicking methods

global unique continuation from a half space for the schrodinger equation abstract we obtain a global unique continuation result for the differential inequality i t u v x u in r n 1 this is the first result on global unique continuation for the schrodinger equation with time independent potentials v x in r n our method is based on a new type of carleman estimates for the operator i t on r n 1 as a corollary of the result we also obtain a new unique continuation result for some parabolic equations

demosaicing by successive approximation in this paper we present a fast and high performance algorithm for color filter array cfa demosaicing cfa demosaicing is formulated as a problem of reconstructing correlated signals from their downsampled versions with an opposite phase the major contributions of this work include 1 a new iterative demosaicing algorithm in the color difference domain and 2 a spatially adaptive stopping criterion for suppressing color misregistration and zipper artifacts in the demosaiced images we have compared the proposed demosaicing algorithm with two current state of the art techniques reported in the literature ours outperforms both of them on demosaicing performance and computational cost

unique continuation type theorem for the self similar euler equations abstract we prove a unique continuation type theorem for the self similar euler equations in r 3 assuming the time periodicity namely if a time periodic solution v y s of the time dependent self similar euler equations has the property that v 0 s 0 for all s 0 s 0 where s 0 is the time period and y 0 is a local extremal point of v y s near the origin then v y s 0 for all y s r 3 0 s 0 a similar result holds for more general system with arbitrary coefficients and also for the inviscid incompressible magnetohydrodynamic mhd system as a consequence we obtain new criteria for the absence of the discretely self similar singularities for the 3d euler equations and the inviscid 3d mhd

on the boundary strichartz estimates for wave and schrodinger equations abstract we consider the l t 2 l x r estimates for the solutions to the wave and schrodinger equations in high dimensions for the homogeneous estimates we show l t 2 l x estimates fail at the critical regularity in high dimensions by using stable levy process in r d moreover we show that some spherically averaged l t 2 l x estimate holds at the critical regularity as a by product we obtain strichartz estimates with angular smoothing effect for the inhomogeneous estimates we prove double l t 2 type estimates

an edge sensing generic demosaicing algorithm with application to image resampling in this paper we introduce a new demosaicing algorithm that can be used for various sensor images captured by digital cameras equipped with various red green blue color filter arrays our algorithm enhances the universal demosaicing algorithm of lukac et al by defining a new spectral interpolation model that exploits not only the information on the color of pixels but also the relative distance between neighboring pixels within an image moreover we include an edge detection model that makes our algorithm adaptive and reduces the presence of color shifts and artifacts a series of tests has been made on images of the kodak database and our algorithm performs better than the universal demosaicing algorithm with regard to both subjective and objective evaluation the versatility of our demosaicing algorithm is also highlighted through an application to the issue of color image resampling and we obtain conclusive experimental results

rendezvous search on the interval and the circle two people are placed randomly and independently on a street of unit length they attempt to find each other in the shortest possible expected time we solve this problem assuming each searcher knows where he or she is on the street for monotonic density functions for the initial placement this includes the uniform pdf as a special case this gives an example of a rendezvous search problem where there is no advantage in being allowed to use asymmetric strategies we also solve some corresponding problems for the circle when asymmetric strategies are permitted one of these shows that it can sometimes be optimal for one player to wait for the other to find him

uniqueness properties of solutions to schrodinger equations nx j 1 2 u x 2 x 0 harmonic functions in the unit ball x r n x 2 since harmonic functions are still real analytic in x r n x 1 in fact it is well known that if p x d is a linear elliptic differential operator with real analytic coefficients andp x d u 0 in a open set r n then u is real analytic in hence the s u c p also holds for such solutions through the work of hadamard 28 on the uniqueness of the cauchy problem which is closely related to the strong unique continuation property discussed earlier it became clear for applications in nonlinear problems that it would be desirable to establish the strong unique continuation property for operators whose coefficients are not necessarily real analytic oreven c the first results in this direction were found in the pioneering work of carleman 9 when

hardy uncertainty principle convexity and parabolic evolutions we give a new proof of the l2 version of hardy s uncertainty principle based on calculus and on its dynamical version for the heat equation the reasonings rely on new log convexity properties and the derivation of optimal gaussian decay bounds for solutions to the heat equation with gaussian decay at a future time we extend the result to heat equations with lower order variable coefficient

fractal strichartz estimate for the wave equation abstract we consider strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions in r 3 1 we obtain the sharp estimate and in higher dimensions improve the previous results

strichartz estimates for the euler equations in the rotational framework abstract we consider the initial value problems of the incompressible euler equations in the rotational framework we obtain the optimal range of the strichartz estimate for the linear group associated with the coriolis forces as an application we prove that the lifespan of the solution can be taken arbitrarily large provided that the speed of rotation is sufficiently high

rendezvous search on the line we present two new results for the asymmetric rendezvous problem on the line we first show that it is never optimal for one player to be stationary during the entire search period in the two player rendezvous then we consider the meeting time of n players in the worst case and show that it has an asymptotic behavior of n 2 o log n

a note on unique continuation for the schrodinger equation abstract we show a unique continuation result for the differential inequality i t u u v u where v is a time dependent potential our results extend those in c e kenig and c d sogge 1988 7 to include potentials contained in mixed norm spaces l t p l x s also we obtain some endpoint inhomogeneous strichartz estimates for the schrodinger equation

inhomogeneous strichartz estimates for the schrodinger equation we study strichartz estimates for the solution of the cauchy problem associated with the inhomogeneous free schrodinger equation in the case when the inital data is equal to zero proving some new estimates for certain exponents and giving counterexamples for some others