mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

the dixmier map for nilpotent super lie algebras in this article we prove that there exists a dixmier map for nilpotent super lie algebras in other words if we denote by mathrm prim mathcal u mathfrak g the set of graded primitive ideals of the enveloping algebra mathcal u mathfrak g of a nilpotent lie superalgebra mathfrak g and mathcal a d 0 the adjoint group of mathfrak g 0 we prove that the usual dixmier map for nilpotent lie algebras can be naturally extended to the context of nilpotent super lie algebras i e there exists a bijective map i mathfrak g 0 mathcal a d 0 rightarrow mathrm prim mathcal u mathfrak g defined by sending the equivalence class of a functional to a primitive ideal i of mathcal u mathfrak g and which coincides with the dixmier map in the case of nilpotent lie algebras moreover the construction of the previous map is explicit and more or less parallel to the one for lie algebras a major difference with a previous approach cf 18 one key fact in the construction is the existence of polarizations for super lie algebras generalizing the concept defined for lie algebras as a corollary of the previous description we obtain the isomorphism mathcal u mathfrak g i lambda simeq rm cliff q k otimes a p k where p q rm dim mathfrak g 0 mathfrak g 0 lambda 2 rm dim mathfrak g 1 mathfrak g 1 lambda we get a direct construction of the maximal ideals of the underlying algebra of mathcal u mathfrak g and also some properties of the stabilizers of the primitive ideals of mathcal u mathfrak g

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

numerical algorithms for diffusion reaction problems with non classical conditions abstract parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years in this paper new high order algorithms for the linear diffusion reaction problem are derived the convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion reaction equations with these non classical conditions

bayesian methods for pharmacokinetic models in dynamic contrast enhanced magnetic resonance imaging this paper proposes a new method for estimating kinetic parameters of dynamic contrast enhanced magnetic resonance imaging dce mri based on adaptive gaussian markov random fields kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries asymptotic results for standard errors from likelihood based nonlinear regression are compared with those derived from the posterior distribution using bayesian estimation with and without neighborhood information application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of bayesian analysis combined with adaptive gaussian markov random fields provides improved convergence behavior and more consistent morphological and functional statistics

existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α norm abstract this paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the norm the linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators and the nonlinear part satisfies some lipschitz conditions with respect to the norm by using a fixed point theorem of sadovskii we establish some existence results which generalize the recent conclusions on this issue in the end the obtained results will be applied to a class of partial differential equations with nonlocal conditions

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

numerical schemes for one dimensional parabolic equations with nonstandard initial condition parabolic partial differential equations with nonstandard initial condition feature in the mathematical modelling of many phenomena while a significant body of knowledge about the theory and numerical methods for parabolic partial differential equations with classical initial condition has been accumulated not much has been extended to parabolic partial differential equations with nonstandard initial condition in this paper finite difference approximations to the solution of one dimensional parabolic equation with nonstandard initial condition are studied several finite difference schemes are presented for solving a parabolic partial differential equation with nonlocal time weighting initial condition these schemes are based on the forward time centred space explicit formula the backward time centred space implicit technique the crank nicolson implicit formula the crandall s implicit scheme and the saulyev s 2 2 explicit methods the results of a numerical experiment are presented

reaction diffusion equations with nonlocal boundary and nonlocal initial conditions in this paper we investigate the existence multiplicity and asymptotic behavior of solutions for a reaction diffusion equation under nonlocal boundary and nonlocal initial conditions a distinctive feature of this type of boundary and initial conditions is that the parabolic equation may possess multiple solutions even if the reaction function is smooth including linear functions of special concern is the asymptotic behavior of these multiple solutions in relation to the solutions of the corresponding steady state problem which may also possess multiple solutions in some special cases both the time dependent and the steady state problems possess an infinite number of solutions and each of the time dependent solutions converges to one of the steady state solutions

on maximal subalgebras of central simple malcev algebras let f be a field of characteristic different from two and a a central sim ple non lie malcev algebra over f our purpose is to determine the maximal subalgebras of a with respect to inclusion maximal subalgebras of simple lie algebras over an algebraically closed field have been studied by dynkin 3 41 and maximal subalgebras of central simple associative alternative and special jordan algebras have been studied by racine 121 racine s results on octonion algebras will be relevant in our investigation 1

three level techniques for one dimensional parabolic equation with nonlinear initial condition in this paper a boundary value problem for one dimensional heat equation is considered under the constraint of a nonlocal initial condition in place of the classical specification of initial data we impose the nonlocal initial condition efficient higher order algorithms are developed for solving this parabolic partial differential equation with nonstandard initial condition several three level finite difference schemes are presented these schemes are based on the modification of the centred time centred space explicit formula the three level 1 3 1 explicit technique the sixth order 1 3 3 explicit method and the dufort frankel finite difference scheme numerical computations combined with a simple iteration procedure of some examples are given to demonstrate the efficiency and accuracy of the new algorithms

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

mathematical treatment of the magnetic confinement in a current carrying stellarator the model studied concerns the case of a stellarator machine and the magnetic confinement is modeled by using averaging methods and suitable vacuum coordinates this is shown to lead to a two dimensional grad shafranov type problem for the averaged poloidal flux function various problems are considered and it is pointed out that corresponding problems for models based on tokamak machines are essentially similar

maximal subalgebras of associative superalgebras abstract the maximal subalgebras of the finite dimensional central simple associative superalgebras possibly endowed with a superinvolution are determined this relies on the corresponding description by m racine in the ungraded case which is completed here too

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

impulsive degenerate nonlinear parabolic functional differential inequalities abstract the aim of the paper is to give a theorem about impulsive degenerate strong nonlinear parabolic functional differential inequalities in arbitrary parabolic domain and two corollaries about weak and strong inequalities the paper is a direct generalization and a continuation among other things of the author s previous work the results obtained in this paper can be applied for some impulsive problems in the theories of diffusion and heat conduction with better effects than analogous known classical parabolic problems

wavelet based schemes for linear advection dispersion equation abstract in this paper two wavelet based adaptive solvers are developed for linear advection dispersion equation the localization properties and multilevel structure of the wavelets in the physical space are used for adaptive computational methods for solution of equation which exhibit both smooth and shock like behaviour the first framework is based on wavelet galerkin and the second is based on multiscale decomposition of finite element method coiflet wavelet filter is incorporated in both the methods the main advantage of both the adaptive methods is the elimination of spurious oscillations at very high peclet number

strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functionals abstract in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 the author studied strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with particular functionals our purpose here is to extend results in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with arbitrary functionals the results obtained in this paper can be applied in the theories of diffusion and heat conduction

simple accurate and efficient revisions to maccormack and saulyev schemes high peclet numbers abstract stream water quality modeling often involves numerical methods to solve the dynamic one dimensional advection dispersion reaction equations adre there are numerous explicit and implicit finite difference schemes for solving these problems and two commonly used schemes are the maccormack and saulyev schemes this paper presents simple revisions to these schemes that make them more accurate without significant loss of computation efficiency using advection dominated high peclet number problems as test cases performances of the revised schemes are compared to performances of five classic schemes forward time centered space ftcs backward time centered space btcs crank nicolson and the traditional maccormack and saulyev schemes all seven of the above numerical schemes were tested against analytical solutions for pulse and step inputs of mass to a steady flow in a channel and performances were considered with respect to stability accuracy and computational efficiency results indicated that both the modified saulyev and the maccormack schemes which are named the saulyevc and maccormackc schemes respectively greatly improved the prediction accuracy over the original ones the computation efficiency in terms of cpu time was not impacted for the saulyevc scheme the maccormackc scheme demonstrated increased time consumption but was still much faster than implicit schemes

the two level finite difference schemes for the heat equation with nonlocal initial condition abstract in this paper the two level finite difference schemes for the one dimensional heat equation with a nonlocal initial condition are analyzed as the main result we obtain conditions for the numerical stability of the schemes in addition we revise the stability conditions obtained in 21 for the crank nicolson scheme we present several numerical examples that confirm the theoretical results within linear as well as nonlinear problems in some particular cases it is shown that for small regions of the time step size values the explicit ftcs scheme is stable while certain implicit methods such as crank nicolson scheme are not

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

primitive superalgebras with superinvolution abstract our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras 5 6 10 and to classify primitive superrings with superinvolution having a minimal one sided superideal we were led to this problem by our work on finite dimensional central simple jordan superalgebras over fields of characteristic not 2 9 see also 7 of course just as symmetric elements give rise to jordan superalgebras skewsymmetric elements give rise to lie superalgebras 8 4 the results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution 5 chap i 6 chaps ii iii 1 chap x 10 chap 2 some of the results have been announced in 13

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

controllability of systems with a general nonlocal condition abstract in this work we are concerned with the controllability of first order distributed systems with a general nonlocal condition specifically by a general nonlocal condition we understand a nonlocal condition modeled in terms of an inclusion in this context assuming that the underlying linear system is approximately controllable we present three types of conditions under which the nonlinear system is also approximately controllable

maximal subalgebras of simple modular lie algebras abstract the maximal graded subalgebras of the restricted simple lie algebras of cartan type w n s n h n and k n are studied the notion of an r subalgebra and that of an s subalgebra are introduced for maximal subalgebras all maximal r subalgebras are described completely the number of conjugacy classes representatives of conjugacy classes and the dimensions of all r subalgebras are found an invariant description of graded s subalgebras is also obtained

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

an integral constrained parabolic problem with applications in thermochronology we investigate an inverse source problem with an integral constraint for a parabolic equation the constraint is motivated by an application in thermochronology a branch of geology the existence and uniqueness of weak solutions are established by means of the rothe method and an energy method respectively the elliptic problem resulting from the time discretization is solved by homogenizing the integral constraint the implicit scheme used in the proof of existence lends itself readily for numerical studies and we present the results of numerical experiments we also report on the errors and convergence rates

on the covariance of two noncentral f random variables and the variance of the estimated liner discriminant function summary the covariance of two noncentral f random variables with a common covariance matrix is obtained from which the variance of their difference follows easily an application of this latter result in discriminant analysis is then given

maximal subalgebras of lie superalgebras of cartan type over fields of characteristic zero this paper aims to characterize the maximal graded subalgebras of lie superalgebras of cartan type w s s and h over fields of characteristic zero all maximal graded subalgebras are completely determined by virtue of a constructive method and their isomorphism classes dimension formulas are given except for maximal s subalgebras in the exceptional situation the classification of maximal s subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical lie algebras

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

spatially regularized estimation for the analysis of dynamic contrast enhanced magnetic resonance imaging data competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast enhanced magnetic resonance imaging data we present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori a multi compartment approach is considered which is translated into a restricted least square model selection problem this is done by using a set of basis functions for a given set of candidate rate constants the form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment using a spatial elastic net estimator we chose a sparse set of basis functions per voxel and hence rate constants of compartments the spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently the proposed estimation method is evaluated for simulated images and applied to an in vivo dataset copyright 2013 john wiley sons ltd

three validation metrics for automated probabilistic image segmentation of brain tumours the validity of brain tumour segmentation is an important issue in image processing because it has a direct impact on surgical planning we examined the segmentation accuracy based on three two sample validation metrics against the estimated composite latent gold standard which was derived from several experts manual segmentations by an em algorithm the distribution functions of the tumour and control pixel data were parametrically assumed to be a mixture of two beta distributions with different shape parameters we estimated the corresponding receiver operating characteristic curve dice similarity coefficient and mutual information over all possible decision thresholds based on each validation metric an optimal threshold was then computed via maximization we illustrated these methods on mr imaging data from nine brain tumour cases of three different tumour types each consisting of a large number of pixels the automated segmentation yielded satisfactory accuracy with varied optimal thresholds the performances of these validation metrics were also investigated via monte carlo simulation extensions of incorporating spatial correlation structures using a markov random field model were considered

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

estimating kinetic parameter maps from dynamic contrast enhanced mri using spatial prior knowledge dynamic contrast enhanced magnetic resonance dce mr imaging can be used to study microvascular structure in vivo by monitoring the abundance of an injected diffusible contrast agent over time the resulting spatially resolved intensity time curves are usually interpreted in terms of kinetic parameters obtained by fitting a pharmacokinetic model to the observed data least squares estimates of the highly nonlinear model parameters however can exhibit high variance and can be severely biased as a remedy we bring to bear spatial prior knowledge by means of a generalized gaussian markov random field ggmrf by using information from neighboring voxels and computing the maximum a posteriori solution for entire parameter maps at once both bias and variance of the parameter estimates can be reduced thus leading to smaller root mean square error rmse since the number of variables gets very big for common image resolutions sparse solvers have to be employed to this end we propose a generalized iterated conditional modes icm algorithm operating on blocks instead of sites which is shown to converge considerably faster than the conventional icm algorithm results on simulated dce mr images show a clear reduction of rmse and variance as well as in some cases reduced estimation bias the mean residual bias mrb is reduced on the simulated data as well as for all 37 patients of a prostate dce mri dataset using the proposed algorithm average computation times only increase by a factor of 1 18 871 ms per voxel for a gaussian prior and 1 51 1 12 s per voxel for an edge preserving prior compared to the single voxel approach 740 ms per voxel

uniqueness of solutions of parabolic semilinear nonlocal boundary problems abstract the purpose of the paper is to give two theorems about the uniqueness of solutions of parabolic semilinear nonlocal boundary problems the paper is a continuation of previous papers by byszewski and the generalization of some results from r rabczuk introduction to differential inequalities pwn warsaw 1976 polish j chabrowski on nonlocal problems for parabolic equations nagoya math j 93 1984 109 131 the theorems obtained in this paper can be applied in the theories of diffusion and heat conduction with better effects than the analogous theorems about parabolic initial boundary problems and than the analogous theorems about parabolic periodic boundary problems

weighted finite difference techniques for the one dimensional advection diffusion equation various numerical techniques will be developed and compared for solving the one dimensional advection diffusion equation with constant coefficient these techniques are based on the two level finite difference approximations the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the new methods are more accurate and are more efficient than the conventional techniques these schemes are free of numerical diffusion the results of a numerical experiment are presented and the accuracy and central processor cpu time needed are discussed and compared

finite difference solutions for parabolic equations with the time weighting initial conditions abstract a class of nonlinear parabolic boundary value problems with time weighting initial condition is considered instead of studying the existence uniqueness and continuous dependence of the solution upon the data we give a brief review of the known results and then concentrate on the performance of the backward euler and crank nicolson finite difference schemes 1 the results of some numerical examples are presented which demonstrate the efficiency and rapid convergence

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

on the lie structure of a prime associative superalgebra abstract in this paper some results on the lie structure of prime superalgebras are discussed we prove that with the exception of some special cases for a prime superalgebra a over a ring of scalars with 1 2 if l is a lie ideal of a and w is a subalgebra of a such that w l w then either l z or w z likewise if v is a submodule of a and v l v then either v z or l z or there exists an ideal of a m such that 0 m a v this work extends to prime superalgebras some results of i n herstein c lanski and s montgomery on prime algebras

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis