a new super kp system and a characterization of the jacobians of arbitrary algebraic super curves a set of super commuting vector fields is defined on the super grassmannians a characterization of the jacobian varieties of super curves super schottky problem is established in the following manner every finite dimensional integral manifold of these vector fields has a canonical structure of the jacobian variety of an algebraic super curve and conversely the jacobian variety of an arbitrary algebraic super curve is obtained in this way the vector fields restricted on the super grassmannian of index 0 0 give a completely integrable system of partial super differential equations which gives a new supersymmetric generalization of the kp system thus every finite dimensional solution of this new system gives rise to a jacobian variety of an algebraic super curve the correspondence between this super grassmannian and the group of monic super pseudo differential operators of order zero the super sato correspondence is also established table of

titchmarsh s asymptotic formula for periodic eigenvalues and an extension to the p laplacian an asymptotic formula for periodic eigenvalues due to titchmarsh is taken to a higher degree of accuracy using a prufer transformation method not depending on floquet theory with the idea of the rotation number this method is then extended to the p laplacian

relationship between the moyal kp and the sato kp hierarchies the formula describing the isomorphism between the moyal kp and the sato kp hierarchies is given we obtain the conserved densities of the dispersionless kp hierarchy by taking the limit k to 0 of the conserved quantities derived in the sato approach

first eigenvalue of the p laplacian under integral curvature condition abstract we give various estimates of the first eigenvalue of the p laplace operator on closed riemannian manifold with integral curvature conditions

global solution branches for equations involving nonhomogeneous operators of p laplace type abstract it is shown that if is not an eigenvalue of an associated p laplacian then the equation div x u u p 2 u f x u u with nonhomogeneous which is assumed to behave asymptotically as the function generating the associated p laplacian has a global branch of solutions u also the case of modified p laplace operators and generalizations thereof are discussed

sequential ordinal modeling with applications to survival data summary this paper considers the class of sequential ordinal models in relation to other models for ordinal response data markov chain monte carlo mcmc algorithms based on the approach of albert and chib 1993 journal of the american statistical association88 669 679 are developed for the fitting of these models the ideas and methods are illustrated in detail with a real data example on the length of hospital stay for patients undergoing heart surgery a notable aspect of this analysis is the comparison based on marginal likelihoods and training sample priors of several nonnested models such as the sequential model the cumulative ordinal model and weibull and log logistic models

eigenvalues of the radial p laplacian with a potential on 0 brown and reichel recently established the existence of eigenvalues for the p laplacian on r when the potential q is either i large and positive or ii sufficiently large and negative limit circle case at infinity their methods imposed extra restrictions on q in this paper these restrictions are removed in addition the case where q decays at infinity is also shown to produce negative eigenvalues and a condition is given under which there are only a finite number of such eigenvalues

two reduction of the super kp hierarchy recursion relations are established for the residues of fractional powers of a two reduced super kp operator making use of the baker akhiezer function these show the integrability of the two reduced even or bosonic flows of the super kp hierarchy similar recursion relations are also proven for the residues of operators associated with the odd or fermionic flows of the mulase rabin super kp hierarchy due to the presence of a spectral parameter and its fermionic partner in the baker akhiezer function these recursion relations should be relevant to any attempt to prove or disprove a recent proposal that the integrable hierarchy underlying two dimensional quantum supergravity is the mulase rabin super kp hierarchy

approximation numbers singular values this paper introduces a generalisation of the notion of singular value for hilbert space operators to more general banach spaces it is shown that for a simple integral operator of hardy type the singular values are the eigenvalues of a non linear sturm liouville equation and coincide with the approximation numbers of the operator finally asymptotic formulas for the singular numbers are deduced

supersymmetric kadomtsev petviashvili hierarchy ghost symmetry structure reductions and darboux backlund solutions this paper studies manin radul supersymmetric kadomtsev petviashvili hierarchy mr skp in three related aspects i we find an infinite set of additional ghost symmetry flows spanning the same anti commutation algebra as the ordinary mr skp flows ii the latter are used to construct consistent reductions skpr 2 m 2 of the initial unconstrained mr skp hierarchy which involves a nontrivial modification for the fermionic flows iii for the simplest constrained mr skp hierarchy skp12 12 we show that the orbit of darboux backlund transformations lies on a supersymmetric toda lattice being a square root of the standard one dimensional toda lattice and also we find explicit wronskian ratio solutions for the super tau function

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

characterization of jacobian varieties in terms of soliton equations pour dans le demi espace superieur de siegel h g soit x c g z g z g la variete abelienne principalement polarisee correspondante et soit z z m e z gexp 2 i t mz i t m m la fonction theta de riemann pour x les deux conditions a et b pour x sont equivalentes a 1 il existe des vecteurs a 1 a 2 a 3 c g a 1 0 et une forme quadratique q t i j 1 3 q ij t i t j q ij c tel que pour c g t t exp q t t 1 a 1 t 2 a 2 t 3 a 3 donne une solution a l equation de kadomtsev petviashvili sous la forme d hirota d 1 4 3d 2 2 4d 1 d 3 0 2 le diviseur de x est irreductible b x est isomorphe a la variete jacobienne d une courbe lisse complete de genre g sur c

bifurcation problems for the laplacian in ⁿ in this paper we consider the bifurcation problem div ivulp 2vu ag x julp 2u f a x u in rn with p 1 we show that a continuum of positive solutions bifurcates out from the principal eigenvalue a1 of the problem div ivuip 2vu ag x ulp 2u here both functions f and g may change sign

existence of radial solutions for an asymptotically linear p laplacian problem abstract we prove that an asymptotically linear dirichlet problem which involves the p laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the p derivative of the nonlinearity includes at least the first j radial eigenvalues of the p laplacian operator the main tools that we use are a uniqueness result for the p laplacian operator and bifurcation theory

positive solutions for a class of elliptic equations abstract in this paper the existence and bifurcation of positive solutions for a class of elliptic equations involving the p laplacian are studied by using the sub and super solution method and the topological degree argument

on the existence of sign changing radial solutions to nonlinear p laplacian equations in rn abstract a class of nonlinear equations r n 1 u p 2 u r n 1 w r f u on 0 1 where 1 p is considered we study the existence of sign changing solutions to this problem some sufficient conditions for such solutions with the prescribed number of zeros are developed we generalize the result of naito and tanaka 2008 to the radial solutions of a class of nonlinear p laplacian equations in r n some related issues on the half line will be also discussed

additional symmetries for super kp hierarchies abstract with the use of vacuum wave functions for the super kp hierarchies manin radul and jacobian versions we study the additional symmetries for such integrable hierarchies

oscillation and interlacing for various spectra of the p laplacian abstract we consider the eigenvalue problem p u r q u p 1 sgn u a e on 0 b where b 0 p 1 p is the p laplacian q r l 1 0 b r 0 and r a variety of boundary conditions will be imposed at 0 and b but the main focus is on dirichlet neumann and periodic anti periodic conditions in the linear case p 2 there are well known oscillation and interlacing results for the eigenvalues of the above problem with these boundary conditions and we explore similarities and differences between this case and the nonlinear case with p 2 we will see that several new phenomena occur in the periodic anti periodic problems for example with separated boundary conditions the structure of the spectrum when p 2 is the same as when p 2 but this is not true in the periodic anti periodic cases we also consider the set of half eigenvalues and the fucik spectrum of the problem these concepts are useful for solving jumping nonlinearity problems and we show that new phenomena also appear here in addition to analogues of those occurring for the usual eigenvalues

nonparametric estimates of standard error the jackknife the bootstrap and other methods summary we discuss several nonparametric methods for attaching a standard error to a point estimate the jackknife the bootstrap half sampling subsampling balanced repeated replications the infinitesimal jackknife influence function techniques and the delta method the last three methods are shown to be identical all the methods derive from the same basic idea which is also the idea underlying the common parametric methods extended numerical comparisons are made for the special case of the correlation coefficient

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

global bifurcation for nonlinear equations abstract using a bifurcation result on noncompact branches of solutions in an abstract setting we establish the existence of global bifurcation for the following nonlinear equation div a u p 2 u 0 b u p 2 u q x u u subject to dirichlet boundary conditions under certain assumptions on a b and q when 0 is not an eigenvalue of the above divergence form

cohomological structure in soliton equations and jacobian varieties on etudie la structure des orbites du systeme dynamique definie par la hierarchie kp totale on montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une algebre commutative le systeme dynamique kp restreint a chaque orbite determine un systeme dynamique de mouvements lineaires sur lui par rapport a la structure lineaire du groupe de cohomologie

on some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the p laplacian on a disk we discuss several properties of eigenvalues and eigenfunctions of the p laplacian on a ball subject to zero dirichlet boundary conditions among main results in two dimensions we show the existence of nonradial eigenfunctions which correspond to the radial eigenvalues also we prove the existence of eigenfunctions whose shape of the nodal set cannot occur in the linear case p 2 moreover the limit behavior of some eigenvalues as p 1 and p is studied

a local bifurcation theorem for degenerate elliptic equations with radial symmetry abstract in this work we provide local bifurcation results for equations involving the p laplacian in balls we analyze the continua c n of radial solutions emanating from n p 0 n p being the radial eigenvalues of p first we show that the only nontrivial solutions close to n p 0 lie on a continuous curve thus extending the crandall rabinowitz theorem second it is proved that c n n p 0 splits into two unbounded connected pieces characterized by their nodal properties thus sharpening previous results

bounds for the positive eigenvalues of the p laplacian with decaying potential an upper bound is obtained for the positive eigenvalues of the p laplacian with decaying potential on 0 the bound is expressed in terms of the potential and is shown to be the best possible of its kind

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

bifurcation and admissible solutions for the hessian equation abstract we study the following eigenvalue problem of k hessian equation s k d 2 u k f u in b u 0 on b global bifurcation result is established for this problem as applications of the bifurcation result we determine the intervals of for the existence nonexistence uniqueness and multiplicity of radially symmetric k admissible solutions for this problem

p laplacian problems with jumping nonlinearities we consider the p laplacian boundary value problem 1 p u x f x u x u x a e x 0 1 2 c00u 0 c01u 0 c10u 1 c11u 1 where p 1 is a fixed number p s s p 2s s r and for each j 0 1 cj0 cj1 0 the function f 0 1 r2 r is a caratheodory function satisfying for x s t 0 1 r2 x p s e x s t f x s t x p s e x s t s 0 where l1 0 1 and e has the form e x s t x e s t with l1 0 1 0 e 0 and limr e r r1 p 0 this condition allows the nonlinearity in 1 to behave differently as u such a nonlinearity is often termed jumping related to 1 2 is the problem 3 p u a p u b p u p u in 0 1 together with 2 where a b l1 0 1 r and u x max u x 0 for x 0 1 this problem is positively homogeneous and jumping values of for which 2 3 has a nontrivial solution u will be called half eigenvalues while the corresponding solutions u will be called half eigenfunctions we show that a sequence of half eigenvalues exists the corresponding half eigenfunctions having certain nodal properties and we obtain certain spectral and degree theoretic properties of the set of half eigenvalues these properties lead to existence and nonexistence results for the problem 1 2 we also consider a related bifurcation problem and obtain a global bifurcation result similar to the well known rabinowitz global bifurcation theorem this then leads to a multiplicity result for 1 2 when the functions a and b are constant the set of half eigenvalues is closely related to the fucik spectrum of the problem and equivalent solvability results are obtained using the two approaches however when a and b are not constant the half eigenvalue approach yields stronger results

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

n extended superelliptic integrable systems a supersymmetric extension for an arbitrary number of odd parameters of the stationary kdv equation is studied we call this an n extended super kdv it is shown that it is related to superelliptic curves and thereafter the complete ring of superdifferential operators commuting with the associated schrodinger operator is constructed

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

computing eigenvalues and fucik spectrum of the radially symmetric p laplacian eigenvalue problems for the radially symmetric p laplacian are discussed we present algorithms which compute a given number of eigenvalues and fucik curves together with the corresponding eigenfunctions the second order p laplacian equation is transformed into a first order system by a generalized prufer transformation to the first order system we apply shooting algorithms newton s method and in case of the fucik curves a predictor corrector method our approach requires analytical and numerical treatment of generalized sine functions singular as well as regular problems are treated and a detailed error analysis for the approximation of singular problems by regular ones are given numerical results are presented

interval estimation for individual categories in cumulative logit models we derive and compute confidence intervals for probabilities of categories for ordinal responses in cumulative logit link models using frequentist bayesian and bootstrap approaches the three approaches are evaluated by their coverage probabilities and are illustrated for longitudinal assessment of graded heart valve prosthesis regurgitation following aortic valve replacement

the riemann liouville integral and continuous kp hierarchy extension of the standard construction of the kadomtsev petviashvili kp hierarchy by the use of riemann liouville integral is given in consequence we obtain the new classes of integer as well as fractional graded kp hierarchies which are further investigated the fractional calculus leads to the new generalization of the w algebra

the second eigenfunction of the p laplacian on the disk is not radial abstract in this paper we prove that the second eigenfunction of the p laplacian p 1 on the disk is not radial our proof is a combination of asymptotic analysis for p and the application of interval arithmetic

supertori are algebraic curves super riemann surfaces of genus 1 with arbitrary spin structures are shown to be the sets of zeroes of certain polynomial equations in projective superspace we conjecture that the same is true for arbitrary genus properties of superelliptic functions and super theta functions are discussed the boundary of the genus 1 super moduli space is determined

explicit solutions of supersymmetric kp hierarchies supersolitons and solitinos wide classes of explicit solutions of the manin radul and jacobian supersymmetric kp hierarchies are constructed by using line bundles over complex supercurves based on the riemann sphere their construction extends several ideas of the standard kp theory such as wave functions equations and functions thus supersymmetric generalizations of n soliton solutions including a new purely odd solitino solution as well as rational solutions are found and characterized

unilateral global bifurcation phenomena and nodal solutions for p laplacian in this paper we establish a dancer type unilateral global bifurcation result for one dimensional p laplacian problem p u m t p u g t u t 0 1 u 0 u 1 0 under some natural hypotheses on the perturbation function g 0 1 r r r we show that k p is a bifurcation point of the above problem and there are two distinct unbounded continua ck and ck consisting of the bifurcation branch ck from k p 0 where k p is the k th eigenvalue of the linear problem corresponding to the above problem as the applications of the above result we study the existence of nodal solutions for the following problem p u f t u 0 t 0 1 u 0 u 1 0 moreover based on the bifurcation result of girg and takac 2008 13 we prove that there exist at least a positive solution and a negative one for the following problem div p u f x u in u 0 on

bifurcation phenomena associated to the p laplace operator on determine la structure de l ensemble des solutions u de u x p 2 u x x f u u p 2 u sur 0 1 telles que u 0 u 1 0 ou p 1 et r on demontre que les solutions avec k zeros sont uniques quand 1 2

additional symmetries of supersymmetric kp hierarchies we investigate the additional symmetries of several supersymmetric kp ierarchiess the skp hierarcy of manin and radul the skp2 hierarchy and the jacobian skp hierarchy in all three cases we find that the algebra of symmetries is isomorphic to the algebra of supperdifferential operators or equivalentlysw1 these results seem to suggest that despite their realization depending on the dynamics the additional symmetries are kinematical in nature

solvability of the super kp equation and a generalization of the birkhoff decomposition the unique solvability of the initial value problem for the total hierarchy of the super kadomtsev petviashvili system is established to prove the existence we use a generalization of the birkhoff decomposition which is obtained by replacing the loop variable and loop groups in the original setting by a super derivation operator and groups of infinite order super micro i e pseudo differential operators to show the uniqueness we generalize the fact that every flat connection admits horizontal sections to the case of an infinite dimensional super algebra bundle defined over an infinite dimensional super space the usual kp system with non commutative coefficients is also studied the kp system is obtained from the super kp system by reduction modulo odd variables on the other hand the first modified kp equation can be obtained from the super kp system by elimination of odd variables thus the super kp system is a natural unification of the kp system and the modified kp systems

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

algebraic study on the super kp hierarchy and the ortho symplectic super kp hierarchy bilinear residue formulas are established for the super kp hierarchy and the ortho symplectic super kp hierarchy furthermore superframes corresponding to the ortho symplectic super kp hierarchy are completely characterized soliton solutions to the super kp hierarchy are given

principal eigenvalues and an anti maximum principle for homogeneous fully nonlinear elliptic equations we study the fully nonlinear elliptic equation 0 1 f d2u du u x f in a smooth bounded domain under the assumption that the nonlinearity f is uniformly elliptic and positively homogeneous recently it has been shown that such operators have two principal half eigenvalues and that the corresponding dirichlet problem possesses solutions if both of the principal eigenvalues are positive in this paper we prove the existence of solutions of the dirichlet problem if both principal eigenvalues are negative provided the second eigenvalue is positive and generalize the anti maximum principle of clement and peletier p clement l a peletier an anti maximum principle for second order elliptic operators j differential equations 34 2 1979 218 229 to homogeneous fully nonlinear operators

eigenvalue analysis for the p laplacian convective perturbation abstract in this paper a detailed analysis of the eigenvalue problem under convection u p 2 u c u p 2 u u p 2 u 0 u 0 u 1 0 d d x is performed the analysis is based on a complete study of the phase space of the family of equations u p 2 u a u p 2 u b u p 2 u 0 a b constants

geometry of superconformal manifolds the main facts about complex curves are generalized to superconformal manifolds the results thus obtained are relevant to the fermion string theory and in particular they are useful for computation of determinants of super laplacians which enter the string partition function

the geometry of the super kp flows a supersymmetric generalization of the krichever map is used to construct algebro geometric solutions to the various super kadomtsev petviashvili skp hierarchies the geometric data required consist of a suitable algebraic supercurve of genusg generallynot a super riemann surface with a distinguished point and local coordinates z there and a generic line bundle of degreeg 1 with a local trivialization near the point the resulting solutions to the manin radul skp system describe coupled deformations of the line bundle and the supercurve itself in contrast to the ordinary kp system which deforms line bundles but not curves two new skp systems are introduced an integrable jacobian system whose solutions describe genuine jacobian flows deforming the bundle but not the curve and a nonintegrable maximal system describing independent deformations of bundle and curve the kac van de leur skp system describes the same deformations as the maximal system but in a different parametrization

global bifurcation and convex solutions for the monge ampere equation abstract we study the following monge ampere equation det d 2 u 1 n f u in u 0 on by bifurcation technique we establish some results about the existence nonexistence uniqueness and multiplicity of convex solutions for this problem our results generalize and improve many important known results from previous literature

automatic solution of sturm liouville problems using the pruess method abstract we develop algorithms based on coefficient approximation for the automatic solution of regular and singular sturm liouville problems

analytical and numerical results for the fucik spectrum of the laplacian nontrivial solutions of u u vu 0 in rn with zero dirichlet condition on are studied the collection of the pairs v is the so called fucik spectrum f a new variational formulation for parts of f is presented and analyzed based on this formulation a minimization algorithm for the computation of a part of f is developed alternatively an approach using an implicit function argument is discussed analytically and via newton s method also numerically by combining the variational minimization method with newton s method a new bifurcation result is first observed numerically and then proved rigorously by replacing the variational minimization method by the mountain pass algorithm higher curves in f are found numerically several numerical results are discussed including a further example of the previously recorded phenomenon of crossing of fucik curves originating from different eigenvalues

tau function formalism for supersymmetric kp hierarchies we consider the manin radul and jacobian supersymmetric kp hierarchies from the point of view of the tau function formalism solutions of their associated systems of sato equations are characterized in terms of correlation functions of supersymmetric vertex operators of superghost type the expression of the wave functions of these hierarchies in terms of tau functions is obtained and the corresponding bilinear identities are established explicit methods for generating soliton and rational solutions are given

multiple solutions for nonlinear dirichlet problems via bifurcation and additional results abstract in this paper we study the existence of multiple solutions for semilinear elliptic boundary value problems first when the nonlinearity is asymptotically linear and then when it has an arbitrary behavior for large values of the argument our proofs use extensively the global bifurcation theorem and bifurcation from infinity additionally when we can apply the lyapunov schmidt reduction method we show the existence of multiple solutions we give an exact number of solutions and we provide qualitative properties of these solutions

computing the first eigenpair of the p laplacian in annuli abstract we propose a method for computing the first eigenpair of the dirichlet p laplacian p 1 in the annulus a b x r n a x b n 1 for each t a b we use an inverse iteration method to solve two radial eigenvalue problems one in the annulus a t with the corresponding eigenvalue t and boundary conditions u a 0 u t and the other in the annulus t b with the corresponding eigenvalue t and boundary conditions u t 0 u b next we adjust the parameter t using a matching procedure to make t coincide with t thereby obtaining the first eigenvalue p hence by a simple splicing argument we obtain the positive l normalized radial first eigenfunction u p the matching parameter is the maximum point of u p in order to apply this method we derive estimates for t and t and we prove that these functions are monotone and locally lipschitz continuous moreover we derive upper and lower estimates for the maximum point which we use in the matching procedure and we also present a direct proof that u p converges to the l normalized distance function to the boundary as p we also present some numerical results obtained using this method

eigenvalues for radially symmetric fully nonlinear singular or degenerate operators abstract in this paper we present a one dimensional and radial theory for the existence of eigenvalues and eigenfunctions for fully nonlinear elliptic 1 homogeneous operators 1 a general theory for the first eigenvalue and eigenfunction exists in the frame of viscosity solutions but in this particular case a simpler theory can be established that extends via degree theory to obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeros