smooth solutions of the euler and navier stokes equations from the a posteriori analysis of approximate solutions abstract the main result of morosi and pizzocchero 2012 is presented in a variant based on a c formulation of the cauchy problem in this approach the a posteriori analysis of an approximate solution gives a bound on the sobolev distance of any order between the exact and the approximate solution

spectra of wess zumino witten models with arbitrary simple groups we consider the wess zumino witten two dimensional sigma models with fields taking values in an arbitrary connected but not necessarily simply connected simple lie groupg the quantum states of the theory are realized geometrically as sections of a line bundle over the loop grouplg the action of the current algebra of the theory is decomposed into highest weight representations by explicit construction of the highest weight states this solves for the spectrum of the models as a by product we obtain modular invariant partition functions of the theory on tori the present paper extends the results of 7 where the casesg su 2 andso 3 were treated

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

on asymptotics in case of linear index 2 differential algebraic equations asymptotic properties of solutions of general linear differential algebraic equations daes and those of their numerical counterparts are discussed new results on the asymptotic stability in the sense of lyapunov as well as on contractive index 2 daes are given the behavior of the backward differentiation formula bdf implicit runge kutta irk and projected implicit runge kutta pirk methods applied to such systems is investigated in particular we clarify the significance of certain subspaces closely related to the geometry of the dae asymptotic properties like a stability and l stability are shown to be preserved if these subspaces are constant moreover algebraically stable irk dae are b stable under this condition the general results are specialized to the case of index 2 hessenberg systems

kinematics of yang mills solitons in su 2 yang mills theory then monopole configuration space is a bundle with fibers isomorphic to u 1 u 1 and state vectors for which each monopole has chargen e 2 are homogeneous of degreen with respect to each u 1 translations and rotations are defined for individual monopoles in then monopole space the commutator of two translations is found to be a u 1 transformation that agrees for large monopole separation with the analogous phase change accompanying the translation of a charged point particle in an external magnetic field the theory developed here is applied in a companion paper to prove a spin statistics theorem for monopoles in su 2 yang mills theory

decomposition approaches to integration without a measure extending the idea of even and lehrer 2014 3 we discuss a general approach to integration based on a given decomposition system equipped with a weighting function and a decomposition of the integrated function we distinguish two type of decompositions sub decomposition based integrals in economics linked with optimization problems to maximize the possible profit and super decomposition based integrals linked with costs minimization we provide several examples both theoretical and realistic to stress that our approach generalizes that of even and lehrer 2014 3 and also covers problems of linear programming and combinatorial optimization finally we introduce some new types of integrals related to optimization tasks

conditioning and dichotomy in differential algebraic equations the relationship between the dichotomy of the solution space for a differential algebraic system and the well conditioning of associated boundary value problems is investigated this work extends results that are known for regular explicit ordinary differential equations and it follows the presentation by de hoog and mattheij siam j numer anal 24 1987 pp 89 105

adjoint sensitivity analysis for differential algebraic equations algorithms and software an efficient numerical method for sensitivity computation of large scale differential algebraic systems is developed based on the adjoint method issues that are critical for the implementation are addressed complexity analysis and numerical results demonstrate that the adjoint sensitivity method is advantageous over the forward sensitivity method for applications with a large number of sensitivity parameters and few objective functions

new answers to an old question in the theory of differential algebraic equations in the context of linear differential algebraic equations daes one finds different associated explicit ordinary differential equations odes among them essential underlying and inherent explicit regular ones abbreviated euodes and ierodes euodes have been introduced in 1991 for index 2 daes in hessenberg form by means of special transformations ierodes result within the framework of the projector based decoupling each such explicit ode is occasionally considered to rule the flow of the dae the question to which extend euodes and ierodes are related to each other has been asked promptly after 1991 for index 2 hessenberg form daes answers have been given in 2005 saying that euodes represent somehow condensed ierodes recently euodes have been indicated for general arbitrary index daes and it has been proved that they are condensed ierodes the understanding of the relation between the ierode and the euodes enables to uncover the stability behavior of the dae flow in the present paper we show that both the ierodes and euodes of a dae with arbitrary high index do not at all depend on derivatives of the right hand side we consider adjoint pairs of daes and provide generalizations of the classical lagrange identity furthermore we address lyapunov spectra and lyapunov regularity

fermionic quantization and configuration spaces for the skyrme and faddeev hopf models the fundamental group and rational cohomology of the configuration spaces of the skyrme and faddeev hopf models are computed physical space is taken to be a compact oriented 3 manifold either with or without a marked point representing an end at infinity for the skyrme model the codomain is any lie group while for the faddeev hopf model it is s 2 it is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons of the model within generalizations of the frameworks of finkelstein rubinstein and sorkin fermionic quantization of skyrmions is possible only if the target group contains a symplectic or special unitary factor while fermionic quantization of hopfions is always possible geometric interpretations of the results are given

chern simons gauge theory and projectively flat vector bundles on 421 1421 1421 1 we consider a vector bundle on teichmuller space which arises naturally from witten s analysis of chern simons gauge theory and define a natural connection on it in the case when the gauge group isu 1 we compute the curvature showing in particular that the connection is projectively flat

superadditive and subadditive transformations of integrals and aggregation functions we propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non negative reals in particular of integrals with respect to monotone measures we discuss special properties of the proposed transforms and links between some distinguished integrals superadditive transformation of the choquet integral as well as of the shilkret integral is shown to coincide with the corresponding concave integral recently introduced by lehrer similarly the transformation of the sugeno integral is studied moreover subadditive transformation of distinguished integrals is also discussed

adjoint sensitivity analysis for differential algebraic equations the adjoint dae system and its numerical solution an adjoint sensitivity method is presented for parameter dependent differential algebraic equation systems daes the adjoint system is derived along with conditions for its consistent initialization for daes of index up to two hessenberg for stable linear daes stability of the adjoint system for semi explicit daes or of an augmented adjoint system for fully implicit daes is shown in addition it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system

local optimization of dynamic programs with guaranteed satisfaction of path constraints an algorithm is proposed for locating a feasible point satisfying the kkt conditions to a specified tolerance of feasible inequality path constrained dynamic programs pcdp within a finite number of iterations the algorithm is based on iteratively approximating the pcdp by restricting the right hand side of the path constraints and enforcing the path constraints at finitely many time points the main contribution of this article is an adaptation of the semi infinite program sip algorithm proposed in mitsos 2011 to pcdp it is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first order kkt conditions of the pcdp to a specified tolerance the main assumptions are i availability of a nonlinear program nlp local solver that generates a kkt point of the constructed approximation to pcdp at each iteration if this problem is indeed feasible ii existence of a slater point of the pcdp that also satisfies the first order kkt conditions of the pcdp to a specified tolerance iii all kkt multipliers are nonnegative and uniformly bounded with respect to all iterations the performance of the algorithm is analyzed through two numerical case studies

transfer of boundary conditions for daes of index 1 in this paper the concept of abramov s method for transferring boundary conditions posed for regular ordinary differential equations odes is applied to index 1 differential algebraic equations daes having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of abramov s method we consider boundary value problems for index 1 linear daes both with constant and varying leading matrices we describe the relations defining the subspaces of solutions satisfying the prescribed boundary conditions at one end of the interval the index 1 daes which realize the transfer are given and their properties are studied the results are reformulated for inhomogeneous index 1 daes as well

an adjoint variable method for wideband second order sensitivity analysis through fdtd we propose an efficient adjoint variable method avm for estimating wideband second order response sensitivities using the finite difference time domain fdtd approach our avm approach reduces the number of required simulations for computing the hessian matrix of the desired objective function from o n 2 to only n 1 where n is the number of designable parameters all first order sensitivities are also estimated as a by product our sensitivity technique is illustrated through 1 d 2 d and 3 d electromagnetic examples involving both dispersive and nondispersive materials the accuracy of our avm approach is verified through comparison with analytical sensitivity results or sensitivities estimated using the accurate but computationally intensive central finite difference cfd approximations

on the stability of the abramov transfer for differential algebraic equations of index 1 the transfer of boundary conditions for ordinary differential equations developed by abramov zh vychisl mat mat fiz 1 1961 pp 542 545 is a stable method for representing the solution spaces of linear boundary value problems instead of boundary value problems matrix valued initial value problems are solved when integrating these differential equations the inner independence of the columns of the solution matrix and hence of the solutions of the resulting linear system of equations remains valid balla and marz have generalized abramov s transfer for homogenized index 1 differential algebraic equations siam j numer anal 33 1996 pp 2318 2332 in this article a direct version of the abramov transfer for inhomogeneous linear mbox index 1 differen linebreak 4 tial algebraic equations is developed and the numerical stability of this method is proved

generalized derivatives of dynamic systems with a linear program embedded dynamic systems with a linear program lp embedded can be found in control and optimization of bioreactor models based on dynamic flux balance analysis dfba derivatives of the dynamic states with respect to a parameter vector are essential for open and closed loop dynamic optimization and parameter estimation of such systems these derivatives given by a forward sensitivity system may not exist because the optimal value of a linear program as a function of the right hand side of the constraints is not continuously differentiable therefore nonsmooth analysis must be applied which provides optimality conditions in terms of subgradients for convex functions or clarke s generalized gradient for nonconvex functions this work presents an approach to compute the necessary information for nonsmooth optimization i e an element of the generalized gradient moreover a numerical implementation of the results is introduced the approach is illustrated through a large scale dynamic flux balance analysis example

linear subspaces for linear daes of index 1 abstract in this paper the representation of linear subspaces of solutions of index 1 daes a x y b x y 0 is given it is shown that the solutions of adjoint systems are strongly related to the subspaces

efficient gradient computation for dynamical models data assimilation is a fundamental issue that arises across many scales in neuroscience ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fmri data assimilation involves inverting a generative model that can not only explain observed data but also generate predictions typically the model is inverted or fitted using conventional tools of convex optimization that invariably extremise some functional norms minimum descriptive length variational free energy etc generally optimisation rests on evaluating the local gradients of the functional to be optimized in this paper we compare three different gradient estimation techniques that could be used for extremising any functional in time i finite differences ii forward sensitivities and a method based on iii the adjoint of the dynamical system we demonstrate that the first order gradients of a dynamical system linear or non linear can be computed most efficiently using the adjoint method this is particularly true for systems where the number of parameters is greater than the number of states for such systems integrating several sensitivity equations as required with forward sensitivities proves to be most expensive while finite difference approximations have an intermediate efficiency in the context of neuroimaging adjoint based inversion of dynamical causal models dcms can in principle enable the study of models with large numbers of nodes and parameters

a general relation between kink exchange and kink rotation the normal correlation between spin and statistics is shown to be valid for arbitrary kinks among them thesu n skyrmions forn 3 it is assumed in the proof that no gauge ambiguity attaches to the values of the underlying scalar field and that conversely each configuration of this field is represented quantum mechanically by a hilbert subspace of dimension precisely one

adjoint sensitivity analysis for time dependent partial differential equations with adaptive mesh refinement a new adjoint sensitivity analysis approach is presented for time dependent partial differential equations with adaptive mesh refinement the new approach called adda combines the best features of both the adjoint of the discretization ad and discretization of the adjoint da approaches it removes the obstacles of applying ad to adaptive methods and in contrast to da requires for its use only a minimal amount of knowledge about the formulation of adjoint pdes and their boundary conditions the effectiveness and efficiency of adda are demonstrated for several numerical examples

a note on the superadditive and the subadditive transformations of aggregation functions we expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions necessary and sufficient conditions ensuring that a transformation of a proper aggregation function is again proper are deeply studied and exemplified relationships between these transformations are also studied

on the regularization of a class of nontransferable differential algebraic equations abstract this paper deals with linear differential algebraic equations which arise by coupling ordinary differential equations with solution invariants boundary value problems for these equations are essentially ill posed a parametrization into transferable equations is shown to present a regularization results about convergence rates for exact and noisy data are presented

symmetry groups of state vectors in canonical quantum gravity in canonical quantum gravity the diffeomorphisms of an asymptotically flat hypersurface s not connected to the identity but trivial at infinity can act nontrivially on the quantum state space because state vectors are invariant under diffeomorphisms that are connected to the identity the group of inequivalent diffeomorphisms is a symmetry group of states associated with s this group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on s it is calculated for all hypersurfaces of the form s s3 g point where the removed point is thought of as infinity on s and the symmetry group s is the zeroth homotopy group of the group of diffeomorphisms of s3 g fixing a point and frame denoted 0 difff s3 g before calculating 0 difff s3 g it is necessary to find 0 of the group of diffeomorphisms once 0 diff s3 g is known 0 diffx0 s3 g is calculated using a fiber bundle involving diff s3 g diffx0 s3 g and s3 g finally a fiber bundle involving difff s3 g

sensitivity analysis of odes daes using the taylor series method this paper studies the applicability of the taylor method for the sensibility analysis of odes and daes extended automatic differentiation rules are introduced for the calculus of partial derivatives of taylor series the numerical method is implemented using an efficient variable step variable order scheme finally some numerical tests are presented showing the benefits of the formulation

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

stability of computational methods for constrained dynamics systems many methods have been proposed for numerically integrating the differential algebraic systems arising from the euler lagrange equations for constrained motion these are based on various problem formulations and discretizations we offer a critical evaluation of these methods from the standpoint of stability nconsidering a linear model we first give conditions under which the differential algebraic problem is well conditioned this involves the concept of an essential underlying ode we review a variety of reformulations which have been proposed in the literature and show that most of them preserve the well conditioning of the original problem then we consider stiff and nonstiff discretizations of such reformulated models in some cases the same implicit discretization may behave in a very different way when applied to different problem formulations acting as a stiff integrator on some formulations and as a nonstiff integrator on others we present the approach of projected invariants as a method for yielding problem reformulations which are desirable in this sense

superdecomposition integrals this study introduces and discusses a new class of integrals based on superdecompositions of integrated functions including an analysis of their relationship with decomposition integrals which were introduced recently by even and lehrer the proposed superdecomposition integrals have several properties that are similar or dual with respect to decomposition integrals but they also have some significant differences the convex integral is obtained by considering all possible superdecompositions with no constraints on the applied sets which can be treated as the greatest convex homogeneous functional that is bounded from above by the measure we consider the relationship with the universal integral of klement et al is also discussed finally some possible generalizations are outlined

on approximate solutions of the equations of incompressible magnetohydrodynamics abstract inspired by an approach proposed previously for the incompressible navier stokes ns equations we present a general framework for the a posteriori analysis of the equations of incompressible magnetohydrodynamics mhd on a torus of arbitrary dimension d this setting involves a sobolev space of infinite order made of c vector fields with vanishing divergence and mean on the torus given any approximate solution of the mhd cauchy problem its a posteriori analysis with the method of the present work allows one to infer a lower bound on the time of existence of the exact solution and to bound from above the sobolev distance of any order between the exact and the approximate solution in certain cases the above mentioned lower bound on the time of existence is found to be infinite so one infers the global existence of the exact mhd solution we present some applications of this general scheme the most sophisticated one lives in dimension d 3 with the abc flow perturbed magnetically as an initial datum and uses for the cauchy problem a galerkin approximate solution in 124 fourier modes we illustrate the conclusions arising in this case from the a posteriori analysis of the galerkin approximant these include the derivation of global existence of the exact mhd solution with the abc datum when the dimensionless viscosity and resistivity are equal and stay above a critical value

sensitivity analysis of uncertain dynamic systems using set valued integration we present an extension of set valued integration to enable efficient sensitivity analysis of parameter dependent ordinary differential equation ode systems using both the forward and adjoint me

on the regularization of index 2 differential algebraic equations abstract boundary value problems for linear differential algebraic equations daes with time varying coefficients a t x t b t x t q t tractable with index 2 are considered these daes contain differentiation problems and lead therefore to essentially ill posed problems we show that a parametrization proposed by marz is a regularization in the sense of tikhonov convergence rates for noisy data are derived moreover for the so called pencil regularization analogous results are derived in the case of a time independent nullspace n a t

software and algorithms for sensitivity analysis of large scale differential algebraic systems sensitivity analysis for dae systems is important in many engineering and scientific applications the information contained in the sensitivity trajectories is useful for parameter estimation optimization model reduction and experimental design in this paper we present algorithms and software for sensitivity analysis of large scale dae systems of index up to two the new software provides for consistent initialization of the solutions and the sensitivities interfaces seamlessly with automatic differentiation for the accurate evaluation of the sensitivity equations and is capable via mpi of exploiting the natural parallelism of sensitivity analysis as well as providing an efficient solution in sequential computations

constant coefficient differential algebraic operators and the kronecker form abstract we consider constant coefficient differential algebraic equations from an operator theoretic point of view we show that the kronecker form allows to determine the nullspace and range of the corresponding differential algebraic operators this yields simple matrix theoretic characterizations of features like closed range and fredholmness

on the discrete adjoints of adaptive time stepping algorithms we investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation ad by differentiating the time step controller and the error estimator of the original algorithm reverse mode ad generates spurious adjoint derivatives of the time steps the resulting discrete adjoint models become inconsistent with the adjoint ode and yield incorrect derivatives to regain consistency one has to cancel out the contributions of the non physical derivatives in the discrete adjoint model we demonstrate that the discrete adjoint models of one step explicit adaptive algorithms such as the runge kutta schemes can be made consistent with their continuous counterparts using simple code modifications furthermore we extend the analysis to cover second order adjoint models derived through an extra forward mode differentiation of the discrete adjoint code several numerical examples support the mathematical derivations

using krylov methods in the solution of large scale differential algebraic systems in this paper a new algorithm for the solution of large scale systems of differential algebraic equations is described it is based on the integration methods in the solver dassl but instead of a direct method for the associated linear systems which arise at each time step we apply the preconditioned gmres iteration in combination with an inexact newton method the algorithm along with those in dassl is implemented in a new solver called daspk we outline the algorithms and strategies used and discuss the use of the solver we develop and analyze some preconditioners for a certain class of dae stems and finally demonstrate the application of daspk on two example problems

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

linear differential algebraic equations in spaces of integrable functions on developpe une l 2 theorie pour des equations differentielles algebriques lineaires t x t a t x t b t x t f t t a b x t r m

efficient computation of sensitivities for ordinary differential equation boundary value problems for models described by ordinary differential equation boundary value problems ode bvps we derive adjoint equations for sensitivity analysis giving explicit forms for the boundary conditions of the adjoint boundary value problem the solutions of the adjoint equations are used to efficiently compute gradients of both integral form and pointwise constraints existence and stability results are given for the adjoint system and its numerical solution the use of the method is demonstrated for a simple example where it is seen that the method is particularly advantageous for problems with more than a few parameters

the wess zumino term and fermionic solitons in 1 2 witten derived important consequences of the topological structure of models we rederive them from the canonical viewpoint and outline a systematic approach to similar questions

on a least squares collocation method for linear differential algebraic equations the aim of this note is to extend some results on least squares collocation methods and to prove the convergence of a least squares collocation method applied to linear differential algebraic equations some numerical examples are presented

least squares collocation for linear higher index differentialalgebraic equations differentialalgebraic equations with higher index give rise to essentially ill posed problems therefore their numerical approximation requires special care in the present paper we state the notion of ill posedness for linear differentialalgebraic equations more precisely based on this property we construct a regularization procedure using a least squares collocation approach by discretizing the pre image space numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index 1 differentialalgebraic equations convergence is shown for a limited class of linear higher index differentialalgebraic equations

on polynomial chaos expansion via gradient enhanced l 1 minimization gradient enhanced uncertainty quantification uq has received recent attention in which the derivatives of a quantity of interest qoi with respect to the uncertain parameters are utilized to improve the surrogate approximation polynomial chaos expansions pces are often employed in uq and when the qoi can be represented by a sparse pce 1 minimization can identify the pce coefficients with a relatively small number of samples in this work we investigate a gradient enhanced 1 minimization where derivative information is computed to accelerate the identification of the pce coefficients for this approach stability and convergence analysis are lacking and thus we address these here with a probabilistic result in particular with an appropriate normalization we show the inclusion of derivative information will almost surely lead to improved conditions e g related to the null space and coherence of the measurement matrix for a successful solution recovery further we demonstrate our analysis empirically via three numerical examples a manufactured pce an elliptic partial differential equation with random inputs and a plane poiseuille flow with random boundaries these examples all suggest that including derivative information admits solution recovery at reduced computational cost an approach for sparse polynomial chaos pc expansions including derivative information is presented method relies on 1 minimization to solve for the pc coefficients formal analysis is presented to guarantee the stability and convergence of gradient enhanced 1 minimization three examples presented to illustrate cost accuracy improvements achieved by gradient enhanced 1 minimization

on the existence of aggregation functions with given super additive and sub additive transformations abstract in this note we study restrictions on the recently introduced super additive and sub additive transformations a a and a a of an aggregation function a we prove that if a has a slightly stronger property of being strictly directionally convex then a a and a is linear dually if a is strictly directionally concave then a a and a is linear this implies for example the existence of pairs of functions f g sub additive and super additive on 0 n respectively with zero value at the origin and satisfying relatively mild extra conditions for which there exists no aggregation function a on 0 n such that a f and a g

forward and adjoint sensitivity analysis with continuous explicit runge kutta schemes abstract we study the numerical solution of tangent linear first and second order adjoint models with high order explicit continuous runge kutta pairs the approaches currently implemented in popular packages such as sundials or daspkadjoint are based on linear multistep methods for adaptive time integration of nonlinear models interpolation of the forward model solution is required during the adjoint model simulation we propose to use the dense output mechanism built in the continuous runge kutta schemes as a highly accurate and cost efficient interpolation method in the inverse problem run we implement our approach in a fortran library called denserks which is found to compare well to other similar software on a number of test problems

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

stability criteria for differential algebraic equations with multiple delays and their numerical solutions abstract this paper is concerned with the asymptotic stability of differential algebraic equations with multiple delays and their numerical solutions first we give a sufficient condition for delay independent stability after characterizing the coefficient matrices that satisfy this stability condition we propose some practical checkable criteria for asymptotic stability then we investigate the stability of numerical solutions obtained by methods and bdf methods finally solvability and stability of a class of weakly regular delay differential algebraic equations are analyzed

boundary conditions and their transfer for differential algebraic equations of index 1 abstract for the homogeneous linear index 1 tractable dae we give the characterization of the linear subspace defined by a homogeneous linear relationship prescribed at an arbitrarily fixed point

linear functional minimization for inverse modeling heterogeneous aquifers typically consist of multiple lithofacies whose spatial arrangement significantly affects flow and transport the estimation of these lithofacies is complicated by the scarcity of data and by the lack of a clear correlation between identifiable geologic indicators and attributes we introduce a new inverse modeling approach to estimate both the spatial extent of hydrofacies and their properties from sparse measurements of hydraulic conductivity and hydraulic head our approach is to minimize a functional defined on the vectors of values of hydraulic conductivity and hydraulic head fields defined on regular grids at a user determined resolution this functional is constructed to i enforce the relationship between conductivity and heads provided by the groundwater flow equation ii penalize deviations of the reconstructed fields from measurements where they are available and iii penalize reconstructed fields that are not piece wise smooth we develop an iterative solver for this functional that exploits a local linearization of the mapping from conductivity to head this approach provides a computationally efficient algorithm that rapidly converges to a solution a series of numerical experiments demonstrates the robustness of our approach

the choquet integral with respect to a level dependent capacity we present a generalization of choquet integral in which the capacity depends also on the value of the aggregated variables we show that as particular cases of our generalization of choquet integral there are the sugeno integral the sipos integral and the cumulative prospect theory functional we also show that many concepts such as mobius transform importance index interaction index k order capacities and owa operators introduced in the research about choquet integral can be generalized in the considered context

on approximate solutions of the incompressible euler and navier stokes equations abstract we consider the incompressible euler or navier stokes ns equations on a torus t d in the functional setting of the sobolev spaces h 0 n t d of divergence free zero mean vector fields on t d for n d 2 1 we present a general theory of approximate solutions for the euler ns cauchy problem this allows to infer a lower bound t c on the time of existence of the exact solution u analyzing a posteriori any approximate solution u a and also to construct a function n such that u t u a t n n t for all t 0 t c both t c and n are determined solving suitable control inequalities depending on the error of u a the fully quantitative implementation of this scheme depends on some previous estimates of ours on the euler ns quadratic nonlinearity morosi and pizzocchero 2010 in press 7 8 to keep in touch with the existing literature on the subject our results are compared with a setting for approximate euler ns solutions proposed in chernyshenko et al 2007 1 as a first application of the present framework we consider the galerkin approximate solutions of the euler ns cauchy problem with a specific initial datum considered in behr et al 2001 9 in this case our methods allow amongst else to prove global existence for the ns cauchy problem when the viscosity is above an explicitly given bound