symmetries of distributional domain wall geometries generalizing the lie derivative of smooth tensor fields to distribution valued tensors we examine the killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries the chosen geometries are rigorously the distributional thin wall limit of self gravitating scalar field configurations representing thick domain walls and the permanence and or the rising of symmetries in the limit process is studied we show that for all the thin wall space times considered the symmetries of the distributional curvature tensors turns out to be the killing symmetries of the pullback of the metric tensor to the surface where the singular part of these tensors is supported remarkably enough for the nonreflection symmetric domain wall studied these killing symmetries are not necessarily symmetries of the ambient space time on both sides of the wall

symmetries of the energy momentum tensor of spherically symmetric lorentzian manifolds matter collineations of spherically symmetric lorentzian manifolds are considered these are investigated when the energy momentum tensor is nondegenerate and also when it is degenerate we have classified space times admitting higher symmetries and space times admitting so 3 as the maximal isometry group for the nondegenerate case we obtain either four six seven or ten independent matter collineations in which four are isometries and the rest are proper the results of the previous paper sharif and sehar gen relativ gravit 35 1091 2003 are recovered as a special case it is worth noting that we have also obtained two cases where the energy momentum tensor is degenerate but the group of matter collineations is finite dimensional i e four or ten

fluid space times and conharmonic symmetries the conharmonic curvature tensor is considered as an invariant of the conharmonic transformation defined by ishii and the necessary and sufficient conditions for the conharmonic curvature tensor in a perfect fluid space time to be divergence free has been obtained conharmonic motion conharmonic collineation and conharmonic curvature collineation are introduced as subcases of conformal motion conformal collineation and weyl conformal collineation respectively and relations of conharmonic symmetries with inheriting symmetries are investigated in the case of an existing conharmonic killing vector along the flow vector along the anisotropy vector and perpendicular to both in an anisotropic fluid space time it is found that no equation of state is singled out unless the conharmonic killing vector is also a curvature inheritance vector conditions are obtained for the symmetries of the anisotropic fluid space time admitting a conharmonic killing vector to be inherited in the case of a conharmonic sym

symmetries of the energy momentum tensor of cylindrically symmetric static space times we investigate matter symmetries of cylindrically symmetric static space times these are classified for both cases when the energy momentum tensor is nondegenerate and also when it is degenerate it is found that the nondegenerate energy momentum tensor gives either three four five six seven or ten independent matter collineations in which three are isometries and the rest are proper the worth mentioning cases are those where we obtain the group of matter collineations finite dimensional even the energy momentum tensor is degenerate these are either three four five or ten some examples are constructed satisfying the constraints on the energy momentum tensor

affine collineations in space time the existence of affine collineations in space time is discussed and the types of space time admitting proper affine collineations is displayed the close connection between such space times and their holonomy structure and local decomposability is established affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space time

convergence of multidimensional cascade algorithm a necessary and sufficient condition on the spectrum of the restricted transition operator is given for the convergence in l 2 bbb r d of the multidimensional cascade algorithm for any starting function phi 0 whose shifts form a partition of unity

the bidual of the compact operators let x be a banach space such that x has the radon nikodym property if x also has the approximation property then the banach algebra b x of all bounded linear operators on x is isometrically isomorphic as an algebra to the double dual bk x of the banach algebra of compact operators on x when bk x is provided with the first arens product the chief result of this paper is a converse to the above statement the converse is formulated in a strong fashion and a number of other results including a formula for the second arens product are also given

on m ideals of compact operators in lorentz sequence spaces abstract let x d v p and y d w q be lorentz sequence spaces we investigate when the space k x y of compact linear operators acting from x to y forms or does not form an m ideal in the space of bounded linear operators we show that k x y fails to be a non trivial m ideal whenever p 1 or p q in the case when 1 p q we establish a general essential condition guaranteeing that k x y is not an m ideal in contrast we prove that non trivial m ideals k x y do exist whenever 1 p q and we give a description of them

the equivalence of darmois israel and distributional method for thin shells in general relativity a distributional method to solve the einstein s field equations for thin shells is formulated the familiar field equations and jump conditions of darmois israel formalism are derived a careful analysis of the bianchi identities shows that for cases under consideration they make sense as distributions and lead to jump conditions of darmois israel formalism

on ideals of compact operators satisfying them r s inequality abstract letr s 0 1 we prove that a banach spacexsatisfies them r s inequality i e formula where is the canonical projection ofx ontox wheneverr s 2 1 and there exists a norm one projectionpon l x with ker p k x satisfying formula we characterize the last property of k x in l x by a strong version of the metric compact approximation property ofx our results extend some well known results onm ideals

special conformal killing vector space times and symmetry inheritance viscous heat conducting fluid and anisotropic fluid space times admitting a special conformal killing vector sckv are studied and some general theorems concerning the inheritance of the symmetry associated with the sckv are proved in particular for viscous fluid space times it is shown that i if the sckv maps fluid flow lines into fluid flow lines then all physical components of the energy momentum tensor inherit the sckv symmetry or ii if the lie derivative along a sckv of the shear viscosity term ab is zero then again we have symmetry inheritance all space times admitting a sckv and satisfying the dominant energy condition are found apart from the vacuum pp wave solutions which are the only vacuum solutions that can admit a sckv the energy momentum tensor associated with these space times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid no perfect fluid space times can admit a sckv these sckv space t

affine conformal vectors in space time all space times admitting a proper affine conformal vector acv are found by using a theorem of hall and da costa it is shown that such space times either i admit a covariantly constant vector timelike spacelike or null and the acv is the sum of a proper affine vector and a conformal killing vector or ii the space time is 2 2 decomposable in which case it is shown that no acv can exist unless the space time decomposes further furthermore it is proved that all space times admitting an acv and a null covariantly constant vector which are necessarily generalized pp wave space times must have ricci tensor of segre type 2 1 1 it follows that among space times admitting proper acv the einstein static universe is the only perfect fluid space time there are no non null einstein maxwell space times and only the pp wave space times are representative of null einstein maxwell solutions otherwise the space times can represent anisotropic fluids and viscous heat conducting fluids but only with restricted equations of state in each case

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

incorporation of space time symmetries in einstein s field equations in the search for exact solutions to einstein s field equations the main simplification tool is the introduction of space time symmetries motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry the method is being expressed in a covariant formalism using the framework of a double congruence the basic notion on which it is based is that of the geometrization of a general symmetry as a special application of our general method we consider the case of a space like conformal killing vector field on the space time manifold regarding special types of matter fields new perspectives in general relativity are discussed

convergence of cascade algorithms by frequency approach abstract starting with an initial function 0 the cascade algorithm generates a sequence q a n 0 n 1 by cascade operator q a defined by q a f z d a f m a function is refinable if it satisfies q a the refinable functions play an important role in wavelet analysis and computer graphics the cascade algorithm is the main approach to approximate the refinable functions and to study their properties this note establishes a sufficient condition in terms of fourier transforms of the initial function 0 and the refinable function for the convergence of cascade algorithm our results apply to the case where neither the initial function is compactly supported nor the refinement mask is finitely supported as a byproduct we prove that any compactly supported refinable function has a positive sobolev regularity exponent provided it is in l 2

on the general structure of ricci collineations for type b warped space times a complete study of the structure of ricci collineations for type b warped space times is carried out this study can be used as a method to obtain these symmetries in such space times special cases as 2 2 reducible space times and plane and spherical symmetric space times are considered specifically

addendum symmetries of the energy momentum tensor in recent papers j math phys 44 5142 2003 45 1518 2003 45 1532 2004 we have discussed matter symmetries of nonstatic spherically symmetric space times static plane symmetric space times and cylindrically symmetric static space times these have been classified for both cases when the energy momentum tensor is nondegenerate and also when it is degenerate here we add up some consequences and the missing references about the ricci tensor

collineations of a symmetric 2 covariant tensor ricci collineations the infinitesimal transformations that leave invariant a two covariant symmetric tensor are studied the interest of these symmetry transformations lays in the fact that this class of tensors includes the energy momentum and ricci tensors we find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional lie algebra but in some cases exhibiting a higher degree of degeneracy this class is infinite dimensional and may fail to be a lie algebra as an application we study the ricci collineations of a type b warped spacetime

classification of static plane symmetric space times according to their matter collineations in this paper we classify static plane symmetric space times according to their matter collineations these have been studied for both cases when the energy momentum tensor is nondegenerate and also when it is degenerate it turns out that the nondegenerate case yields either four five six seven or ten independent matter collineations in which four are isometries and the rest are proper there exists three interesting cases where the energy momentum tensor is degenerate but the group of matter collineations is finite dimensional the matter collineations in these cases are either four six or ten

stability implies convergence of cascade algorithms in sobolev space this article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in sobolev space to which the refinable function vector belongs an example of hermite interpolants is presented to illustrate the result

affine collineations in general relativity and their fixed point structure a general discussion of affine vector fields collineations in space time is given following a previous article by hall and da costa some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established some preliminary results regarding homothetic symmetries in two and three dimensional space times are also given the impossibility of reducing an affine algebra containing proper affine vector fields to homothetic or killing vector fields by means of a change of compatible metric is demonstrated

compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas in this paper for any d d dilation matrix m we demonstrate in a constructive way that we can construct compactly supported tight m wavelet frames and orthonormal m wavelet bases in l2 rd of exponential decay which are derived from compactly supported m refinable functions such that they can have both arbitrarily high smoothness and any preassigned order of vanishing moments this paper improves several results in battle comm math phys 110 1987 601 bownik j fourier anal appl 7 2001 489 grochenig and ron proc amer math soc 126 1998 1101 lemarie j math pures appl 67 1988 227 and strichartz constr approx 9 1993 327

matter collineations the inverse symmetry inheritance problem matter collineations as a symmetry property of the energy momentum tensor tab are studied from the point of view of the lie algebra of vector fields generating them most attention is given to space times with a degenerate energy momentum tensor some examples of matter collineations are found for dust fluids including szekeres s space times and null fluid space times

fraisse limits in functional analysis we provide a unified approach to fraisse limits in functional analysis including the gurarij space the poulsen simplex and their noncommutative analogs we obtain in this general framework many known and new results about the gurarij space and the poulsen simplex and at the same time establish their noncommutative analogs particularly we construct noncommutative analogs of universal operators in the sense of rota

collineations of godel type space times ricci collineations for godel type space times are studied the members of this family of metrics admitting these symmetries are identified it is shown that these space times do not admit homothetic vector fields also the unique affine collineation associated to godel type space times is exhibited

geometrization of a general collineation geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities shear vorticity expansion of the congruence of the vector field generating the collineation it is shown that the generic form of a collineation is l gab 2 gab hab where hab is a traceless symmetric tensor a general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed

eigenvalues of spl darr 2 h and convergence of the cascade algorithm this paper is about the eigenvalues and eigenvectors of spl darr 2 h the ordinary fir filter h is a convolution with a vector h h o h n which is the impulse response the operator spl darr 2 downsamples the output y h x keeping the even numbered components y 2n where h is represented by a constant diagonal matrix this is a toeplitz matrix with h k on its kth diagonal the odd numbered rows are removed in spl darr 2 h the result is a double shift between rows yielding a block toeplitz matrix with 1 spl times 2 blocks iteration of the filter is governed by the eigenvalues if the transfer function h z spl sigma h k z sup k has a zero of order p at z 1 corresponding to spl omega spl pi then spl darr 2 h has p special eigenvalues 1 2 1 4 1 2 sup p we show how each additional zero at spl pi divides all eigenvalues by 2 and creates a new eigenvector for spl lambda 1 2 this eigenvector solves the dilation equation spl phi t 2 spl sigma h k spl phi 2t k at the integers t n the left eigenvectors show how 1 t t sup p 1 can be produced as combinations of spl phi t k the dilation equation is solved by the cascade algorithm which is an infinite iteration of m spl darr 2 2h convergence in l sup 2 is governed by the eigenvalues of t spl darr 2 2hh sup t corresponding to the response 2h z h z sup 1 we find a simple proof of the necessary and sufficient condition for convergence

curvature collineations in general relativity ii this paper is the second of a set of two papers on curvature collineations in general relativity the first paper presented the mathematical basis of curvature collineations and a possible approach to their study this paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space time it is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here this together with the geometrical approach favored in this paper leads to a rather general discussion of the problem which it is hoped does not obscure those physical aspects of the situation that are important in einstein s theory

almost square banach spaces abstract we single out and study a natural class of banach spaces almost square banach spaces in an almost square space we can find given a finite set x 1 x 2 x n in the unit sphere a unit vector y such that x i y is almost one these spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2 we provide several examples and characterizations of almost square spaces we prove that non reflexive spaces which are m ideals in their biduals are almost square we show that every separable space containing a copy of c 0 can be renormed to be almost square a local and a weak version of almost square spaces are also studied

collineations of the ricci tensor ricci collineations for the ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of rab r such that rab 0 for a b it turns out that the only collineations admitted by this tensor can be ten six or four and there does not appear any case in between

curvature inheritance symmetry in riemannian spaces with applications to fluid space times katzin et al g h katzin j levine and w r davis j math phys 10 617 1969 introduced curvature collineations cc defined by a vector satisfying l rbcda 0 where rbcda is the riemann curvature tensor of a riemannian space vn and l denotes the lie derivative they proved that a cc is related to a special conformal motion which implies the existence of a covariant constant vector field unfortunately recent study indicates that the existence of a covariant constant vector restricts vn to a very rare special case with limited physical use in particular for a fluid space time with special conformal motion either stiff or unphysical equations of state are singled out moreover perfect fluid space times do not admit special conformal motions this information was not available in 1969 when cc symmetry was introduced in this paper cc is generalized to another symmetry called curvature inheritance ci satisfying l rbcda 2 rbcda where is a scalar function we prove that a proper

norm preserving extensions of functionals and denting points of convex sets let w and z be banach spaces and let x subset w and y subset z be closed subspaces let mathcal l be a subspace of mathcal l w z the banach space of bounded linear operators from w to z containing x otimes y we describe for x in x and y in y all norm preserving extensions of x otimes y in x otimes y ast to the space mathcal l in terms of convergence of convex combinations we also characterize denting points of bounded convex subsets of banach spaces in similar terms various applications are presented

symmetries of bianchi i space times all diagonal proper bianchi i space times are determined which admit certain important symmetries it is shown that for homothetic motions conformal motions and kinematic self similarities the resulting space times are defined explicitly in terms of a set of parameters whereas affine collineations ricci collineations and curvature collineations if they are admitted they determine the metric modulo certain algebraic conditions in all cases the symmetry vectors are explicitly computed the physical and the geometrical consequences of the results are discussed and a new anisotropic fluid physically valid solution which admits a proper conformal killing vector is given

spacelike conformal killing vectors and spacelike congruences necessary and sufficient conditions are derived for space time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na these conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four velocity of the observer employed at any given point of the congruence it is shown that either the expansion or the rotation of this spacelike congruence must vanish if dna dp 0 where p denotes arc length measured along the integral curves of na and also that there exist no proper spacelike homothetic motions with constant expansion propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid fluid space times are studied in detail a relation is established between spacelike conformal motions and material curves in the fluid if a fluid space time admits a spacelike conformal killing vector parallel to na and