wave based transfer matrix method for dynamic response of large net structures abstract wave based method for dynamic responses of net structures can provide analytic out of plane responses in full frequency range helping to avoid the problem of control spillover comparing with traditional modal analysis however as the scale of the net structure increases more computing resources are required here a wave based method inspired by transfer matrix method is proposed for both orthogonal and non orthogonal symmetric net structures according to the symmetric characteristics of the net structure we first divide the whole structure into several periodic elements and calculate the transfer matrix of the periodic element by using the basic wave based method then by multiplying transfer matrixes of the periodic element and using all the boundary condition of net structure the out of plane displacments of the net structure can be finally obtained our proposed wave based transfer matrix method is proved to be more accurate and efficient than the finite element analysis for large net structures

a miyawaki type lift for textit gspin 2 10 let mathfrak t 2 resp mathfrak t be the hermitian symmetric domain of textit spin 2 10 resp e 7 3 in previous work compos math 152 2 223 254 2016 we constructed holomorphic cusp forms on mathfrak t from elliptic cusp forms with respect to textit sl 2 mathbb z by using such cusp forms we construct holomorphic cusp forms on mathfrak t 2 which are similar to miyawaki lift constructed by ikeda duke math j 131 469 497 2006 in the context of symplectic groups it is conditional on the conjectural jacquet langlands correspondence from textit pgso 2 10 to textit pgso 6 6

the cohomology group associated with jacobi cusp forms over cayley numbers we consider the cohomology group associated with jacobi cusp forms over cayley numbers as an example of the general theory of the cohomology groups associated with cusp forms developed by eichler and shimura the theory establishes isomorphisms between the cohomology groups and the vector spaces of vector valued cusp forms and then expresses their common dimensions in terms of certain geometric invariants in the corresponding quotient spaces this is an analogue of the riemann roch theorem applied to the cases of vector valued modular forms

matrix analysis of statically and kinematically indeterminate frameworks abstract the paper is concerned with the structural mechanics of assemblies of bars and pinjoints particularly where they are simultaneously statically and kinematically indeterminate the physical significance of the four linear algebraic vector subspaces of the equilibrium matrix is examined and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces in particular this algorithm gives full details of any states of self stress and modes of inextensional deformation which an assembly may possess a scheme is devised for the segregation of inextensional modes into rigid body modes up to six of these may be allowed by the foundation constraints and internal mechanisms in some circumstances a state of self stress may impart first order stiffness to an inextensional mode a matrix method for detecting this effect is devised and it is shown that if there is no state of self stress which imparts first order stiffness to a given mode then that mode can undergo rather large distortion which involves either zero change in length of the bars or possibly changes in length of third or higher order in the displacements the significance of negative stiffness as indicated by the matrix method is discussed the paper contains simple examples which illustrate all of the main points of the work

invariant differential operators and eigenspace representations on an affine symmetric space let g h be an affine symmetric space of split rank r let d be a preferred polynomial algebra of g invariant differential operators on g h generated by r elements we show that the space of k finite joint eigenfunctions of d on g h form an admissible g k module which is called an eigenspace representation the main content of this paper is description of the algebras of invariant differential operators and determination of the eigenspace representations on g h we also obtain a poisson transform for t spherical eigenfunctions on g h by eisenstein integrals

hyperbolic weyl groups and the four normed division algebras we study the weyl groups of hyperbolic kac moody algebras of over extended type and ranks 3 4 6 and 10 which are intimately linked with the four normed division algebras k r c h o respectively a crucial role is played by integral lattices of the division algebras and associated discrete matrix groups our findings can be summarized by saying that the even subgroups w of the kac moody weyl groups w are isomorphic to generalized modular groups over k for the simply laced algebras and to certain finite extensions thereof for the non simply laced algebras this hints at an extended theory of modular forms and functions

dimensions of spaces of generalized spherical functions generalized spherical functions are defined to be joint eigenfunctions of some invariant differential operators with fixed k type on both sides on a semisimple lie group one of our main results is the same dimension formula for all spaces of generalized spherical functions which is independent of eigenvalues the other main result is proof of the existence of a global basis for all spaces of generalized spherical functions which is holomorphic in the parameter for the eigenvalues as an application we calculate the distribution characters of k bi finite eigenfunctions of the center of enveloping algebra for split groups

statical and dynamical response of cable nets abstract the statical and the dynamical behaviour of cable nets is studied fully constrained and underconstrained cable nets are considered the conditions for initial stability and the prestressing of the nets are formulated a method for the analysis of the nodal displacements and the change in the internal forces in the cables due to static loads is proposed the cases where linear algebra can be used are discussed the method is extended to consider the dynamical behaviour of the net its free dynamical response and forced vibration are investigated

a series of unitary irreducible representations induced from a symmetric subgroup of a semisimple lie group letg h be a semisimple symmetric space generalizing results of flensted jensen we give a sufficient condition for the existence of irreducible closed invariant subspaces of the unitary representations ofg induced from unitary finite dimensional representations ofh this provides a method of constructing unitary irreducible representations ofg and we show by examples that for some irreducible admissible representations ofg this method exhibits not previously known unitarity

zero stiffness tensegrity structures tension members with a zero rest length allow the construction of tensegrity structures that are in equilibrium along a continuous path of configurations and thus exhibit mechanism like properties equivalently they have zero stiffness the zero stiffness modes are not internal mechanisms as they involve first order changes in member length but are a direct result of the use of the special tension members these modes correspond to an infinitesimal affine transformation of the structure that preserves the length of conventional members they hold over finite displacements and are present if and only if the directional vectors of those members lie on a projective conic this geometric interpretation provides several interesting observations regarding zero stiffness tensegrity structures

the theory of jacobi forms over the cayley numbers m eie and a kriegabstract as a generalization of the classical theory of jacobi forms we discussjacobi forms on xc8 which are related with integral cayley numbers usingthe selberg trace formula we give a simple explicit formula for the dimensionof the space of jacobi forms the orthogonal complement of the space of cuspforms is shown to be spanned by certain types of eisenstein series