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

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

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

the prime graph on class sizes of a finite group has a bipartite complement abstract let g be a finite group and let cs g denote the set of sizes of the conjugacy classes of g the prime graph built on cs g that we denote by g is the simple undirected graph whose vertices are the prime divisors of the numbers in cs g and two distinct vertices p q are adjacent if and only if pq divides some number in cs g a rephrasing of the main theorem in 8 is that the complement g of the graph g does not contain any cycle of length 3 in this paper we generalize this result showing that g does not contain any cycle of odd length i e it is a bipartite graph in other words the vertex set v g of g is covered by two subsets each inducing a complete subgraph a clique as an immediate consequence setting g to be the maximum size of a clique in g the inequality v g 2 g holds for every finite group g

conservative numerical methods for x f x abstract two distinctly different numerical methods are developed for solving the conservative initial value problem x f x x o dot x o both methods conserve exactly the same total energy as does the given differential equation computer examples are described and

zeros of brauer characters and linear actions of finite groups small primes abstract we describe the finite groups whose p brauer character table for p 2 or p 3 does not contain any zero this completes the analysis in 6 where we considered the case p 5

analytic solution of the gravity anomaly of irregular 2d masses with density contrast varying as a 2d polynomial function the analytic solution of the gravity anomaly caused by a 2d irregular mass body with the density contrast varying as a polynomial function in the horizontal and vertical directions is extrapolated from a historical version in which the analytic solution for the gravity anomaly was given only at the origin of the coordinate system to any point for the density function in terms of variables relative to that origin to calculate the gravity anomaly at stations that are not at origins a coordinate transformation is performed in which case the polynomial density contrast function must also be expressed in the transformed coordinates or a transformed solution must be obtained these analytic solutions can be obtained at any station using 1 a solution transformation method in which the density function and boundary of a mass body are kept intact or 2 a coordinate transformation method in which polynomial coefficient and boundary of a mass body are transformed accordingly the issue of singularity and instability of the analytic methods has been related to case studies caution should be exercised in modeling or interpreting the gravity survey data using the analytic methods for large target distance to target size ratios outside the range of numerical stability compared with other published methods the analytic solution results agree very well with other numerical or seminumerical methods indicating the solution is correct and can be applied for any gravity anomaly calculation caused by an irregular 2d mass body with the density contrast approximated as a polynomial function of horizontal position and or vertical position when the observation is within the range of numerical stability

incomplete vertices in the prime graph on conjugacy class sizes of finite groups abstract given a finite group g consider the prime graph built on the set of conjugacy class sizes of g denoting by 0 the set of vertices of this graph that are not adjacent to at least one other vertex we show that the hall 0 subgroups of g which do exist are metabelian

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

a characterization of the prime graphs of solvable groups abstract let g denote the set of prime divisors of the order of a finite group g the prime graph of g denoted g is the graph with vertex set g with edges p q e g if and only if there exists an element of order pq in g in this paper we prove that a graph is isomorphic to the prime graph of a solvable group if and only if its complement is 3 colorable and triangle free we then introduce the idea of a minimal prime graph we prove that there exists an infinite class of solvable groups whose prime graphs are minimal we prove the 3k conjecture on prime divisors in element orders for solvable groups with minimal prime graphs and we show that solvable groups whose prime graphs are minimal have fitting length 3 or 4

efficient gravity inversion of basement relief using a versatile modeling algorithm abstractwe have developed a novel approach to compute in an efficient and versatile way the gravity anomaly produced by an arbitrary discrete 3d distribution of density contrast the method allows adjustable precision and is particularly suited for the interpretation of sedimentary basins because the gravity field decays with the square of the distance we use a discrete green s operator that may be made much smaller than the whole study area for irregularly positioned observations this discrete green s operator must be computed just at the first iteration and because each of its horizontal layers presents a center of symmetry only one eighth of its total elements need to be calculated furthermore for gridded data on a plane this operator develops translation symmetry for the whole region of interest and has to be computed just once for a single arbitrary observation position the gravity anomaly is obtained as the product of this small operator by any arbitrary density contrast distribution in

magnetic anomaly fourier spectrum of a 3d gaussian source i obtain a closed form expression for the total field magnetic anomaly generated by a 3d gaussian magnetization distribution the solution is evaluated by a novel contour integration in the complex wavenumber domain the spatial domain solution is then computed by a numerical inverse fourier transform this calculated field can be used to interpret magnetic data because a 3d gaussian function can represent a compact and smooth source the method moreover allows for calculation of the fourier components as a function of the distance between the depth of the source and the height of the observation level the solution is thus useful for the inverse problem spectral analysis or data continuation

zeros of brauer characters and linear actions of finite groups let g be a finite group and p a prime number greater than 3 it is known that if every irreducible p brauer character of g does not vanish on any p element of g then g is solvable the primary aim of this work is to describe the structure of groups satisfying the above condition among other more specific properties we show that the p length of g is at most 2 the bound being the best possible the structural results are obtained as an application of the main theorem in this paper that deals with particular linear actions of solvable groups on finite vector spaces

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

gravitational attraction of a rectangular prism with depth dependent density the gravity effect produced by two and three dimensional bodies with nonuniform density contrast has been treated by several authors one of the first attempts in this direction made by cordell 1973 who developed a method to compute the gravity effect due to a two dimensional prism whose density decreases exponentially with depth a different approach was proposed by murthy and rao 1979 they extended the line integral method to obtain the gravity effect for bodies of arbitrary cross sections with density contrast varying linearly with depth chai and hinze 1988 have derived a wavenumber domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth recently rao 1990 has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial

automatic energy momentum conserving time integrators for hyperelastic waves an energy momentum conserving time integrator coupled with an automatic finite element algorithm is developed to study longitudinal wave propagation in hyperelastic layers the murnaghan strain energy function is used to model material nonlinearity and full geometric nonlinearity is considered an automatic assembly algorithm using algorithmic differentiation is developed within a discrete hamiltonian framework to directly formulate the finite element matrices without recourse to an explicit derivation of their algebraic form or the governing equations the algorithm is illustrated with applications to longitudinal wave propagation in a thin hyperelastic layer modeled with a two mode kinematic model solution obtained using a standard nonlinear finite element model with newmark time stepping is provided for comparison

2 d inversion of gravity data using sources laterally bounded by continuous surfaces and depth dependent density a description is given of numerical methods for 2 d gravity modeling and nonlinear inversion the forward model solution is suitable for calculating the gravity anomaly caused by a 2 d source body with depth dependent density that is laterally bounded by continuous surfaces and can easily accommodate different kinds of geologic structures the weighted and damped discrete nonlinear inverse method addressed here can invert both density and geometry of the source body both modeling and inversion methods are illustrated with several examples using synthetic and two field gravity data sets one over a sulfide ore body and other across a sedimentary basin a sensitivity analysis is carried out for the resulting solutions by means of the resolution covariance and correlation matrices providing insight into the capabilities and limitations of the inversion method the inversion of synthetic data provides meaningful results showing that the method is robust in the presence of noise its sensitivity analysis i

2 d gravity modeling with analytically defined geometry and quadratic polynomial density functions new methods for 2 d modeling of gravity anomaly data are developed following an approach that uses both analytic and numerical methods of integration the forward model solution developed here is suitable to calculate the gravity effect caused by a 2 d source body bounded either laterally or vertically by continuous functions in our models the density contrast is defined by a second order polynomial function of depth and distance along the profile we present several examples to show that our models are capable of accommodating a broad variety of geologic structures

gravity inversion using open reject and shape of anomaly fill criteria a gravity inversion method is developed by iteratively applying open reject and fill o r f criteria within a model space comprising a great many rectangular prisms each prism is assigned a density contrast the modeling procedure consists of filling some prisms while leaving others empty only one element is filled for each pass generally elements are added only to the periphery of the growing model models can be allowed to grow in any combination of directions or in all directions by application of a shape of anomaly fill criterion the model rapidly attains a form which yields gravity approximating the given gravity scaled down by some constant factor as the model continues to grow this scale factor approaches unity the method readily yields inverse models comprising several thousand individual prisms examples presented here give applications to 2 d problems the method is readily applicable to 212 d and 3 d problems as well overhanging elements are obtained by appropriate use of model

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

conservation properties of a time fe method part iv higher order energy and momentum conserving schemes in the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite dimensional hamiltonian systems with symmetry is shown the result of this development is the enhanced galerkin eg finite element method in time the conservation of the eg method is generally related to its collocation property total energy conservation in particular is obtained by a new projection technique the eg method is moreover based on objective time discretization of the used strain measure this paper is concerned with particle dynamics and semi discrete non linear elastodynamics the related numerical examples show good performance in presence of stiffness as well as for calculating large strain motions copyright 2005 john wiley sons ltd

singularity removal a refinement of resistivity modeling techniques modeling techniques commonly exhibit errors of 3 to 10 percent or more in the calculation of apparent resistivities over earth models for which analytic solutions are easily available a singularity occurs in the solution of any elliptic partial differential equation for which the forcing function is not smooth the inability to adequately represent in discrete space a discontinuous function in this case the delta function describing the introduction of current at a point commonly results in numerical error near the source of a modeled singularity inspection of an integrated finite difference method for modeling the dc resistivity geophysical technique indicates much of the error encountered is of singular origin a procedure is herein detailed by which the singularity is mathematically removed from the modeling process and reintroduced as a last step thus preventing it from contributing to the numerical error using this procedure the average error in apparent resistivity values for a model of a polar dipole traverse over a nonconducting sphere is reduced by 40 percent for a dipole dipole traverse of a two layer model the error decreases by 75 percent and in the case of a wenner profile of a model of a vertically faulted earth the average error is diminished by 90 percent

high precision fourier forward modeling of potential fields we analyzed the numerical forward methods in the fourier domain for potential fields existing fourier domain forward methods applied the standard fast fourier transform fft algorithm to inverse transform a conjugate symmetrical spectrum into a real field it had significant speed advantages over space domain forward methods but suffered from problems including aliasing imposed periodicity and edge effect usually grid expansion was needed to reduce these errors which was equivalent to the numerical evaluation of the oscillatory fourier integral using the trapezoidal rule with smaller steps we tested a high precision fourier domain forward method based on a combined use of shift sampling technique and gaussian quadrature theory the trapezoidal rule applied by the standard fft algorithm to evaluate the continuous fourier transform was modified by introducing a shift parameter by choosing optimum values of as gaussian quadrature nodes we developed a gauss fft method for fourier forward modeling of potential fields no grid expansion was needed the sources can be set near the boundary of the fields or even go beyond the boundary the gauss fft method converged to the space domain solution much faster than the standard fft method with grid expansion forward modeling results almost identical to space domain ones can be obtained in less time numerical examples of both simple and complex 2d and 3d source forward modeling revealed the reliability and adaptability of the method

groups whose prime graph on conjugacy class sizes has few complete vertices abstract let g be a finite group and let g denote the prime graph built on the set of conjugacy class sizes of g in this paper we consider the situation when g has few complete vertices and our aim is to investigate the influence of this property on the group structure of g more precisely assuming that there exists at most one vertex of g that is adjacent to all the other vertices we show that g is solvable with fitting height at most 3 the bound being the best possible moreover if g has no complete vertices then g is a semidirect product of two abelian groups having coprime orders finally we completely characterize the case when g is a regular graph

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

gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth we present a new stable gravity inversion method applied to the mapping of an interface separating two homogeneous media in contrast with previous similar methods it does not impose an overall smoothness on the estimated interface to stabilize the solution the density contrast between the media is assumed to be known the interpretation model for the upper medium consists of rectangular juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated the true interface is assumed to be flat everywhere except at faults to incorporate this attribute into the estimated relief we developed an iterative process in which three kinds of constraints are imposed on parameters 1 proximity between values of adjacent parameters 2 lower and upper bounds to parameters and 3 proximity between the values of parameters and fixed numerical values starting with an initial solution which presents an overall smooth relief the method enhances initially estimated

forward modeling of gravity data using finite volume and finite element methods on unstructured grids abstractminimum structure inversion is one of the most effective tools for the inversion of gravity data however the standard gauss newton algorithms that are commonly used for the minimization procedure and that employ forward solvers based on analytic formulas require large memory storage for the formation and inversion of the involved matrices an alternative to the analytical solvers are numerical ones that result in sparse matrices this sparsity suits gradient based minimization methods that avoid the explicit formation of the inversion matrices and that solve the system of equations using memory efficient iterative techniques we have developed several numerical schemes for the forward modeling of gravity data using the finite element and finite volume methods on unstructured grids in the finite volume method a delaunay tetrahedral grid and its dual voronoi grid are used to find the primary solution i e gravitational potential at the centers and vertices of the tetrahedra respectively cel

three dimensional fourier gravity inversion with arbitrary density contrast the use of variable density contrasts in gravity inversion has gained increasing importance in recent years due to the necessity of constructing more realistic models of geophysical structures such as sedimentary basins linear quadratic and exponential variations either in the space or in the frequency domain are the basis of several methods see among others the papers by granser 1987 chai and hinze 1988 reamer and ferguson 1989 and rao et al 1990 guspi 1990 used polynomial density depth functions for inverting gravity anomalies into 2 d polygons in the space domain

continuous finite element methods which preserve energy properties for nonlinear problems abstract continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations schemes are constructed that give high orders of accuracy time discretization algorithms for the cahn hilliard klein gordon korteweg de vries and schrodinger equations are presented comparisons are made with existing schemes

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

how to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties abstract for a fairly general class of second order accurate algorithms a sub stepping procedure is described which achieves fourth order accuracy while retaining the stability conservation properties and implementation of the underlying second order method two features render the proposed approach especially attractive from a computational perspective over conventional fourth order methods first the improved fourth order accuracy is attained merely by two additional residual evaluations with no changes in the implementation of the underlying second order method in particular no additional storage or extra computations of high order gradients are required second for hamiltonian systems the stability properties and possible conservation properties of the underlying second order method such as energy momentum and symplectic character are preserved the new technique is applied to a number of standard algorithms for elastodynamics structural and rigid body dynamics in particular when applied to the recently proposed second order accurate energy momentum method this approach results in a fourth order accurate energy linear and angular momentum conserving algorithm for general hamiltonian systems

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

inversion modeling of gravity with prismatic mass bodies a combined method for forward and inverse modeling of gravity data is presented based on the fourier transform of poisson s equation the forward modeling is suitable for observation points above within and below causative masses with any prescribed density distribution the inversion is linearized in the spatial domain by superimposing numerous prismatic bodies each having constant but different density and fixed geometry our inversion algorithm adopts a sampling window to reduce memory storage and computations testing with synthetic and field data demonstrates that a successful inversion can be obtained from crudely estimated a priori density distributions and uncertainties lateral variations in density are well resolved but depth resolution often requires better constrained a priori information under various a priori conditions our modeling indicates that sediment density tends to vary exponentially with depth in the san jacinto basin southern california

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

on the classification of finite dimensional irreducible modules for affine bmw algebras in this paper we classify the finite dimensional irreducible modules for affine bmw algebra over an algebraically closed field with arbitrary characteristic

3d vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3d variable density contrast three dimensional rectangular prisms are building blocks for calculating gravity anomalies from irregular 3d mass bodies with spatially variable density contrasts a 3d vector gravity potential is defined for a 3d rectangular prism with density contrast varying in depth and horizontally the vertical component of the gravity anomaly equals the flux of the 3d vector gravity potential through the enclosed surface of the prism thus the 3d integral for the gravity anomaly is reduced to a 2d surface integral in turn a 2d vector gravity potential is defined the vertical component of the gravity anomaly equals the net circulation of the 2d vector gravity potential along the enclosed contour bounding the surfaces of the prism the 3d integral for the gravity anomaly is reduced to 1d line integrals further analytical or numerical solutions can then be obtained from the line integrals depending on the forms of the density contrast functions if an analytical solution cannot be obtained the line integral method is semianalytical requiring numerical quadratures to be carried out at the final stages singularity and discontinuity exist in the algorithm and the method of exclusive infinitesimal sphere or circle is effective to remove them then the vector potential line integral method can calculate the gravity anomaly resulting from a rectangular prism with density contrast varying simply in one direction and sophisticatedly in three directions the advantage of the method is that the constraint to the form of the density contrast is greatly reduced and the numerical calculation for the gravity anomaly is fast

morita equivalence for cyclotomic bmw algebras abstract in this paper we determine explicitly the singular parameters for cyclotomic bmw algebras b r n over an arbitrary field equivalently we give a criterion for b r n being morita equivalent to the direct sum of some ariki koike algebras this generalizes konig and xi s work on brauer algebras 14 theorem 7 3 and our previous work on brauer and birman murakami wenzl algebras 20 proposition 2 15

conservation properties of a time fe method part ii time stepping schemes for non linear elastodynamics in the present paper one step implicit integration algorithms for non linear elastodynamics are developed the discretization process rests on galerkin methods in space and time in particular the continuous galerkin method applied to the hamiltonian formulation of semidiscrete non linear elastodynamics lies at the heart of the time stepping schemes algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals we newly introduce the assumed strain method in time which enables the design of energy momentum conserving schemes and which can be interpreted as temporal counterpart of the well established assumed strain method for finite elements in space the numerical examples deal with quasi rigid motion as well as large strain motion copyright 2001 john wiley sons ltd

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

gravity inversion of an interface above which the density contrast varies exponentially with depth mapping of an interface above which the density contrast varies exponentially with depth as is common at the basement surface of sedimentary basins is efficiently achieved by a theoretically precise gravity method which can be applied to either profile data or twodimensional data the contrast in mass above the interface is modeled by an array of vertical rectangular prisms with density contrasts varying exponentially with depth gravity anomalies due to the prisms are calculated in the wavenumber domain and then converted to the space domain the precision of the inverse numerical fourier transform in this procedure is significantly increased by a shift sampling technique based on the discrete fourier deviation equation depth to the interface is determined by iterative adjustment of the vertical extent of the prisms in accordance with observed gravity anomaly data the basement surface of the los angeles basin california calculated by this method closely duplicates the published configuration based

gravity interpretation using fourier transforms and simple geometrical models with exponential density contrast the decrease of density contrast in sedimentary basins can often be approximated by an exponential function theoretical fourier transforms are derived for symmetric trapezoidal vertical fault vertical prism syncline and anticline models this is desirable because there are no equivalent closed form solutions in the space domain for these models combined with an exponential density contrast these transforms exhibit characteristic minima maxima and zero values and hence graphical methods have been developed for interpretation of model parameters after applying end corrections to improve the discrete transforms of observed gravity data the transforms are interpreted for model parameters this method is first tested on two synthetic models then applied to gravity anomalies over the san jacinto graben and los angeles basin

character degree graphs with no complete vertices abstract let be a graph in which each vertex is non adjacent to another different one we show that if g is a finite solvable group with abelian fitting subgroup and with character degree graph g then g is a direct product of subgroups having a disconnected character degree graph in particular is a join of disconnected graphs we deduce also that solvable groups with abelian fitting subgroup have a character degree graph with diameter at most 2

the gravity anomaly of two dimensional sources with continuous density distribution and bounded by continuous surfaces the gravity anomaly of a complicated two dimensional 2 d source having arbitrary surfaces and density varying in either horizontal or vertical direction is calculated using a combination of closed form solutions and numerical integration the surfaces and density can be defined by continuous or piecewise continuous two dimensional functions in the integration interval for example the anomalies for intrusions or folded sedimentary units having an arbitrary density in the horizontal direction and a polynomial density distribution in the vertical direction can be calculated using surfaces represented by functions of the horizontal dimension when modeling dipping layered intrusions or sedimentary beds the surfaces are represented by functions of the vertical dimension in which case the density can be an arbitrary function of depth and a polynome function of horizontal coordinate the accuracy of the method is defined by the user the method gives simple and general equations to calculate anomalies of c

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

a bayesian approach to modeling 2d gravity data using polygons abstractwe apply a bayesian markov chain monte carlo formalism to the gravity inversion of a single localized 2d subsurface object the object is modeled as a polygon described by five parameters the number of vertices a density contrast a shape limiting factor and the width and depth of an encompassing container we first constrain these parameters with an interactive forward model and explicit geologic information then we generate an approximate probability distribution of polygons for a given set of parameter values from these we determine statistical distributions such as the variance between the observed and model fields the area the center of area and the occupancy probability the probability that a spatial point lies within the subsurface object we introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties we apply our techniques to synthetic data sets and a natural data set collected across the rio grande gorge bridge i

on independent sets in the class graph of a finite group we prove that in the class graph of a finite group there is no independent set of three vertices

linear inversion of gravity data for 3 d density distributions we have developed an improved levenburg marquart technique to rapidly invert bouguer gravity data for a 3 d density distribution as a source of the observed field this technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user where such information is not available objective models are generated the technique estimates the density distribution within the source volume using a least squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential householder transformations the source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density this discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution convergence of the solution to the system is tightly controlled by a damping pa

a finite element model for a higher order shear deformable beam theory the theory for a higher order shear deformable beam model is first developed it is based on a higher order displacement model and incorporates linear and quadratic variation of transverse normal strain and transverse shearing strain respectively through the beam thickness the effects of the transverse normal and shear stresses are included in the definition of the material s constitutive law the warping of the transverse normal cross section of the beam is automatically incorporated in the mathematical model the question of selecting a shear correction coefficient as in a first order shear deformable timoshenko theory does not arise a linear two noded finite element model of this theory is introduced and developed next both static and free vibration results of this theory are presented and compared with those of euler and timoshenko theories for various boundary and loading conditions