from canonical tensor operators of su 3 and 3 to bi orthogonal coupling coefficients explicit expansion expansion of the matrix elements of su 3 and canonical tensor operators in terms of the bi orthogonal coupling coefficients and overlaps of the draayer akiyama construction are considered special bi orthogonal extremal isoscalar factors with subscripts as multiplicity labels and proportional to q racah q 6j coefficients or the generalized wilson rahman rational bi orthogonal functions in terms of balanced or hypergeometric series are used as a natural basis for extremal matrix elements of the highest weight component of the canonical tensor operators of su 3 in the generating function approach of biedenharn lohe and louck the expansion that is obtained triple sum together with previously derived asymmetric seed isofactors and elementary overlaps gives the explicit overlap coefficients and can be used to derive su 3 and canonical tensor operators as well as new explicit normalized seed isofactors with regge type symmetry specified for the minimal null space case

goal oriented error control in adaptive mixed fem for signorini s problem abstract this paper outlines goal oriented finite element error control for signorini s problem the discretization is based on a mixed formulation proposed by hlavacek et al which is extended to higher order polynomials a duality argument based on a variational inequality is applied which allows for the estimates in h as well as hp adaptivity numerical results confirm the applicability of the theoretical findings

transformation formula for a double clausenian hypergeometric series its q analogue and its invariance group a transformation formula for a double basic hypergeometric series of type 1 2 20 2 2 is derived this transformation yields a double series analogue of sears transformation for a terminating 3 2 series in the limit q 1 the formula reduces to a transformation for a terminating double clausenian hypergeometric series of unit argument one of the proper kampe de feriet series f1 2 20 2 2 1 1 this formula is a double series analogue of whipple s terminating 3f2 transformation this transformation gives rise to a transformation group the invariance group acting on the parameters of the double series the invariance group is examined and shown to be a subgroup of a double copy of the symmetries of the square

a note on the classification of the zeros of angular momentum coefficients closed form expressions for polynomial or nontrivial zeros of degree one of the clebsch gordan 3 j and the racah 6 j coefficients are presented and a conjecture regarding closed form formulas for the same is made

a reflective newton method for minimizing a quadratic function subject to bounds on some of the variables we propose a new algorithm a reflective newton method for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables this method applies to a general indefinite quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem our new method exhibits strong convergence properties global and quadratic convergence and appears to have significant practical potential strictly feasible points are generated experimental results on moderately large and sparse problems support the claim of practicality for large scale problems

higher order fem for the obstacle problem of the p laplacian a variational inequality approach abstract we consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p laplacian differential operator for p 1 we prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity moreover we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions all our results contain the known results for the linear case of p 2 we present numerical results on the improved convergence rates of adaptive schemes mesh size adaptivity with and without polynomial degree adaptation for the singular case of p 1 5 and for the degenerated case of p 3

comparison of mixed h p bem stabilized and non stabilized for frictional contact problems we present boundary integral equation procedures for contact problems with tresca or coulomb friction which are based on mixed formulations where besides the displacement also the traction on the contact boundary part appears as a lagrange multiplier this approach allows for an easy and efficient way to perform an h p be method by the use of biorthogonal basis functions this is especially suited for applying the semi smooth newton ssn method which is a very efficient solver superior to standard algorithm like uzawa with an adaptive algorithm we perform locally mesh refinements and increase of polynomial degrees for the be solution thus correctly representing the contact phenomena we also present as stabilized version of our mixed h p bem scheme with gauss lobatto lagrange basis which circumvents the discrete inf sup condition numerical results supporting our theory are reported

towards the canonical tensor operators of uq 3 ii the denominator function problem the explicit denominator normalization function of the canonical tensor operators of the quantum algebra uq 3 corresponding to the maximal null space case is derived ab initio in terms of double basic hypergeometric series which cannot be obtained as any q extension of the su 3 denominator polynomial gb 1 x in terms of multiple double or triple balanced hypergeometric series introduced by biedenharn louck and their collaborators although their q 1 versions are shown being equivalent the corresponding orthonormal seed isoscalar factors of the coupling wigner clebsch gordan coefficients of uq 3 and su 3 with multiple irreducible representations are presented conjectured expression of the q polynomials which ratios appear in the uq 3 and new su 3 denominator functions for an arbitrary value of the canonical multiplicity label t of the repeating irreducible representations in terms of multiple partition dependent q series extension of the maximal and minimal null space versions i

transformation and reduction formulae for double q clausen series of type φ1 1 μ1 2 λ abstract the sears transformations are employed to establish several general series transformations for double q clausen hypergeometric series of type 1 1 1 2 these transformations yield further a number of reduction and summation formulae on the double basic hypergeometric series

some formulae for double clausenian functions abstract for certain f q s s p r r x y functions with p r 3 and q s 2 reduction and transformation formulae under various conditions upon variables and parameters are derived from an euler integral representation that requires one relation between parameters

transformation and summation formulas for double hypergeometric series abstract a number of new transformation formulas for double hypergeometric series are presented the series appearing here are the so called kampe de feriet functions of type f1 1 20 3 4 1 1 and f0 2 21 2 2 1 1 the transformation formulas relate such double series to a single hypergeometric series of 4f3 1 type by specializing certain parameters a list of new summation formulas for f0 2 21 2 2 1 1 series is obtained the origin of the results comes from studying symmetries of the 9 j coefficient appearing in quantum theory of angular momentum

stabilized mixed hp bem for frictional contact problems in linear elasticity we analyze stabilized mixed hp boundary element methods for frictional contact problems for the lame equation the stabilization technique circumvents the discrete inf sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables we prove a priori convergence rates in the case of tresca friction using gauss legendre lagrange polynomials as test and trial functions for the lagrange multiplier additionally a residual based a posteriori error estimate for a more general class of discretizations is derived it in particular applies to discretizations based on bernstein polynomials for the discrete lagrange multiplier which we also analyze the discretization and the a posteriori error estimate are extended to the case of coulomb friction several numerical experiments underline our theoretical results demonstrate the behavior of the method and its insensitivity to the scaling and perturbations of the stabilization term

transformation and summation formulae for kampe de feriet series abstract euler s two transformations are employed to establish several general transformation formulae for double hypergeometric series these transformations yield further a number of reduction formulae for kampe de feriet series of types f 1 0 1 1 f 1 0 0 2 and f 1 0 2 0 by specializing certain parameters a list of new summation formulae for these kampe de feriet series are obtained

statistical analysis of word initial voiceless obstruents preliminary data a statistical procedure for classifying word initial voiceless obstruents is described the data set to which the analysis was applied consisted of monosyllabic words starting with a voiceless obstruent each word was repeated six times in the carrier phrase i can say again by each of ten speakers fast fourier transforms ffts using a 20 ms hamming window were calculated every 10 ms from the onset of the obstruent through the third cycle of the following vowel each fft was treated as a random probability distribution from which the first four moments mean variance skewness and kurtosis were computed moments were calculated from linear and bark transformed spectra data were pooled across vowel contexts for speakers of a given gender and input to a discriminant analysis using the moments calculated from the linear spectra 92 of the voiceless stops were classified correctly when dynamic aspects of the stop were included even more important the model constructed from the males data correctly classified about 94 of the voiceless stops produced by the female speakers classification of the voiceless fricatives when all places of articulation were included in the analysis did not exceed 80 correct when the moments from either the linear or bark transformed scales were used however classification of only the voiceless sibilants was 98 correct when the moments from the bark transformed spectra were used as with the stops the classification model held across gender

coupling coefficients of so n and integrals involving jacobi and gegenbauer polynomials the expressions for the coupling coefficients 3j symbols for most degenerate symmetric representations of orthogonal groups so n in a canonical basis with so n restricted to so n 1 and different semicanonical or tree bases with so n restricted to so n so n n n n are considered respectively in context of integrals involving triplets of the gegenbauer and the jacobi polynomials since the directly derived triple hypergeometric series do not reveal the apparent triangle conditions of the 3j symbols they are rearranged using their relation with semistretched isofactors of the second kind for the complementary chain sp 4 su 2 su 2 and analogy with the stretched 9j coefficients of su 2 into formulae with more rich limits for summation intervals and obvious triangle conditions the isofactors of class one representations of orthogonal groups or class two representations of unitary groups and of course the related integrals involving triplets of the gegenbauer and the jacobi polynomials turn into double sums in the cases of canonical so n so n 1 or u n u n 1 and semicanonical so n so n 2 so 2 chains as well as into the 4f3 1 series under more specific conditions some ambiguities of the phase choice of the complementary group approach are adjusted as well as problems with an alternating sign parameter of so 2 representations in the so 3 so 2 and so n so n 2 so 2 chains

multiple hypergeometric functions and 9 j coefficients it is well known that the 9 j recoupling coefficient appearing in the quantum theory of angular momentum has 72 symmetries however the triple sum series expression for the 9 j coefficient exhibits none of these symmetries here a stretched 9 j coefficient for which a closed form single term expression exists is considered and the type of summation theorems the triple sum series reduces is investigated for any of the 72 symmetries apart from well known single summation theorems for hypergeometric functions this analysis gives rise to new summation theorems for double and triple hypergeometric functions

hypergeometric series related to the 9 j coefficient of su 1 1 abstract we study various expressions for the 9 j coefficient of su 1 1 with an emphasis on multiple hypergeometric series an orthogonal polynomial in two discrete variables is associated to the 9 j coefficient some applications are considered dealing with formulas in which the 9 j coefficient appears as a connection or expansion coefficient and discussing some transformation formulas for double and triple hypergeometric series of unit argument

coupling regularization and adaptive hp bem for the solution of a delamination problem in this paper we couple regularization techniques with the adaptive hp version of the boundary element method hp bem for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions as a model example we treat the delamination of composite structures with a contaminated interface layer this problem has a weak formulation in terms of a nonsmooth variational inequality the resulting hemivariational inequality is first regularized and then discretized by an adaptive hp bem we give conditions for the uniqueness of the solution and provide an a priori error estimate furthermore we prove the very first a posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation thus enabling hp adaptivity various numerical experiments illustrate the behavior strengths and limitations of the proposed high order approximation scheme

multiplicity free uq n coupling coefficients the coupling wigner clebsch gordan coefficients of the unitary quantum algebras uq n are considered the tensorial properties of the generator powers and their ordered products used in the explicit projectors and weight lowering procedures are established different expressions for the multiplicity free isofactors of uq n coupling coefficients those coupling an arbitrary and symmetric representations are derived explicit expression of the arbitrary isofactors in terms of their boundary values are proposed proportionality of the semistretched isofactors to the stretched q recoupling coefficients of uq n 1 q analogues of 9j symbols is demonstrated the stretched isofactors of uq 3 are expressed in terms of clebsch gordan coefficients of uq 2

invariance groups of transformations of basic hypergeometric series we show that certain two term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups for the transformations of nonterminating 3 2 series and those of terminating balanced 4 3 series these invariance groups are symmetric groups for transformations of 2 1 series the invariance group is the dihedral group of order 12 transformations of terminating 3 2 series are described by means of some subgroup of s6 and finally the invariance group of transformations of very well poised nonterminating 8 7 series is shown to be isomorphic to the weyl group of a root system of type d5

the dual hahn q polynomials in the lattice and the q algebras and the dual q hahn polynomials in the non uniform lattice are obtained the main data for these polynomials are calculated the square of the norm of the coefficients of the three term recurrence relation etc as well as the lattice representation as a q hypergeometric series the connection with the clebsch gordan coefficients of the quantum algebras and is also given

6j symbols for symmetric representations of so n as the double series the corrected triple sum expression of alisauskas 1987 j phys a math gen 20 35 for the recoupling racah coefficients 6j symbols of the symmetric most degenerate representations of the orthogonal groups so n previously derived from the fourfold sum expression of alisauskas also related to the result of hormes and junker 1999 j phys a math gen 32 4249 is rearranged into three new different double sum expressions related to the hypergeometric kampe de feriet type series and a new triple sum expression with preferable summation condition the regge type symmetry of special 6j symbols of the orthogonal groups so n in terms of special kampe de feriet f1 41 3 series is revealed the recoupling coefficients for antisymmetric representations of symplectic group sp 2n are derived using their relation with the recoupling coefficients of the formal orthogonal group so 2n

explicit canonical tensor operators and orthonormal coupling coefficients of su 3 the canonical unit su 3 tensor operators are constructed by means of the stretched coupling of the auxiliary maximal and minimal null space tensor operators with the renormalization factors expressed in terms of the denominator functions of biedenharn gustafson lohe louck and milne the matrix elements of the maximal null space tensor operators are expressed with the help of the modified projection operators of asherova and smirnov the self conjugate minimal null space tensor operators are expressed in terms of the group generators with the help of the weight lowering operator technique the corresponding extreme isoscalar factors of the clebsch gordan wigner coefficients are used as constructive elements of the explicit recursive expression for the general orthonormal isoscalar factors of su 3 with its considerable simplication for the boundary values of parameters the general isofactors are also expanded in the different ways in terms of their boundary values the new classes of the generaliz

semiclassical mechanics of the wigner 6j symbol the semiclassical mechanics of the wigner 6j symbol is examined from the standpoint of wkb theory for multidimensional integrable systems to explore the geometrical issues surrounding the ponzano regge formula the relations among the methods of roberts and others for deriving the ponzano regge formula are discussed and a new approach based on the recoupling of four angular momenta is presented a generalization of the yutsis type of spin network is developed for this purpose special attention is devoted to symplectic reduction the reduced phase space of the 6j symbol the 2 sphere of kapovich and millson and the reduction of poisson bracket expressions for semiclassical amplitudes general principles for the semiclassical study of arbitrary spin networks are laid down some of these were used in our recent derivation of the asymptotic formula for the wigner 9j symbol

a note on the triple sum series for the 9j coefficient it is shown that the triple sum series of jucys and bandzaitis angular momentum theory in quantum physics vilnius mokslas 1977 for the 9j coefficient can be identified with a formal triple hypergeometric series due to lauricella saran srivastava g lauricella rend circ mat palermo 7 111 1893 l saran ganita 5 77 1954 h m srivastava ganita 5 97 1964

on clebsch gordan coefficients and matrix elements of representations of the quantum algebra uq su2 clebsch gordan coefficients and matrix elements of irreducible representations of the quantum algebra uq su2 were considered in several papers in particular a few expressions for them were derived an approach to clebsch gordan coefficients and to matrix elements of representations of uq su2 on the base of the theory of basic hypergeometric functions is given this approach allows one to obtain q analogs of all well known classical expressions for clebsch gordan coefficients most of them were absent new symmetry relations generating functions and recurrence formulas for clebsch gordan coefficients of uq su2 are obtained unlike other papers clebsch gordan coefficients and matrix elements are considered on the base of minimal theoretical constructions in fact without using the notion of a c algebra and of a hopf algebra

solutions of diophantine equations and degree one polynomial zeros of racah coefficients it is shown that the complete set of polynomial zeros of degree one of the racah coefficients can be obtained only from the full eight parameter solution of the multiplicative diophantine equation xyz uvw subject to the constraint z x y u v w all other parametric solutions obtained are shown to represent only proper subsets of the complete set

mixed finite element methods of higher order for model contact problems this paper presents mixed finite element methods of higher order for a simplified signorini problem and an idealized frictional problem the discretization is based on a mixed variational formulation proposed by haslinger et al which is extended to higher order finite elements to guarantee the unique existence of the solution of the mixed method a discrete inf sup condition is proven approximation results of the p method of finite elements and some inverse estimates for higher order polynomials are applied numerical results confirm the theoretical findings

acoustic characteristics of english fricatives this study constitutes a large scale comparative analysis of acoustic cues for classification of place of articulation in fricatives to date no single metric has been found to classify fricative place of articulation with a high degree of accuracy this study presents spectral amplitudinal and temporal measurements that involve both static properties spectral peak location spectral moments noise duration normalized amplitude and f2 onset frequency and dynamic properties relative amplitude and locus equations while all cues except locus equations consistently serve to distinguish sibilant from nonsibilant fricatives the present results indicate that spectral peak location spectral moments and both normalized and relative amplitude serve to distinguish all four places of fricative articulation these findings suggest that these static and dynamic acoustic properties can provide robust and unique information about all four places of articulation despite variation in speaker vowel context and voicing

group theoretical basis of some identities for the generalized hypergeometric series it is shown that thomae s identity between two 3f2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group s5 is an invariance group of this series a similar result is proved for the terminating saalschutzian 4f3 series where s6 is shown to be the invariance group of this series or s5 if one parameter is eliminated by using the saalschutz condition here bailey s identity is realized as a permutation of appropriately defined parameters finally the set of three term relations between 3f2 series of unit argument discovered by thomae j thomae j reine angew math 87 26 1879 and systematized by whipple f j whipple proc london math soc 23 104 1925 is shown to be transformed into itself under the action of the group s6 where is a two element group the 12 left cosets of s6 with respect to the invariance group s5 are the structural elements underlying the three

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

a note on the convergence of certain families of multiple hypergeometric series abstract in this sequel to an earlier work on the subject the authors present a further analysis of the convergence problem of kampe de feriet s double hypergeometric series and also of lauricella s multiple hypergeometric series when the arguments take on values on the boundaries of the known open regions of convergence of these series

on the algebra of coupled so 3 tensors the commutation relation for coupled so 3 tensor operators is constructed this gives rise to a lie algebra for which 9j symbols appear in the structure constants in an example it is shown how an exceptional lie subalgebra can be realized the closure requirement for the exceptional lie algebra does not seem to be related to nontrivial 9j symbols but rather to vanishings of relations involving 6j symbols

automatic generation of hypergeometric identities by the beta integral method in this article hypergeometric identities or transformations for p 1fp series and for kampe de feriet series of unit arguments are derived systematically from known transformations of hypergeometric series and products of hypergeometric series respectively using the beta integral method in an automated manner based on the mathematica package hyp as a result we obtain some known and some identities which seem to not have been recorded before in literature

new transformation and reduction formulae for double q clausen series abstract the sears transformations for non terminating 3 2 series are applied to derive several general series transformations for another two double q clausen series of type 2 0 1 2 and 2 0 0 3 further new transformations and reduction formulae are established for the basic clausen hypergeometric series in particular several bibasic reduction formulae are obtained

on the triple sum formula for wigner 9j symbols we give a new proof of the triple sum formula for wigner 9j symbols due to alisauskas and jucys the proof uses explicit expressions for the coupling kernels recently introduced by the author parts of our results generalize to general recoupling coefficients

another proof of the triple sum formula for wigner 9j symbols we give a simple proof of the alisauskas jucys triple sum formula for wigner 9j symbols

polynomial zeros of the 9 j coefficient it is shown that there exist polynomial or non trivial zeros for the 9 j coefficient a simple closed form expression for the polynomial zeros of degree one of the 9 j coefficient is derived from the triple sum series due to jucys and bandzaitis 1977 polynomial zeros of degree one of the 9 j coefficient are generated from either this closed form expression or from a set of parametric solutions of the multiplicative diophantine equations xyz uvw

towards the canonical tensor operators of uq 3 i the maximal null space case generalizing the su 3 canonical tensor operator concept biedenharn and louck to the quantum algebra uq 3 the wigner clebsch gordan coefficients of uq 3 with repeating irreducible representations are considered extremal projectors of the quantum algebra uq 3 in terms of the ordered generator polynomials are used for evaluation of the bilinear combinations of the uq 3 canonical isoscalar factors explicit expressions of the uq 3 isofactors corresponding to the maximal null space case of the uq 3 unit canonical tensor operators and their normalization factors denominator functions are presented the transposition and conjugation phase factors for the su 3 and uq 3 canonical isofactors are correlated with phases and zeros of boundary isofactors invariance of the canonical isofactors or absence of such invariance under interchange of the tensor operator and the initial or final state parameters is correlated with the existence and invariance or numerical degeneracy of the usual splitting

two hypergeometric summation formulae related to 9 j coefficients two summation formulae for special kampe de feriet functions f1 10 3 with variables 1 1 are proved

an algorithm to generate the polynomial zeros of degree one of the racah coefficients an algorithm is presented to enumerate the polynomial zeros of degree 1 of the racah 6j coefficients this algorithm is based on a diophantine equation linear in two variables obtained from a condition satisfied by the parameters in the parametrical formula of brudno for the polynomial zeros of degree 1 of the 6j coefficient

on the zeros of 3j coefficients polynomial degree versus recurrence order for 3j coefficients of su 2 two quantities the degree n and the order m are defined the first the polynomial degree n is well known as the number of terms in the polynomial part of the single sum expression of the 3j coefficient minus one the second the recurrence order m is new from an exhaustive computer search for non trivial zeros of 3j coefficients it follows that both quantities play an important role in classifying the zeros explicit formulae for all zeros of order 1 are obtained and several new infinite sequences of zeros related to pell equations are presented

hp adaptive ipdg tdg fem for parabolic obstacle problems for a parabolic obstacle problem two equivalent hp fem discretization methods based on interior penalty discontinuous galerkin in space and discontinuous galerkin in time are presented the first approach is based on a variational inequality vi formulation and the second approach on a mixed method in which the non penetration condition is resolved by a lagrange multiplier the discrete lagrange multiplier is a linear combination of biorthogonal basis functions allowing to write the discrete vi constraints as a set of complementarity problems employing a penalized fischer burmeister non linear complementarity function the discrete mixed problem can be solved by a locally q quadratic converging semi smooth newton ssn method the hierarchical a posteriori error estimator for the vi formulation which under the saturation assumption is both efficient and reliable allows hp adaptivity the numerical experiments show improved convergence compared to uniform and h adaptive meshes furthermore an a priori error estimate is given for the vi formulation

racah polynomials and a three term recurrence relation for the racah coefficients a three term recurrence relation is derived for the racah coefficients or 6 j symbols based on a set of orthogonal polynomials called racah polynomials that generalise these coefficients this relation is shown to be a consequence of the well known biedenharn elliot identity

generalized basic hypergeometric functions and the q analogues of 3 j and 6 j coefficients the racah wigner algebra for the quantum group suq 2 is developed to derive explicit expressions for the q analogues of the van der waerden racah wigner and majumdar forms of the 3 j coefficient given in terms of sets of basic hypergeometric functions interrelationships between the members of a given set of 3 phi 2 are established using the reversal of series or the q to q 1 operation starting with the van der waerden set using three transformations of 3 phi 2s 12 other sets including the racah wigner and majumdar sets have been obtained in the simpler case of the q analogue of the 6 j coefficients two sets of 4 phi 3s related to each other by reversal of series are obtained

stretched 9 j coefficients and summation theorems it is well known that the 9 j coefficient has 72 symmetries and that its simplest known form is the triple sum series which exhibits none of these symmetries a study of the expressions for the stretched 9 j coefficients stretched in the sense that that one or more of its six triangle inequality components are stretched via the triple sum series shows the existence of the 2f1 1 3f2 1 and the 4f3 1 summation theorems and reveals some new summation theorems as well

biorthogonal basis functions in hp adaptive fem for elliptic obstacle problems abstract in this paper the discretization of a non symmetric elliptic obstacle problem with h p adaptive h 1 conforming finite elements is discussed for this purpose a higher order mixed finite element discretization is introduced where the dual space is discretized via biorthogonal basis functions the h p adaptivity is realized via automatic adaptive mesh refinement based on a residual a posteriori error estimation which is also derived in this paper the use of biorthogonal basis functions leads to unilateral box constraints and componentwise complementarity conditions enabling the highly efficient application of a quadratically converging semi smooth newton scheme which can be modified to ensure global convergence h p adaptivity usually implies meshes with hanging nodes and varying polynomial degrees which have to be handled appropriately within the h 1 conforming finite element discretization this is typically done by using so called connectivity matrices in this paper a procedure is proposed which efficiently computes these matrices for biorthogonal basis functions finally the applicability of the theoretical findings is demonstrated with several numerical experiments

mixed finite element methods for two body contact problems this paper presents mixed finite element methods of higher order for two body contact problems of linear elasticity the discretization is based on a mixed variational formulation proposed by haslinger et al which is extended to higher order finite elements the main focus is on the convergence of the scheme and on a priori estimates for the h and the p method for this purpose a discrete inf sup condition is proven which guarantees the stability of the mixed method numerical results confirm the theoretical findings

normalized uq sl 3 gel fand weyl zetlin basis and new summation formulas for q hypergeometric functions an explicit realization of the normalized gel fand weyl zetlin gwz basis for uq sl 3 in terms of polynomial functions in three variables real or complex is given the construction uses two different realizations of the uq sl 3 unnormalized gwz basis which were given previously and whose transformation properties were not known it turns out that finding these properties enables us to find the gwz dependent proportionality constant between these two realizations the scalar product is also fixed by this in both unnormalized realizations and then by normalization the normalized gwz states are obtained as by products new summation formulas are obtained which seem new also for q 1 the main new formula is a double sum which is given in terms of the proportionality constant mentioned above this double sum can be written as single sum over a q 3f2 hypergeometric function or as a q hypergeometric function of two variables

four sets of 3f2 1 functions hahn polynomials and recurrence relations for the 3 j coefficients the wigner racah and majumdar sets of 3f2 1 are derived from the symmetric van der waerden set of 3f2 1 for the 3 j coefficient using a transformation due to erdelyi and weber 1952 which is also used to relate the 3 j coefficient to a discrete orthogonal hahn polynomial the four recurrence relations one old and three new obtained by karlin and mcgregor 1961 for the hahn polynomial are used to derive recurrence relations for the 3 j coefficient two of which have been shown to be useful in the exact recursive evaluation of the 3 j coefficients by schulten and gordon

an entry of ramanujan on hypergeometric series in his notebooks example 7 after entry 43 in chapter xii of the first notebook of srinivasa ramanujan is proved and more generally a summation theorem for 3f2 a a x 1 a 1 a n 1 where n is a nonnegative integer is derived

group theoretical basis for the terminating 3f2 1 series it is shown that a recursive use of the transformation for a terminating 3f2 1 series used by weber and erdelyi 1952 which belongs as shown by whipple 1925 to a set of equivalent 3f2 1 functions obtained by thomae 1979 results in a 72 element group associated with 18 terminating series the generators conjugacy classes invariant subgroups characters and dimensions of irreducible representations for this group are presented

the multiple sum formulas for 12j coefficients of su 2 and uq 2 the expressions for 12j coefficients of the both kinds without and with braiding of the su 2 group and the quantum algebra uq 2 are considered using dougall s summation formula of the very well poised hypergeometric 5f4 1 series and its q generalization several fourfold sum formulas with each sum related to the balanced 5f4 1 or 5 4 series for the q 12j coefficients of the second kind without braiding are derived applying q generalizations of rearrangement formulas of the very well poised hypergeometric 6f5 1 series which correspond to a new expression for the clebsch gordan coefficients of su 2 and uq 2 the new expressions with five sums of the 4f3 1 and 3f2 1 or 4 3 and 3 2 type are derived for the q 12j coefficients of the first kind with braiding instead of the usual expansions in terms of q 6j coefficients stretched and doubly stretched q 12j coefficients as triple double or single sums related to composed or separate hypergeometric 4f3 1 and 5f4 1 or 4 3 and 5 4 seri

transformation and summation formulas for kampe de feriet seriesf0 31 1 1 1 abstract the double hypergeometric kampe de feriet series f 0 3 1 1 1 1 depends upon 9 complex parameters we present three cases with 2 relations between those 9 parameters and show that under these circumstances f 0 3 1 1 1 1 can be written as a 4 f 3 1 series some limiting cases of these transformation formulas give rise to new summation results for special f 0 3 1 1 1 1 s the actual transformation results arose out of the study of 9 j coefficients

overlaps of the biorthogonal 3 coupling coefficients and related basic hypergeometric and other q factorial series the intermediate expansion technique is developed for the overlap coefficients of different biorthogonal coupled states and coupling coefficients of the quantum algebra and group su 3 with repeating irreducible representations and the role of separate basic and classical hypergeometric functions is demonstrated some expansion coefficients such as new prime overlap functions equivalent to the bilinear combinations of the different boundary isofactors are expressed in terms of the balanced saalschutzian basic or classical hypergeometric series these new overlap functions their analytical inversion some known triangular expansion matrices transition matrices related to definite racah coefficients the well poised or series and compositions of q factorial series resembling the well poised and series or equivalent to and series provide themselves as generators for mutual expansion of different non orthonormal systems of and su 3 isofactors which may be orthonormalized to the paracanonical or with a definite caution canonical version

transformation formulas for double hypergeometric series related to 9 j coefficients and their basic analogs in a recent paper alisauskas deduced different triple sum expressions for the 9 j coefficient of su 2 and suq 2 for a singly stretched 9 j coefficient these reduce to different double sum series using these distinct series we deduce a set of new transformation formulas for double hypergeometric series of kampe de feriet type and their basic analogs these transformation formulas are valid for rather general parameters of the series although a common feature is that all the series appearing here are terminating it is also shown that the transformation formulas deduced here generate a group of transformation formulas thus yielding an invariance group or symmetry group of particular double series

some multiple hypergeometric transformations and associated reduction formulas the main object of the present paper is to derive various classes of double series identities and to show how these general results would apply to yield some known or new reduction formulas for the appell kampe de feriet and lauricella hypergeometric functions of several variables a number of closely related linear generating functions for the classical jacobi polynomials are also investigated

algorithms for the polynomial zeros of degree 2 of the 3 j and the 6 j coefficients simple algorithms which are based on the principle of factorisation of an integer are proposed to generate the polynomial zeros of degree 2 of the 3 j and 6 j coefficients

acoustic cue weighting in the singleton vs geminate contrast in lebanese arabic the case of fricative consonants this paper is the first reported investigation of the role of non temporal acoustic cues in the singleton geminate contrast in lebanese arabic alongside the more frequently reported temporal cues the aim is to explore the extent to which singleton and geminate consonants show qualitative differences in a language where phonological length is prominent and where moraic structure governs segment timing and syllable weight twenty speakers ten male ten female were recorded producing trochaic disyllables with medial singleton and geminate fricatives preceded by phonologically short and long vowels the following acoustic measures were applied on the medial fricative and surrounding vowels absolute duration intensity fundamental frequency spectral peak and shape dynamic amplitude and voicing patterns of medial fricatives and vowel quality and voice quality correlates of surrounding vowels discriminant analysis and receiver operating characteristics roc curves were used to assess each acoustic cue s contribution to the singleton geminate contrast classification rates of 89 and roc curves with an area under the curve rate of 96 confirmed the major role played by temporal cues with non temporal cues contributing to the contrast but to a much lesser extent these results confirm that the underlying contrast for gemination in arabic is temporal but highlight tense fortis as a secondary feature

a p version finite element method for nonlinear elliptic variational inequalities in 2d this article introduces and analyzes a p version fem for variational inequalities resulting from obstacle problems for some quasi linear elliptic partial differential operators we approximate the solution by controlling the obstacle condition in images of the gauss lobatto points we show existence and uniqueness for the discrete solution up from the p version for the obstacle problem we prove the convergence of up towards the solution with respect to the energy norm and assuming some additional regularity for the solution we derive an a priori error estimate in numerical experiments the p version turns out to be superior to the h version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation

on the polynomial zeros of the clebsch gordan and racah coefficients it is shown that the symbolic binomial expansions for the clebsch gordan and racah coefficients are exact for n 1 where n 1 indicates the number of terms in the series expansions when exact these binomial forms reveal polynomial zeros of degree one which are trivial structure zeros hitherto considered as non trivial zeros along with polynomial zeros of degree or 2

a simple derivation of the quantum clebsch gordan coefficients for su 2 q to su 2 q the quantum deformation of su 2 the van der waerden method for calculating the clebsch gordan cg coefficients is genaralized the polynomial basis for irreducible representations of su 2 q the relevant polynomial invariants and the deduction of the q analog of the cg coefficients are given