simplified frequency domain expressions for potential fields of arbitrary three dimensional bodies models based on homogeneous polyhedral bodies offer great flexibility in representing the potential fields of complex geologic sources however existing expressions for the gravity and magnetic fields of such bodies suffer from two disadvantages first the surface of the body must be specified as a set of triangular facets which makes input to a modeling program rather awkward second each facet of the body must be rotated into a special position which generates substantial computational overhead and makes the analytic expressions difficult to interpret in this paper pedersen s fourier transform expressions for the potential fields due to homogeneous polyhedral bodies are recast in a simpler coordinate invariant form the resulting expressions are then rewritten as a sum of contributions from each vertex of the body this greatly simplified form is used as the basis for a modeling program that is substantially faster and more straightforward than existing programs furthermore the analytic expres

toward a three dimensional automatic interpretation of potential field data via generalized hilbert transforms fundamental relations the paper extends to three dimensions 3 d the two dimensional 2 d hilbert transform relations between potential field components for the 3 d case it is shown that the hilbert transform is composed of two parts with one part acting on the x component and one part on the y component as for the previously developed 2 d case it is shown that in 3 d the vertical and horizontal derivatives are the hilbert transforms of each other the 2 d cauchy riemann relations between a potential function and its hilbert transform are generalized for the 3 d case finally the previously developed concept of analytic signal in 2 d can be extended to 3 d as a first step toward the development of an automatic interpretation technique for potential field data

direct products of groups and regular orbits abstract we prove the following result let p be a prime and let g be a finite p solvable group that is a direct product of two non cyclic subgroups of coprime order and let v be some faithful irreducible module for g over some field in characteristic p then g has a regular orbit that is there exists some v v such that c g v 1

consistent sets of estimates for regressions with correlated or uncorrelated measurement errors in arbitrary subsets of all variables over the last decade the problem of measurement errors in the independent variables of a regression equation has attracted renewed interest among econometricians in the fifties and sixties the problem was considered to be more or less hopeless due to its inherent underidentification e g theil 1971 apart from instrumental variables the most frequently cited textbook solution was wald s method of grouping wald 1940 recent insight into the properties of the method of grouping can be interpreted as making this method worthless in most practical cases pakes 1982 since about 1970 new approaches to the problem have been explored basically along three lines viz embedding the error ridden equation into a set of multiple equations e g zellner 1970 goldberger 1972 into a set of simultaneous equations e g hsiao 1976 geraci 1976 and using the dynamics of the equation if present e g maravall and aigner 1977 in view of the underidentification of the basic model it is clear that all these methods invoke additional information of some kind if this information takes the form of exact or stochastic knowledge of certain parameters in the model the construction of consistent estimators is fairly straightforward e g fuller 1980 kapteyn and wansbeek 1984 for an overview of the state of the art see aigner et al 1984 an approach somewhat orthogonal to the ones described above has been to take the model as it is and to use prior ideas about the size of the measurement errors to diagnose how serious the probem is examples are blomqvist 1972 hodges and moore 1972 and davies and hutton 1975 leamer 1983 starts from the opposite direction by asking how serious the measurement error problem has to be in order to render the data useless for inference that is to say when measurement error is large enough to make it impossible to put bounds on regression parameters in an empirical example he shows that even very small measurement errors in some explanatory variables would open up the possibility of perfectly collinear explanatory variables and hence make the data useless for statistical inference at least without additional prior information the most systematic analysis of the information loss caused by measurement error is due to klepper and leamer 1984 they start out by invoking a minimal amount of prior information and then ask the question under what conditions it is still possible to make some inferences regarding the vector of unknown regression parameters p in the special case where the measurement errors are assumed uncorrelated and the k 1 estimates of 3 obtained by regressing each of the k 1 variables involved i e the one dependent variable and the k independent variables on the remaining k variables are all in the same orthant one can bound the ml estimates of p in that case the convex hull of the k 1 regressions contains all possible ml estimates and any point in the hull is a possible ml estimate if the k 1 regressions are not all in the same orthant then the set of ml estimates is unbounded in that case klepper and leamer 1984 introduce extra prior information which allows them to bound the set of maximum likelihood estimates the prior information comes in two forms firstly a researcher is supposed to be able to specify a maximum value of r2 if all exogenous variables were measured accurately it is shown that if this maximum is low enough one can again bound the set of ml estimates by a convex hull secondly if

a multiple level set method for 3d inversion of magnetic data abstractwe have developed a multiple level set method for inverting magnetic data produced by weak induced magnetization only the method is designed to deal with a specific class of 3d magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies we adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies each having a uniform magnetic susceptibility embedded in a nonmagnetic background this representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies because each body may take on a variety of shapes and we may not know the number of bodies a priori either we use multiple level set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level set f

bounding the effects of proxy variables on regression coefficients we consider a regression in which one of the observed variables is a proxy for some unobserved true variable given a lower bound for the correlation between the proxy and the unobserved true variable for which it substitutes we derive intervals in which the coefficients of the unobserved true regression must lie regardless of any other correlations involving unobserved variables or disturbances we present a simple solution for the important special case in which only the signs of the coefficients are of concern and one seeks the smallest correlation between the proxy and the true variable that guarantees the correctness of the signs of the coefficients in the proxy regression we also present an algorithm for extending these results to the multiple proxy problem attemprs to confront economic theories with data are often hampered by the problem that some of the relevant variables are unavailable or even unobservable in the case of regression models it is customary to substitute proxies for the unavailable variables though the coefficients in the proxy regression will not coincide with those in the regression of the dependent variable on the true explanatory variables it is clear by continuity that the differences will be small if each proxy is sufficiently highly correlated with the unobserved true variable for which it substitutes even if its error is correlated with other errors or variables moreover in many instances the theory predicts not the magnitudes but only the signs of the regression coefficients correct inferences will then be drawn from the model provided that the pairwise correlations between the proxies and the true variables are high enough to guarantee that the signs of the regression coefficients would be unchanged if the proxies were replaced by the true variables in applications econometricians can generally assess those pairwise correlations subjectively but how high do they need to be in this paper we present a complete answer to this question when only one variable is a proxy and describe an algorithm for determining the required correlations when there are several proxies the effects of proxy variables have been extensively studied in the special case of errors in variables eiv in which the differences between the proxies and the corresponding true variables the measurement errors are independent of the true variables of each other and of the disturbances in the true regression we require no such independence in the eiv case it is sometimes possible to guarantee correctness of the signs of the coefficients even without prior information about the variances of the measurement errors for example if the coefficient vector from the direct regression and the coefficient vectors from the reverse regressions as one varies the left side variable all lie in the same orthant then the coefficient vector in the true regression must also lie in that orthant see

set identified linear models we analyze the identification and estimation of parameters satisfying the incomplete linear moment restrictions e z x y e z u z where z is a set of instruments and u z an unknown bounded scalar function we first provide empirically relevant examples of such a set up second we show that these conditions set identify where the identified set b is bounded and convex we provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters we derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar sargan condition third we provide new results on the asymptotics of analog estimates constructed from the identification results when b is a strictly convex set we also construct a test of the null hypothesis 0 2 b whose size is asymptotically correct and which relies on the minimization of the support function of the set b 0 results of some monte carlo experiments are presented

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

large character degrees of solvable groups with abelian sylow 2 subgroups abstract we prove that if g is a solvable group with abelian sylow 2 subgroups the index of the fitting subgroup of g is at most the square of the largest irreducible character degree of g

inversion for magnetic anomalies of arbitrary three dimensional bodies two dimensional profile inversion techniques for magnetic anomalies are widely used in exploration geophysics but until now the three dimensional 3 d methods available have been restricted in their geologic applicability dependent upon good initial values or limited by the capabilities of existing computers we have developed a fully 3 d inversion algorithm intended for routine application to large data sets the algorithm based on a fourier transform expression for the magnetic field of homogeneous polyhedral bodies hansen and wang 1998 is a 3 d generalization of compudepth o brien 1972 like compudepth the new inversion algorithm employs thespatial equivalent of frequency domain autoregression to determine a series of coefficients from which the depths and locations of polyhedral vertices are calculated by solving complex polynomials these vertices are used to build a 3 d geologic model application to the medicine lake volcano aeromagnetic anomaly resulted in a geologically reasonable

bounding parameters in a linear regression model with a mismeasured regressor using additional information this paper discusses a linear regression model with a mismeasured regressor in which the measurement error is correlated with both the latent variable and the regression error we use a linear structure to capture the correlation between the measurement error and the latent variable this paper shows that the variance of the latent variable is very useful for revealing information on the parameters which otherwise cannot be obtained with such a nonclassical measurement error the main result is that the finite bounds on the parameters can be found using the variance of the latent variable regardless of how severely the measurement error and the regression error are correlated if the mismeasured regressor contains enough information on the latent one this paper also discusses the special but interesting case of the latent variable being dichotomous in this case the mean of the latent variable may even reveal information on the correlation between the measurement error and the regression error all the bounds developed in the paper are tight

a polynomial bound for the orders of primitive solvable groups the structure of primitive solvable permutation groups has bee r thoroughly investigated since galois relying on the known structure theorems we determine the largest order a n of a primitive solvable group of degree ii theorem 3 in the course of the proof we obtain the largest order a n of a transitive solvable group of degree n as well theorem 2 although the formula describing the exact value of i is quite complicated we are able to give an asymptotic evaluation it turns out thar the order of a primitive solvable group of degree n is bounded by 24 12 for a constant c 3 24399 theorem i a similar asymptotic estimate obtained recentiy by babai cameron and pilfy 111 shows that the orders of those primitive permutation groups of degree iz in which all nonabelian simple sections have orders less than a iixed integer k are bounded by n where c c k depends on k only related estimates under the assumption of the classification of finite simple groups are given by cameron 2 strong motivation for such asymptotic estimates comes from recent results of luks 151 on the complexity of graph isomorphism testing the results of the present paper have immediate application to graphs of vaience k p we mean that the field multiplication can be defined on the k dimensional vector space over gf p so that this equ ality holds 127 002 8693 82 g g i27 i so2 gg g

large orbits in coprime actions of solvable groups let g be a solvable group of automorphisms of a finite group k if g and k are coprime then there exists an orbit of g on k of size at least g it is also proved that in a solvable group the largest normal subgroup is the intersection of at most three hall subgroups