continuum modeling of the mechanical and thermal behavior of discrete large structures in the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss like repetitive structures once the actual structure is specified the construction procedure can be outlined by the following three steps a all sets of parallel members are identified b unidirectional effective continuum properties are derived for each of these sets and c orthogonal transformations are finally used to determine the contribution of each set to the overall effective continuum properties of the structure here the properties includes mechanical stiffnesses thermal coefficients of thermal expansions and material densities once expanded descriptions of the steps b and c are done the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods

yang mills connections over manifolds with grassmann structure let m be a manifold with grassmann structure i e with an isomorphism of the cotangent bundle t m e h with the tensor product of two vector bundles e and h we define the notion of a half flat connection w in a vector bundle w m as a connection whose curvature f s2e 2h end w 2t m end w under appropriate assumptions for example when the grassmann structure is associated with a quaternionic kahler structure on m half flatness implies the yang mills equations inspired by the harmonic space approach we develop a local construction of holomorphic half flat connections w over a complex manifold with holomorphic grassmann structure equipped with a suitable linear connection any such connection w can be obtained from a prepotential by solving a system of linear first order odes the construction can be applied for instance to the complexification of hyper kahler manifolds or more generally to hyper kahler manifolds with admissible torsion and to their higher spin analogs it yields solutions

on symmetry reductions of topological cohomological yang mills theories general aspects of symmetry reductions of topological cohomological yang mills theories are discussed it is shown that cohomological quantum field theories associated with the nahm equations can be derived from the donaldson witten theory by a symmetry reduction with respect to a three dimensional abelian group

magnificent four with colors we study the rank n magnificent four theory which is the supersymmetric localization of u n super yang mills theory with matter a super group u n n gauge theory on a calabi yau fourfold our theory contains the higher rank donaldson thomas theory of threefolds we conjecture an explicit formula for the partition function mathcal z and report on the performed checks the partition function mathcal z has a free field representation surprisingly it depends on the coulomb and mass parameters in a simple way we also clarify the definition of the instanton measure

shear deformation plate continua of large double layered space structures abstract a simple method is presented to model large rigid jointed lattice structures as continuous elastic media with couple stresses using energy equivalence in our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a taylor series about a suitable chosen origin the strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua equivalent continua for single layered grids double layered grids and three dimensional lattices are then obtained

q ary cascaded gmw sequences cascaded gmw sequences over gf q of arbitrary characteristic are investigated their periods are derived as compared with the existing results on such sequences substantially extended and improved theorems concerning their linear spans and autocorrelation functions are obtained a criterion and an algorithm for constructing cascaded gmw sequences that have much larger linear spans than gmw sequences with the same periods are given these provide a new class of complex valued sequences which have larger linear spans and two valued autocorrelation functions

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

new construction for families of binary sequences with optimal correlation properties we present a construction in a closed form for an optimal family of 2 sup m binary sequences of period 2 sup 2m 1 with respect to welch s 1974 bound whenever there exists a balanced binary sequence of period 2 sup m 1 with ideal autocorrelation property using the trace function this construction enables us to reinterpret a small set of kasami and no 1988 sequences as a family constructed from m sequences new optimal families of binary sequences are constructed from the legendre sequences of mersenne prime period hall s sextic residue sequences and miscellaneous sequences of unknown type in addition we enumerate the number of distinct families of binary sequences which are constructed from a given binary sequence by this method

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

on the moyal deformation of nahm equations in seven dimensions we show how the reduced anti self dual yang mills equations to seven dimensions described by the nahm equations can be carried over to the weyl wigner moyal formalism in the process some new solutions for the cases of gauge groups su 2 and sl 2 r are explicitly obtained

trace representation of legendre sequences of mersenne prime period in this correspondence it is shown that legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2 sup n elements whenever p 2 sup n 1 is prime for some n spl ges 3

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

autocorrelation values of generalized cyclotomic sequences of order two the generalized cyclotomic sequence of order two has several good randomness properties and behaves like the legendre sequence in several aspects we calculate the autocorrelation values of the generalized cyclotomic sequence of order two our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly

oxidation of self duality to 12 dimensions and beyond using partial curvature flows and the transitive action of subgroups of rm o d mathbb z on the indices 1 ldots d of the components of the yang mills curvature in an orthonormal basis we obtain a nested system of equations in successively higher dimensions d each implying the yang mills equations on d dimensional riemannian manifolds possessing special geometric structures this matryoshka of self duality equations contains the familiar self duality equations on riemannian fourfold as well as their generalisations on complex kahler threefold and on seven and eight dimensional manifolds with g2 and spin 7 holonomy the matryoshka allows enlargement oxidation to a remarkable system in 12 dimensions invariant under sp 3 there are hints that the underlying geometry is related to the sextonions a six dimensional algebra between the quaternions and octonions

effective constitutive relations for large repetitive frame like structures abstract effective mechanical properties for large repetitive frame like structures are derived using straight forward combinations of strength of material orthogonal transformation techniques once the actual structure is identified symmetry considerations are used in order to identify its independent property constants the actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps a all bask planar lattices are identified b effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods and c orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure

anti self duality of curvature and degeneration of metrics with special holonomy we study the structure of noncollapsed gromov hausdorff limits of sequences mni of riemannian manifolds with special holonomy we show that these spaces are smooth manifolds with special holonomy off a closed subset of codimension 4 additional results on the the detailed structure of the singular set support our main conjecture that if the mni are compact and a certain characteristic number c mni is bounded independent of i then the singularities are of orbifold type off a subset of real codimension at least 6

generalization of gmw sequences and no sequences gmw sequences and families of no sequences are generalized generalized gmw sequences have ideal autocorrelation and balance properties and generalized no sequences also have optimal correlation properties in terms of welch s lower bound the linear spans of the generalized gmw and no sequences appear to be large although there is not at present a closed form expression for the linear span a count of the numbers of cyclically distinct generalized gmw sequences and generalized no sequences that can be constructed is provided generalized gmw sequences have also been found in the literature by klapper et al 1993 under the name cascaded gmw sequences

topological twists of supersymmetric algebras of observables we explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras namely given a supersymmetric factorization algebra with a choice of a topological supercharge we construct an algebra over the operad of little disks we also explain the role of the twisting homomorphism allowing us to construct an algebra over the operad of framed little disks finally we give a complete classification of topological supercharges and twisting homomorphisms in dimensions 1 through 10

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

seiberg witten monopole equations on noncommutative r4 it is well known that due to vanishing theorems there are no nontrivial finite action solutions to the abelian seiberg witten sw monopole equations on euclidean four dimensional space r4 we show that this is no longer true for the noncommutative version of these equations i e on a noncommutative deformation r 4 of r4 there exist smooth solutions to the sw equations having nonzero topological charge we introduce action functionals for the noncommutative sw equations and construct explicit regular solutions all our solutions have finite energy we also suggest a possible interpretation of the obtained solutions as codimension four vortex like solitons representing d p 4 and d p 4 branes in a dp dp brane system in type ii superstring theory

binary sequences with optimal autocorrelation sequences have important applications in ranging systems spread spectrum communication systems multi terminal system identification code division multiple access communication systems global positioning systems software testing circuit testing computer simulation and stream ciphers sequences and error correcting codes are also closely related in this paper we give a well rounded treatment of binary sequences with optimal autocorrelation we survey known ones and construct new ones

complex sequences over gf p sup m with a two level autocorrelation function and a large linear span new complex sequences with elements are proposed that have constant absolute values of 1 the periodic autocorrelation functions of these sequences are shown to be two level the sequences are generated by three consecutive mapping processes the number of sequences of fixed length is determined which is larger than the number of binary sequences for cryptographical reasons the large linear span of the sequences is of great interest the linear span of the new sequences is examined and is proven to be larger than the linear span of complex m sequences if the parameters of the mapping processes are appropriately chosen the formula for generating the sequences is generalized to enlarge the linear span of sequences

g2 manifolds and associative submanifolds via semi fano 3 folds we construct many new topological types of compact g 2 manifolds i e riemannian 7 manifolds with holonomy group g 2 to achieve this we extend the twisted connected sum construction first developed by kovalev and apply it to the large class of asymptotically cylindrical calabi yau 3 folds built from semi fano 3 folds constructed previously by the authors in many cases we determine the diffeomorphism type of the underlying smooth 7 manifolds completely we find that many 2 connected 7 manifolds can be realised as twisted connected sums in a variety of ways raising questions about the global structure of the moduli space of g 2 metrics many of the g 2 manifolds we construct contain compact rigid associative 3 folds which play an important role in the the higher dimensional enumerative geometry gauge theory calibrated submanifolds approach to defining deformation invariants of g 2 metrics by varying the semi fanos used to build different g 2 metrics on the same 7 manifold we can change the number of rigid associative 3 folds we produce

the linear complexity of some binary sequences with three level autocorrelation binary sequences with good autocorrelation are needed in many applications a construction of binary sequences with three level autocorrelation was recently presented this construction is generic and powerful in the sense that many classes of binary sequences with three level autocorrelation could be obtained from any difference set with singer parameters the objective of this paper is to determine both the linear complexity and the minimal polynomial of two classes of binary sequences i e the class based on the singer difference set and the class based on the gmw difference set

special quantum field theories in eight and other dimensions we build nearly topological quantum field theories in various dimensions we give special attention to the case of eight dimensions for which we first consider theories depending only on yang mills fields two classes of gauge functions exist which correspond to the choices of two different holonomy groups in so 8 namely su 4 and spin 7 the choice of su 4 gives a quantum field theory for a calabi yau fourfold the expectation values for the observables are formally holomorphic donaldson invariants the choice of spin 7 defines another eight dimensional theory for a joyce manifold which could be of relevance in m and f theories relations to the eight dimensional supersymmetric yang mills theory are presented then by dimensional reduction we obtain other theories in particular a four dimensional one whose gauge conditions are identical to the non abelian seiberg witten equations the latter are thus related to pure yang mills self duality equations in 8 dimensions as well as to the n 1 d 10 super yang mills theory we also exhibit a theory that couples 3 form gauge fields to the second chern class in eight dimensions and interesting theories in other dimensions