on a liouville type equation with sign changing weight in this paper we study the existence nonexistence and multiplicity of non negative solutions for the family of problems u a x e f x u u h 0 where is a bounded domain in r2 and 0 is a parameter the coefficient a x is allowed to change sign the techniques used in the proofs are a combination of upper and lower solutions the trudingermoser inequality and variational methods note that when f x u 0 the equation is of liouville type

infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry abstract we present a new approach to studying a parametric nonlinear dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is concave i e p 1 sublinear near zero and convex i e p 1 superlinear near the reaction term is not assumed to be odd we show that for all small values of the parameter 0 the problem has infinitely many nodal solutions

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

combined effects of concave and convex nonlinearities in elliptic equation on rn abstract in this paper we consider the existence of two positive solutions of the elliptic equation on r n with concave and convex nonlinearities

bayesian design of experiments using approximate coordinate exchange abstractthe construction of decision theoretical bayesian designs for realistically complex nonlinear models is computationally challenging as it requires the optimization of analytically intractable expected utility functions over high dimensional design spaces we provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm this methodology uses a gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps it has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables numbers of runs and randomization restrictions in contrast to existing approaches to bayesian design the method can find multi variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility the methodology is demonstrated on

an interleaved iterative criterion for h matrices abstract a non parameter iterative method for generalized diagonally dominant matrices i e h matrices was proposed by li et al l li h niki m sasanabc a non parameter criterion for generalized diagonally dominant matrices int j comput math 71 1999 267 275 in this paper we provide an improved algorithm by means of interleaved iteration the new method is always convergent and needs fewer iterations than that of li et al we also provide a corresponding algorithm for a general matrix which decreases the wasteful computations when the given matrix is not an h matrix several numerical examples for the effectiveness of the proposed algorithms are presented

on semilinear elliptic equations involving concave convex nonlinearities and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign changing weight function with the help of the nehari manifold we prove that there are at least two positive solutions for eq e f in bounded domains

limits as p of p laplacian concave convex problems abstract we study the behavior as p of the sequel of positive weak solutions of the concave convex problem p div u p 2 u u q p u r p in u 0 in u 0 on where r n is a bounded domain 0 and the exponents q r satisfy lim p q p p 1 q lim p r p p 1 r with 0 q 1 r we characterize any positive uniform limit of a sequence of weak solutions of p as a viscosity solution of min u max u q u r u 0 in notice that the limit process decouples the nonlinearity we obtain existence non existence and global multiplicity of positive viscosity solutions of the limit problem in terms of the parameter

nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity abstract we are concerned with existence nonexistence and multiplicity of nonnegative solutions for the elliptic problem u a x u q b x u p in u 0 on where is a bounded domain in r n r 0 q 1 p 2 1 and a b are bounded functions with b x 0 and a x changes its sign

bayesian optimal design for ordinary differential equation models with application in biological science bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of nonlinear ordinary differential equations the motivation is an experime

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

blow up rates of radially symmetric large solutions abstract this paper adapts a technical device going back to j lopez gomez optimal uniqueness theorems and exact blow up rates of large solutions j differential equations 224 2006 385 439 to ascertain the blow up rate of the unique radially symmetric large solution given through the main theorem of j lopez gomez uniqueness of radially symmetric large solutions discrete contin dyn syst supplement dedicated to the 6th aims conference poitiers france 2007 pp 677 686 the requested underlying estimates are based upon the main theorem of s cano casanova j lopez gomez existence uniqueness and blow up rate of large solutions for a canonical class of one dimensional problems on the half line j differential equations 244 2008 3180 3203 precisely we show that if is a ball or an annulus f c 0 is positive and non decreasing v c 0 c 2 0 satisfies v 0 0 v u 0 v u 0 for every u 0 and v u h u p 1 as u for some h 0 and p 1 then for each 0 u u f dist x v u u possesses a unique positive large solution in l which must be radially symmetric by uniqueness and we can estimate the exact blow up rate of l x at in terms of p h and f see theorem 1 1

positive solutions of superlinear elliptic equations abstract in this paper we study the existence of two positive solutions of superlinear elliptic equations without assuming the conditions which have been used in the literature to deduce either the p s condition or a priori bounds of positive solutions the first solution is proved as the minimal positive solution while the second one is obtained as the limit of a gradient flow whose starting point is properly chosen the dependence of the minimal solution upon a parameter is also considered

exact multiplicity and bifurcation diagrams of positive solutions of a one dimensional multiparameter prescribed mean curvature problem abstract we study the exact multiplicity and bifurcation diagrams of positive solutions u c 2 l l c l l of the one dimensional multiparameter prescribed mean curvature problem u x 1 u x 2 u p u q l x l u l u l 0 where 0 is a bifurcation parameter l 0 the radius of the one dimensional ball l l is an evolution parameter and 0 p q are two constants we prove that the problem has at most two positive solutions for any 0 p q and l 0 in addition if 0 p q q p p 1 2 p 1 we give a classification of totally three qualitatively different bifurcation diagrams on the u plane for any l 0 for any fixed p 0 and q q p p 2 2 2 p 3 we prove that there exist positive l l such that the bifurcation diagrams on the u plane are individually qualitatively different for the cases i 0 l l or l l ii l l iii l l l

adaptive design optimization a mutual information based approach to model discrimination in cognitive science discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science resolving this issue begins with designing maximally informative experiments to this end the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps when the models under consideration are nonlinear as is often the case in cognitive science this problem can be impossible to solve analytically without simplifying assumptions however as we show in this letter a full solution can be found numerically with the help of a bayesian computational trick derived from the statistics literature which recasts the problem as a probability density simulation in which the optimal design is the mode of the density we use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of bayesian posterior estimates as a proof of concept we offer a simple example application to an experiment on memory retention

the choice of variables in multivariate regression a non conjugate bayesian decision theory approach we consider the choice of explanatory variables in multivariate linear regression our approach balances prediction accuracy against costs attached to variables in a multivariate version of a decision theory approach pioneered by lindley 1968 we also employ a non conjugate proper prior distribution for the parameters of the regression model extending the standard normal inverse wishart by adding a component of error which is unexplainable by any number of predictor variables thus avoiding the determinism identified by dawid 1988 simulated annealing and fast updating algorithms are used to search for good subsets when there are very many regressors the technique is illustrated on a near infrared spectroscopy example involving 39 observations and 300 explanatory variables this demonstrates the effectiveness of multivariate regression as opposed to separate univariate regressions it also emphasises that within a bayesian framework more variables than observations can be utilised

on the global structure of the set of positive solutions of some semilinear elliptic boundary value problems abstract in this work we analyze the structure of the set of positive solutions of a class of semilinear boundary value problems it is shown that the global continuum of positive solutions emanating from the trivial equilibrium at the principal eigenvalue of the linearization is constituted by a regular curve if the slope of the kinetic at the trivial solution is large enough and is convex the same result holds if the support region of the species is a bounded simply connected domain of r 2 close to a convex domain in a sense to be precised later to prove these results we have to find out the exact width of the boundary layer of a singular perturbation problem the results about the singular perturbation problem are new and of great interest by themselves

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

stochastic optimization on continuous domains with finite time guarantees by markov chain monte carlo methods we introduce bounds on the finite time performance of markov chain monte carlo mcmc algorithms in solving global stochastic optimization problems defined over continuous domains it is shown that mcmc algorithms with finite time guarantees can be developed with a proper choice of the target distribution and by studying their convergence in total variation norm this work is inspired by the concept of finite time learning with known accuracy and confidence developed in statistical learning theory

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

combined effects in nonlinear problems arising in the study ofanisotropic continuous media the paper deals with the study of a lane emden fowler equation with dirichlet boundary condition and variable potential functions the analysis developed in this paper combines monotonicity methods with variational arguments

on a dirichlet problem with p q laplacian and parametric concave convex nonlinearity abstract a homogeneous dirichlet problem with p q laplace differential operator and reaction given by a parametric p convex term plus a q concave one is investigated a bifurcation type result describing changes in the set of positive solutions as the parameter 0 varies is proven since for every admissible the problem has a smallest positive solution u both monotonicity and continuity of the map u are studied

on spectral asymptotics and bifurcation for elliptic operators with odd superlinear term on considere le probleme aux valeurs propes semi lineaire lu f x u u dans u 0 sur ou est un sous ensemble ouvert borne de r n n 1 a frontiere lisse ou l est un operateur uniformement elliptique dans formellement auto adjoint et f une application continu de r r

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

an iterative criterion for h matrices we provide an algorithmic characterization of h matrices when a is an h matrix this algorithm determines a positive diagonal matrix d such that ad is strictly row diagonally dominant in effect d is produced iteratively by quantifying and

optimal bayesian design by inhomogeneous markov chain simulation we consider decision problems defined by a utility function and an underlying probability model for all unknowns the utility function quantifies the decision maker s preferences over consequences the optimal decision maximizes the expected utility function where the expectation is taken with respect to all unknowns that is future data and parameters in many problems the solution is not analytically tractable for example the utility function might involve moments that can be computed only by numerical integration or simulation also the nature of the decision space i e the set of all possible actions might have a shape or dimension that complicates the maximization the motivating application for this discussion is the choice of a monitoring network when the optimization is performed over the high dimensional set of all possible locations of monitoring stations possibly including choice of the number of locations we propose an approach to optimal bayesian design based on inhomogeneous markov

existence of solutions for perturbed fractional p laplacian equations abstract the purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p laplacian operator as follows p s u v x u p 2 u a x u r 2 u b x u q 2 u in r n where is a real parameter p s is the fractional p laplacian operator with 0 s 1 p p r min q p s and v a b r n 0 are three positive weights using variational methods we obtain nonexistence and multiplicity results for the above mentioned equations depending on and according to the integrability properties of the ratio a q p b r p our results extend the previous work of autuori and pucci 2013 5 to the fractional p laplacian setting furthermore we weaken one of the conditions used in their paper hence the results of this paper are new even in the fractional laplacian case

critical point theory on partially ordered hilbert spaces we develop some abstract critical point theory in order to prove that boundary value problems like the model problem formula on a bounded domain rn 2 p 2n n 2 have infinitely many sign changing solutions uk k n which are not comparable that is uk ul and uk ul change sign for k l we also show that there are no subsolutions u such that u uk for some k and u is positive somewhere a corresponding nonexistence result applies to supersolutions related results on the existence of sign changing solutions hold for other classes of nonlinearities

a bifocal measure of expected ambiguity in bayesian nonlinear parameter estimation we present a novel approach to define and calculate the expected uncertainty of bayesian parameter estimates prior to collecting any observational data this can be used to design investigation techniques or experiments that minimize expected uncertainty our approach accounts fully for nonlinearity in the parameter observation relationship which is neither the case for the bayesian d and a optimality criteria most commonly used in experimental design nor the case for most other derivative or information matrix based experimental design techniques our method is based on analyzing pairs of parameter estimates thus forming a bifocal measure of ambiguity derivatives of observable data with respect to parameter values are neither required nor calculated for linear models our new measure is equivalent to expected posterior variance and it is closely related to expected posterior variance in nonlinear models

decision theoretic sensitivity analysis for complex computer models when using a computer model to inform a decision it is important to investigate any uncertainty in the model and determine how that uncertainty may impact on the decision in probabilistic sensitivity analysis model users can investigate how various uncertain model inputs contribute to the uncertainty in the model output however much of the literature focuses only on output uncertainty as measured by variance the decision problem itself often is ignored even though uncertainty as measured by variance may not equate to uncertainty about the optimum decision consequently traditional variance based measures of input parameter importance may not correctly describe the importance of each input we review a decision theoretic framework for conducting sensitivity analysis that addresses this problem because computation of these decision theoretic measures can be impractical for complex computer models we provide efficient computational tools using gaussian processes we give an illustration in the fiel

on the oscillations of the solution curve for a class of semilinear equations abstract we consider positive solutions of the dirichlet problem u u sin u 0 x b u 0 for x b where b is unit ball in r n is a positive parameter let 1 denote the principal eigenvalue of the laplacian on b with zero boundary conditions we show that for 1 n 5 the problem has infinitely many positive solutions at 1 while for n 6 the problem has at most finitely many solutions at any

optimal design via curve fitting of monte carlo experiments abstract this article explores numerical methods for stochastic optimization with special attention to bayesian design problems a common and challenging situation occurs when the objective function in bayesian applications the expected utility is very expensive to evaluate perhaps because it requires integration over a space of very large dimensionality our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations by exploiting smoothness of the expected utility surface and borrowing information from neighboring design points the central idea is that of implementing stochastic optimization by curve fitting of monte carlo samples this is done by simulating draws from the joint parameter sample space and evaluating the observed utilities fitting a smooth surface through these simulated points serves as estimate for the expected utility surface the optimal design can then be found deterministically in this article we introduce a general algorithm for cu

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

multiple solutions to p laplacian problems with concave nonlinearities in this paper we study the p laplacian type elliptic problems with concave nonlinearities using some asymptotic behavior of f at zero and infinity three nontrivial solutions are established

self corrective iterations sci for generalized diagonally dominant matrices a suggestive indicator is proposed for predicting whether a given complex or real square matrix a is or is not a generalized diagonally dominant matrix gddm by which we mean if a can be brought into a strictly diagonally dominant matrix by post multiplying some diagonal matrix d based on the indicator three self corrective iterative algorithms sci are presented for determining if an irreducible a is or is not a gddm and at the same time delivering the matrix d in case when a is a gddm the basic idea is to push a towards being strictly diagonally dominant when the indicator suggests that a is likely a gddm or towards being off diagonally dominant otherwise among the three algorithms each has their own feature one takes the fewest number of iterations but the most amount of work per iteration one takes the most number of iterations but the least amount of work per iteration and the third one strikes a balance between the two extremes it is shown that the algorithms will terminate in finite many steps under the assumption that a has no zero entries and the comparison matrix of a is nonsingular comparing with existing methods new algorithms are more efficient as demonstrated on known difficult examples in the literature newly designed random matrices as well as matrices from the university of florida sparse matrix collection

simulation based optimal bayesian experimental design for nonlinear systems the optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction particularly in situations where experiments are time consuming and expensive to conduct we propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation based models in particular we focus on finding sets of experiments that provide the most information about targeted sets of parameters our framework employs a bayesian statistical setting which provides a foundation for inference from noisy indirect and incomplete data and a natural mechanism for incorporating heterogeneous sources of information an objective function is constructed from information theoretic measures reflecting expected information gain from proposed combinations of experiments polynomial chaos approximations and a two stage monte carlo sampling method are used to evaluate the expected information gain stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high dimensional settings these algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics

compact sobolev embeddings and positive solutions to a quasilinear equation with mixed nonlinearities abstract in this paper we study the existence and multiplicity results of nontrivial positive solutions to the following quasilinear elliptic equation on r n when n 2 p u k x u r 1 v x u q 1 here k x v x 0 are suitable potentials 1 p r q and 0 is a parameter to study this problem some compact embedding results regarding m v q p r n l k r r n are proved that unify and extend some recent results of the author 12 13 14

nonlinear elliptic equations with an asymptotically linear reaction term abstract we examine nonlinear elliptic problems driven by the p laplacian and with a reaction term which asymptotically at exhibits a p 1 linear growth 1 p using tools from critical point theory and from morse theory we prove existence theorems and we provide information about the sign of the solutions

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

a new criterion for the h matrix property for many applications it is very useful to know whether a matrix is an h matrix or not recently some iterative tests have been proposed for distinguishing h matrix in this paper we propose a new method for being able to distinguish only a scalar times column vector numerical evidence for the effectiveness of the proposed algorithm is presented

normalized ground states for the nls equation with combined nonlinearities abstract we study existence and properties of ground states for the nonlinear schrodinger equation with combined power nonlinearities u u u q 2 u u p 2 u in r n n 1 having prescribed mass r n u 2 a 2 under different assumptions on q p a 0 and r we prove several existence and stability instability results in particular we consider cases when 2 q 2 4 n p 2 q p i e the two nonlinearities have different character with respect to the l 2 critical exponent these cases present substantial differences with respect to purely subcritical or supercritical situations which were already studied in the literature we also give new criteria for global existence and finite time blow up in the associated dispersive equation

bayesian optimal design via interacting particle systems we propose a new stochastic algorithm for bayesian optimal design in nonlinear and high dimensional contexts following peter muller we solve an optimization problem by exploring the expected utility surface through markov chain monte carlo simulations the optimal design is the mode of this surface considered a probability distribution our algorithm relies on a particle method to efficiently explore high dimensional multimodal surfaces with simulated annealing to concentrate the samples near the modes we first test the method on an optimal allocation problem for which the explicit solution is available to compare its efficiency with a simpler algorithm we then apply our method to a challenging medical case study in which an optimal protocol treatment needs to be determined for this case we propose a formalization of the problem in the framework of bayesian decision theory taking into account physicians knowledge and motivations we also briefly review further improvements and alternatives

multiplicity of positive solutions for p laplace equation with superlinear type nonlinearity abstract in this work we consider the problem p r p u u p u q u 0 in b r 0 u 0 on b r 0 where p 2 p np n p and b r 0 is the open ball of radius r centered about the origin in r n n 3 under the condition that p 1 q p 2 n p 1 we show that there exists r 0 such that p r admits atleast two solutions for all r r and no solution if r this extends the results of nonlinear anal tma 10 8 1986 755 to the case of p laplace equation

on elliptic problems involving critical hardy sobolev exponents and sign changing function abstract in this paper we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical hardy sobolev exponent and a sign changing function some existence results are obtained by splitting the nehari manifold and by exploring some properties of the best hardy sobolev constant together with an approach developed by brezis and nirenberg

existence uniqueness and blow up rate of large solutions for a canonical class of one dimensional problems on the half line this paper shows the existence and the uniqueness of the positive solution l t of the singular boundary value problem u t f t h u t t 0 u 0 u 0 where f is a continuous non decreasing function such that f 0 0 and h is a non negative function satisfying the keller osserman condition moreover it also ascertains the exact blow up rate of l t at t 0 in the special case when there exist h 0 and p 1 such that h u hup for sufficiently large u naturally the blow up rate of the problem in such a case equals its blow up rate for the very special but important case when h u hup for all u 0 so our results are substantial improvements of some previous findings of j lopez gomez uniqueness of large solutions for a class of radially symmetric elliptic equations in s cano casanova j lopez gomez c mora corral eds spectral theory and nonlinear analysis with applications to spatial ecology world scientific 2005 pp 75 110 and j lopez gomez optimal uniqueness theorems and exact blow up rates of large solutions j differential equations 224 2006 385 439

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

nondegeneracy and uniqueness of positive solutions for robin problem of second order ordinary differential equations and its applications abstract this article studies positive solutions of robin problem for semi linear second order ordinary differential equations nondegeneracy and uniqueness results are proven for homogeneous differential equations necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations

optimal experimental design for another s analysis abstract we consider the optimal design of experiments in which estimation and design are performed by different parties the parties are assumed to share similar goals as reflected by a common loss function but they may have different prior beliefs after presenting a few motivating examples we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation we also consider the problem of optimal allocation for given overall sample sizes we present results under both squared error loss and a logarithmic utility paying attention to the differences between one and two prior optimal designs an asymmetric discrepancy measure features repeatedly in our development and we question the extent of its role in optimal two prior design

radial solutions of dirichlet problems with concave convex nonlinearities abstract we prove the existence of a double infinite sequence of radial solutions for a dirichlet concave convex problem associated with an elliptic equation in a ball of r n we are interested in relaxing the classical positivity condition on the weights by allowing the weights to vanish the idea is to develop a topological method and to use the concept of rotation number the solutions are characterized by their nodal properties

an iterative test for h matrix abstract for many applications it is very useful to know whether a matrix is an h matrix or not harada et al proposed simple algorithm which is produced iteratively a positive diagonal matrix d in bishan li et al linear algebra appl 271 1998 179 190 this method is useful when matrix a is an h matrix and when a is not an h matrix a wasteful computation is necessary in this paper to conquer this drawback we propose a new algorithm

finite difference approximate solutions for a mixed sub superlinear equation in ben mabrouk and ben mohamed 2006 a ben mabrouk m l ben mohamed on some critical and slightly super critical sub superlinear equations far east j appl math 23 1 2006 73 90 special volume of pdes a ben mabrouk m l ben mohamed nodal solutions for some nonlinear elliptic equations appl math comp in press doi 10 1016 j amc 2006 08 003 it has proved some theoretical results dealing with some boundary value problem du f u 0 in b and u 0 on b where b is a domain in r d with smooth boundary in the present paper we perform a difference scheme method to approximate the solution of a nonlinear evolutionary problem associated to the elliptic problem studied in ben mabrouk and ben mohamed 2006 we give at the end some numerical implementations based on a mixed sublinear superlinear term of the form f u u p email protected u q 1u

optimal observation times in experimental epidemic processes this article describes a method for choosing observation times for stochastic processes to maximise the expected information about their parameters two commonly used models for epidemiological processes are considered a simple death process and a susceptible infected si epidemic process with dual sources for infection spreading within and from outwith the population the search for the optimal design uses bayesian computational methods to explore the joint parameter data design space combined with a method known as moment closure to approximate the likelihood to make the acceptance step efficient for the processes considered a small number of optimally chosen observations are shown to yield almost as much information as much more intensively observed schemes that are commonly used in epidemiological experiments analysis of the simple death process allows a comparison between the full bayesian approach and locally optimal designs around a point estimate from the prior based on asymptotic results the robustness of the approach to misspecified priors is demonstrated for the si epidemic process for which the computational intractability of the likelihood precludes locally optimal designs we show that optimal designs derived by the bayesian approach are similar for observational studies of a single epidemic and for studies involving replicated epidemics in independent subpopulations different optima result however when the objective is to maximise the gain in information based on informative and non informative priors this has implications when an experiment is designed to convince a naive or sceptical observer rather than consolidate the belief of an informed observer some extensions to the methods including the selection of information criteria and extension to other epidemic processes with transition probabilities are briefly addressed

on the singular second order elliptic equation abstract let m g be a smooth and compact riemannian manifold with dimensions n 3 this paper deals with the existence of nontrivial solutions for a nonlinear second order elliptic equation with a singular term and critical sobolev growth we provide a geometric application of this singular equation

on the evolution and qualitative behaviors of bifurcation curves for a boundary value problem abstract we study the evolution and qualitative behaviors of bifurcation curves of positive solutions for u x u 1 sin u u p 1 x 1 u 1 u 1 0 where 0 is a bifurcation parameter and p 1 is an evolution parameter on the u plane we prove that the bifurcation curve has exactly one turning point where the curve turns to the left for p 2 it is a monotone curve for p 2 it has at least two turning points for 1 p p 1 2 cos 1 sin 1 1 2 cos 1 sin 1 1 629 and it has infinitely many turning points for p 1 hence we are able to determine the exact number of positive solutions in particular we give complete descriptions of the structure of bifurcation curves when p 2 we also give some numerical simulations of bifurcation curves for p 1

simple proof of stationary phase method and application to oscillatory bifurcation problems abstract we consider the nonlinear eigenvalue problem u t f u t u t 0 t i 1 1 u 1 0 where f u f 1 u u 3 sin u 3 u f u f 2 u u u p sin u q 0 p 1 1 q p 2 and 0 is a bifurcation parameter it is known that in this case is parameterized by the maximum norm u of the solution u associated with and is written as we simplify the argument of the stationary phase method and show the asymptotic formulas for for f 1 u and f 2 u as and 0 in particular the shape of bifurcation diagram of for f 1 u seems to be new

existence and multiplicity results for quasilinear elliptic exterior problems with nonlinear boundary conditions abstract in this paper we study a class of quasilinear elliptic exterior problems with nonlinear boundary conditions existence of ground states and multiplicity results are obtained via variational methods

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

optimal predictive model selection often the goal of model selection is to choose a model for future prediction and it is natural to measure the accuracy of a future prediction by squared error loss under the bayesian approach it is commonly perceived that the optimal predictive model is the model with highest posterior probability but this is not necessarily the case in this paper we show that for selection among normal linear models the optimal predictive model is often the median probability model which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1 2 of being in a model the median probability model often differs from the highest probability model

asymptotic length of bifurcation curves related to inverse bifurcation problems abstract we consider the nonlinear eigenvalue problem u t f u t 0 u t 0 t i 1 1 u 1 u 1 0 where f u u g u and 0 is a parameter our interest is the asymptotic length l g of the bifurcation curve g u 0 by the notion of l g we will propose a new framework of inverse bifurcation problems precisely we consider whether it is possible to characterize the unknown nonlinear term g u by l g if g u g 1 u u 2 sin u or g 2 u u 1 2 sin u then the bifurcation curves g i i 1 2 are continuous functions of 0 and g i 2 4 as furthermore they intersect the line 2 4 infinitely many times as in this paper by establishing the precise asymptotic formula for g i for 1 we obtain the precise asymptotic length l g i of g i for 1 then we consider the set g c 2 r g 2 4 as and study the existence and non existence of g whose asymptotic formula for l g is equal to those of l g i up to the second term

decision analysis by augmented probability simulation we provide a generic monte carlo method to find the alternative of maximum expected utility in a decision analysis we define an artificial distribution on the product space of alternatives and states and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives after drawing a sample from the artificial distribution we may use exploratory data analysis tools to approximately identify the optimal alternative we illustrate our method for some important types of influence diagrams

criteria for generalized diagonally dominant matrices and m matrices abstract we provide new necessary and sufficient conditions for verifying strictly generalized diagonally dominant matrices by applying the inverse of a partitioned matrix and obtain some criteria for identifying nonsingular m matrices

compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity we study the branch of semistable and unstable solutions i e those whose morse index is at most 1 of the dirichlet boundary value problem u f x 1 u 2 on a bounded domain n which models among other things a simple electrostatic microelectromechanical system mems device we extend the results of 11 relating to the minimal branch by obtaining compactness along unstable branches for 1 n 7 on any domain and for a large class of permittivity profiles f we also show the remarkable fact that powerlike profiles f x x can push back the critical dimension n 7 of this problem by establishing compactness for the semistable branch on the unit ball also for n 8 and as long as as a byproduct we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for in a natural range in all these results the conditions on the space dimension and on the power of the profile are essentially sharp 2007 wiley periodicals inc

three positive solutions for dirichlet problems involving critical sobolev exponent and sign changing weight abstract in this paper we study the decomposition of the nehari manifold via the combination of concave and convex nonlinearities furthermore we use this result and the lusternik schnirelman category to prove that a semilinear elliptic equation involving a sign changing weight function has at least three positive solutions

four positive solutions for a semilinear elliptic equation involving concave and convex nonlinearities abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation with the help of the nehari manifold and the center mass function we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole