pv cohomology of the pinwheel tilings their integer group of coinvariants and gap labeling in this paper we first remind how we can see the hull of the pinwheel tiling as an inverse limit of simplicial complexes anderson and putnam in ergod th dynam sys 18 509 537 1998 and we then adapt the pv cohomology introduced in savinien and bellissard ergod th dynam sys 29 997 1031 2009 to define it for pinwheel tilings we then prove that this cohomology is isomorphic to the integer cech cohomology of the quotient of the hull by s1 which let us prove that the top integer cech cohomology of the hull is in fact the integer group of coinvariants of the canonical transversal of the hull the gap labeling for pinwheel tilings is then proved and we end this article by an explicit computation of this gap labeling showing that mu t left c xi mathbb z right frac 1 264 mathbb z left frac 1 5 right

paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

spaces with almost euclidean dehn function we prove that any proper geodesic metric space whose dehn function grows asymptotically like the euclidean one has asymptotic cones which are non positively curved in the sense of alexandrov thus are mathrm cat 0 this is new already in the setting of riemannian manifolds and establishes in particular the borderline case of a result about the sharp isoperimetric constant which implies gromov hyperbolicity our result moreover provides a large scale analog of a recent result of lytchak and the author which characterizes proper mathrm cat 0 in terms of the growth of the dehn function at all scales we finally obtain a generalization of this result of lytchak and the author namely we show that if the dehn function of a proper geodesic metric space is sufficiently close to the euclidean dehn function up to some scale then the space is not far in a suitable sense from being mathrm cat 0 up to that scale

almost compact fuzzy sets in fuzzy topological spaces abstract the study of almost compact fuzzy topological spaces was initiated by concilio and gerla 4 which was followed by further investigations of the same in 11 the present paper aspires for an extension of the same concept to fuzzy sets in a fuzzy topological space we characterize almost compact fuzzy sets in terms of the concept of fuzzy filterbase some properties of such sets are established using the concepts of fuzzy ds closure and fuzzy ds cluster points of fuzzy filterbase

dynamic response of planar cracks in an infinitely long piezoelectric strip the problem of determining the electro elastic fields around an array of parallel planar cracks in an infinitely long piezoelectric strip is considered the cracks acted upon by dynamic loads are either electrically impermeable or permeable a semi analytic method based on the theory of exponential fourier transformation is presented for solving the problem in the laplace transform domain the laplace transforms of the jumps in the displacements and electric potential across opposite crack faces are determined by solving a system of hypersingular integral equations once these displacement and electric potential jumps are obtained the displacements and electric potential and other physical quantities of interest such as the crack tip stress and electric displacement intensity factors can be recovered with the help of a suitable algorithm for inverting laplace transforms the stress and electric displacement intensity factors are computed for some specific cases of the problem

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

the domino problem of the hyperbolic plane is undecidable in this paper we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles the problem was raised by a paper of raphael robinson in 1971 in his famous simplified proof that the general tiling problem is undecidable for the euclidean plane initially proved by robert berger in 1966

a note on compactness in a fuzzy setting abstract the concept of filter basis in a fuzzy setting is defined and investigated fuzzy filter bases are then used to introduce the notion of compactness in fuzzy setting the expected basic properties of compactness are explored

limit theorems for self similar tilings we study deviation of ergodic averages for dynamical systems given by self similar tilings on the plane and in higher dimensions the main object of our paper is a special family of finitely additive measures for our systems an asymptotic formula is given for ergodic integrals in terms of these finitely additive measures and as a corollary limit theorems are obtained for dynamical systems given by self similar tilings

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

on some weaker forms of fuzzy continuous and fuzzy open mappings on fuzzy topology spaces abstract the purpose of the present paper is to study some weaker forms of fuzzy continuous and fuzzy open maps between fuzzy topological spaces along with the introduction and investigations of a new class of non fuzzy continuous maps this latter type of mappings is seen to be independent of the other non continuous functions discussed here all these functions are characterized and certain properties concerning them are proved finally a comparative study as to their mutual dependence and interrelations under different conditions is taken up

the isoperimetric problem for pinwheel tilings in aperiodic pinwheel tilings of the plane there exist unions of tiles with ratio area perimeter 2 arbitrarily close to that of a circle such approximate circles can be constructed with arbitrary center and any sufficiently large radius the existence of such circles follows from the metric on pinwheel space being almost euclidean at large distances ifp andq are points separated by large euclidean distancer then the shortest path along tile edges fromp toq has lengthr o r

convergence of random walks on the circle generated by an irrational rotation fix 0 1 consider the random walk on the circle s1 which proceeds by repeatedly rotating points forward or backward with probability 1 2 by an angle 2 this paper analyzes the rate of convergence of this walk to the uniform distribution under discrepancy distance the rate depends on the continued fraction properties of the number 2 we obtain bounds for rates when is any irrational and a sharp rate when is a quadratic irrational in that case the discrepancy falls as k 1 2 up to constant factors where k is the number of steps in the walk this is the first example of a sharp rate for a discrete walk on a continuous state space it is obtained by establishing an interesting recurrence relation for the distribution of multiples of which allows for tighter bounds on terms which appear in the erd s turan inequality

regular production systems and triangle tilings we discuss regular production systems as a tool for analyzing tilings in general as an application we give necessary and sufficient conditions for a generic triangle to admit a tiling of and show that almost every triangle that admits a tiling is weakly aperiodic we pause for informal discussion of a variety of other applications such as non quasi isometric maps between regular tilings non periodic archimedean tilings growth and decidability most generally regular production systems provide a model for the organized growth of surfaces along a front subject to local rules

cohomology of canonical projection tilings we define the cohomology of a tiling as the cocycle cohomology of its associated groupoid and consider this cohomology for the class of tilings which are obtained from a higher dimensional lattice by the canonical projection method in schlottmann s formulation we prove the cohomology to be equivalent to a certain cohomology of the lattice we discuss one of its qualitative features namely that it provides a topological obstruction for a generic tiling to be substitutional we develop and demonstrate techniques for the computation of cohomology for tilings of codimension smaller than or equal to 2 presenting explicit formulae these in turn give computations for the k theory of certain associated non commutative c algebras

dynamic response of a cracked piezoelectric ceramic under arbitrary electro mechanical impact the dynamic response of a cracked piezoelectric ceramic under in plane electric and anti plane mechanical impact is investigated by the integral transform method the electric and mechanical loads are assumed to be arbitrary functions of time it is shown that the dynamic crack tip stress and electric displacement fields still have a square root singularity numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field on the other hand the dynamic response of the electric field is determined solely by the applied electric field the electric field will promote or retard the propagation of the crack depending on the time elapsed since the application of the external electro mechanical loads

on some near fuzzy continuous functions between fuzzy topological spaces abstract the concepts of fuzzy almost strongly continuous fuzzy continuous fuzzy weekly continuous and fuzzy weakly continuous are introduced and studied in the light of the concept of q coincidence in a fuzzy setting together with the concept of q neighbourhoods the notions of fuzzy neighbourhoods and fuzzy neighbourhoods are defined to investigate the characterizations and properties of these functions finally a comparative study regarding the mutual interrelations among these maps along with fuzzy continuous maps is made

non periodic tessellations with unit and non unit pisot inflation factors non periodic planar patterns generated by deterministic inflation rules are described several types of patterns with both unit and non unit pisot numbers as inflation factors are formed by triangular prototiles when the inflation factor is the silver mean the patterns can be obtained by superimposing two subpatterns and some of them can be converted into face to face patterns the geometric constructions corresponding to 12 fold symmetry are also studied the fourier transform of point masses placed in vertex positions of the transformed subpatterns exhibit two fold four fold and six fold symmetries although the peaks with highest intensities are situated in rings with apparent octagonal and dodecagonal symmetries

spaces of tilings finite telescopic approximations and gap labeling the continuous hull of a repetitive tiling t in d with the finite pattern condition fpc inherits a minimal d lamination structure with flat leaves and a transversal open image in new window which is a cantor set this class of tiling includes the penrose the amman benkker ones in 2d as well as the icosahedral tilings in 3d we show that the continuous hull with its canonical d action can be seen as the projective limit of a suitable sequence of branched oriented and flat compact d manifolds as a consequence the longitudinal cohomology and the k theory of the corresponding c algebra open image in new window are obtained as direct limits of cohomology and k theory of ordinary manifolds moreover the space of invariant finite positive measures can be identified with a cone in the d th homology group canonically associated with the orientation of d at last the gap labeling theorem holds given an invariant ergodic probability measure on the hull the corresponding integrated density of states ids of any selfadjoint operators affiliated to open image in new window takes on values on spectral gaps in the module generated by the occurrence probabilities of finite patches in the tiling

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

exactly solvable disordered sphere packing model in arbitrary dimensional euclidean spaces we introduce a generalization of the well known random sequential addition rsa process for hard spheres in d dimensional euclidean space mathbb r d we show that all of the n particle correlation functions of this nonequilibrium model in a certain limit called the ghost rsa packing can be obtained analytically for all allowable densities and in any dimension this represents the first exactly solvable disordered sphere packing model in an arbitrary dimension the fact that the maximal density ensuremath phi ensuremath infty 1 2 d of the ghost rsa packing implies that there may be disordered sphere packings in sufficiently high d whose density exceeds minkowski s lower bound for bravais lattices the dominant asymptotic term of which is 1 2 d indeed we report on a conjectural lower bound on the density whose asymptotic behavior is controlled by 2 ensuremath 0 778 65 dots d thus providing the putative exponential improvement on minkowski s 100 year old bound our results suggest that the densest packings in sufficiently high dimensions may be disordered rather than periodic implying the existence of disordered classical ground states for some continuous potentials

quaquaversal tilings and rotations we construct a hierarchical tiling of 3 dimensional euclidean space based on a triangular prism using repeated rotations about orthogonal axes by angles 2 m and 2 n to analyze the structure of the tiling we are led to determine the group g m n generated by such a pair of rotations for m n 3 and for m 3 n 4

a hierarchical strongly aperiodic set of tiles in the hyperbolic plane we give a new construction of strongly aperiodic set of tiles in h 2 exhibiting a kind of hierarchical structure simplifying the central framework of margenstern s proof that the domino problem is undecidable in the hyperbolic plane margenstern 2008 16

a multidimensional critical factorization theorem the critical factorization theorem is one of the principal results in combinatorics on words it relates local periodicities of a word to its global periodicity in this paper we give a multidimensional extension of it more precisely we give a new proof of the critical factorization theorem but in a weak form where the weakness is due to the fact that we loose the tightness of the local repetition order in exchange we gain the possibility of extending our proof to the multidimensional case indeed this new proof makes use of the theorem of fine and wilf that has several classical generalizations to the multidimensional case

design of broadband planar arrays based on the optimization of aperiodic tilings antenna arrays based on aperiodic tilings have been shown to exhibit low sidelobe levels and modest bandwidths over which grating lobes are suppressed in addition compared to conventional periodic arrays these arrays are naturally thinned i e mean inter element spacing is greater than the generation of these arrays involves placing array elements at the locations of the vertices of an aperiodic tiling to obtain a realizable design the entire array is then scaled and truncated to achieve a desired minimum element spacing and aperture size this paper demonstrates that it is possible to greatly extend the bandwidth of these arrays by incorporating a simple perturbation scheme into the basic array generation process the implementation of this perturbation scheme is straightforward and it lends itself well to being combined with an optimization technique such as the genetic algorithm it is successfully used to generate arrays that have large bandwidths peak sidelobe level db with no grating lobes of up to a minimum element spacing of moreover the flexibility of this technique will be further demonstrated by introducing a slight variation of the basic scheme that is capable of generating arrays with extremely wide bandwidths an example will be presented for an array design that has a bandwidth corresponding to a minimum element spacing of up to

np problems are tractable in the space of cellular automata in the hyperbolic plane in this paper we define cellular automata on a grid of the hyperbolic plane that is based on the tessellation obtained from the regular pentagon with right angles owing to the properties of that grid we show that 3 sat can be solved in polynomial time in that peculiar setting then we extend that result for any np problem on this ground several directions are indicated

on nearly compact and 0 rigid fuzzy sets in fuzzy topological spaces abstract this paper intends to initiate the study of nearly compact and rigid fuzzy sets in a fuzzy topological space these two classes of fuzzy sets are seen to be properly contained in the class of fuzzy compact sets and properly contain the class of fuzzy almost compact sets several characterizations and certain other properties of these two types of fuzzy sets are established by using the concepts of fuzzy closures and closures of fuzzy sets and fuzzy filterbases

some remarks on lo rs fuzzy compactness abstract in this paper we define lo rs fuzzy compact fuzzy sets we study some properties of lo rs fuzzy compact spaces and lo rs fuzzy compact fuzzy sets we give some characterizations of these notions by fuzzy regularly open sets and fuzzy regularly closed sets we prove that lo rs fuzzy compactness is preserved under a fuzzy almost continuous and fuzzy almost open mapping

subgroups ofso 3 associated with tilings abstract we give a thorough analysis of those subgroups ofso 3 generated by rotations about perpendicular axes by 2 pand 2 q a corollary is that such a group is the free product of the cyclic groups of rotations about the separate axes if and only ifp q 3 and are both odd these groups are naturally associated with a family of hierarchical tilings of euclidean 3 space

large time behavior of disturbed planar fronts in the allen cahn equation abstract we consider the allen cahn equation in r n with n 2 and study how a planar front behaves when arbitrarily large but bounded perturbation is given near the front region we first show that the behavior of the disturbed front can be approximated by that of the mean curvature flow with a drift term for all large time up to t using this observation we then show that the planar front is asymptotically stable in l r n under spatially ergodic perturbations which include quasi periodic and almost periodic ones as special cases as a by product of our analysis we present a result of a rather general nature which states that for a large class of evolution equations the unique ergodicity of the initial data is inherited by the solution at any later time

the pinwheel tilings of the plane prototiles in euclidean n space en for n 2 the prototiles are usually required to be rather nice topologically at least homeomorphs of the closed unit ball one then makes arbitrarily many congruent copies called tiles of these prototiles and considers all ways called tilings that such tiles may provide a simultaneous covering and packing of en a tiling is thus an unordered collection of tiles for which the union is all of en but such that the interiors of each pair of tiles do not intersect wang s original problem was to determine if it was possible to have a finite set of prototiles with associated tilings of space for which all the tilings were nonperiodic a tiling is nonperiodic if it is not invariant under any single simultaneous translation of its tiles this was settled in the affirmative in the thesis of wang s student robert berger 1

a strongly aperiodic set of tiles in the hyperbolic plane we construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane such a set of tiles does admit a tiling but admits no tiling with an infinite cyclic symmetry this can also be regarded as a regular production system 5 that does admit bi infinite orbits but admits no periodic orbits

symmetries of quasicrystals we consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant rings instead of bragg peaks they can be distinguished from glasses by self similarity of the pattern of radii of the rings

a universal cellular automaton on the heptagrid of the hyperbolic plane with four states in this paper we construct a new weakly universal cellular automaton on the ternary heptagrid this significantly improves the previous result obtained by the same author in the same grid with six states this time the number of states is four this is the best result up to date for cellular automata in the hyperbolic plane with true planar motions

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

tiling spaces are inverse limits let m be an arbitrary riemannian homogeneous space and let be a space of tilings of m with finite local complexity relative to some symmetry group and closed in the natural topology then is the inverse limit of a sequence of compact finite dimensional branched manifolds the branched manifolds are finite unions of cells constructed from the tiles themselves and the group this result extends previous results of anderson and putnam of ormes radin and sadun of bellissard benedetti and gambaudo and of gahler in particular the construction in this paper is a natural generalization of gahler s

almost compactness in fuzzy topological spaces abstract we introduce and study almost compactness for fuzzy topological spaces we show that the almost continuous image of an almost compact fuzzy topological space is almost compact moreover we show that generally almost compactness for fuzzy topological spaces is not product invariant but if x and y are almost fuzzy topological spaces and x is product related to y then their fuzzy topological product is almost compact

fuzzy s continuous functions and semilocally connected fuzzy topological spaces abstract the concept of s continuous functions kohli 1978 is translated in fuzzy setting into two concepts fuzzy s continuous functions and fuzzy os continuous functions the concepts of semiconnected functions kohli 1978 and semilocally connected spaces kohli 1978 do the same interactions between those concepts in fuzzy setting and fuzzy continuity chang 1968 are discussed also characterizations of semilocally connected and semilocally o connected fuzzy topological spaces in terms of fuzzy s continuous functions and fuzzy os continuous functions respectively are obtained

meyer s concept of quasicrystal and quasiregular sets this paper relates two mathematical concepts of long range order of a set of atoms each of which is based on restrictions on the set of interatomic distances a set in n is ameyer set if is a delone set and there is a finite setf such that lambda lambda subseteq lambda f text y meyer proposed that such sets include the possible structures of quasicrystals he obtained a structure theory for such sets which reformulates results that he obtained in harmonic analysis around 1970 and which relates these sets to cut and project sets in geometric crystallography v i galiulin introduced the concept ofquasiregular set which is a set such that both and are delone sets this paper shows that these two concepts are identical

an algorithm for two dimensional mesh generation based on the pinwheel tiling we propose a new two dimensional meshing algorithm called pinw able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges this technique is based on an extension of pinwheel tilings proposed by radin and conway see c radin ann of math 2 139 1994 pp 661 702 we prove that the algorithm produces triangles of bounded aspect ratio this kind of mesh would be useful in cohesive interface finite element modeling when the crack propagation path is an outcome of a simulation process

spatial convergence of crack nucleation using a cohesive finite element model on a pinwheel based mesh we consider the use of initially rigid cohesive interface models in a two dimensional dynamic finite element solution of a fracture process our focus is on convergence of finite element solutions to a solution of the undiscretized medium as the mesh spacing x and therefore time step t tends to zero we propose the use of pinwheel meshes which possess the isoperimetric property that for any curve c in the computational domain there is an approximation to c using mesh edges that tends to c including a correct representation of its length as the grid size tends to zero we suggest that the isoperimetric property is a necessary condition for any possible spatial convergence proof in the general case that the crack path is not known in advance conversely we establish that if the pinwheel mesh is used the discrete interface first activated in the finite element model will converge to the initial crack in the undiscretized medium finally we carry out a mesh refinement experiment to check convergence of both nucleation and propagation our results indicate that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to other types of meshes copyright 2006 john wiley sons ltd

some stronger forms of fuzzy continuous mapping on fuzzy topological spaces abstract the paper is devoted to the introduction and study of the concepts of certain classes of functions between fuzzy topological spaces each of these functions presents a stronger form of the fuzzy continuous functions these maps have been characterized and investigated mainly in the light of the notions of q neighbourhoods quasi coincidence fuzzy closure and ds neighbourhoods they have also been compared as to their mutual dependence as also with regard to their interactions with certain other fuzzy non continuous functions

on fuzzy compactness in this paper we characterize well known fuzzy compactness see 3 4 9 and 10 using the notion of fuzzy upper limit see 5 also we give and study new fuzzy compactness in fuzzy topological spaces

directed family of fuzzy sets and fuzzy perfect maps the present paper deals with the perfect functions in fuzzy setting fuzzy filter bases of fuzzy sets are also studied vis a vis such functions finally certain fuzzy topological properties are taken up for their study with regard to fuzzy perfect functions

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

the transient response of a piezoelectric strip with a vertical crack under electromechanical impact load in this paper the dynamic electromechanical response of a piezoelectric strip with a central crack vertical to the boundary was investigated based on the superposition principle and integral transform techniques the present problem was reduced to the solution of two pairs of dual integral equations to accommodate the finite size of the strip two diaerent fourier transforms about the x and y coordinates were assumed the solution was obtained in the laplace transformed domain in terms of fredholm integral equations of the second kind by a modified copson s method the laplace inversion was then carried out to obtain the resulting dynamic stress and electric displacement intensities unlike the findings observed in the static fracture behavior of piezoelectric materials the present study indicates that the dynamic electric field will retard or promote the crack propagation at the diaerent loading stages furthermore the dynamic electric response is proportional to the electric impact and is independent of the applied mechanical impact it is also shown that both the mechanical and electric response around the crack tip are greatly influenced by the free boundaries of the piezoelectric strip 7 2000 elsevier science ltd all rights reserved

on a conjecture on bidimensional words we prove that given a double sequence w over the alphabet a i e a mapping from z2 to a if there exists a pair n0 m0 z2 such that pw n0 m0 1 100n0m0 then w has a periodicity vector where pw is the complexity function in rectangles of w

effective beam forming networks for large arbitrary array of antennas a deterministic and effective strategy to reduce as much as possible the number of amplitude controls points in large arrays is herein proposed and applied to cases of practical interest the proposed strategy exploits two important concepts the first one coming from a special class of aperiodic tiling and the second one based on nufft non uniform fast fourier transform techniques the first one allows designing innovative front end architectures made of a reduced number of control points while nufft algorithms lead to computationally effective synthesis procedures the overall results and design guidelines allow to achieve simplified beamforming networks derived from aperiodic tilings and to know the performances that can be achieved using this approach particularly in case of low sidelobe requirements to confirm the usefulness of the proposed tools numerical examples are discussed conclusion follows

rapid convergence to frequency for substitution tilings of the plane this paper concerns self similar tilings of the euclidean plane we consider the number of occurrences of a given tile in any domain bounded by a jordan curve for a large class of self similar tilings including many well known examples we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain which depend only on the jordan curve

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules