the doublet representation of non hilbert eigenstates of the hamiltonian ii we find the minimal mathematical structure to represent quantum eigenstates with complex eigenvalues with no need of analytic continuation these eigenvectors build doublets in non hilbert spaces we construct exact solutions for the friedrichs model that continuously join the ones of the free hamiltonian we extend the wigner operator to these non hilbert spaces and enlarge the concept of normalized vectors via the definition of the doublets making use of these doublets we describe systems whose states have initial conditions out of hilbert space

relativistic gamow vectors the friedrichs model has often been used in order to obtain explicit formulas for eigenvectors associated to complex eigenvalues corresponding to lifetimes such eigenvectors are called gamow vectors and they acquire meaning in extensions of the conventional hilbert space of quantum theory to the so called rigged hilbert space in this paper gamow vectors are constructed for a solvable model of an unstable relativistic field as a result we obtain a time asymmetric relativistic extension of the fock space this extension leads to two distinct poincare semigroups the time reversal transformation maps one semigroup to the other as a result the usual pct invariance should be extended we show that irreversibility as expressed by dynamical semigroups is compatible with the requirements of relativity

a symmetric formulation of coupled bem fem in solving responses of submerged elastic structures for large degrees of freedom this work presents a symmetric formulation for the coupling of boundary element method bem with finite element method fem to compute responses of submerged elastic structures in a heavy acoustic medium the acoustic loading derived from bem is formulated in a symmetric complex matrix the symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals the structural equation is represented by fem the fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods consequently the computational efficiency of the proposed coupled fem bem is significantly increased the proposed method involving 20 000 degrees of freedom can be implemented on a personal computer numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

on the rhs description of resonances and virtual states we discuss the role of the m ller wave operators in a rigged hilbert space rhs model for resonances we also construct a new rhs of analytic functions valid for the description of resonances and virtual states these become generalized state vectors in a general physically realizable representation

a generalized weyl correspondence ii some general results after defining a generalized weyl correspondence we give some general results these are presented as comments on a theorem they mainly refer to the finite dimensional unbounded and non self adjoint cases

when is the wigner function of multidimensional systems nonnegative it is shown that for systems with an arbitrary number of degrees of freedom a necessary and sufficient condition for the wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form this result generalizes the one obtained by hudson rep math phys 6 249 1974 for one dimensional systems

coupling bem with fem by a direct computation of the boundary stiffness matrix the boundary stiffness matrix characterizing in a discretized form the response of the boundary to given dirichlet boundary conditions allows the coupling between bem and fem the paper presents an approach based on the direct computation of the stiffness matrix from the potential function related to a given dirichlet boundary condition the method produces a symmetric stiffness matrix as for the singular galerkin boundary element method but does not need to compute hypersingular integrals in addition the method uses only the nodal values of the boundary potential but does not need discretized values of the normal gradient at the boundary as for usual boundary element methods which reduces the number of matrices to be constructed the regularization of the integrals is achieved by means used for simply singular integrals introduced for the collocation boundary element method an example of application is produced in the case of the solution of laplace equation within a plane domain

gaussian interval quadrature formulae for tchebycheff systems for any given system of continuously differentiable functions u k k 1 2n that constitute an extended tchebycheff system of order 2 on a b we prove the existence and uniqueness of the gaussian interval quadrature formula based on n weighted integrals over nonoverlapping subintervals of a b of preassigned lengths this supplies an analogue of the result of krein about canonical representation of linear positive functionals

the generalized weyl correspondence and time dependent stochastic processes the definition and some general properties of the generalized weyl correspondence between stochastic processes and operator valued real functions on a hilbert space plus a trace class operator are given the relation between the derivatives of an operator valued function and the derivative of the corresponding stochastic process are studied when the operator valued function is the position or momentum in the heisenberg picture a condition for the positivity of the joint distribution functions of the corresponding process is given provided that the evolution hamiltonian be quadratic in the position and momentum finally the case of an arbitrary hamiltonian evolution for the position operator is studied and the two dimensional density functions of the process is related to the wigner function associated to some state and a necessary condition for the positivity of the densities is given

dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures in this work we propose dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures a novel framework for intersubject registration of diffusion tensor imaging dti data sets this framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures including white matter wm gray matter gm and spaces containing cerebrospinal fluid csf currently most dti based spatial normalization algorithms emphasize alignment of anisotropic structures while some diffusion derived metrics such as diffusion anisotropy and tensor eigenvector orientation are highly informative for proper alignment of wm other tensor metrics such as the trace or mean diffusivity md are fundamental for a proper alignment of gm and csf boundaries moreover it is desirable to include information from structural mri data e g t1 weighted or t2 weighted images which are usually available together with the diffusion data the fundamental property of dr tamas is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally another important feature of dr tamas is a symmetric time varying velocity based transformation model which enables it to account for potentially large anatomical variability in healthy subjects and patients the performance of dr tamas is evaluated with several data sets and compared with other widely used diffeomorphic image registration techniques employing both full tensor information and or dti derived scalar maps our results show that the proposed method has excellent overall performance in the entire brain while being equivalent to the best existing methods in wm

minimal irreversible quantum mechanics the decay of unstable states abstract brownian motion is modelled by a harmonic oscillator brownian particle interacting with a continuous set of uncoupled harmonic oscillators the interaction is linear in the coordinates and the momenta the model has an analytical solution that is used to study the time evolution of the reduced density operator it is derived in a closed form in the one particle sector of the model the irreversible behavior of the brownian particle is described by a reduced density matrix

extreme structural response analysis of truss structures under material uncertainty via linear mixed 0 1 programming this paper concerns the extreme structural response analysis of truss structures taking the possible uncertainties of young s moduli of the bars into consideration the uncertainty of young s modulus is described by a non probability but bounded interval model with the use of this uncertain model it is shown that the structural responses such as nodal displacement and bar stress will attain their extreme values when young s moduli of the bars take either their upper or lower bound value based on this conclusion and simultaneous analysis and design formulation a linear mixed 0 1 programming problem can be constructed to find the extreme values of the structural response by the well established branch and bound approach with global optimality the proposed approach is applied to several test problems for the demonstration of its validity

interval and subinterval perturbation finite element boundary element method for low frequency uncertain analysis of structural acoustic systems abstract uncertainties exist widely in the structural acoustic systems due to the physical imperfections model inaccuracies and system complexities to deal with the uncertainties the interval perturbation and subinterval perturbation techniques for the first time are extended and integrated into the hybrid finite element boundary element method ipfem bem in this work firstly the structural part of structural acoustic systems is modeled using finite element method fem and acoustic cavity is modeled by boundary element method bem then the interval perturbation technique is introduced to establish the interval perturbation equations of the system for large uncertainty levels the interval of parameters is divided into smaller sub intervals to improve the accuracy of proposed ipfem bem sub interval perturbation finite element boundary element method sipfem bem the proposed ipfem bem and sipfem bem are verified by two numerical examples the results obtained by ipfem bem sipfem bem and monte carlo method are compared it is found that ipfem bem and sipfem bem is reliable for the frequency response analysis of structural acoustic systems with small or large uncertain levels

single and multiple shell uniform sampling schemes for diffusion mri using spherical codes in diffusion mri dmri a good sampling scheme is important for efficient acquisition and robust reconstruction diffusion weighted signal is normally acquired on single or multiple shells in q space signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue or the laboratory coordinate frame the electrostatic energy minimization eem method originally proposed for single shell sampling scheme in dmri was recently generalized to multi shell schemes called generalized eem geem geem has been successfully used in the human connectome project however eem does not directly address the goal of optimal sampling i e achieving large angular separation between sampling points in this paper we propose a more natural formulation called spherical code sc to directly maximize the minimal angle between different samples in single or multiple shells we consider not only continuous problems to design single or multiple shell sampling schemes but also discrete problems to uniformly extract sub sampled schemes from an existing single or multiple shell scheme and to order samples in an existing scheme we propose five algorithms to solve the above problems including an incremental sc isc a sophisticated greedy algorithm called iterative maximum overlap construction imoc an 1 opt greedy method a mixed integer linear programming method and a constrained non linear optimization method to our knowledge this is the first work to use the sc formulation for single or multiple shell sampling schemes in dmri experimental results indicate that sc methods obtain larger angular separation and better rotational invariance than the state of the art eem and geem the related codes and a tutorial have been released in dmritool 1 1 https diffusionmritool github io tutorial qspacesampling html

a survey of non probabilistic uncertainty treatment in finite element analysis the objective of this paper is to critically review the emerging non probabilistic approaches for uncertainty treatment in finite element analysis the paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis first the applicability of the non probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint the necessary conditions for a useful application of the non probabilistic concepts are determined and are proven to be complementary rather than competitive to the classical probabilistic approach the second part of the paper focuses on numerical aspects of the interval finite element method it describes two principal strategies for the implementation i e the anti optimisation and the interval arithmetic approach and gives a state of the art of the interval finite element algorithms available from literature it is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output and the main sources of this conservatism are identified a numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built up benchmark structure

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

time evolution of the wigner function in this paper we give a partial answer to the problem when does an initially non negative wigner function remain non negative under the effect of the time evolution we show that for pure states this is the case for linear systems only to prove this we use the fact that the wigner function is non negative if and only if the wavefunction is gaussian we also prove that the green s solution of the evolution equation of the wigner function which in the framework of probability theory corresponds to the conditional probability density takes on negative values we utilize a theorem about moments borrowed from pawula we conclude that the wigner phase space formulation of quantum mechanics cannot receive a genuine probabilistic interpretation

dr buddi diffeomorphic registration for blip up blip down diffusion imaging method for correcting echo planar imaging distortions we propose an echo planar imaging epi distortion correction method dr buddi specialized for diffusion mri which uses data acquired twice with reversed phase encoding directions often referred to as blip up blip down acquisitions dr buddi can incorporate information from an undistorted structural mri and also use diffusion weighted images dwi to guide the registration improving the quality of the registration in the presence of large deformations and in white matter regions dr buddi does not require the transformations for correcting blip up and blip down images to be the exact inverse of each other imposing the theoretical blip up blip down distortion symmetry may not be appropriate in the presence of common clinical scanning artifacts such as motion ghosting gibbs ringing vibrations and low signal to noise the performance of dr buddi is evaluated with several data sets and compared to other existing blip up blip down correction approaches the proposed method is robust and generally outperforms existing approaches the inclusion of the dwis in the correction process proves to be important to obtain a reliable correction of distortions in the brain stem methods that do not use dwis may produce a visually appealing correction of the non diffusion weighted images but the directionally encoded color maps computed from the tensor reveal an abnormal anatomy of the white matter pathways

a description of virtual scattering states in the rigged hilbert space formulation of quantum mechanics we define a pair of gel fand triplets i hi i i 1 2 where the linear spaces i are formed by suitably chosen entire analytic functions on the riemann surface associated to the transformation z2 virtual scattering states are well defined as pairs of functionals respectively in 1 and 2

parameter perturbation method for dynamic responses of structures with uncertain but bounded parameters based on interval analysis the study was intended to evaluate the range of dynamic responses of structures with uncertain but bounded parameters by using the parameter perturbation method the uncertain parameters were modeled as an interval vector the first order perturbation quantities of responses of the perturbed system were obtained through the parameter perturbation method and then taking advantage of interval mathematics a new algorithm to estimate the response interval was presented comparisons between the parameter perturbation method and the probabilistic approach from mathematical proofs and numerical simulations were performed the numerical results are in agreement with the mathematical proofs the response range given by the parameter perturbation method encloses that obtained by the probabilistic approach the results also show good robustness of the proposed method

block matching distortion correction of echo planar images with opposite phase encoding directions by shortening the acquisition time of mri echo planar imaging epi enables the acquisition of a large number of images in a short time compatible with clinical constraints as required for diffusion or functional mri however such images are subject to large local distortions disrupting their correspondence with the underlying anatomy the correction of those distortions is an open problem especially in regions where large deformations occur we propose a new block matching registration method to perform epi distortion correction based on the acquisition of two epi with opposite phase encoding directions ped it relies on new transformations between blocks adapted to the epi distortion model and on an adapted optimization scheme to ensure an opposite symmetric transformation we present qualitative and quantitative results of the block matching correction using different metrics on a phantom dataset and on in vivo data we show the ability of the block matching to robustly correct epi distortion even in strongly affected areas

how to correct susceptibility distortions in spin echo echo planar images application to diffusion tensor imaging diffusion tensor imaging is often performed by acquiring a series of diffusion weighted spin echo echo planar images with different direction diffusion gradients a problem of echo planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility this results in distorted diffusion tensor maps to resolve this we suggest acquiring two images for each diffusion gradient one with bottom up and one with top down traversal of k space in the phase encode direction this achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas the resulting dt maps exhibit considerably higher geometric fidelity as assessed by comparison to an image volume acquired using a conventional 3d mr technique

antioptimization of structures with large uncertain but non random parameters via interval analysis non probabilistic interval modeling of uncertain but non random parameters for structures is developed in this paper for antioptimization analysis consisting in determining the least favorable responses the uncertain but non random parameter is considered to be a deterministic variable belonging to a set modeled as an interval the least favorable static displacement bound estimation for structures with uncertain but non random parameters is transformed into solving interval linear equations for small interval parameters the width of interval being small the uncertainties of interval parameters are treated as the perturbed quantities around the midpoint of interval parameters by means of the interval matrix central notation and the natural interval extension interval perturbation method for estimating the static displacement bound of structures with interval parameters was presented in the recent study by qiu et al 1 for large interval parameters a subinterval perturbation method for estimating the static displacement bound of structures with interval parameters is put forward in the study the numerical results show that a subinterval perturbation method yields tighter bounds than those yielded by the interval perturbation method

interval analysis of structures with uncertain but bounded axial stiffness abstract a method to evaluate the static response of structures with interval axial stiffnesses is proposed the procedure overcomes the drawbacks arising in traditional interval analysis due to dependency phenomenon the inversion of the interval stiffness matrix is pursued by means of a novel approximate relationship based on an interval valued sherman morrison woodbury formula numerical results on truss and frame structures evidence the accuracy and the effectiveness of the proposed approach to evaluate bounds of displacements and internal forces

a generalized weyl correspondence applications a so called generalized weyl correspondence is defined among random variables on one side and linear operators in a separable hilbert space h on the other besides such a correspondence there is a relation among states on h considered as positive nuclear operators on h and the distribution functions of the random variables by adding some new assumptions several relations are shown later we study two particularly interesting cases in the first we connect dichotomic random variables with number operators in a grassmann algebra h and nuclear operators on h with probability measures in the set of all sequences made up of zero and one in the second case we relate states between stochastic and quantum electrodynamics

a rigged hilbert space for the free radiation field we here construct a rigged hilbert space suitable for the description of the free radiation field in a box and in the coulomb gauge we prove the continuity of the main observables on this structure

analysis of uncertain structural systems using interval analysis the imprecision or uncertainty present in many engineering analysis design problems can be modeled using probabilistic fuzzy or interval methods this work considers the modeling of uncertain structural systems using interval analysis by representing each uncertain input parameter as an interval number a static structural analysis problem can be expressed in the form of a system of linear interval equations in addition to the direct and gaussian elimination based solution approaches a combinatorial approach based on an exhaustive combination of the extreme values of the interval numbers and an inequality hased method are presented for finding the solution of interval equations the range or interval of the solution vector response parameters is found to increase with increasing size of the problem in all of the methods an interval truncation approach is proposed to limit the growth of intervals of response parameters so that realistic and accurate solutions can be obtained in the presence of large amounts of uncertainty numerical examples are presented to illustrate the computational aspects of the methods and also to indicate the importance of the truncation approach in practical problems the utility of interval methods in predicting the extreme values of the response parameters of structures is discussed