connectedness at infinity of complete kahler manifolds one of the main purposes of this paper is to prove that on a complete k ahler manifold of dimension m if the holomorphic bisectional curvature is bounded from below by 1 and the minimum spectrum lambda 1 m ge m 2 then it must either be connected at infinity or isometric to bbb r times n with a specialized metric with n being compact generalizations to complete k ahler manifolds satisfying a weighted poincar e inequality are also being considered

an extended identifiability in aquifer parameter identification and optimal pumping test design an extended identifiability called identifiability is developed for groundwater modeling and management some fundamental concepts are developed for establishing a criterion in connection with the problem of optimal experimental design such as the design of an optimum pumping test to assist aquifer parameter identification in practice the quantity and quality of data prohibits a unique solution of the inverse problem of parameter identification the proposed identifiability is based upon the concept of weak uniqueness the determination of the admissibility of a given design is formulated as a nonlinear programming problem the original constrained problem is transformed into solving a sequence of unconstrained problems by a penalty function method numerical experiments are conducted to illustrate the proposed concept and algorithm

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

recursive programs and denotational semantics in absolute logics of programs abstract it has been proposed by meyer kfouri and others to extend the so called nonstandard logics of programs approach nlp henceforth to recursive programs and denotational semantics in some natural way the key step in doing nlp is selecting a semantics for programs which in the present paper is denotational semantics and then forming its kpu absolute version absoluteness is a set theoretic property of logics if a logic l is not absolute then some formulas of l do not speak about the models of l but about something else if a logic has this strange property then it is impossible to find a complete inference system for it and this because of purely administrative reasons which might not correspond to any of the inherent properties of the original situation we are modeling in devising this logic etc this administrative incompleteness is only one of the undesirable side effects of nonabsoluteness in nlp the purpose of constructing and studying absolute versions of logics is aimed at among other things the removal of these undesirable properties the absolute version of denotational semantics will turn out to be based on 2 sorted first order logic or more concretely on the usual nonstandard or weak second order logic some of the most relevant features of this logic are the ability to compare realistic existing program verification methods create new more powerful and still realistic ones completeness etc to mention only a very few

on the heat kernel of the bergmann metric on algebraic varieties the restriction of the standard fubini study metric of ycpn l to m m is an incomplete kahler metric g called the bergmann metric let us consider the operators d and 3 defined on c1 functions and c1 1 forms on m m respectively we define the domain 9y d of d to be the set of c1 functions 2 f defined on m m such that both f and df are in l similarly we define the domain 92 6 of to be the set of c1 1 forms co such that both co and 2 6 o are in l we then define the laplacian a with respect to the bergmann metric by a d with domain 9 a given by the set of c2 functions f such that f e 9 d and df e 6 the main purpose of this paper is to show that

a simple and efficient space domain implementation of the turning bands method given a correlation function c x with x in rn the turning bands method tbm for n 2 and 3 constructs realizations of an n dimensional and stationary process y n o c x from appropriately summed line processes therefore an implementation of tbm calls naturally for fast and accurate generations of line realizations these have generally been generated by a spectral approach since the fourier transform of the line covariances is linked in a very simple fashion to the n dimensional fourier transform of c x however we show that in many instances a space domain implementation of tbm with line realizations obtained from a circulant embedding method has advantages over a spectral implementation in that without increase in computational costs 1 the line realizations display exactly the required covariance structure 2 knowledge of the spectral density of the process y is not required and 3 fine tuning of line process parameters is not needed

semantic models for total correctness and fairness assertional s rings are introduced to provide an algebraic setting in which the finite and infinite behavior of nondeterministic programs can be expressed and reasoned about this includes expressing the fair infinite behavior of nondeterministic iterative programs and reasoning about termination under various fairness assumptions we also address the question of when the reasoning techniques are semantically complete

classification of negatively pinched manifolds with amenable fundamental groups we give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups namely they are precisely the mobius band and the products of r with the total spaces of flat vector bundles over closed infranilmanifolds

comparison theorem for kahler manifolds and positivity of spectrum the first part of this paper is devoted to proving a comparison theorem for kahler manifolds with holomorphic bisectional curvature bounded from below the model spaces being compared to are m m and m in particular it follows that the bottom of the spectrum for the laplacian is bounded from above by m2 for a complete m dimensional kahler manifold with holomorphic bisectional curvature bounded from below by 1 the second part of the paper is to show that if this upper bound is achieved and when m 2 then it must have at most four ends

on the notion of expressiveness and the rule of adaptation abstract in this note two issues concerning completeness of hoare like proof systems which seem unrelated at first sight are brought together expressiveness of the assertion language and the rule of adaptation these different issues are connected by investigating soundness and relative completeness of four published versions of the rule of adaptation with help of some general techniques for reasoning about expressiveness

inverse groundwater modeling with emphasis on model parameterization 1 this study develops an inverse method aiming to circumvent the subjective decision regarding model parameterization and complexity in inverse groundwater modeling the number of parameters is included as a decision variable along with parameter values a parameterization based on b spline surfaces bss is selected to approximate transmissivity and genetic algorithms were selected to perform error minimization a transform based on linear least squares lls is developed so that different parameterizations may be combined by standard genetic algorithm operators first three applications with isotropic anisotropic and zoned aquifer parameters are examined in a single objective optimization problem and the estimated transmissivity is found to be near the true one interestingly in the anisotropic case the algorithm converged to a solution with an anisotropic distribution of control points next a single objective optimization with regularization penalizing complex models is considered and last the problem is expressed in a multiobjective optimization framework moo where the goals are simultaneous minimization of calibration error and model complexity the result of moo is a pareto set of potential solutions where the user can examine the tradeoffs between calibration error and model complexity and select the most suitable model by comparing calibration with prediction errors it appears that the most promising models are the ones near a region where the rate of decrease of calibration error as model complexity increases drops bend of error curve this is a useful result of practical interest in real inverse modeling applications

incorporation of prior information on parameters into nonlinear regression groundwater flow models 1 theory prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem two scales of prior information can be available 1 prior information having known reliability that is bias and random error structure and 2 prior information consisting of best available estimates of unknown reliability a regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved although biased parameter estimates approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias which is almost always much smaller than that resulting from standard ridge regression it is shown that if both scales of prior information are available then a combined regression analysis may be made

stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology conditioning on head observations a stochastic methodology to evaluate the predictive uncertainty in well capture zones in heterogeneous aquifers with uncertain parameters is presented the approach is based on the generalized likelihood uncertainty estimation methodology the hydraulic conductivity is modeled as a random space function allowing for the uncertainty that stems from the imperfect knowledge of the parameters of the correlation structure parameters are sampled from prior distributions and are used for the generation of a large number of hydraulic conductivity fields which are subsequently used to solve the groundwater flow equation a likelihood is calculated for every simulation based on some goodness of fit measure between simulated heads and available observations using inverse particle tracking a capture zone is determined which is assigned the likelihood calculated for that particular simulation statistical analysis of the ensemble of all simulations enables the predictive uncertainty of the well capture zones to be defined results are presented for a hypothetical test case and different likelihood definitions used in the conditioning process the results show that the delineated capture zones are most sensitive to the mean hydraulic conductivity and the variance whereas the integral scale of the variogram is the parameter with the smallest influence for all likelihood measures the prior uncertainty is reduced considerably by introducing the observation heads but the reduction is most effective for the very selective likelihood definition the method presented can be used in real applications to quantify the uncertainty in the location and extent of well capture zones when little or no information is available about the hydraulic properties through the conditioning on head observations

on the recovery of multiple flow parameters from transient head data the problem of estimating groundwater flow parameters from head measurements and other ancillary data is fundamental to the process of modelling a groundwater system we consider here a new method that allows for the simultaneous computation of multiple parameters as the unique minimum of a convex functional

total correctness in nonstandard logics of programs abstract we show that termination is a first order notion if approached via nonstandard logics of programs nlp we give explicit first order characterizations of the program verifying power of the well known manna cooper method for proving total correctness assertions tca s similar characterization is given to the intermittent assertions method w r t tca s a comparison of the tca proving powers of distinguished methods or logics of programs is also attempted we also show that nlp provides new methods which are strictly stronger than the manna cooper method in the end we turn to partial correctness issues related to the main body of the paper

a new formulation for transmissivity estimation with improved global convergence properties a new formulation is proposed for the estimation of transmissivity in confined aquifers based on head measurements this formulation consists of a formulation which minimizes a weighted residual norm of the gradient of the measured and observed head the weighting is the square of the estimated transmissivity we show by theoretical analysis and numerical experimentation the improved global convergence properties and characteristics of stability under head measurement uncertainty exhibited by the new formulation we conclude that the new formulation may be superior to conventional head residual formulations or may be useful as an added term to conventional formulations the formulation is further demonstrated by a field scale application to the friuli aquifer in italy

ten years of hoare s logic a survey part ii nondeterminism a survey of various results concerning the use of hoare s logic in proving correctness of nondeterministic programs is presented various proof systems together with the example proofs are given and the corresponding soundness and completeness proofs of the systems are discussed programs allowing bounded and countable nondeterminism are studied proof systems deal with partial and total correctness freedom of failure and the issue of fairness the paper is a continuation of part i by apt 1981 where various results concerning hoare s approach to proving correctness of sequential programs are presented

evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall runoff models influence of calibration data variability and length on model credibility the success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature quantity and quality of the data used the objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model also the data should be chosen so as to contain as much valuable information about the process as possible in this paper we compare the performance of two maximum likelihood estimators the amle which assumes the presence of first lag autocorrelated homogeneous variance errors and the hmle which assumes the presence of uncorrelated inhomogeneous variance errors to the commonly used simple least squares criterion sls the model calibrated was the soil moisture accounting model of the u s national weather service s river forecast system sma nwsrfs the results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates furthermore the sensitivity of the estimation results to various characteristics of the calibration data such as hydrologic variability and length are substantially reduced

complete manifolds with positive spectrum ii in this paper we continued our investigation of complete manifolds whose spectrum of the laplacian has an optimal positive lower bound in particular we proved a splitting type theorem for n dimensional manifolds that have a finite volume end this can be viewed as a study of the equality case of a theorem of cheng

coupled inverse problems in groundwater modeling 1 sensitivity analysis and parameter identification some basic concepts and methods for solving the coupled inverse problem in groundwater modeling are presented in a series of two papers because there are crossover effects between state variables and parmeters coupled inverse problems are different from single inverse problems in several aspects especially in the selection of objective functions identifiability and experimental design this paper discusses the general definition of coupled inverse problems posed in the framework of multiobjective optimization in order to obtain gradient vectors of objective functions as well as all sensitivity coefficients a general procedure for deriving the adjoint state equations and their associated conditions is described using the rules of adjoint operation presented in this paper the derivation of adjoint problems becomes very easy even for nonlinear and transient coupled problems as examples the adjoint problem of flow mass transport or flow heat transport the adjoint problem of saltwater intrusion and the adjoint problem of two phase flow are derived numerical experiments on a two dimensional flow mass transport problem are given to explain the procedure of sensitivity analysis and parameter identification for coupled problems the hydraulic conductivity can be identified by using observations of head and or solute concentration

equational logic of circular data type specification abstract iteration theories introduced by bloom elgot and wright in 1980 formalize the equational properties of the strong behaviors of flowchart algorithms we show that the same equational properties are shared by the functors used to specify circular data types lehmann and smyth 1981 have shown how to specify circular data types such as stacks as fixed points of certain functors the called gw functors for example the set of stacks of elements in the set a is a solution to the equation in the variable x x f a x where f x x 1 a x is the functor on set taking the pair a x to the disjoint union of the singleton set 1 and the product a x such equations have initial solutions f a which in turn determine a solution functor f the equational properties of the operation f f are precisely captured by the axioms for iteration theories more precisely we show how the structure th c of all functors c n c p n p 0 on the category c forms an iteration theory and conversely any identity valid in all such structures is valid in the class of all iteration theories

bayesian calibration of a large scale geothermal reservoir model by a new adaptive delayed acceptance metropolis hastings algorithm 1 the aim of this research is to estimate the parameters of a large scale numerical model of a geothermal reservoir using markov chain monte carlo mcmc sampling within the framework of bayesian inference all feasible parameters that are consistent with the measured data are summarized by the posterior distribution and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution it appears to be computationally infeasible to use the standard metropolis hastings algorithm mh to sample the high dimensional computationally expensive posterior distribution to improve the sampling efficiency a new adaptive delayed acceptance mh algorithm adamh is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced order model this use of adaptivity differs from existing adaptive mcmc algorithms that tune proposal distributions of the metropolis hastings algorithm mh though adamh also implements that technique for the 3 d geothermal reservoir model we present here adamh shows a great improvement in the computational efficiency of the mcmc sampling and promising results for parameter estimation and uncertainty quantification are obtained this algorithm could offer significant improvement in computational efficiency when implementing sample based inference in other large scale inverse problems

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

definability by programs in first order structures introduction ti 1 preliminarv detinitilms and results algebraic characterizations of the unwind property a structure with the unwind property for every iterative but not every recursive 1 program the truth table property structures with the truth table property but not the unwind property for every iterative program 4ppendix 1 the pebble game on infinite dags ippendix 2 remaining proofs references

simultaneous inversion of hydrogeologic and thermal data 1 theory and application using hydraulic head data one goal in solving the inverse problem in groundwater hydrology is to obtain parameter estimates for use in a simulation model a philosophy about the inverse is adopted here that takes the form of constructing a variety of models under different norms large differences in parameter estimates obtained using different norms suggests the possibility of an incorrect interpretational model an optimization procedure is used that is based on the constrained simplex method this algorithm easily handles constraints does not require derivatives of the functional with respect to the parameters and can be employed to minimize complicated functionals the algorithm produces a cluster of search points in parameter space about the global minimum of the objective function each of these points generates data that matches observed values within a prescribed tolerance the centroid of the search points is taken as the best estimate of the parameters the covariances of the estimated parameters and estimated data can also be computed this inverse technique is applied to a sparse inaccurate hydraulic head data set observed at downie slide british columbia canada for this cross sectional problem with noisy data and a strong drift component interpolation of hydraulic head values using kriging techniques was not possible the domain is represented as a homogeneous isotropic medium four parameters are estimated the free surface position of the water table and three boundary conditions further simulations using a synthetic data set with assumed properties similar to that of downie slide show that with noise free data and an adequate spacing between measurement points it is possible to interpolate an unbiased estimate of hydraulic head data at all nodes in the equivalent discretized domain when the inverse technique is applied the hydraulic conductivity structure is correctly identified the implications for downie slide are that in order to resolve more than a simple hydraulic conductivity structure accurate field measurements of hydraulic head a better spacing between measurements and more detailed knowledge of the boundary conditions are required

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

inverse stochastic moment analysis of steady state flow in randomly heterogeneous media 1 nonlocal stochastic moment equations have been used successfully to analyze steady state and transient flow in randomly heterogeneous media conditional on measured values of medium properties we present a nonlinear geostatistical inverse algorithm for steady state flow that makes it possible to further condition such analyses on measured values of state variables our approach accounts for all scales of spatial variability resolvable by the computational grid it is based on recursive finite element approximations of exact nonlocal first and second conditional moment equations hydraulic conductivity is parameterized geostatistically on the basis of measured values at discrete locations and unknown values at discrete pilot points prior estimates of pilot point values are obtained optionally by generalized kriging posterior estimates at pilot points and optionally at measurement points are obtained by calibrating mean flow against measured values of head the parameters are projected onto a computational grid via kriging maximum likelihood calibration allows estimating not only hydraulic but also optionally unknown variogram parameters with or without prior information about the former the approach yields covariance matrices for parameter estimation as well as head and flux prediction errors the latter being obtained a posteriori we implement our inverse approach on highly and mildly heterogeneous media under superimposed mean uniform and convergent flows in a bounded two dimensional domain our examples illustrate how conductivity and head data act separately and jointly to reduce parameter estimation errors and to model predictive uncertainty we also evaluate the functional form of the log conductivity variogram and its parameters using likelihood based model discrimination criteria

multimodel bayesian analysis of groundwater data worth we explore the way in which uncertain descriptions of aquifer heterogeneity and groundwater flow impact one s ability to assess the worth of collecting additional data we do so on the basis of maximum likelihood bayesian model averaging mlbma by accounting jointly for uncertainties in geostatistical and flow model structures and parameter hydraulic conductivity as well as system state hydraulic head estimates given uncertain measurements of one or both variables previous description of our approach was limited to geostatistical models based solely on hydraulic conductivity data here we implement the approach on a synthetic example of steady state flow in a two dimensional random log hydraulic conductivity field with and without recharge by embedding an inverse stochastic moment solution of groundwater flow in mlbma a moment equations based geostatistical inversion method is utilized to circumvent the need for computationally expensive numerical monte carlo simulations the approach is compatible with either deterministic or stochastic flow models and consistent with modern statistical methods of parameter estimation admitting but not requiring prior information about the parameters it allows but does not require approximating lead predictive statistical moments of system states by linearization while updating model posterior probabilities and parameter estimates on the basis of potential new data both before and after such data are actually collected

some questions about expressiveness and relative completeness in hoare s logic abstract a well known result of cook asserts the completeness of hoare s logic for while programs relative to any expressive structure in this paper we present a wide and natural class of structures whose members are either expressive or make hoare s logic strongly incomplete relative to them in the sense that a trivially true partial correctness assertion is not hoare derivable from the first order theory of the structure the definition of this class is related to the so called unwind property for while programs and its behaviour follows from quite general sufficient conditions for strong relative incompleteness we state also two questions about the connections among inexpressiveness relative incompleteness and strong relative incompleteness and point out the seeming difficulty of answering them

ends of locally symmetric spaces with maximal bottom spectrum let x be a symmetric space of non compact type and gnx a locally sym metric space then the bottom spectrum l1 gnx satisfies the inequality l1 gnx e l1 x we show that if equality l1 gnx l1 x holds then gnx has either one end which is necessarily of infinite volume or two ends one of infinite volume and another of finite vol ume in the latter case gnx is isometric to r 1 n endowed with a multi warped metric where n is compact

weak second order characterizations of various program verification systems abstract we show the equivalence of leivant s characterization of floyd hoare logic in weak second order logic leivant 1985 with both csirmaz s 1980 and sain s 1985 characterizations of floyd hoare logic in nonstandard logics of programs our method allows us to spell out the precise role of the comprehension axiom in weak second order logic we then prove similar results for other program verification systems suggested by burstall and pnueli and identify exactly the comprehension axioms corresponding to those systems

iteration theories of synchronization trees synchronization trees are shown to form an iteration theory in a natural way the class of grove iteration theories is introduced the regular synchronization trees are shown to be the free theories in the subclass of synchronization theories moreover the bisimulation equivalence classes of regular synchronization trees are shown to be the free synchronization theories satisfying an infinite idempotency law

strategic placement of localization devices such as pilot points and anchors in inverse modeling schemes 1 localization schemes using devices such as pilot points or anchors localization devices are used in inversion schemes as a tool for gleaning information from measurements that can be used to constrain inversion schemes with the added benefit in the form of a potential for reduction in the number of parameters employed in the inversion scheme this paper proposes and demonstrates a method for strategic placement of the localization devices the method combines stochastic singular value decomposition with parameter rejection methods to produce a map of intensity scores which allows the inverse modeler to place the localization devices at locations defined by their probability for producing informative probabilistic constraints on the statistical distributions of the target variables we also show that the method can be used for selecting measurement locations when designing data acquisition campaigns the method is demonstrated for the case of steady state flow in a heterogeneous conductivity field using mad method of anchored distributions in summary the proposed localization scheme intends to increase the information gleaned from measurements while reducing the associated computational costs associated with stochastic inversion

a simple dynamic logic abstract a system of dynamic predicate logic is presented it allows nonstandard modelling of time which makes recursive axiomatization possible and is essentially one sorted the same elements code data and time which makes the system reasonably simple and transparent the system is subjected to usual mathematical considerations in particular it is shown to be equivalent to the three sorted system due to andreka nemeti and sain 1982 a conservation result for the latter system is obtained as a by product

efficient posterior exploration of a high dimensional groundwater model from two stage markov chain monte carlo simulation and polynomial chaos expansion 1 this study reports on two strategies for accelerating posterior inference of a highly parameterized and cpu demanding groundwater flow model our method builds on previous stochastic collocation approaches e g marzouk and xiu 2009 and marzouk and najm 2009 and uses generalized polynomial chaos gpc theory and dimensionality reduction to emulate the output of a large scale groundwater flow model the resulting surrogate model is cpu efficient and serves to explore the posterior distribution at a much lower computational cost using two stage mcmc simulation the case study reported in this paper demonstrates a two to five times speed up in sampling efficiency

hydrologic characterization of heterogeneous geologic media with an inverse method based on iterated function systems one way to estimate the hydrologic properties of heterogeneous geologic media is to invert well test data using multiple observation wells pressure transients observed during a well test are compared to the corresponding values obtained by numerically simulating the test using a mathematical model the parameters of the mathematical model are varied and the simulation repeated until a satisfactory match to the observed pressure transients is obtained at which point the model parameters are accepted as providing a possible representation of the hydrologic property distribution restricting the search to parameters that represent self similar fractal hydrologic property distributions can improve the inversion process far fewer parameters are needed to describe a hierarchical medium improving the efficiency and robustness of the inversion additionally each parameter set produces a hydrologic property distribution with a hierarchical structure which mimics the multiple scales of inversion create fractal sets known as attractors using an iterated function system ifs an attractor is mapped to a distribution of transmissivity and storativity in the mathematical model thus the ifs inverse method searches for the parameters of the ifs typically tens of parameters rather than the values of the hydrologic property distribution directly typically hundreds to thousands of parameters applicationmore of the ifs inverse method to synthetic data shows that the method works well for simple heterogeneities application to field data from a sand clay sedimentary sequence and a fractured granite produces reasonable results 26 refs 32 figs 5 tabs less

recursive programs as definitions in first order logic despite the reputed limitations of first order logic it is easy to state and prove almost all interesting properties of recursive programs within a simple first order theory by using an approach we call first order programming logic unlike higher order logics based on fixed point induction first order programming logic is founded on deductive principles that are familiar to most programmers informal structural induction arguments such as termination proofs for lisp append mccarthy s 91 function and ackermann s function have direct formalizations within the system the essential elements of first order programming logic are 1 the data domain d must be a finitely generated set that explicitly includes the undefined object bot representing nontermination as well as ordinary data objects 2 recursive programs over d are treated as logical definitions augmenting a first order theory ofthe data domain 3 the interpretation of a recursive program is the least fixed point of the function

hoare s logic for nondeterministic regular programs a nonstandard approach abstract this paper studies hoare s logic for nondeterministic regular programs with unbounded nondeterminism from the point of view of nonstandard dynamic logic we define a so called continuous semantics which allows certain infinitely long computations and compare it with usual semantics proving among other things the equivalence of both over reasonable data types we also establish a completeness theorem for hoare s calculus relative to continuous semantics thereby generalizing a previous result of csirmaz the proof makes use of a normal form for regular programs which is perhaps interesting in its own right

a continuous time inverse operator for groundwater and contaminant transport modeling model identifiability general identifiability conditions are derived for the model coefficients of the spatially discretized continuous time diffusion equation these conditions in turn determine some sufficient and necessary conditions for the existence and uniqueness of the continuous time inverse operator described in a previous article the identifiability conditions are in terms of the initial conditions and the flux vector containing boundary condition information and the eigenspace of the spatially discretized system the derivation of these conditions gives some insight into the location of the solution of the inverse problem in terms of the direct operator under investigation in the space of the laplace transform and limited insight into the stability of the solution near that location

on flowchart theories part ii the nondeterministic case abstract we give a calculus for nondeterministic flowchart schemes similar to the calculus of polynomials it uses a formal representation of flowchart schemes and a natural equivalence on these formal representations the algebraic structure involved is a matrix theory endowed with an axiomatized repetition

a complete logic for reasoning about programs via nonstandard model theory ii in part i of the present paper w z defined the first order dynamic language dld of type d in definition 13 3 defined a decidable proof concept i prn for dld and in theorem 2 we proved that kn pm is a strongly complete inferenr e system for dld that is for every theory th and formula qj of first order dynamic language we have th q iff th i cc by j ynamic logic of type d we understand dld bn pm here we investigate further properties of our dynamic logic its expressive power how it can be used for various purposes how it can be adapted to various situations then we investigate floyd s method using the framework of dl a complete characterization of the amount of information implicitly contained in floyd s method will be found but several questions remain open in this line the proof method i is proved to be strictly stronger than floyd s method in section 6 different semantics programming are compared in section 7 within the framework of dl comkrisons with several approaches related ill several ways are given in sections 7 9

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

the unwind property in certain algebras in the present paper we investigate abstract algebras having the so called unwind property i e algebras where every total computable function can be defined by open formulas in an adequate first order language a method of proving the unwind property is given for a special kind of algebra applying this method we prove that there exists a structure satisfying the unwind property for all flow charts but not for recursive procedures we prove also that algebraically closed and real closed fields with infinite degrees of transcendence over their prime subfields satisfy the unwind property for all schemas

varieties of iteration theories the equational properties of iteration when combined with composition and pairing are captured by the notion of iteration theory which was introduced in siam j comput 9 1980 pp 26 45 9 1980 pp 525 540 we believe although all of our evidence will not be exhibited here that every iterative construction satisfies at least the properties of iteration theories in this paper axiomatizations are given for several varieties of iteration theories which occur naturally in the semantics of programming languages i e those generated by theories of trees j comput sys sci 16 1978 pp 362 399 theories of sequacious functions proc 1973 colloquium vol 80 studies in logic north holland amsterdam 1975 pp 175 230 theories of partial functions and theories of both sequacious and partial functions with distinguished predicates we show which additional equations must be added to the axioms for iteration theories comput ling comput lang 14 1980 pp 183 207 in order to

a continuous time inverse operator for groundwater and contaminant transport modeling deterministic case the value of time dependent data in the calibration of numerical models of groundwater flow has been recently highlighted in the literature in this paper the background for a new development in the inverse problem is placed and a new operator for inversion of the spatially discretized diffusion equation is introduced the motivation for the development of an inverse problem solution procedure which uses information in transient data is illustrated with a focused review of recent literature such an approach which implicitly incorporates the continuous time dependency of the flow model is then presented this approach is based upon the new concept of inverting the model after the for example finite element spatial discretization but before the typically finite difference temporal discretization of the model not afterward as has been done in the past the laplace transform is used to replace discretization in time of the system of ordinary differential equations to discretization in the laplace variable of the algebraic system in laplace space the existence of the deterministic solution in the laplace transform space does not require knowledge of the eigenvalues of the diffusion matrix but only the specification of the laplace variables near zero a simple numerical example from the literature is used to generate a set of three simplified test cases upon which the proposed method is tested the implications of the theoretical investigation and the results of the numerical experiments are discussed with a view toward prospects of practical implementation

maximal bottom of spectrum or volume entropy rigidity in alexandrov geometry li and wang j differ geom 58 501 534 2001 j differ geom 62 143 162 2002 proved a splitting theorem for an n dimensional riemannian manifold with ric ge n 1 and the bottom of spectrum lambda 0 m frac n 1 2 4 for an n dimensional compact manifold m with ric ge n 1 with the volume entropy h m n 1 ledrappier and wang j differ geom 85 461 477 2010 proved that the universal cover widetilde m is isometric to the hyperbolic space mathbb h n we will prove analogue theorems for alexandrov spaces

coupled inverse problems in groundwater modeling 2 identifiability and experimental design parameter identifiability and experimental design in the context of solving the coupled inverse problem in groundwater modeling are considered in part 2 of the two paper series the following three new definitions of extended identifiability for a distributed parameter system are presented interval identifiability ini prediction equivalence identifiability pei and management equivalence identifiability mei the uniqueness requirement of the inverse solution is relaxed by these definitions an identified parameter is said to be extendedly identifiable if it is able to satisfy an accuracy requirement in a specific application of the model when a generalized least squares norm is used the proposed identifiabilities are applicable to any coupled problems in which the state variables and parameters may have different order of magnitudes a salient feature of the new definitions is that the extended identifiabilities are closely related to experimental design consequently the sufficiency of an experimental design for assuring a given level of an extended identifiability can be estimated prior to field experiments the methodology developed can be used to determine the reliability of an experimental design even for nonlinear models a numerical example on the management of a wastewater disposal is given to explain how the concepts and methods presented in this paper can be used for solving practical problems

development of objective oriented groundwater models 1 robust parameter identification 1 when the structure of an aquifer is complex and unknown determining the complexity of model structure and identifying its spatially distributed parameters become very difficult this two paper series describes an approach for objective oriented model construction that can identify a model with simplified structure and assure its reliability for predetermined model applications the theoretical basis of the methodology includes the definition of structure error the conditions of structure reducibility the calculation of the worst case parameter wcp and the solution of a generalized inverse problem in the first paper of the series we extend the basic theory established in our previous works from zonation parameterization to any kind of parameterization the extension makes the methodology more general and complete we present an effective direct search algorithm that can form a nonnested structure series with an optimized pattern for solving the generalized inverse problem we use numerical examples to show how the wcp depends on the structure complexity prior information boundary conditions and the objectives of model application generally speaking with more prior information simpler boundary conditions fewer objectives and lower accuracy requirement the wcp will have a simpler shape as a result a reliable model can be identified with less observation data in part 2 of this series we will give the conditions of structure reducibility and the method for robust experimental design a robust experimental design is independent of the true parameter and can provide sufficient information for identifying an objective oriented model