beta integers as natural counting systems for quasicrystals recently discrete sets of numbers the integers have been proposed as numbering tools in quasicrystalline studies indeed there exists a unique numeration system based on the irrational in which the integers are all real numbers with no fractional part these integers appear to be quite appropriate for describing some quasilattices relevant to quasicrystallography when precisely is equal to golden mean to or to i e when is one of the self similarity ratios observed in quasicrystalline structures as a matter of fact integers are natural candidates for coordinating quasicrystalline nodes and also the bragg peaks beyond a given intensity in corresponding diffraction patterns they could play the same role as ordinary integers do in crystallography in this paper we prove interesting algebraic properties of the sets when is a quadratic unit pv number a class of algebraic integers which includes the quasicrystallographic cases we completely characterize their respective meyer additive and multiplicative properties where f and g are finite sets and also their respective galois conjugate sets these properties allow one to develop a notion of a quasiring we hope that in this way we will initiate a sort of algebraic quasicrystallography in which we can understand quasilattices which be module on a quasiring in we give also some two dimensional examples with

the algebraic theory of quasicrystals with five fold symmetries an algebraic binary operation is introduced into quasicrystals admitting five fold symmetry in terms of this many quasicrystals displaying full pentagonal or icosahedral symmetry are seen to be finitely generated examples are given in dimensions 1 2 3 and 4 the operation of left quasicrystal addition is affine linear the monoid generated by these operators is discussed and a presentation for it given in the generic case

classification of voronoi and delone tiles of quasicrystals iii decagonal acceptance window of any size this paper is the last of a series of three articles presenting a classification of vornoi and delone tilings determined by point sets quasicrystals built by the standard projection of the root lattice of type a4 to a two dimensional plane spanned by the roots of the coxeter group h2 dihedral group of order 10 the acceptance window for in the present paper is a regular decagon of any radius 0 r there are 14 distinct vt sets of voronoi tiles and 6 sets dt of delone tiles up to a uniform scaling by the factor and the number of voronoi tiles in different quasicrystal tilings varies between 3 and 12 similarly the number of delone tiles is varying between 4 and 6 there are 7 vt sets of the generic type and 7 of the singular type the latter occur for seven precise values of the radius of the acceptance window quasicrystals with acceptance windows with radii in between these values have constant vt sets only the relative densities and arrangement of the tiles in the tilings change similarly we distinguish singular and generic sets dt of delone tiles

lie algebras associated with one dimensional aperiodic point sets the set of points of a one dimensional cut and project quasicrystal or model set while not additive is shown to be multiplicative for appropriate choices of acceptance windows this leads to the definition of an associative additive graded composition law and permits the introduction of lie algebras over such aperiodic point sets these infinite dimensional lie algebras are shown to be representatives of a new type of semi direct product induced lie algebras

a new method for estimating subgroup means under misclassification summary this paper considers the estimation of the subgroup means of a response variable when the individuals in a random sample are allocated to the subgroups or classes by a fallible device a double sampling scheme under which we determine also the true classes of the individuals in a subsample is utilized a simple distributional free estimator is proposed and the associated large sample properties are also derived the proposed estimator is also demonstrated by simulation studies to be more efficient than selen s estimator 1986

tiles in quasicrystals with quartic irrationality in 2003 pelantova and twarock did research into the number of and types of tiles found in 1 dimensional cut and project quasicrystals associated with 7 order symmetry in this paper we extend this to symmetries of order 9 degree 3 as well as orders 15 16 20 and 24 degree 4 some discussion of the next case order 11 degree 5 is given

minimal distances in quasicrystals a general expression is derived for the minimal distance between points of a cut and project quasicrystal in with a convex acceptance window the study of minimal distances amounts to the study of one dimensional quasicrystals and their rescalings which occur in for an n dimensional ball as the exact value of is calculated for any radius for close to a ball a simple formula is given for all upper and lower bounds for are found the latter are easy to use even when is of a complicated shape

optimum shape design against flutter of a cantilevered column with an end mass of finite size subjected to a non conservative load abstract optimum design for dynamic stability of slender cantilevered columns subjected to a follower force due to a rocket thrust is investigated the aim is to determine the tapering of the column which maximizes the critical value of the rocket thrust at which flutter is initiated under the constraint of constant length and volume of the column the rocket thrust is assumed to be produced by a solid rocket motor mounted at the tip end of the column the rocket motor is simplified as a massive ball with the same material density as the column based on experimental evidence 1 2 it is argued that a mathematical model without damping gives the practical stability limit if internal and external damping is small and the rocket thrust acts only in a short interval of time optimum columns are determined for various sizes of the end ball rocket motor for small sizes the critical thrust can be significantly increased by optimization about eight times by practical experimental realizable values of the mass ratio mass of end ball mass of column the critical thrust can only be increased 1 3 1 4 times which is similar to the case of a pure conservative dead end load also it is found that the great sensitivity to small changes in design parameters which significantly complicates optimization of the pure beck s column is not present for practical values of it is argued then that the pure beck s column should be considered as a theoretical limit case of vanishing end mass

tiles in quasicrystals with cubic irrationality we determine completely all tiles of one dimensional cut and project quasicrystals which have a cubic irrationality as self similarity factor and are given in terms of connected rectangular acceptance windows it is shown that there are at least five and at most nine tiles and they are indicated explicitly depending on the lengths of the two acceptance windows in terms of which the quasicrystals are defined

sensitivity analysis for problems of dynamic stability abstract in mechanics as well as in physics the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters problems of dynamic stability for non conservative systems involve determination of eigenvalues and eigenvectors for these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses the main question relates to the change in flutter load as a function of change in stiffness mass boundary conditions or load distribution discretized as well as non discretized examples are presented in details

quasicrystals and icosians a family of quasicrystals of dimensions 1 2 3 4 governed by the root lattice e8 is constructed the use of the icosian ring found in the quaternions with coefficients in q square root 5 allows simultaneous interpretation of the construction both in physical space and as a result of the standard cut and projection method in double dimension icosians are seen to provide a natural co ordination scheme for these quasicrystals nested sequences of quasicrystals form systems whose symmetries are all derivable from inflational and reflective symmetries directly related to the arithmetic of the icosians the use of coxeter diagrams clarifies the amazing relationship of e8 and quasicrystal symmetries and leads to the fundamental chain e8 contains implies d6 contains implies a4 contains implies a1 a1 that underlies five fold symmetry in quasicrystals decomposition of quasicrystals into concentric shells and a counting formula for the cardinalities of these shells is discussed

adjusting for errors in classification and measurement in the analysis of partly and purely categorical data abstract this article examines a method of adjusting subgroup means when there are errors both in the allocation of elements to the subgroups and in the measurement of the response the advantages with the method are that it is simple it is also applicable when there are many subgroups and it requires no distributional assumptions for the response variable the method is compared to the maximum likelihood method for a dichotomous response and an example from the swedish level of living survey is given

vibration and stability of annular plates in non linear creep conditions abstract this paper presents a study on the influence of the physical non linearity of material in creep conditions on vibration and stability of non uniform annular plates subjected to a follower force radially distributed at the outer edge the stability analysis requires first the calculation of a membrane stress distribution and then the application of the kinetic stability criterion making use of small superposed vibrations the differential equations of the membrane and vibration states have been integrated by means of the transfer matrix method which allowed the determination of the relationships between the real and imaginary parts of the complex frequency and compressive force characteristic curves the results have been presented in numerous figures

inflation centres of the cut and project quasicrystals a rather general form of the conventional cut and project scheme is used to define quasicrystals as point sets in real n dimensional euclidean space the inflation or equivalently the self similarity properties of such quasicrystals are studied here assuming only the convexity of the acceptance window our result is a description of inflation centres of all types in a quasicrystal and a proof that our description is complete there are no other inflation centres for any chosen quasicrystal point internal inflation centre u its inflation properties are given as a set of scaling factors it turns out that the scaling factors form a one dimensional quasicrystal with a u dependent acceptance window scaling window the intersection of the scaling windows associated with all points of a quasicrystal is the one dimensional quasicrystal of universal internal scaling symmetries its acceptance window is the interval external inflation centres of a cut and project quasicrystal are those which are not among quasicrystal points their complete description is given analogically to the description of the internal ones imposing some additional requirements on the scaling factors between any two adjacent quasicrystal points one finds a countable infinity of external inflation centres the scaling factors belonging to any such centre u form an infinite u dependent subset of points of the quasicrystal with acceptance window containing

affine extension of noncrystallographic coxeter groups and quasicrystals unique affine extensions haff2 haff3 and haff4 are determined for the noncrystallographic coxeter groups h2 h3 and h4 they are used for the construction of new mathematical models for quasicrystal fragments with tenfold symmetry the case of haff2 corresponding to planar point sets is discussed in detail in contrast to the cut and project scheme we obtain by construction finite point sets which grow with a model specific growth parameter

the torus parametrization of quasiperiodic li classes the torus parametrization of quasiperiodic local isomorphism classes is introduced and used to determine the number of elements in such a class with special symmetries or inflation properties the method is explained in an illustrative fashion for some widely used tiling classes with golden mean rescaling namely for the fibonacci chain one dimensional the triangle and penrose patterns two dimensional and for kramer s and danzer s icosahedral tilings three dimensional we obtain a rather complete picture of the orbit structure within these classes and also discuss various general results

estimating strata means in double sampling with corrections based on second phase sampling an estimator for strata means is presented for double sampling for stratification where the first phase strata estimates are corrected by second phase subsampling a variance estimator is derived for the estimated strata weights and for the adjusted strata means these are compared with two bootstrap variance estimators in a simulation study the stratum mean estimator has negligible bias and either bootstrap variance estimator is clearly better than the classical estimator in estimating the true variance the variability of the strata weights is most reliably estimated by the classical variance estimator

self similar delone sets and quasicrystals in this paper we answer the question whether any delone set invariant under quasiaddition of berman and moody can be identified with a cut and project quasicrystal for any such set we find an acceptance window which is bounded but has only convex interior the cut and project quasicrystal is then identified with an affine image of constructive methods used in the paper allow one in principle to put bounds on from a given fragment of a delone set

densities minimal distances and coverings of quasicrystals quasicrystals are generalizaions of lattices in this spirit we consider here three kinds of geometric properties of mathematical models of quasicrystals minimal distances between quasicrystal points covering radii of quasicrystals and the densities of quasicrystal points

proving the deterministic period breaking of linear congruential generators using two tile quasicrystals we describe the design of a family of aperiodic prngs aprngs we show how a one dimensional two tile cut and project quasicrystal 2tqc used in conjunction with lcgs in an aprng generates an infinite aperiodic pseudorandom sequence in the suggested design any 2tqc corresponding to unitary quadratic pisot number combined with either one or two different lcgs can be used