gravity interpretation using the mellin transform the mellin transform of the gravity effect of a buried sphere and two dimensional horizontal circular cylinder and the first horizontal derivative of the gravity effect of a two dimensional thin fault layer are derived the transformed functions are bounded by two asymptotes they are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters the application of the mellin transform is tested on simulated models as well as on two field examples 1 the humble dome gravity anomaly near houston usa and 2 the louga gravity anomaly usa

an extension of kesten s criterion for amenability to topological markov chains abstract the main results of this note extend a theorem of kesten for symmetric random walks on discrete groups to group extensions of topological markov chains in contrast to the result in probability theory there is a notable asymmetry in the assumptions on the base that is it turns out that under very mild assumptions on the continuity and symmetry of the associated potential amenability of the group implies that the gurevic pressures of the extension and the base coincide whereas the converse holds true if the potential is holder continuous and the topological markov chain has big images and preimages finally an application to periodic hyperbolic manifolds is given

products of random matrices and generalised quantum point scatterers to every product of 2 2 matrices there corresponds a one dimensional schrodinger equation whose potential consists of generalised point scatterers products of random matrices are obtained by making these interactions and their positions random we exhibit a simple one dimensional quantum model corresponding to the most general product of matrices in sl 2 we use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms

advantages of using the vertical gradient of gravity for 3 d interpretation gravity gradiometric data or gravity data transformed into vertical gradient can be efficiently processed in three dimensions for delineating density discontinuities model studies performed with the combined use of maxima of analytic signal and of horizontal gradient and the euler deconvolution techniques on the gravity field and its vertical gradient demonstrate the superiority of the latter in locating density contrasts particularly in the case of interfering anomalies where the use of gravity alone fails the gravity gradient is able to provide useful information with satisfactory accuracy

multiple weighted estimates for commutators of multilinear singular integrals with non smooth kernels abstract multilinear commutators and iterated commutators generated by the multilinear singular integrals with non smooth kernels and bmo functions are studied by the weighted estimates of a class of new variant maximal operators and the sharp maximal functions the multiple weighted norm inequalities for such operators are obtained in particular some previous results in anh and duong 2010 1 lerner et al 2009 4 perez et al 2011 5 are improved or extended significantly

local holder regularity for solutions of elliptic systems in this note we prove local l p regularity for the highest order derivatives of an elliptic system of arbitrary order in nondivergence form where the coefficients of the principal part are taken in the space of sarason vanishing mean oscillation vmo lower order coefficients and the known term belong to suitable lebesgue spaces as

morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in cn abstract we prove the morrey boundedness and compactness characterization of integral commutators with singular kernel of calderon zygmund type on pseudo convex domains in c n our results extend some of the ones of krantz li in 16 17

distribution of orbits in r 2 of a finitely generated group of sl 2 r in this work we study the asymptotic distribution of the non discrete orbits of a finitely generated group acting linearly on bbb r 2 to do this we establish new equidistribution results for the horocyclic flow on the unitary tangent bundle of the associated surface

linearized least squares method for interpretation of potential field data from sources of simple geometry we present a new method for interpreting isolated potential field gravity and magnetic anomaly data a linear equation involving a symmetric anomalous field and its horizontal gradient is derived to provide both the depth and nature of the buried sources in many currently available methods either higher order derivatives or postprocessing is necessary to extract both pieces of information therefore data must be of very high quality in contrast for gravity work with our method only a first order horizontal derivative is needed and the traditional data quality is sufficient our proposed method is similar to the euler technique it uses a shape factor instead of a structural index to characterize the buried sources the method is tested using theoretical anomaly data with and without random noise in all cases the method adequately estimates the location and the approximate shape of the source the practical utility of the method is demonstrated using gravity and magnetic field examples from the united states and zimbabwe

a least squares minimization approach to depth determination from numerical horizontal gravity gradients the sphere and the horizontal cylinder models can be very useful in quantitative interpretation of gravity data measured in a small area over buried structures several graphical and numerical methods have been developed by many workers for interpreting the residual gravity anomalies caused by these models to find the depth of most geologic structures excellent reviews are given in saxov and nygaard 1953 and bowin et al 1986 the numerical approaches odegard and berg 1965 gupta 1983 sharma and geldart 1968 lines and treitel 1984 and shaw and agarwal 1990 may have advantages in theory and practice over graphical depth estimation techniques pick et al 1973 nettleton 1976 telford et al 1976 however effective quantitative interpretation procedures using the least squares method based on the analytical expression of simple numerical horizontal gravity gradient anomalies are yet to be developed

classification of joinings for kleinian groups we classify all locally finite joinings of a horospherical subgroup action on g when g psl2 r or psl2 c and is a geometrically finite zariski dense subgroup of g this generalizes ratner s 1983 joining theorem for the case when is a lattice in g

on the least squares residual anomaly determination this paper discusses an approach to determine the least squares optimum order of the regional surface which when subtracted from the bouguer gravity anomaly data minimizes distortion of the residual component of the field the least squares method was applied to theoretical composite gravity fields each consisting of a constant residual component sphere or vertical cylinder and a regional component of different order using successively increasing orders of polynomial regionals for residual determination the overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables similarity between residual maps of the lowest orders verified by good correlation may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component the residual map of the lower order in this well correlated doublet is considered the most plausible one and may be used

a least squares minimization approach to shape determination from gravity data the gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape shape factor and depth related variables with an amplitude coefficient related to mass abdelrahman and el araby 1993 few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles these methods include a walsh transform approach shaw and agarwal 1990 and the employment of a correlation factor between successive least squares residuals abdelrahman and el araby 1993 in the present note a least squares minimization approach to shape factor determination from a residual gravity anomaly profile is presented the problem of the shape factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f q 0

global morrey regularity of strong solutions to the dirichlet problem for elliptic equations with discontinuous coefficients abstract well posedness is proved in the space w2 p w1 p0 for the dirichlet problem equation omitted if the principal coefficients aij x of the uniformly elliptic operator belong to vmo l

compactness for the commutators of singular integral operators with rough variable kernels abstract let t be the singular integral operator with variable kernel defined by t f x p v r n x x y x y n f y d y where x y is homogeneous of degree zero in the second variable y and s n 1 x z d z 0 for any x r n in this paper the authors prove that if l r n l q s n 1 for some q 2 n 1 n then the commutator generated by a cmo r n function and t and the associated lacunary maximal operator are compact on l 2 r n the associated continuous maximal commutator is also considered

a new method for shape and depth determinations from gravity data we have developed a simple method to determine simultaneously the shape and depth of a buried structure from residualized gravity data using filters of successive window lengths the method is similar to euler deconvolution but it solves for shape and depth independently the method involves using a relationship between the shape factor and the depth to the source and a combination of windowed observations the relationship represents a parametric family of curves window curves for a fixed window length the depth is determined for each shape factor the computed depths are plotted against the shape factors representing a continuous monotonically increasing curve the solution for the shape and depth of the buried structure is read at the common intersection of the window curves this method can be applied to residuals as well as to the bouguer gravity data of a short or long profile length the method is applied to theoretical data with and without random errors and is tested on a known field example from the united states in all cases the shape and depth solutions obtained are in good agreement with the actual ones

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

l p bounds for the commutators of singular integrals and maximal singular integrals with rough kernels the commutator of convolution type calderon zygmund singular integral operators with rough kernels p v x n are studied the authors established the l p 1 p boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition h1 sn 1 mr 2000 subject classification 42b20 42b25 42b99

solvability for schrodinger equations with discontinuous coefficients abstract we consider the l p solvability for divergence and non divergence form schrodinger equations with discontinuous coefficients as an application we give the global morrey regularity for divergence and non divergence form schrodinger operators with vmo coefficients in a bounded domain

a mostly elementary proof of morrey space estimates for elliptic and parabolic equations with vmo coefficients abstract in recent years there has been considerable interest in extending the well known calderon zygmund estimates for the laplacian to more general equations in particular equations with highest order coefficients lying in the sarason space vmo in addition the analogous estimates with morrey spaces replacing lebesgue spaces have been considered these morrey space estimates have been proved by refining the proofs for the l p estimates we shall show that the morrey space estimates follow from the l p estimates via an elementary argument which is very similar to that used by campanato

calderon zygmund operators with non doubling measures in this survey the authors review some basic results on calderon zygmund theory on r d with the non doubling radon measure instead of the usual doubling condition the measure is only assumed to satisfy some growth condition that is there exist positive con stants n 0 d a ndc such that b x r cr n for all x r d and r 0 in this setting the results that we review are the following the hardy space h 1 and the regularized bmo space rbmo some interpolation results related to h 1 a nd rbmo the calderon zygmund decomposition the t 1 theorem and the properties of the calderon zygmund op erator on lebesgue spaces and hardy spaces cotlar s inequality and the boundedness of the maximal calderon zygmund operator the behaviors of the multilinear calderon zygmund op erator on lebesgue spaces weighted norm inequalities for the calderon zygmund operator the boundedness of the commutator generated by the calderon zygmund operator and rbmo function moreover some new progress obtained recently is also included

the application of walsh transforms to interpret gravity anomalies due to some simple geometrically shaped causative sources a feasibility study walsh functions are a set of complete and orthonormal functions of nonsinusoidal waveform in contrast to sinusoidal waveforms whose amplitudes may assume any value between 1 to 1 walsh functions assume only discrete amplitudes of or 1 which form the kernel function of the walsh transform because of this special nature of the kernel computation of the walsh transform of a given signal is simpler and faster than that of the fourier transform the properties of the fourier transform in linear time are similar to those of the walsh transform in dyadic time the fourier transform has been widely used in interpretation of geophysical problems considering various aspects of the walsh transform an attempt has been made to apply it to some gravity data a procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources viz a sphere a horizontal cylinder and a 2 d vertical prism of large depth extent the technique has been applied to data from the published literature to evaluate its applicability and the results are in good agreement with the more conventional ones

characterizations of morrey type besov and triebel lizorkin spaces with variable exponents abstract in this paper morrey type besov and triebel lizorkin spaces with variable exponents are introduced then equivalent quasi norms of these new spaces in terms of peetre s maximal functions are obtained finally applying those equivalent quasi norms the authors obtain the atomic molecular and wavelet decompositions of these new spaces

characterization of the central campanato space via the commutator operator of hardy type abstract let 1 p and 1 p 1 n then a function f l loc p r n is said to belong to the central campanato space c p r n if f c p r n sup r 0 1 b 0 r 1 b 0 r b 0 r f f b 0 r p d x 1 p where b 0 r denotes the ball centered at 0 with radius r 0 and f b 0 r 1 b 0 r b 0 r f y d y there are many known characterizations of c p r n for 0 1 n the aim of this paper is to introduce some characterizations of c p r n for 1 p 0 via the boundedness of commutator operators of hardy type some more explicit decompositions of these operators and the space c p r n which are different from that of 0 are here proposed to overcome the difficulties caused by 0 moreover some further interesting boundedness for the hardy type operators is also obtained

gravity interpretation using correlation factors between successive least squares residual anomalies the correlation factors between successive least squares residual or regional gravity anomalies from a buried sphere a two dimensional 2 d horizontal cylinder and a vertical cylinder and the first horizontal derivative of the gravity from a 2 d thin faulted layer are computed correlation values are used to determine the depth to the center of the buried structure and the radius of the sphere or the cylinder and the thickness of the fault are estimated the method can be applied not only to residuals but also to the bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order the method is easy to apply and may be automated if desired it can also be applied to the derivative anomalies of the gravity field the validity of the method is tested on two field examples from the united states and denmark

three least squares minimization approaches to depth shape and amplitude coefficient determination from gravity data three different least squares approaches are developed to determine successively the depth shape shape factor and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly by defining the anomaly value g max at the origin on the profile the problem of depth determination is transformed into the problem of solving a nonlinear equation f z 0 formulas are derived for spheres and cylinders knowing the depth and applying the least squares method the shape factor and the amplitude coefficient are determined using two simple linear equations in this way the depth shape and amplitude coefficient are determined individually from all observed gravity data a procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources the method is applied to synthetic data with and without random errors in all the cases examined the maximum error in depth shape and amplitude coeffic

shape and depth solutions from gravity data using correlation factors between successive least squares residuals the gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape shape factor and depth variables with an amplitude coefficient related to the mass correlation factors between successive least squares residual gravity anomalies from a buried vertical cylinder horizontal cylinder and sphere are used to determine the shape and depth of the buried geologic structure for each shape factor value the depth is determined automatically from the correlation value the computed depths are plotted against the shape factor representing a continuous correlation curve the solution for the shape and depth of the buried structure is read at the common intersection of correlation curves this method can be applied to a bouguer anomaly profile consisting of a residual component caused by local structure and a regional component this is a powerful technique for automatically separating the bouguer data into residual and regional polynomial components this method is tested on theoretical examples and a field example in both cases the results obtained are in good agreement with drilling results

weighted norm inequality for the singular integral with variable kernel and fractional differentiation abstract for 0 1 let d be the fractional differentiation operator and t be the singular integral operator with variable kernel which is defined by t f x r n x x y x y n f y d y let t and t denote the adjoint of t and the pseudo adjoint of t respectively let t 1 t 2 denote the product of t 1 and t 2 t 1 t 2 denote the pseudo product of t 1 and t 2 in this paper we give the weighted norm inequalities for commutators of these singular integral operators and the fractional differentiation operator d finally we extend all results to the morrey spaces

interior estimates in morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients abstract let us consider the nondivergence form elliptic equation a ij u x i x j in this paper we show that if the known term belongs to the morrey space l p then the second derivatives of the w 2 p solution u belong to the same space next we derive a c 1 loc regularity result that is related to a recent work by caffarelli

invariant radon measures for horocycle flows on abelian covers we classify the ergodic invariant radon measures for horocycle flows on d covers of compact riemannian surfaces of negative curvature thus proving a conjecture of m babillot and f ledrappier an important tool is a result in the ergodic theory of equivalence relations concerning the reduction of the range of a cocycle by the addition of a coboundary

invariant radon measures on measured lamination space let s be an oriented surface of genus g 0 with m 0 punctures and 3g 3 m 2 we classify all radon measures on the space of measured geodesic laminations which are invariant under the action of the mapping class group of s

a least squares approach to depth determination from gravity data the present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form f z 0 formulas have been derived for a sphere vertical and horizontal cylinders and for a vertical fault thin plate approximation the procedure is applied to synthetic data with and without random errors finally a field example is presented in which the depth to a fault is estimated at 3 8 km and verified from drilling results

commutators and generalized local morrey spaces abstract in this paper we study the behavior of hardy littlewood maximal operator and the action of commutators in generalized local morrey spaces l m x 0 p r n and generalized morrey spaces m p r n

sharp bounds for the commutators with variable kernels of fractional differentiations and bmo sobolev spaces abstract for 0 1 and b i bmo we introduce a new class of commutators with fractional differentiations and variable kernels which is defined by b t f x r n x x y x y n b x b y f y d y in this paper we give the sharp l 2 norm inequalities for the rough operators b t with x z l r n l q s n 1 q 2 n 1 n satisfying the mean zero value condition in its second variable in the sense that the exponent q 2 n 1 n is optimal if strengthen the smoothness of x z in its second variable we prove weight norm inequalities for these operators our results recover a previous result of murray and extend a previous result of calderon

a least squares minimization approach to depth determination from moving average residual gravity anomalies we have developed a least squares minimization method to estimate the depth of a buried structure from moving average residual gravity anomalies the method involves fitting simple models convolved with the same moving average filter as applied to the observed gravity data as a result our method can be applied not only to residuals but also to the bouguer gravity data of a short profile length the method is applied to synthetic data with and without random errors the validity of the method is tested in detail on two field examples from the united states and senegal