equilibria for the n vortex problem in a general bounded domain abstract this article is concerned with the study of existence of stationary solutions for the dynamics of n point vortices in an idealised fluid constrained to a bounded two dimensional domain which is governed by a hamiltonian system i d x i d t h y i z 1 z n i d y i d t h x i z 1 z n where z i x i y i i 1 n under selected conditions on the vorticities i and various topological and geometrical assumptions on here h z j 1 n j 2 h z j i j 1 i j n i j g z i z j is the so called kirchhoff routh path function in particular we will prove that h has a critical point if it is possible to align the vortices along a line such that the signs of the i are alternating and i is non increasing we are also able to derive a critical point of h if j j j 2 i j j i j i j for all j 1 n j 2 and is not simply connected

enhanced local texture feature sets for face recognition under difficult lighting conditions making recognition more reliable under uncontrolled lighting conditions is one of the most important challenges for practical face recognition systems we tackle this by combining the strengths of robust illumination normalization local texture based face representations distance transform based matching kernel based feature extraction and multiple feature fusion specifically we make three main contributions 1 we present a simple and efficient preprocessing chain that eliminates most of the effects of changing illumination while still preserving the essential appearance details that are needed for recognition 2 we introduce local ternary patterns ltp a generalization of the local binary pattern lbp local texture descriptor that is more discriminant and less sensitive to noise in uniform regions and we show that replacing comparisons based on local spatial histograms with a distance transform based similarity metric further improves the performance of lbp ltp based face recognition and 3 we further improve robustness by adding kernel principal component analysis pca feature extraction and incorporating rich local appearance cues from two complementary sources gabor wavelets and lbp showing that the combination is considerably more accurate than either feature set alone the resulting method provides state of the art performance on three data sets that are widely used for testing recognition under difficult illumination conditions extended yale b cas peal r1 and face recognition grand challenge version 2 experiment 4 frgc 204 for example on the challenging frgc 204 data set it halves the error rate relative to previously published methods achieving a face verification rate of 88 1 at 0 1 false accept rate further experiments show that our preprocessing method outperforms several existing preprocessors for a range of feature sets data sets and lighting conditions

critical points of the n vortex hamiltonian in bounded planar domains and steady state solutions of the incompressible euler equations we prove the existence of critical points of the n vortex hamiltonian h kr x 1 ldots x n sum n i 1 gamma 2 i h x i sum genfrac 0pt i j 1 j ne k n gamma i gamma jg x i x j 2 sum i 1 n gamma i psi 0 x i in a bounded domain omega subset mathbb r 2 which may be simply or multiply connected here g denotes the green function for the dirichlet laplace operator in omega more generally a hydrodynamic green function and h the robin function moreover psi 0 in mathcal c 1 overline omega is a harmonic function on omega we obtain new critical points x x 1 dots x n for n 3 or n 4 under conditions on the vorticities gamma i in mathbb r setminus 0 these critical points correspond to point vortex equilibria of the euler equation in vorticity form the case gamma i 1 i of counterrotating vortices with identical vortex strength is included the point vortex equilibria can be desingularized to obtain smooth steady sta

analytical formulae for the kirchhoff routh path function in multiply connected domains explicit formulae for the kirchhoff routh path functions or hamiltonians governing the motion of n point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero the method uses the schottky klein prime function to find representations of the hydrodynamic green s function in multiply connected circular domains the green s function is then used to construct the associated kirchhoff routh path function the path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains illustrative examples are presented for the case of single vortex motion in multiply connected domains

extension of the furuta inequality and ando hiai log majorization abstract ando and hiai have obtained many excellent log majorization results for power means of positive semidefinite matrices one of these results ensures matrix norm inequalities for unitarily invariant norms which are considered as complementary to the golden thompson inequality firstly we show an extension of the furuta inequality by using itself secondary by using techniques due to ando and hiai and also using this extension of the furuta inequality we extend some results on log majorization

ordinal measures for image correspondence we present ordinal measures of association for image correspondence in the context of stereo linear correspondence measures like correlation and the sum of squared difference between intensity distributions are known to be fragile ordinal measures which are based on relative ordering of intensity values in windows rank permutations have demonstrable robustness by using distance metrics between two rank permutations ordinal measures are defined these measures are independent of absolute intensity scale and invariant to monotone transformations of intensity values like gamma variation between images we have developed simple algorithms for their efficient implementation experiments suggest the superiority of ordinal measures over existing techniques under nonideal conditions these measures serve as a general tool for image matching that are applicable to other vision problems such as motion estimation and texture based image retrieval

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

harmonic radius and concentration of energy hyperbolic radius and liouville s equations d u e u and d u u n 2 n 2 the conformal radius of a simply connected planar domain omega is defined as r x 1 f x where f denotes a riemann map from omega to the unit disk mapping the given point x to the origin beyond geometric function theory the conformal radius has various applications in partial differential equations therefore it is desirable to extend it to multiply connected and higher dimensional domains we discuss two natural extensions 1 the harmonic radius is defined in terms of the green s function its maximum points the harmonic centers play an important role in variational problems involving concentration of energy they are of the following form sup left int limits omega f u u in h 0 1 omega int omega nabla u 2 leqslant varepsilon 2 right as varepsilon to 0 the solutions concentrate at a harmonic center our examples include bernoulli s free boundary problem the plasma problem and the elastic membrane with a movable obstacle an efficient method

a converse inequality of higher order weighted arithmetic and geometric means of positive definite operators in this paper we consider weighted arithmetic and geometric means of higher orders constructed by the symmetrization method appeared in ando li mathias s definition of multi variable geometric means and the arithmetic geometric mean inequality of higher order weighted version we establish a converse inequality of higher order weighed arithmetic and geometric means via specht ratio

the fixed energy problem for a class of nonconvex singular hamiltonian systems we consider a noncompact hypersurface h in r2n which is the energy level of a singular hamiltonian of strong force type under global geometric assumptions on h we prove that it carries a closed characteristic as a consequence of a result by hofer and viterbo on the weinstein conjecture in cotangent bundles of compact manifolds our theorem contains as particular cases earlier results on the fixed energy problem for singular lagrangian systems of strong force type

convexity of solutions of semilinear elliptic equations on considere le probleme elliptique suivant u f u dans u m sur ou est un domaine convexe de r 2 et m est soit une constante reelle soit on etablit que pour une bonne fonction monotone g t pout toute solution u on a g u est strictement convexe dans

periodic solutions of the n vortex hamiltonian system in planar domains abstract we investigate the existence of collision free nonconstant periodic solutions of the n vortex problem in domains c these are solutions z t z 1 t z n t n of the first order hamiltonian system z k t i z k h z t k 1 n where the hamiltonian h has the form h z 1 z n 1 2 j k 1 j k n log 1 z j z k f z the function f n r depends on the regular part of the hydrodynamic green s function and is unbounded from above f z if z k for some k the hamiltonian is unbounded from above and below it is singular not integrable energy surfaces are not compact and not known to be of contact type using singular perturbation techniques and conley index theory we prove the existence of a family of periodic solutions z r t 0 r r 0 with arbitrarily small minimal period t r 0 as r 0 the solutions are close to the singular set of h our result applies in particular to generic bounded domains which may be simply or multiply connected it also applies to certain unbounded domains depending on the domain there are multiple such families

global continua of periodic solutions of singular first order hamiltonian systems of n vortex type the paper deals with singular first order hamiltonian systems of the form begin aligned gamma k dot z k t j nabla z k h z t quad z k t in omega subset mathbb r 2 k 1 dots n end aligned where j in mathbb r 2 times 2 defines the standard symplectic structure in mathbb r 2 gamma 1 dots gamma n in mathbb r setminus 0 are given and the hamiltonian h is of n vortex type begin aligned h z 1 dots z n frac 1 2 pi sum genfrac 0 0pt j k 1 j ne k n gamma j gamma k log left z j z k right f z end aligned this is defined on the configuration space z 1 ldots z n in omega n z j ne z k text for j ne k of n different points in the domain omega subset mathbb r 2 the function f omega n rightarrow mathbb r may have additional singularities near the boundary of omega n we prove the existence of a global continuum of periodic solutions z t z 1 t dots z n t in omega n that emanates after introducing a suitable singular limit scaling from a relative equilibrium z t in mathbb r 2n of the n vortex problem in the whole plane where f 0 examples for z include thomson s vortex configurations or equilateral triangle solutions the domain omega need not be simply connected a special feature is that the associated action integral is not defined on an open subset of the space of 2 pi periodic h 1 2 functions the natural form domain for first order hamiltonian systems this is a consequence of the singular character of the hamiltonian our main tool in the proof is a degree for s 1 equivariant gradient maps that we adapt to this class of potential operators

a 3d feature descriptor recovered from a single 2d palmprint image design and development of efficient and accurate feature descriptors is critical for the success of many computer vision applications this paper proposes a new feature descriptor referred to as don for the 2d palmprint matching the descriptor is extracted for each point on the palmprint it is based on the ordinal measure which partially describes the difference of the neighboring points normal vectors don has at least two advantages 1 it describes the 3d information which is expected to be highly stable under commonly occurring illumination variations during contactless imaging 2 the size of don for each point is only one bit which is computationally simple to extract easy to match and efficient to storage we show that such 3d information can be extracted from a single 2d palmprint image the analysis for the effectiveness of ordinal measure for palmprint matching is also provided four publicly available 2d palmprint databases are used to evaluate the effectiveness of don both for identification and the verification our method on all these databases achieves the state of the art performance

n vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh poisson and the lane emden fowler equations we prove the existence of equilibria of the n vortex hamiltonian in a bounded domain omega subset mathbb r 2 which is not necessarily simply connected on an arbitrary bounded domain we obtain new equilibria for n 3 or n 4 if has an axial symmetry we obtain a symmetric equilibrium for each n in mathbb n we also obtain new stream functions solving the sinh poisson equation delta psi rho sinh psi in with dirichlet boundary conditions for 0 small the stream function psi rho induces a stationary velocity field v rho solving the euler equation in on an arbitrary bounded domain we obtain velocitiy fields having three or four counter rotating vortices if has an axial symmetry we obtain for each n a velocity field v rho that has a chain of n counter rotating vortices analogous to the mallier maslowe row of counter rotating vortices in the plane our methods also yield new nodal solutions for other semilinear dirichlet problems in particular for the lane emden fowler equation delta u u p 1 u in with p large

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

kantorovich type operator inequalities via the specht ratio abstract as a converse of the arithmetic and geometric mean inequality specht gave the ratio of the arithmetic one by the geometric one in 1960 we can reap the rich harvest of the specht ratio in operator theory in this paper we shall present other characterizations of the chaotic order and the usual one associated with kantorovich type inequalities via the specht ratio among others as an application of the grand furuta inequality we show that if a and b are positive operators and k a 1 k for some k 1 then a b is equivalent to s k 2 p 1 s 2 s a p b p holds for all p 1 s 1 such that p 1 1 s where the specht ratio sk r is defined for each r 0 as s k r k r 1 k r k r 1 re log k k 0 k 1 and s 1 r 1

log majorization and complementary golden thompson type inequalities abstract we obtain a log majorization result for power means of positive semidefinite matrices this implies matrix norm inequalities for unitarily invariant norms which are considered as complementary to the golden thompson one other log majorization results are also obtained we give logarithmic trace inequalities and determinant inequalities as applications of our log majorizations

bifurcation of periodic solutions from a ring configuration in the vortex and filament problems this paper gives an analysis of the movement of n 1 almost parallel filaments or vortices starting from a polygonal equilibrium of n vortices with equal circulation and one vortex at the center of the polygon we find bifurcation of periodic solutions the bifurcation result makes use of the orthogonal degree in order to prove the global bifurcation of periodic solutions depending on the circulation of the central vortex in the case of the filament problem these solutions are periodic traveling waves