eigenvalue multiplicity in quartic graphs abstract let g be a connected cubic graph of order n with as an eigenvalue of multiplicity k we show that i if 1 0 then k 1 2 n with equality if and only if 1 and g is the petersen graph ii if 1 then k 1 2 n 1 with equality if and only if g k 4 iii if 0 then k 1 2 n 1 with equality if and only if g 2 k 3

complete lagrange family for the cube in finite element interpolations abstract noting a vagueness in the serendipity definition the complete lagrange family for the cube and the mixed complete lagrange family are introduced the unisolvent lagrange interpolations over rectangular finite elements are then presented definitively in hierarchy ranking expressions so that the polynominal completeness is realized with appropriately necessary minimum nodes the corresponding interpolation bases in the conventional form can easily be derived through the basis transformation without matrix inversion

on multiple eigenvalues of trees abstract let t be a tree of order n 6 with as a positive eigenvalue of multiplicity k star complements are used to show that i if k n 3 then 1 ii if 1 then without restriction on k t has k 1 pendant edges that form an induced matching the results are used to identify the trees with a non zero eigenvalue of maximum possible multiplicity

indecomposable representations of the nonlinear lie algebras on the two state heisenberg weyl basis the indecomposable representations of the nonlinear lie algebras of vector type r 0 1 one of which is generated by two angular momentum operators j0 j2 and any component of an irreducible tensor operator of rank 1 t 1 0 1 of an so 3 group are studied in detail we give the explicit expressions for the infinite dimensional indecomposable representations of r which further subduce the infinite dimensional indecomposable representations on the invariant subspaces and induce the finite dimensional or infinite dimensional indecomposable irreducible representations on the quotient spaces as special cases the standard angular momentum representations of r are given also

becchi rouet stora tyutin structure of polynomial poisson algebras the becchi rouet stora tyutin brst structure of polynomial poisson algebras is investigated it is shown that poisson algebras provide nontrivial models where the full brst recursive procedure is needed quadratic poisson algebras may already be of arbitrarily high rank explicit examples are provided for which the first terms of the brst generator are given the calculations are cumbersome but purely algorithmic and have been treated by means of the computer algebra system reduce our analysis is classical nonquantum throughout

on nonlinear angular momentum theories their representations and associated hopf structures nonlinear sl 2 algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases we construct their unitary irreducible representations in such a general context the linear sl 2 case as well as its q deformation are easily recovered as specific examples two other physically interesting applications corresponding to the so called higgs and quadratic algebras are also considered we show that these two nonlinear algebras can be equipped with a hopf structure

semi radial singularity mapping theory for line singularities in fracture mechanics abstract fundamental theory of the semi radial singularity mapping dealing with line singularities in the stress and strain is presented explicitly the brick type semi radial singularity mapping element as well as the wedge type one are proposed element familization is then described based on the conventional polynomial interpolations for the cube and simplex with examinations of the elaborate trial function spaces

on eigenvalue multiplicity and the girth of a graph suppose that g is a connected graph of order n and girth g n let k be the multiplicity of an eigenvalue of g sharp upper bounds for k are n g 2 when 1 0 and n g otherwise the graphs attaining these bounds are described

singular element construction using a mapping technique conformal mapping regularizes in the new plane the singular stress field around the crack tip so conventional finite elements can be used in the transformed plane the inverse mapping of the above elements gives another class of mapped elements the crack tip mapped element is a singular element thus using various elements the parent elements in the mapped plane we obtain an infinity of singular elements the product elements these singular elements are introduced naturally and have no defect as many other singular elements have

on bipartite graphs with complete bipartite star complements abstract let g be a bipartite graph with as an eigenvalue of multiplicity k 1 we show that if g has k r s 1 r s as a star complement for then k s 1 moreover if is non main then k s 2 for large enough s we provide examples of graphs in which various bounds on k or s are attained we also describe the bipartite graphs with k 1 s as a star complement for a non main eigenvalue of multiplicity s 1 1

eigenvalue multiplicity in triangle free graphs abstract let g be a connected triangle free graph of order n 5 with 1 0 as an eigenvalue of multiplicity k 1 we show that if d is the maximum degree in g then k n d 1 moreover if k n d 1 then either a g is non bipartite and k 2 3 1 2 2 1 with equality only if g is strongly regular or b g is bipartite and k d 1 with equality only if g is a bipolar cone in each case we discuss the extremal graphs that arise

higher order susy linearized nonlinear heisenberg algebras and coherent states using an iterative construction of the first order intertwining technique we find k parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below e0 it is seen that the natural ladder operators for these systems give place to polynomial nonlinear algebras and it is shown that these algebras can be linearized the coherent states construction is performed in the nonlinear and linearized cases

on some nonlinear extensions of the angular momentum algebra deformations of the lie algebras so 4 so 3 1 and e 3 that leave their so 3 subalgebra undeformed and preserve their coset structure are considered it is shown that such deformed algebras are associative for any choice of the deformation parameters their casimir operators are obtained and some of their unitary irreducible representations are constructed for vanishing deformation the unitary irreducible representations of the deformed algebras transform into those of the corresponding lie algebras that contain each of the so 3 unitary irreducible representations at most once it is also proved that similar deformations of the lie algebras su 3 sl 3 r and of the semidirect sum of an abelian algebra t 5 and so 3 do not lead to associative algebras

some general lagrange interpolations over simplex finite elements with reference to derivative singularities abstract for simplex finite elements the native lagrange family with arbitrarily placed nodes is presented in hierarchy ranking expressions it includes the well known complete lagrange family as well as the mid edge lagrange family to be proposed in this paper this new family enables us to utilize harmonious combinations of interpolations of different orders in finite element analysis as an application of developed simplex interpolations to fracture mechanics where some derivative singularities are needed we then describe the semi radial singularity mapping with examinations of peculiar trial function spaces

analytical integral formulae related to convex quadrilateral finite elements abstract analytical quadrature formulae for rational functions integrated over finite elements with quadrilateral geometry are presented definitively for second order differential equations these formulae produce algebraic finite element relations associated with the isoparametrical or subparametrical rectangular interpolations

the mapped elements for the solution of cracked bodies abstract using a conformal mapping the singular stress field around crack tips is transformed to a regular one with respect to the new variables thus the displacement field is approximated in the mapped plane the inverse mapping gives shape functions which are not polynomials the strain field obtained after a derivation of the displacement field has the appropriate square root singularity the elements constructed by using this procedure are called mapped elements this simple method was applied with excellent results to the solution of a series of problems

boson and differential realizations of polynomial angular momentum algebra the inhomogeneous multiboson and multivariable differential realizations of the polynomial angular momentum algebra of quadratic type l2 which may be seen as the nonlinear extension of an ordinary angular momentum algebra su 2 or its noncompact form su 1 1 are obtained from fock representations of l2 which are related to master representation of l2 on the space of its universal enveloping algebra u l2 or to induced representations on their respective quotient spaces u l2 ii with different left ideals ii

star complements in regular graphs old and new results we survey results concerning star complements in finite regular graphs and note the connection with designs and strongly regular graphs in certain cases we include improved proofs along with new results on stars and windmills as star complements

gauss jacobi quadrature rules for n simplex with applications to finite element methods abstract for numerical integrations over the n simplex the gauss jacobi quadrature operators are presented definitively it is demonstrated in finite element applications that the gauss jacobi quadratures could be highly effective under the isoparametric mapping as well as under the semi radial singularity mapping

quantum brst charge for quadratically nonlinear lie algebras we consider the construction of a nilpotent brst charge for extensions of the virasoro algebra of the form ta tb fabctc vabcdtctd classical algebras in terms of poisson brackets and ta tb habi fabctc vabcd tctd quantum algebras in terms of commutator brackets normal ordering of the product tctd is understood in both cases we assume that the set of generators ta splits into a set hi generating an ordinary lie algebra and remaining generators s such that only thevij are nonvanishing in the classical case a nilpotent brst charge can always be constructed for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent brst charge non trivial examples are the spin 3 algebra with central chargec 100 and theso n extended superconformal algebras with levels 2 n 3

on graphs with complete bipartite star complements abstract let be an eigenvalue of the graph g with multiplicity m a star complement for in g is an induced subgraph g x such that x m and is not an eigenvalue of g x some general observations concerning graphs with the complete bipartite graph k r s r s 2 as a star complement are followed by a complete analysis of the case r 2 s 5 the results include a characterization of the schlafli graph and the construction of all the regular graphs which have k 2 5 as a star complement

strings from n 2 gauged wess zumino witten models we present an algebraic approach to string theory an embedding ofsl 2 1 in a super lie algebra together with a grading on the lie algebra determines a nilpotent subalgebra of the super lie algebra chirally gauging this subalgebra in the corresponding wess zumino witten model breaks the affine symmetry of the wess zumino witten model to some extension of then 2 superconformal algebra the extension is completely determined by thesl 2 1 embedding the realization of the superconformal algebra is determined by the grading for a particular choice of grading one obtains in this way after twisting the brst structure of a string theory we classify all embeddings ofsl 2 1 into lie super algebras and give a detailed account of the branching of the adjoint representation this provides an exhaustive classification and characterization of both all extendedn 2 superconformal algebras and all string theories which can be obtained in this way

the relation between polynomial deformations of sl 2 r and quasi exact solvability a general method based on the polynomial deformations of the lie algebra sl 2 r is proposed in order to exhibit the quasi exact solvability of specific hamiltonians implied by quantum physical models this method using the finite dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on second harmonic generation

fundamental theory of the semi radial singularity mapping with applications to fracture mechanics abstract fundamental theory of the semi radial singularity mapping is presented which yields the necessary singularities in the stress and strain with bounded strain energy in particular the quadrilateral semi radial singularity mapping as well as the triangular one with collapse are described explicitly with some verification example in linear fracture mechanics the trial function spaces due to the conventional polynomial interpolations with these peculiar mappings are examined in detail

generalized lagrange family for the cube with special reference to infinite domain interpolations abstract as a general family allowing arbitrarily placed nodes the generalized lagrange family for the cube is presented in hierarchy ranking expressions this new family contains the well known regular mid edge and complete lagrange families as subfamilies the generalized lagrange interpolations are then applied to the infinite domain and the semi radial infinity mapping is proposed with examinations of elaborate trial function spaces