estimating source location using normalized magnetic source strength calculated from magnetic gradient tensor data abstractfor a number of widely used models normalized source strength nss can be derived from eigenvalues of the magnetic gradient tensor the nss is proportional to a constant q normalized by the nth power of the distance between observation and integration points where q is a shape factor depending upon geometry of the model and n is the structural index the nss is independent of magnetization direction and its amplitude is only affected by the magnitude of magnetization the nss is also a homogenous function and satisfies euler s homogeneity equation therefore euler deconvolution of the nss can be used to estimate source location in our algorithm we use data points enclosed by a square window centered at maxima of the nss for simultaneously estimating the source location and structural index the window size is increased until it exceeds a predefined limit then the most reliable solution is chosen based on some statistical analysis minimum uncertainty one of the advantages of the presented

magnetic interpretation in three dimensions using euler deconvolution magnetic survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using euler s homogeneity relation the method employs gradients either measured or calculated data need not be pole reduced so that remanence is not an interfering factor geologic constraints are imposed by use of a structural index model studies show that the method can locate or outline confined sources vertical pipes dikes and contacts with remarkable accuracy a field example using data from an intensively studied area of onshore britain shows that the method works well on real data from structurally complex areas and provides a series of depth labeled euler trends which mark magnetic edges notably faults with good precision

enumeration based approach to solving parametric linear complementarity problems this paper presents a solution method for parametric linear complementarity problems plcp that relies on an enumeration technique to discover all feasible bases the enumeration procedure is based on evaluating all possible combinations of active constraints and testing for feasibility although the enumeration approach is known to grow exponentially in the number of constraints the formulation of the plcp allows incorporation of cheap rank tests to quickly prune the infeasible directions in the exploration the motivation for the development of the enumeration based plcp solver is that it represents a direct method to solve parametric linear and quadratic optimization problems as well as their mixed integer counterparts these types of problems often arise in the field of model predictive control for linear and hybrid systems the enumeration based plcp solver offers another alternative to compute explicit solutions in the field of hybrid model predictive control that can be extremely effective in some important cases

surface charge algebra in gauge theories and thermodynamic integrability surface charges and their algebra in interacting lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus in the case of exact solutions and symmetries the surface charges are interpreted as a pfaff system integrability is governed by frobenius theorem and the charges associated with the derived symmetry algebra are shown to vanish in the asymptotic context we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended comparison with hamiltonian and covariant phase space methods is made all approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context

the linear dynamic complementarity problem is a special case of the extended linear complementarity problem in this paper we consider some extensions of the linear complementarity problem which is one of the fundamental problems in mathematical programming more specifically we consider the linear dynamic complementarity problem ldcp the generalized linear complementarity problem glcp and the extended linear complementarity problem elcp in this note we show that the ldcp is a special case of the elcp and the glcp

mpc for discrete event systems with soft and hard synchronization constraints discrete event systems with only synchronization and no concurrency also known as timed event graphs or max linear systems have been studied by several authors the synchronization constraints that arise in these discrete event systems are hard i e they cannot be broken under any circumstances in this paper we consider a more extended class of discrete event systems with both hard and soft synchronization constraints i e if necessary some synchronization conditions may be broken but then a penalty is incurred we show how the model predictive control mpc framework which is a very popular controller design method in the process industry can be extended to this class of discrete event systems in general the mpc control design problem for discrete event systems with soft and hard synchronization constraints leads to a non linear non convex optimization problem we show that the optimal mpc strategy can also be computed using an extended linear complementary problem

on the estimation of the structural index from low pass filtered magnetic data abstractthe estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data such as euler deconvolution however these estimates are unstable even in the presence of a weak amount of noise and euler deconvolution of noisy data leads to an underestimation of structural index and depth we have studied how the structural index and depth estimates are affected by applying low pass filtering to the data physically based low pass filters such as upward continuation and integration have been shown to be the best choice over a range of altitudes upward continuation or orders integration filters mainly because their outputs have a well defined physical meaning in contrast mathematical low pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields the c norm criterion is a reliable strategy to produce a stabilized vertical derivative and we disc

enumeration of all wedged equilibrium configurations in contact problem with coulomb friction abstract for a linear structure subjected to the unilateral contact condition with a fixed obstacle we refer to a nontrivial equilibrium state as a wedged configuration finding a wedged configuration is called a wedging problem this paper discusses theoretical properties of solution set of the finite dimensional wedging problem with the coulomb friction and presents numerical methods for computing all the wedged configurations we propose algorithms for enumerating all the finitely many representative solutions with which we can completely describe the solution set of the wedging problem there exists a positive critical friction coefficient defined as the minimum value of friction coefficient with which at least one wedged configuration exists we also propose an algorithm for computing the critical friction coefficient which is based on the bisection method and the second order cone program

unification of euler and werner deconvolution in three dimensions via the generalized hilbert transform the extended euler deconvolution algorithm is shown to be a generalization and unification of 2 d euler deconvolution and werner deconvolution after recasting the extended euler algorithm in a way that suggests a natural generalization to three dimensions we show that the 3 d extension can be realized using generalized hilbert transforms the resulting algorithm is both a generalization of extended euler deconvolution to three dimensions and a 3 d extension of werner deconvolution at a practical level the new algorithm helps stabilize the euler algorithm by providing at each point three equations rather than one we illustrate the algorithm by explicit calculation for the potential of a vertical magnetic dipole

assessing the complete solution set of the planar frictional wedging problem abstract this paper examines the computation of all the infinitely many solutions of the frictional wedging problem in the non coercive context by an algorithm applied to its complementarity formulation our analysis offers insights regarding the mechanical and the geometrical meaning of the solution set we find that the solution structure depends much on the value of the coefficient of friction the evidence indicates that non coercivity implies much longer computation times coefficients of friction at the onset of wedging are computed and related

equivalence of lcp and pls it is our purpose here to show that two prototype models of complementary pivot and fixed point theory and the corresponding path following solution methods are conceptually equivalent

a practical anti cycling procedure for linearly constrained optimization a procedure is described for preventing cycling in active set methods for linearly constrained optimization including the simplex method the key ideas are a limited acceptance of infeasibilities in all variables and maintenance of a working feasibility tolerance that increases over a long sequence of iterations the additional work per iteration is nominal and stalling cannot occur with exact arithmetic the method appears to be reliable based on computational results for the first 53 linear programming problems in thenetlib set

solving nonlinear multicommodity flow problems by the analytic center cutting plane method the paper deals with nonlinear multicommodity flow problems with convex costs a decomposition method is proposed to solve them the approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network it is thus formulated as a shortest path problem and solved with dijkstra s d heap algorithm an implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations computational results show the efficiency of this approach on well known nondifferentiable problems and also large scale randomly generated problems up to 1000 arcs and 5000 commodities

magnetic source parameters of two dimensional structures using extended euler deconvolution the euler homogeneity relation expresses how a homogeneous function transforms under scaling when implemented it helps to determine source location for particular potential field anomalies in this paper we introduce an additional relation that expresses the transformation of homogeneous functions under rotation the combined implementation of the two equations called here extended euler deconvolution for 2 d structures gives a more complete source parameter estimation that allows the determination of susceptibility contrast and dip in the cases of contact and thin sheet sources this allows for the structural index to be correctly chosen on the basis of a priori knowledge about susceptibility and dip the pattern of spray solutions emanating from a single source anomaly can be attributed to interfering sources which have their greatest effect on the flanks of the anomaly these sprays follow different paths when using either conventional euler deconvolution or extended euler deconvolution the paths of these spray solutions cross and cluster close to the true source location this intersection of spray paths is used as a discriminant between poor and well constrained solutions allowing poor solutions to be eliminated extended euler deconvolution has been tested successfully on 2 d model and real magnetic profile data over contacts and thin dikes

on the application of euler deconvolution to the analytic signal standard euler deconvolution is applied to potential field functions that are homogeneous and harmonic homogeneity is necessary to satisfy the euler deconvolution equation itself whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane according to potential field theory the analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function hence the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent euler deconvolution we show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones the consequences of this error in the structural index are equally important whether the structural index is given as input as in standard euler deconvolution or represents an unknown to be solved for the analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions we suggest computing the first vertical derivative of the analytic signal modulus taking into account its nonharmonicity by using a simple finite difference algorithm when the vertical derivative of the analytic signal is computed by finite differences the depth to source and the structural index consistent with known source parameters are in fact obtained

the initial boundary value problem for einstein s vacuum field equation we study the initial boundary value problem for einstein s vacuum field equation we prescribe initial data on an orientable compact 3 dimensional manifold s with boundary and boundary conditions on the manifold t re 0 we assume the boundaries and 0 of s and t to be identified in the natural way furthermore we prescribe certain gauge source functions which determine the evolution of the fields provided that all data are smooth and certain consistency conditions are met on we show that there exists a smooth solution to einstein s equation ric g 0 on a manifold which has after an identification a neighbourhood of s in t s as a boundary the solution is such that s is space like the initial data are induced by the solution on s and in the region of t where the solution is defined t is time like and the boundary conditions are satisfied

local symmetries and constraints the general relationship between local symmetries occurring in a lagrangian formulation of a field theory and the corresponding constraints present in a phase space formulation are studied first a prescription applicable to an arbitrary lagrangian field theory for the construction of phase space from the manifold of field configurations on space time is given next a general definition of the notion of local symmetries on the manifold of field configurations is given that encompasses as special cases the usual gauge transformations of yang mills theory and general relativity local symmetries on phase space are then defined via projection from field configuration space it is proved that associated to each local symmetry which suitably projects to phase space is a corresponding equivalence class of constraint functions on phase space moreover the constraints thereby obtained are always first class and the poisson bracket algebra of the constraint functions is isomorphic to the lie bracket algebra of the local symmetries on the constraint submanifold of phase space the differences that occur in the structure of constraints in yang mills theory and general relativity are fully accounted for by the manner in which the local symmetries project to phase space in yang mills theory all the field independent local symmetries project to all of phase space whereas in general relativity the nonspatial diffeomorphisms do not project to all of phase space and the ones that suitably project to the constraint submanifold are field dependent as by products of the present work definitions are given of the symplectic potential current density and the symplectic current density in the context of an arbitrary lagrangian field theory and the noether current density associated with an arbitrary local symmetry a number of properties of these currents are established and some relationships between them are obtained

the generalized linear complementarity problem and an algorithm to find all its solutions motivated by a number of typical applications a generalization of the classicallinear complementarity problem is presented together with an algorithm to determine the complete solution set the algorithm is based on the double description method for solving linear inequalities and succeeds in describing continuous as well as unbounded solution sets

complementarity modeling of hybrid systems a complementarity framework is described for the modeling of certain classes of mixed continuous discrete dynamical systems the use of such a framework is well known for mechanical systems with inequality constraints but we give a more general formulation which also applies for instance to switching control systems the main theoretical results in the paper are concerned with uniqueness of smooth continuations the solution of this problem requires the construction of a map from the continuous state to the discrete state a crucial technical tool is the so called linear complementarity problem from mathematical programming and we introduce various generalizations of this problem

linear complementarity systems we introduce a new class of dynamical systems called linear complementarity systems the time evolution of these systems consists of a series of continuous phases separated by events which cause a change in dynamics and possibly a jump in the state vector the occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming the framework we describe is suitable for certain situations in which both differential equations and inequalities play a role for instance in mechanics electrical networks piecewise linear systems and dynamic optimization we present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions

determining the distance to magnetic sources abstractthe distance to sources of magnetic field anomalies of a known structural index can be determined by using ratios of the analytic signal amplitudes as of different orders and this can be performed in several different ways local minima of the distance correspond to the source depth if an incorrect structural index has been used then the different methods will yield different depths hence a comparison of the results obtained from the different methods can help us to differentiate between valid and invalid source depths these methods are computationally straightforward and in some of the methods the orders of the as that are used can be chosen based on the noise level of the data some approaches that do not require the a priori specification of the structural index of the source are introduced including methods that use data from two different altitudes obtained by vertical continuation we have applied the methods to aeromagnetic data sets from the giyani and kuruman regions of south

multiridge analysis of potential fields geometric method and reduced euler deconvolution a new method based on 3d multiridge analysis of potential fields assumes a 3d subset in the harmonic region and studies the behavior of potential field ridges which are built by joining extreme points of the analyzed field computed at different altitudes three types of ridges are formed by searching for the zeros of the first horizontal and first vertical derivatives of the potential field types i and ii respectively and the zeros of the potential field itself type iii this method uses a redundant set of ridges called a multiridge set to determine source type and location for homogeneous potential fields generated by simple sources all of the ridges are straight lines converging to the source position this method analyzes the multiridges by using a geometric criterion to find the source position at the intersection of the multiridge set and by solving the three reduced euler equations associated with ridge types i ii and iii the reduced euler type i and ii equations are used to obtain the structural index and the vertical and horizontal source positions equation type iii estimates the horizontal and vertical source positions tests on synthetic as well as the bishop model field yield good results even with noise corrupted data results obtained using magnetic data collected over the wreck of a military ship in the tyrrhenian sea successfully determine its vertical and horizontal positions and the structural index

covariant hamiltonian boundary conditions in general relativity for spatially bounded space time regions we investigate the covariant hamiltonian symplectic structure of general relativity for spatially bounded regions of space time with a fixed time flow vector for existence of a well defined hamiltonian variational principle taking into account a spatial boundary it is necessary to modify the standard arnowitt deser misner hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field the most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the space time region a main result is that we obtain a covariant derivation of dirichlet neumann and mixed type boundary conditions on the gravitational field at a fixed boundary hypersurface together with the associated hamiltonian boundary terms as well we establish uniqueness of these boundary conditions under certain assumptions motivated by the form of the symplectic current our analysis uses a noether charge method which extends and unifies several results developed in recent literature for general relativity as an illustration of the method we apply it to the maxwell field equations to derive allowed boundary conditions and boundary terms for the existence of a well defined hamiltonian variational principle for an electromagnetic field in a fixed spatially bounded region of minkowski space time