gravimagnetic anomaly formulas for polyhedra of spatially linear media formulas for the gravity potential field and field gradient tensor are derived for a polyhedral target body of a spatially linear density medium the formulas also define the magnetic potential and field in the case of a medium of spatially linear magnetization this work generalizes existing solutions for the gravity field of a polyhedral target of linearly varying density the formulas are analyzed for singularities and for numerical error growth error growth with increasing target distance is found to be higher than in the corresponding uniform polyhedral case examination of the error sources reveals that some error reduction is possible on this basis new algorithms of improved error control over existing algorithms are proposed for the linear medium computational results confirm the expected improvement

optimal feedback control for semilinear fractional evolution equations in banach spaces abstract in this paper we study optimal feedback controls of a system governed by semilinear fractional evolution equations via a compact semigroup in banach spaces by using the cesari property the fillippove theorem and extending the earlier work on fractional evolution equations we prove the existence of feasible pairs an existence result of optimal control pairs for the lagrange problem is presented

new scheme for computing the magnetic field resulting from a uniformly magnetized arbitrary polyhedron the magnetic field at any point outside a uniformly magnetized polyhedron of arbitrary shape is obtained by adding the fields resulting from the effective free magnetic poles on each of the polygonal surfaces of the polyhedron for each polygonal surface the components of the field at the point of observation are expressed in terms of new line integrals around the edges of the polygon and the solid angle subtended by the polygon at the point of observation the line integrals are standard elementary forms this new approach makes the numerical evaluation of the magnetic fields for such models much simpler and faster than previously published methods

approximate controllability of partial neutral functional differential systems of fractional order with state dependent delay we prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state dependent delay in an abstract space sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems the results are obtained by using the krasnoselskii schaefer type fixed point theorem with the fractional power of operators an example is provided to illustrate the main results

acceleration of maximum likelihood reconstruction using frequency amplification and attenuation compensation algorithms that calculate maximum likelihood ml and maximum a posteriori solutions using expectation maximization have been successfully applied to spect and pet these algorithms are appealing because of their solid theoretical basis and their guaranteed convergence a major drawback is the slow convergence which results in long processing times the authors present 2 new heuristic acceleration methods for maximum likelihood reconstruction of ect images the first method incorporates a frequency dependent amplification in the calculations to compensate for the low pass filtering of the backprojection operation in the second method an amplification factor is incorporated that suppresses the effect of attenuation on the updating factors both methods are compared to the 1 dimensional line search method proposed by lewitt all 3 methods accelerate the ml algorithm on the authors test images lewitt s method produced the strongest acceleration of the three individual methods however the combination of the frequency amplification with the line search method results in a new algorithm with still better performance under certain conditions an effective frequency amplification can be already achieved by skipping some of the calculations required for ml

on the singularities of the gravity field of a homogeneous polyhedral body the study of the gravity field of arbitrary polyhedral bodies of homogeneous density has provoked a series of publications over the last decades some of the researchers represented an arbitrary three dimensional body in terms of contours obtained by the intersection of horizontal planes with the body

magnetic gradients produced by a 2d homogeneous polygonal source we use a set of analytic equations for calculating horizontal and vertical gradients of the magnetic anomaly produced by a 2d homogeneous magnetic source with a polygonal cross section the magnetization vector of the source is assumed to be constant and known and the anomalous field is assumed to be much smaller than the ambient geomagnetic field in magnitude the derivation begins from an expression of the magnetic potential then we evaluate clockwise integrations to establish the equations a comparison between this analytic approach and a numerical approach using the finite difference method to compute gradients indicates the reliability of the equations the proposed method is numerically efficient and does not present singularity on the edges of the polygon prism except at the vertices where the gradients approach to infinity

approximation of solutions to fractional integral equation in this paper we shall study a fractional integral equation in an arbitrary banach space x we used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem we also prove the existence of global solution the existence and convergence of the faedo galerkin solution to the given problem is also proved in a separable hilbert space with some additional assumptions on the operator a finally we give an example to illustrate the applications of the abstract results

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

accelerated image reconstruction using ordered subsets of projection data the authors define ordered subset processing for standard algorithms such as expectation maximization em for image restoration from projections ordered subsets methods group projection data into an ordered sequence of subsets or blocks an iteration of ordered subsets em is defined as a single pass through all the subsets in each subset using the current estimate to initialize application of em with that data subset this approach is similar in concept to block kaczmarz methods introduced by eggermont et al 1981 for iterative reconstruction simultaneous iterative reconstruction sirt and multiplicative algebraic reconstruction mart techniques are well known special cases ordered subsets em os em provides a restoration imposing a natural positivity condition and with close links to the em algorithm os em is applicable in both single photon spect and positron emission tomography pet in simulation studies in spect the os em algorithm provides an order of magnitude acceleration over em with restoration quality maintained

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

constrained inversion of gravity fields for complex 3 d structures as part of a research program to develop gravity interpretation tools that can be merged with seismic techniques a full 3 d complex structural inversion scheme for possibly multibody polyhedral models has been developed the forward modeling algorithm was adopted from previous work because the inverse problem is generally very ill posed several methods of regularizing the inversion were investigated and a combination of the most useful was adopted the combination includes i a structured matrix formulation for the system equations ii an analytical expression for the jacobian calculation iii first derivative damping iv a choice of damping parameter based on a variation of the trust region method v a weighted scheme for parameter correction and vi complete freezing of degrees of freedom found not to influence the gravity field significantly this combination yields a robust inversion which was successfully demonstrated on data over the galveston island salt dome offshore texas variat

on the initial value problem of fractional evolution equations with noncompact semigroup in this paper we study the initial value problem of fractional semilinear evolution equations with noncompact semigroup in banach spaces the existence of saturated mild solutions and global mild solutions is obtained under weaker conditions particularly we find that the results obtained are also valid for the initial value problem of fractional ordinary differential equations in banach spaces the theorems proved in this paper improve and extend some related conclusions on this topic an example is given to illustrate that our results are valuable

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

gravity anomalies of arbitrary 3d polyhedral bodies with horizontal and vertical mass contrasts up to cubic order abstracta new singularity free analytical formula has been developed for the gravity field of arbitrary 3d polyhedral mass bodies with horizontally and vertically varying density contrast using third order polynomial functions first the observation sites are moved to the origin of the coordinate system then the volume and surface integral theorems are invoked successively to transform the volume integrals into surface integrals over polygonal faces and into line integrals over the edges of the polyhedral mass bodies furthermore singularity free closed form solutions are derived for these line integrals over the edges thus the observation sites can be located inside on or outside the 3d distributions a synthetic prismatic mass body is adopted to verify the accuracy and singularity free property of our newly developed analytical expressions excellent agreements are obtained between our solutions and other published closed form solutions with relative errors in the order of 10 12 to 10 13 in a

parallel application of block iterative methods in medical imaging and radiation therapy some row action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems recently developed block iterative versions of such special purpose methods enable parallel computation when the underlying problem is appropriately decomposed this opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning all in their fully discretized modelling approach since there is more than one way of deriving block iterative versions of any row action method the choice has to be made with reference to the underlying real world problem

fourier forward modeling of vector and tensor gravity fields due to prismatic bodies with variable density contrast abstractprismatic bodies with variable density contrasts are very useful in modeling and inversion of gravity anomalies for sedimentary basins in which some simple mathematical functions offer better approximations for the density depth relationship of the basin fill than a constant density model we have explored fourier domain modeling of vector and tensor gravity anomalies due to 2d and 3d prismatic bodies following a wide class of variable density functions we placed the emphasis on general polynomial models because they provided a flexible way to approximate arbitrary density functions the recently proposed gauss fast fourier transform method was applied to improve the accuracy of inverse fourier transform the numerical performance of the presented method was examined by comparing with space domain analytical seminumerical or completely numerical solutions singularity and numerical stability of the algorithm were also analyzed with ranges of numerical stability for polynomial density models of

closed form formula of magnetic gradient tensor for a homogeneous polyhedral magnetic target a tetrahedral grid example abstracta closed form formula is developed for the full magnetic gradient tensor of a polyhedral body with a homogeneous magnetization vector it is based on the direct derivative technique on the closed form of the magnetic field these analytical expressions are implemented into an easy to use c package which simultaneously calculates the magnetic potential the magnetic field and the full magnetic gradient tensor for magnetic targets modern unstructured tetrahedral grids are adopted to represent the polyhedral body so that our code can deal with arbitrarily complicated magnetic targets a prismatic body is tested to verify the accuracies of our closed form formula excellent agreements are obtained between our closed form solutions and solutions of a prismatic magnetic body with differences up to machine precision a pipeline model is used to demonstrate its capability to deal with complicated magnetic targets this c code is freely available to the magnetic exploration community

the design and implementation of cosen an iterative algorithm for fully 3 d listmode data presents coincidence list ordered set expectation maximisation cosem an algorithm for iterative image reconstruction directly from list mode coincidence acquisition data the cosem algorithm is based on the ordered sets em algorithm for binned data but has several extensions that makes it suitable for rotating two planar detector tomographs the authors develop the cosem algorithm and extend it to include analytic calculation of detection probability noise reducing iterative filtering schemes and on the fly attenuation correction methods the authors present an adaptation of cosem to the varicamvg camera and show results from clinical and phantom studies

analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals the analytical computation of the full gravity tensor from a polyhedral source of homogeneous density is presented with emphasis on its algorithmic implementation the theoretical development is based on the subsequent transition of the general expressions from volume to surface and from surface to line integrals defined along the closed polygons building each polyhedral face however the accurate numerical computation of the obtained transcendental expressions is linked with the relative position of the computation point and its corresponding projections on the plane of each face and on the line of each segment with respect to the polygons defining each face depending on this geometric setup the application of the divergence theorem of gauss leads to the appearance of additional correction terms valid only for these boundary conditions and crucial for the correct numerical evaluation of the polyhedral related gravity quantities at those locations of the computation point a program in fortran is su

comparison of gravimetric formulas for uniform polyhedra the gravitational anomaly of a polyhedral target of uniform density is amenable to analytical solution and has received wide attention we analyze a number of apparently dissimilar solutions for consistency and comment on their suitability for numeric computation consistency is determined by evaluating a method over a special contour for which all methods must agree numerical performance is assessed through operation counts and algorithm classification into vertex line or surface type each type having a known accuracy bound for a given floating point precision we verify performance predictions through model calculations in particular we demonstrate the effectiveness of revised vertex and line algorithms and of a new analytical surface method our scheme of analysis and classification has general application it provides criteria by which existing and novel solutions may be examined for consistency and numerical performance

an analytical expression for the gravity field of a polyhedral body with linearly varying density over the past 24 years the gravity fields of homogeneous polyhedra have been studied extensively paul 1974 barnett 1976 okabe 1979 golizdra 1981 strakhov et al 1986a 1986b gotze and lahmeyer 1988 pohanka 1988 ivan 1990 pohanka 1990 holstein and ketteridge 1996 this intensive scrutiny is well deserved because polyhedra provide a framework in which complex body shapes can be modeled parsimoniously and because the analytic expressions for the gravity fields of uniform polyhedra involve only elementary transcendental functions available as part of the run time library for most computational programming languages

gravimagnetic similarity in anomaly formulas for uniform polyhedra gravitational and magnetic anomalies of an arbitrary target body are linked through poisson s differential relation for a uniform polyhedral target poisson s relation reduces to an algebraic link between gravity and magnetic anomaly formulas the derivation is given in tensor form it identifies for each target facet edge a vector function in terms of which the gravitational and magnetic potential and field anomaly formulas are similarly expressed as appropriately weighted linear combinations this similarity unifies the theory of uniform polyhedral anomalies it benefits analysis and construction of software that naturally embraces all anomalies in a single code the analysis is exemplified by a discussion of singularities and by the adaptation of three gravity field algorithms to the remaining gravitational and magnetic cases while retaining the respective computational advantages of the former gravity field algorithms

event by event image reconstruction from list mode pet data this paper adapts the classical list mode osem and the globally convergent list mode cosem methods to the special case of singleton subsets the image estimate is incrementally updated for each coincidence event measured by the pet scanner events are used as soon as possible to improve the current image estimate and therefore the convergence speed toward the maximum likelihood solution is accelerated an alternative online formulation of the list mode cosem algorithm is proposed first this method saves memory resources by re computing previous incremental image contributions while processing a new pass over the complete dataset this online expectation maximization principle is applied to the list mode osem method as well image reconstructions have been performed from a simulated dataset for the ncat torso phantom and from a clinical dataset results of the classical and event by event list mode algorithms are discussed in a systematic and quantitative way

theoretical study of penalized likelihood image reconstruction for region of interest quantification region of interest roi quantification is an important task in emission tomography e g positron emission tomography and single photon emission computed tomography it is essential for exploring clinical factors such as tumor activity growth rate and the efficacy of therapeutic interventions statistical image reconstruction methods based on the penalized maximum likelihood pml or maximum a posteriori principle have been developed for emission tomography to deal with the low signal to noise ratio of the emission data similar to the filter cut off frequency in the filtered backprojection method the regularization parameter in pml reconstruction controls the resolution and noise tradeoff and hence affects roi quantification in this paper we theoretically analyze the performance of roi quantification in pml reconstructions building on previous work we derive simplified theoretical expressions for the bias variance and ensemble mean squared error emse of the estimated total activity in an roi that is surrounded by a uniform background when the mean and covariance matrix of the activity inside the roi are known the theoretical expressions are readily computable and allow for fast evaluation of image quality for roi quantification with different regularization parameters the optimum regularization parameter can then be selected to minimize the emse computer simulations are conducted for small rois with variable uniform uptake the results show that the theoretical predictions match the monte carlo results reasonably well

a versatile solution for the gravity anomaly of 3d prism meshed bodies with depth dependent density contrast abstractwe have developed a generalized solution for computing the gravity anomalies of 3d irregular mass bodies with complicated density contrast variation the 3d irregular shaped bodies can be approximated flexibly by a collection of finite juxtaposed right rectangular prisms the complicated density contrast variation of each prism can be well represented by a depth dependent polynomial function a novel analytic solution of gravity anomalies due to a right rectangular prism with an arbitrary order of polynomial density contrast function of depth is then derived the solution is singularity free in the upper half space over the prism and its singularity in the lower half space containing the prism is resolved by assigning their limit values to the singular terms the numerical stability of the solution is also evaluated through numerical tests hence the solution can be used to compute the gravity anomalies of 3d irregular bodies with variable density contrasts without singularities when computation

semigroups and some nonlinear fractional differential equations equations of the formd au t dt a au t f t b 1 t u t b r t u t are considered where 0 0 is a family of linear closed operators defined on dense sets in e into e and f is a given abstract nonlinear function defined on 0 t xe r with values in e t 0 it is assumed that a generates an analytic semigroup under suitable conditions on the family of operators b i t i 1 r t 0 and on f we study the existence and uniqueness of the solution of the cauchy problem for the considered equation some properties concerning the stability of solutions are obtained we also give an application for nonlinear partial differential equations of fractional orders

explicit solutions of jacobi and gauss differential equations by means of operators of fractional calculus judging by the remarkably large number of recent publications on fractional calculus and its applications in several widely diverse areas of mathematical physical and engineering sciences the current popularity and importance of the subject of fractional calculus cannot be overemphasized motivated by some of these potentially useful developments many authors have recently demonstrated the usefulness of fractional calculus in the derivation of explicit particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders the main object of the present paper is to show how several interesting contributions on this subject involving a certain class of ordinary differential equations associated with for example the celebrated gauss and jacobi differential equations can be obtained in a unified manner by suitably applying some general theorems on explicit particular solutions of a family of linear ordinary fractional differintegral equations

elastic and piezoelectric fields due to polyhedral inclusions abstract we derive explicit closed form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half space and bi materials our analysis is based on the linear elasticity theory and green s function method the method involves evaluation of volume and surface integrals of harmonic and bi harmonic potentials in case of polyhedra such integrals are expressed through algebraic functions our results generalize numerous studies on this subject and they allow to obtain fully analytical solutions for a number of physical and engineering problems in the limiting case of an infinite space our relations have an essentially more compact form than relations obtained by other authors we present solutions to classical mindlin and cherruti problems we describe the elastic relaxation of a misfitting polygonal quantum dot in bi materials assuming isotropic and vertically isotropic properties it is explained how to analyze non hydrostatic and non uniform inclusions we also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices among other results we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in gaas 0 0 1 and gaas 1 1 1 depending on the orientation of the cube this suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape

2d vector gravity potential and line integrals for the gravity anomaly caused by a 2d mass of depth dependent density contrast using line integrals lis used to calculate the gravity anomaly caused by a 2d mass of complicated geometry and spatially variable density contrast is a computationally efficientalgorithm thatreducesthecalculationfromtwodimensions to one dimension this work has developed a mechanism for defining lis systematically for different types of density functions two dimensional vector gravity potential is defined as a vector the net circulation of which along the closedcontourboundinga2dmass equalsthegravityanomaly caused by the 2d mass two representative types of lis aredefined anliwithanarctangentkernelforanydepth dependent density contrast function which has been studied historically and an li with a simple algebraic kernel for any integrabledensity contrastfunction thepresentworkoffers 1avectorial basedderivationofformulasthatdonotsuffer from the arbitrary sign conventions found in some historical approaches and2asimplealgebraickernelinlineintegrals as an alternative to the historical arctangent kernel with the possibilityofextensiontomoregeneralcases theconceptof 2dvectorgravitypotentialprovidesausefultoolfordefining lis systematically for any mass density function helping us understand how dimensions can be reduced in a calculating gravity anomaly especially when the density contrast varies with space lis have been tested in case studies the maximumdifferencesincalculatedgravityanomaliesbydifferent lis for the case studies were between 5 9310

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

gravimetric analysis of uniform polyhedra analytical formulas for the gravity anomaly of a uniform polyhedral body are subject to numerical error that increases with distance from the target while the anomaly decreases this leads to a limited range of target distances in which the formulas are operational beyond which the calculations are dominated by rounding error we analyze the sources of error and propose a combination of numerical and analytical procedures that exhibit advantages over existing methods namely 1 errors that diminish with distance 2 enhanced operating range and 3 algorithmic simplicity the latter is achieved by avoiding the need to transform coordinates and the need to discriminate between projected observation points that lie inside on or outside a target facet boundary our error analysis is verified in computations based on a published code and on a code implementing our methods the former requires a numerical precision of one part in 1016 double precision in problems of geophysical interest whereas our c

new method for fast computation of gravity and magnetic anomalies from arbitrary polyhedra we show that at any point the gravity field from a solid body bounded by plane surfaces and having uniform density can be computed as a field from a fictitious distribution of surface mass density on the same body the surface mass density at every surface element is equal to the product of the volume density of the body and the scalar product of 1 the unit outward vector normal to that surface element and 2 the position vector of the surface element with respect to the point of observation accordingly the contribution to the gravity field from any plane surface of the body vanishes if the observation point lies in the plane of that surface as a result we can compute the gravity field everywhere including points inside on the surface on an edge or at a corner of the body where more than two surfaces meet this new result lets us compute the gravity field using exactly the same simple procedure as for the magnetic field of a uniformly magnetized object computed from an equivalent surface distr

likelihood maximization for list mode emission tomographic image reconstruction the maximum a posteriori map bayesian iterative algorithm using priors that are gamma distributed due to lange bahn and little is extended to include parameter choices that fall outside the gamma distribution model special cases of the resulting iterative method include the expectation maximization maximum likelihood emml method based on the poisson model in emission tomography as well as algorithms obtained by parra and barrett and by huesman et al that converge to maximum likelihood and maximum conditional likelihood estimates of radionuclide intensities for list mode emission tomography the approach taken here is optimization theoretic and does not rely on the usual expectation maximization em formalism block iterative variants of the algorithms are presented a self contained elementary proof of convergence of the algorithm is included