a material frame approach for evaluating continuum variables in atomistic simulations we present a material frame formulation analogous to the spatial frame formulation developed by hardy whereby expressions for continuum mechanical variables such as stress and heat flux are derived from atomic scale quantities intrinsic to molecular simulation this formulation is ideally suited for developing an atomistic to continuum correspondence for solid mechanics problems we derive expressions for the first piola kirchhoff p k stress tensor and the material frame heat flux vector directly from the momentum and energy balances using localization functions in a reference configuration the resulting p k stress tensor unlike the cauchy expression has no explicit kinetic contribution the referential heat flux vector likewise lacks the kinetic contribution appearing in its spatial frame counterpart using a proof for a special case and molecular dynamics simulations we show that our p k stress expression nonetheless represents a full measure of stress that is consistent with both the system virial and the cauchy stress expression developed by hardy we also present an expanded formulation to define continuum variables from micromorphic continuum theory which is suitable for the analysis of materials represented by directional bonding at the atomic scale

asymptotically almost periodic solutions for abstract neutral integro differential equations we study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro differential equation with unbounded delay a concrete application to partial neutral integro differential equations which arise in the study of heat conduction in fading memory material is considered

estimation of variance of the regression estimator abstract the regression estimator and the ratio estimator are commonly used in survey practice in the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs the ratio estimator is appropriate for populations whose regression line passes close to the origin if the intercept of the regression line is significantly nonzero however it is much less efficient than the regression estimator deng 1984 in general apart from n 2 terms the mean squared error mse of the former is bigger than that of the latter cochran 1977 p 196 given the present computing capacity the computational advantage of the ratio estimator should be less of a concern and the regression estimator will gain wider popularity the main purpose of this article is to provide a theoretical and empirical comparison of several variance estimators for the regression estimator in simple random sampling without replacement the companion problem for the

existence of solutions for impulsive partial neutral functional differential equations this paper is concerned with partial neutral functional differential equations of first and second order with impulses we establish some results of existence of mild solutions for these classes of equations

weighted lq lp estimate with muckenhoupt weights for the diffusion wave equations with time fractional derivatives abstract we present a weighted l q l p theory p q 1 with muckenhoupt weights for the equation t u t x u t x f t x t 0 x r d here 0 2 and t is the caputo fractional derivative of order in particular we prove that for any p q 1 w 1 x a p and w 2 t a q 0 r d u x x p w 1 d x q p w 2 d t n 0 r d f p w 1 d x q p w 2 d t where a p is the class of muckenhoupt a p weights our approach is based on the sharp function estimates of the derivatives of solutions

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

global solutions for abstract neutral differential equations we study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis some concrete applications related to ordinary and partial differential equations are considered

survey design under the regression superpopulation model abstract the construction of sample designs and estimators under a linear regression superpopulation model is considered the anticipated variance the variance of the predictor computed with respect to the sampling design and the superpopulation model is used as a criterion for evaluating probability designs and model unbiased predictors regression predictors that are model unbiased and design consistent are constructed

a priori bounds for degenerate and singular evolutionary partial integro differential equations we study quasilinear evolutionary partial integro differential equations of second order which include time fractional p laplace equations of time order less than one by means of suitable energy estimates and de giorgi s iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems we also show that a maximum principle is valid for such equations

an lq lp theory for the time fractional evolution equations with variable coefficients abstract we introduce an l q l p theory for the semilinear fractional equations of the type 0 1 t u t x a i j t x u x i x j t x f t x u t 0 x r d here 0 2 p q 1 and t is the caupto fractional derivative of order uniqueness existence and l q l p estimates of solutions are obtained the leading coefficients a i j t x are assumed to be piecewise continuous in t and uniformly continuous in x in particular a i j t x are allowed to be discontinuous with respect to the time variable our approach is based on classical tools in pde theories such as the marcinkiewicz interpolation theorem the calderon zygmund theorem and perturbation arguments

maximal regularity for non autonomous schrodinger type equations abstract in this paper we study the maximal regularity property for non autonomous evolution equations t u t a t u t f t u 0 0 if the equation is considered on a hilbert space h and the operators a t are defined by sesquilinear forms a t we prove the maximal regularity under a holder continuity assumption of t a t in the non hilbert space situation we focus on schrodinger type operators a t m t and prove l p l q estimates for a wide class of time and space dependent potentials m

semilinear subdiffusion with memory in the one dimensional case abstract for 0 1 we consider the semilinear integro differential equation on the one dimensional domain a b in the unknown u u x t d t u l 1 u 0 t k t s l 2 u s d s f x t u g x t where d t is the caputo fractional derivative and l 1 and l 2 are uniform elliptic operators with time dependent smooth coefficients under certain structural conditions on the nonlinearity f the global existence and uniqueness of classical solutions to the related initial boundary value problems are established via the so called continuation argument approach the key point is looking for suitable a priori estimates of the solution in the fractional holder spaces

end point maximal regularity and its application to two dimensional keller segel system we prove the maximal l regularity of the cauchy problem of the heat equation in the besov space dot b 1 rho 0 mathbb r n 1 which is not umd space and as its application we establish the time local well posedness of the solution of two dimensional nonlinear parabolic system with the poisson equation in dot b 1 2 0 mathbb r 2 where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time the small data global existence is also obtained in the same class

conditioning ratio estimates under simple random sampling abstract the usual ratio estimates for a population mean use information on an auxiliary variable to improve the estimation the standard randomization analysis however does not take enough account of the observations on the auxiliary variable so estimates and estimated variates can be conditionally biased unless the sample is balanced with respect to the auxiliary variable i propose a method of adjustment for the bias of the estimate and its variance based only on the assumption of simple random sampling which uses an approximate conditional distribution of the estimate given the mean of the auxiliary variable roy all and cumberland 1981 illustrated empirically that the usual random sampling estimates and estimated variances could be badly conditionally biased when samples were obtained that were unbalanced in the auxiliary variate so if the sample mean and population mean both of which are known at the time of analysis are not close it is known that the results are biased but the usual rand

end point maximal l 1 regularity for the cauchy problem to a parabolic equation with variable coefficients we consider maximal l 1 regularity for the cauchy problem to a parabolic equation in the besov space dot b p 1 0 mathbb r n with 1 le p le infty the estimate obtained here is not available by abstract theory of the class of unconditional martingale differences because the end point besov space is included we consider the end point estimate and show that the optimality of maximal regularity in l 1 for the linear parabolic equation with variable coefficients

on a class of abstract neutral functional differential equations abstract by using the theory of semigroups of growth we discuss the existence of mild solutions for a class of abstract neutral functional differential equations a concrete application to partial neutral functional differential equations is considered

conditional statistical inference and quantification of relevance summary we argue that it can be fruitful to take a predictive view on notions such as the precision of a point estimator and the confidence of an interval estimator in frequentist inference this predictive approach has implications for conditional inference because it immediately allows a quantification of the concept of relevance for conditional inference conditioning on an ancillary statistic makes inference more relevant in this sense provided that the ancillary is a precision index not all ancillary statistics satisfy this demand we discuss the problem of choice between alternative ancillary statistics the approach also has implications for the best choice of variance estimator taking account of correlations with the squared error of estimation itself the theory is illustrated by numerous examples many of which are classical

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

boundedness of weak solutions to evolutionary partial integro differential equations with discontinuous coefficients we investigate linear and quasilinear evolutionary partial integro differential equations of second order which include time fractional evolution equations of time order less than one by means of suitable energy estimates and de giorgi s iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems we also show that a maximum principle holds for such equations

prediction models and unequal probability sampling summary prediction models are used to study the horvitz thompson estimator in probabilityproportional to size sampling and six estimators of its variance the variance estimators include the horvitz thompson yates grundy and jackknife statistics as well as two bias robust estimators from prediction theory an empirical study confirms prediction theory s implications about these estimators

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

connecting molecular dynamics to micromorphic theory i instantaneous and averaged mechanical variables abstract this is the first part of an effort to connect molecular dynamics to a well established continuum theory micromorphic theory this effort includes two parts mechanical variables and balance laws in this paper the physical picture of micromorphic theory is introduced a geometric model of an atomic system is presented the microscopic expressions of all the instantaneous mechanical variables in micromorphic theory are derived and related to atomic coordinates and velocities and the corresponding continuum field quantities are obtained through statistical ensemble average the link between the two thoroughly different models is analytically established

atomistic viewpoint of the applicability of microcontinuum theories abstract microcontinuum field theories including micromorphic theory microstructure theory micropolar theory cosserat theory nonlocal theory and couple stress theory are the extensions of the classical field theories for the applications in microscopic space and time scales they have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale this work provides an atomic viewpoint to examine the physical foundations of those well established microcontinuum theories and to justify their applicability through lattice dynamics and molecular dynamics

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

estimation of variance of the ratio estimator summary a general class of estimators of the variance of the ratio estimator is considered which includes two standard estimators vo and v2 and approximates another estimator vh suggested by royall eberhardt 1975 asymptotic expansions for the variances and biases of the proposed estimators are obtained based on this we obtain optimal variance estimators in the class and compare the relative merits of three estimators vo v1 and v2 without any model assumption under a simple regression model a more definite comparison of vo v1 and v2 is made in terms of variance and bias some key word8 asymptotic expansion bias optimal variance estimator ratio estimator superpopulation variance

on a new class of abstract neutral differential equations abstract in this work we introduce a new class of abstract neutral differential equations and study the existence of mild and strict solutions some concrete applications involving partial neutral differential equations are considered

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

long time behavior of nonlinear integro differential evolution equations abstract we study the long time behavior as time tends to infinity of globally bounded strong solutions to certain integro differential equations in hilbert spaces based on an appropriate new lyapunov function and the ojasiewicz simon inequality we prove that any globally bounded strong solution converges to a steady state in a real hilbert space

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

existence of minimizers for a finite strain micromorphic elastic solid we investigate geometrically exact generalized continua of micromorphic type in the sense of eringen the two field problem for the macrodeformation and the affine microdeformation p gl 3 r in the quasistatic conservative load case is investigated in a variational form depending on material constants two existence theorems in sobolev spaces are given for the resulting nonlinear boundary value problems these results comprise existence results for the micro incompressible case p sl 3 r and the cosserat micropolar case p so 3 r in order to treat external loads a new condition called bounded external work has to be included which overcomes the conditional coercivity of the formulation the possible lack of coercivity is related to fracture of the micromorphic solid the mathematical analysis uses an extended korn first inequality the methods of choice are the direct methods of the calculus of variations

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

holder continuous solutions for integro differential equations and maximal regularity we characterize existence and uniqueness of solutions for a linear integro differential equation in holder spaces our method is based on operator valued fourier multipliers the solutions we consider may be unbounded concrete equations of the type we study arise in the modeling of heat conduction in materials with memory

simultaneously model unbiased design unbiased estimation this paper proposes a class of inferential procedures incorporating both design and estimation elements that yield estimates of means that are simultaneously model unbiased and design unbiased classical regression procedures yield conditionally unbiased estimators for the mean conditioning on the model and choice of observation points in contrast design based methods yield estimators that are unconditionally unbiased on matter what the form of the underlying model variance properties of the proposed class are examined and applications to bioavailability water quality from mine run off and finite population regression estimation are considered the proposed procedures perform well especially in the typical case where a model is only approximately correct

on cα holder classical solutions for non autonomous neutral differential equations the nonlinear case abstract in this paper we continue our developments in 19 on the existence of classical solutions for abstract neutral differential equations in the current work we extend the results in 19 for nonlinear neutral differential equations some applications involving nonlinear partial neutral differential equations are presented

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

approximate controllability of semilinear neutral evolution systems with delay this paper considers the approximate controllability for a class of neutral control systems governed by semilinear neutral delayed equations sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition banach contraction mapping principle and techniques on fractional power operators the obtained results improve some existing analogous ones on this topic to some extent an example is presented finally to illustrate the applications of the obtained results

fully nonlinear integrodifferential equations in general banach space on etudie des equations integrodifferentielles non lineaires dans un espace de banach qui peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles non lineaires on considere un probleme aux valeurs limites et initiales