relatively uniformly continuous semigroups on vector lattices abstract in this paper we introduce the notions of relatively uniform continuity and strong continuity with respect to the relatively uniform topology for semigroups on general vector lattices these notions allow us to study semigroups on non locally convex spaces such as l p r for 0 p 1 and non complete spaces such as lip r uc r and c c r we provide examples of relatively uniform continuous semigroups such as the left translation semigroup and the ornstein uhlenbeck semigroup

higher type adjunction inequalities for donaldson invariants we prove new adjunction inequalities for embedded surfaces in four manifolds with non negative self intersection number using the donaldson invariants these formulas are completely analogous to the ones obtained by ozsvath and szabo using the seiberg witten invariants to prove these relations we give a fairly explicit description of the structure of the fukaya floer homology of a surface times a circle as an aside we also relate the floer homology of a surface times a circle with the cohomology of some symmetric products of the surface

the blowup formula for donaldson invariants k k which is calculated in 4 below this formula has been the target of much recent work the abstract fact that there exists such a formula which is independent of x was first proved by c taubes using techniques of t j bryan b and p ozsvath o have independently calculated the coefficients throughb10 x quite recently j morgan and ozsvath have announced a scheme which can recursively compute all of the bk x the special case of the blowup formula for manifolds of simple type see 5 below was first given by p kronheimer and t mrowka however none of the techniques in these cases approach the simplicity of that offered here before presenting the formula we shall first establish notation for the donaldson in variants of a simply connected 4 manifold x with b 1 and odd the hypothesis of simple connectivity is not necessary but makes the exposition easier an orientation of x together with an orientation of h 2 x r is called a homology orientation of x such a homology orientation determines the su 2 donaldson invariant a linear function d dx a x sym h0 x h2 x r

efficient computation of surface fields excited on a dielectric coated circular cylinder an efficient method to evaluate the surface fields excited on an electrically large dielectric coated circular cylinder is presented the efficiency of the method results from the circumferentially propagating representation of the green s function as well as its efficient numerical evaluation along a steepest descent path the circumferentially propagating series representation of the appropriate green s function is obtained from its radially propagating counterpart via watson s transformation and then the path of integration is deformed to the steepest descent path on which the integrand decays most rapidly numerical results are presented that indicate that the representations obtained here are very efficient and valid even for arbitrary small separations of the source and field points this work is especially useful in the moment method analysis of conformal microstrip antennas where the mutual coupling effects are important

diffraction of axisymmetric waves in a borehole by bed boundary discontinuities this paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities the bed boundary is assumed to be horizontal and the inhomogeneities to be axially symmetric in such a geometry an axially symmetric source will produce only axially symmetric waves since the borehole is an open structure the mode spectrum consists of a discrete part as well as a continuum the scattering of a continuum of waves by bed boundaries is difficult to treat the approach used in the past in treating this class of problem has been approximate in nature or highly numerical such as the finite element method we present here a systematic way to approximate the continuum of modes by discrete modes after discretization the scattering problem can be treated simply since the approach is systematic it allows derivation of the solution to any desired degree of accuracy in theory but in practice it is limited by the computational resources available we also show that our appr

the donaldson witten function for gauge groups of rank larger than one we study correlation functions in topologically twisted d 4 supersymmetric yang mills theory for gauge groups of rank larger than one on compact four manifolds x we find that the topological invariance of the generator of correlation functions of brst invariant observables is not spoiled by noncompactness of field space we show how to express the correlators on simply connected manifolds of b 2 x 0 in terms of seiberg witten invariants and the classical cohomology ring of x for manifolds x of simple type and gauge group su n we give explicit expressions of the correlators as a sum over 1 vacua we describe two applications of our expressions one to superconformal field theory and one to large n expansions of su n d 4 supersymmetric yang mills theory

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

stable pseudoanalytical computation of electromagnetic fields from arbitrarily oriented dipoles in cylindrically stratified media computation of electromagnetic fields due to point sources hertzian dipoles in cylindrically stratified media is a classical problem for which analytical expressions of the associated tensor green s function have been long known however under finite precision arithmetic direct numerical computations based on the application of such analytical canonical expressions invariably lead to underflow and overflow problems related to the poor scaling of the eigenfunctions cylindrical bessel and hankel functions for extreme arguments and or high order as well as convergence problems related to the numerical integration over the spectral wavenumber and to the truncation of the infinite series over the azimuth mode number these problems are exacerbated when a disparate range of values is to be considered for the layers thicknesses and material properties resistivities permittivities and permeabilities the transverse and longitudinal distances between source and observation points as well as the source frequency to overcome these challenges in a systematic fashion we introduce herein different sets of range conditioned modified cylindrical functions in lieu of standard cylindrical eigenfunctions each associated with nonoverlapped subdomains of numerical evaluation to allow for stable computations under any range of physical parameters in addition adaptively chosen integration contours are employed in the complex spectral wavenumber plane to ensure convergent numerical integration in all cases we illustrate the application of the algorithm to problems of geophysical interest involving layer resistivities ranging from 1000 wm to 10 8 wm frequencies of operation ranging from 10 mhz down to the low magnetotelluric range of 0 01 hz and for various combinations of layer thicknesses

novel and stable formulations for the response of horizontal coil eccentric antennas in a cylindrically multilayered medium in this paper we present a set of novel and stable formulations to calculate the response of logging tools with horizontal coil antennas in an eccentric borehole straddling cylindrically multilayered formations it can be applied in fast forward computation and the inverse problem for electromagnetic em well logging in deviated and horizontal wells where eccentric scenarios are often encountered our formulations are different from previous ones in following aspects first the tool mandrel can be cylindrically multilayered and the electrical parameters of each layer are arbitrary namely it is not limited to being perfectly metallic second the em propagation in inhomogeneous medium is considered by the generalized reflection and transmission method in place of the transfer matrices the associated generalized reflection and transmission coefficients are expressed by the ratios of bessel or hankel functions that obviate the notorious overflow problem for numerical computation finally a set of linear matrix functions are constructed to solve for the em waves in a borehole based on the concept of the generalized reflection rather than that of the fictitious boundary numerical results in comparison with those from other approaches have demonstrated the validity and stability of our new formulations

closed form green s function representations for mutual coupling calculations between apertures on a perfect electric conductor circular cylinder covered with dielectric layers closed form green s function cfgf representations are developed for tangential magnetic current sources to calculate the mutual coupling between apertures on perfectly conducting circular cylinders covered with dielectric layers the new representations are obtained by first rewriting the corresponding spectral domain green s function representations in a different form so that accurate results for electrically large cylinders and along the axial line of a cylinder can be obtained then the summation over the cylindrical eigenmodes is calculated efficiently finally the resulting expressions are transformed to the spatial domain using a modified two level generalized pencil of function method numerical results are presented showing good agreement when compared to cst microwave studio results

further improvement for fast computation of mixed potential green s functions for cylindrically stratified media a method of fast computation of the mixed potential green s functions mpgfs in spatial domain for cylindrically stratified media has been developed based on the convergence behavior of the mpgfs in spectral domain the discrete complex image method dcim and the extrapolation technique are employed to perform the inverse fourier transform which is different from that of planarly stratified media in order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity the green s functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process for the integral along the deformed sommerfeld integral path with respect to k sub z dcim is used to speed up the computation after the quasistatic components are completely subtracted from the spectral domain green s functions the inverse transform of the remaining parts has an approximated analytical form the proposed method can be used to accurately and efficiently calculate the spatial domain mpgfs which are useful for characterizing conformal patch structures mounted on cylindrically stratified media

bibasic sequences in banach lattices abstract given a schauder basic sequence x k in a banach lattice we say that x k is bibasic if the expansion of every vector in x k converges not only in norm but also in order we prove that in this definition order convergence may be replaced with uniform convergence with order boundedness of the partial sums or with norm boundedness of finite suprema of the partial sums the results in this paper extend and unify those from the pioneering paper order schauder bases in banach lattices by a gumenchuk o karlova and m popov in particular we are able to characterize bibasic sequences in terms of the bibasis inequality a result they obtained under certain additional assumptions after establishing the aforementioned characterizations of bibasic sequences we embark on a deeper study of their properties we show for example that they are independent of ambient space stable under small perturbations and preserved under sequentially uniformly continuous norm isomorphic embeddings after this we consider several special kinds of bibasic sequences including permutable sequences i e sequences for which every permutation is bibasic and absolute sequences i e sequences where expansions remain convergent after we replace every term with its modulus we provide several equivalent characterizations of absolute sequences showing how they relate to bibases and to further modifications of the basis inequality we further consider bibasic sequences with unique order expansions we show that this property does generally depend on ambient space but not for the inclusion of c 0 into l we also show that small perturbations of bibases with unique order expansions have unique order expansions but this is not true if bibases is replaced with bibasic sequences in the final section we consider uo bibasic sequences which are obtained by replacing order convergence with uo convergence in the definition of a bibasic sequence we show that such sequences are very common

the singularities of a fourier type integral in a multicylindrical layer problem the singularities of the integrand of a fourier type integral obtained in solving the multicylindrical layer boundary value problem are discussed the integrand is a function of the radial wavenumber k ip of all the cylindrical layers and the radial wavenumber in the ith layer is related to the axial wavenumber by k ip sqrt k i 2 k 2 where k i is the wavenumber of the i th layer and k z is the axial wavenumber of all the layers which have to be the same by phase matching on the complex k z plane there seemingly are branch points of logarithmic type and algebraic type for k z k i for all the layers however by invoking uniqueness principle in the solution of this boundary value problem one can show that the only singularities on the complex k z plane are the branch point singularity associated with the outermost medium which extends radially to infinity and pole singularities which correspond to discrete guided modes in the multicylindrical medium

an efficient rescaled formulation for tensor green s function computation in cylindrical multilayered media a robust formulation is presented to eliminate overflow underflow and convergence problems that arise the computation of tensor green s functions in cylindrical multilayered media under finite precision arithmetic this is done by first introducing a set of rescaled functions associated to the canonical cylindrical bessel and hankel functions representing standing waves and outgoing waves along the radial direction the rescaled cylindrical functions are designed to avoid the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments in addition a parabolic sommerfeld integration path is constructed in the spectral complex plane to yield a numerical integration with good convergence properties for a wide range of parameter values

heat equation and ergodic theorems for riemann surface laminations we study the dynamics of possibly singular foliations by riemann surfaces the main examples are holomorphic foliations by riemann surfaces in projective varieties we introduce the heat equation relative to a positive partial overline partial closed current and apply it to the directed currents associated with riemann surface laminations possibly with singularities this permits to construct the heat diffusion with respect to various laplacians that could be defined almost everywhere with respect to the partial overline partial closed current we prove two kinds of ergodic theorems for such currents one associated to the heat diffusion and one of geometric nature close to birkhoff s averaging on orbits of a dynamical system here the averaging is on hyperbolic leaves and the time is the hyperbolic time the heat diffusion theorem with respect to a harmonic measure is also developed for real laminations

instanton counting and donaldson invariants for a smooth projective toric surface we determine the donaldson invariants and their wallcrossing in terms of the nekrasov partition function using the solution of the nekrasov conjecture 33 38 3 and its refinement 34 we apply this result to give a generating function for the wallcrossing of donaldson invariants of good walls of simply connected projective surfaces with b 1 in terms of modular forms this formula was proved earlier in 19 more generally for simply connected 4 manifolds with b 1 assuming the kotschick morgan conjecture and it was also derived by physical arguments in 31

theta functions and hodge numbers of moduli spaces of sheaves on rational surfaces we compute generating functions for the hodge numbers of the moduli spaces of h stable rank 2 sheaves on a rational surface s in terms of theta functions for indefinite lattices if h lies in the closure of the ample cone and has self intersection 0 it follows that the generating functions are jacobi forms in particular the generating functions for the euler numbers can be expressed in terms of modular forms and their transformation behaviour is compatible with the predictions of s duality we also express the generating functions for the signatures in terms of modular forms it turns out that these generating functions are also with respect to another developing parameter the generating function for the donaldson invariants of s evaluated on all powers of the point class