precision aware self quantizing hardware architectures for the discrete wavelet transform this paper presents designs for both bit parallel bp and digit serial ds precision optimized implementations of the discrete wavelet transform dwt with specific consideration given to the impact of depth the number of levels of dwt on the overall computational accuracy these methods thus allow customizing the precision of a multilevel dwt to a given error tolerance requirement and ensuring an energy minimal implementation which increases the applicability of dwt based algorithms such as jpeg 2000 to energy constrained platforms and environments additionally quantization of dwt coefficients to a specific target step size is performed as an inherent part of the dwt computation thereby eliminating the need to have a separate downstream quantization step in applications such as jpeg 2000 experimental measurements of design performance in terms of area speed and power for 90 nm complementary metal oxide semiconductor implementation are presented results indicate that while bp designs exhibit inherent speed advantages ds designs require significantly fewer hardware resources with increasing precision and dwt level a four level dwt with medium precision for example while the bp design is four times faster than the digital serial design occupies twice the area in addition to the bp and ds designs a novel flexible dwt processor is presented which supports run time configurable dwt parameters

effect of deviatoric nonassociativity on the failure prediction for elastic plastic materials abstract this paper presents a theoretical study of the effect of nonassociativity of the plastic flow rule on the critical plastic modulus for discontinuous bifurcation in an elastic plastic material nonassociativity in both the spherical and the deviatoric spaces are considered with an emphasis on the effect of nonassociativity in the deviatoric space a particular form of nonassociativity in the deviatoric space is introduced where the projections of the plastic flow direction and the normal to the yield surface are assumed to have the same length but the projection of plastic flow direction is allowed to lag that of the normal by an angle it is shown that even for the simple yield surface of von mises nonassociativity in the deviatoric space can lead to a bifurcation for a load parameter significantly lower than the value predicted with an associated flow rule

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

biorthogonal systems for su4 su2 su2 sun son and sp4 u2 and analytical inversion symmetry analytical inversion symmetry of the biorthogonal systems of su4 contains implies su2 su2 sun contains implies son and sp4 contains implies u2 bases for two parametric covariant and mixed tensor irreducible representation is discovered this symmetry relates the dual isoscalar factors or resubducing coefficients it allowed us to invert by means of a special analytical continuation procedure the non orthogonal isofactors of sun contains implies son for couplings p0 0q to 0 and p10 p20 to 0 as well as the resubducing coefficients transformation brackets for expansion of the su3 contains implies so3 elliott basis states and sp4 contains implies u2 smirnov and tolstoy basis states in terms of the corresponding canonical basis states new expressions for bilinear combinations of sun contains implies son special isofactors are obtained expansion of su3 canonical basis states in terms of su3 contains implies so3 elliott states is found isofactors for coupling of two elliott states are given

discontinuous bifurcation states for associated smooth plasticity and damage with isotropic elasticity abstract for many constitutive equations the tangent tensor consists of a rank one modification to the isotropic elasticity tensor with a total of two elasticity parameters and one parameter describing the current state of inelasticity for small deformations general expressions are derived for the loss of ellipticity the corresponding normal to the bifurcation plane and the mode of discontinuous bifurcation for the velocity gradient if the principal basis of an evolution tensor is used the current stress or strain state is characterized by two additional parameters the small number of material and state parameters makes it feasible to use contour plots to iilustrate all possible combinations that can provide a discontinuous bifurcation these bifurcation maps can be used to illustrate the bifurcation properties of a particular plasticity or continuum damage constitutive model conversely the bifurcation maps can be used in conjunction with experimental data on bifurcation features to assist in the development of constitutive equations that provide the correct failure criterion for a given material under all possible stress paths

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

some 6 j symbols for symplectic and orthogonal groups by cerkaski s method the method devised by cerkaski 1987 has been used for the group sp 2n to find some 6 j symbols for which a single multiplicity index is required this approach possesses some advantages over that based on racah s techniques for so 3 the formulae for the 6 j symbols are comparatively simple and they automatically exhibit the symmetries of jucys 1973 elementary means are used to show that the eigenvalues of casimir s operator c2 for sp 2n are identical to those of c2 for o 2d if the authors take d n and replace the irreps of sp 2n by their transposed counterparts for o 2d where d is integral or half integral this enables the formulae for sp 2n to be used to generate expressions for some 6 j symbols for the orthogonal groups o 2d and so 2d illustrations are provided by so 2l 1 and o 4

combinatorics of transformations from standard to non standard bases in brauer algebras transformation coefficients between standard bases for irreducible representations of the brauer centralizer algebra and split bases adapted to the subalgebra f1 f2 f are considered after providing the suitable combinatorial background based on the definition of the i coupling relation on nodes of the subduction grid we introduce a generalized version of the subduction graph which extends the one given in chilla 2006 j phys a math gen 39 7657 for symmetric groups thus we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space an ordering relation on the grid is also given and then as in the case of symmetric groups the choices of the phases and of the free factors governing the multiplicity separations are discussed

algebraic expressions for some generalised 6 j symbols for so n and g2 a class of generalised 6 j symbols which enter naturally when a second pair of modes epsilon tau 2 is added to the octahedral jahn teller system gamma 8 epsilon tau 2 has been evaluated for the group so 5 the method involves the fictitious boson configurations dwd and can be readily generalised to lwl the resulting 6 j symbols for so 2l 1 can be used to produce others by means of generalisations of the equations satisfied by the ordinary 6 j symbols for so 3 extensions to so 2l 2 and g2 are described as well as the weight space symmetries of jucys 1973 the relation between 6 j symbols and isoscalar factors is illustrated for so 7 contains implies g2

the symmetric group algebraic formulas for some sf 6j symbols and sf sf1 sf2 3jm symbols explicit rank dependent expressions have been obtained for some symmetric group sf 6j symbols and some sf sf1 sf2 3jm symbols using butler s recursion method a key point in deriving these results is the use of the reduced notation introduced by murnaghan to label irreps various symmetries of the 6j and 3jm symbols have been imposed these include the complex conjugation permutation and transpose conjugation we incorporate a new symmetry that arises from the occurrence of the two isomorphic direct product groups sf1 sf2 and sf2 sf1 as subgroups of sf in relation to the tables of 6j and 3jm symbols presented a discussion is given of the symmetric group unitary group duality

strain localization short to long correlation length transition abstract the current study considers the problem of the strain localization as being a dynamic transition in the range of the correlation length using the particle dynamic method within the framework of statistical physics the proposed model re examines the assumptions and simplifications of the traditional quasi static continuum localization theories special attention is focused on the softening regime mystery of the vanishing fault width and the reasons for this pathological result the proposed model suggests an objective and physically acceptable measure of the fault width

two fast architectures for the direct 2 d discrete wavelet transform we propose two architectures for the direct two dimensional 2 d discrete wavelet transform dwt the first one is based on a modified recursive pyramid algorithm mrpa and performs a nonstandard decomposition i e mallat s 1989 tree of an n spl times n image in approximately 2n sup 2 3 clock cycles ccs this result consistently speeds up other known architectures that commonly need approximately n sup 2 ccs furthermore the proposed architecture is simpler than others in terms of hardware complexity subsequently we show how symmetric anti symmetric properties of linear phase wavelet filter bases can be exploited in order to further reduce the vlsi area this is used to design a second architecture that provides one processing unit for each level of decomposition pipelined approach and performs a decomposition in approximately n sup 2 2 ccs in many practical cases even this architecture is simpler than general mrpa based devices having only one processing unit

a partitioned modeling approach with moving jump conditions for localization abstract although many investigations have been performed on localization problems there still exist some pressing issues specifically it is difficult to show in general well posed governing equations based on the essential features of localization phenomena a partitioned modeling approach is proposed here via moving jump conditions for localization problems by taking the initial point of localization as that point where the type of the governing differential equation changes i e a hyperbolic to an elliptic type for dynamic problems and an elliptic to another elliptic type for static problems a moving boundary between localized and non localized deformation zones is defined through jump forms of conservation laws across the boundary as a result localization problems might be considered in the same category as shocks in fluids and solidification in heat transfer to illustrate the proposed procedure one dimensional analytical solutions are given with an emphasis on the definition of boundary conditions and the experimental means to determine model parameters associated with localization future research is then discussed on an extension to general cases

bifurcations in elastic plastic materials abstract when strain softening elastic plastic materials are loaded into the plastic regime they often exhibit deformations that are localized into small regions at some point in the loading process this intense localized deformation limits the formability of materials and will often quickly lead to failure with continued loading localized deformation is often associated with satisfaction of the classical discontinuous bifurcation criterion here we propose that the loss of strong ellipticity criterion should be used in place of the classical discontinuous bifurcation criterion as a necessary condition for localization the application of the strong ellipticity criterion implies that a bifurcation mode associated with loss of positive definiteness of the symmetric part of the acoustic tensor must be identified rather than a mode associated with the first zero eigenvalue of the acoustic tensor itself the eigensystem for the symmetric part of the tangent modulus tensor is obtained for several different plasticity models this eigensystem provides information about deformation modes associated with both diffuse and discontinuous bifurcations material properties boundary conditions and body geometry are all shown to affect the diffuse and localized deformation modes that are generated numerous experimental observations of necking and localization in metal specimens subject to various boundary conditions are explained with the proposed approach

decohesive carrying capacity of a disk under tension and in plane torsion abstract an elastic perfectly plastic circular disk with rigid circular inclusion of the radius a subjected to simultaneous uniform radial tension and in plane torsion is considered external radius of the disk is assumed to be infinitely large just to simplify the boundary conditions limit load carrying capacity of such a disk cannot be reached it is preceded by decohesive carrying capacity dcc defined by infinitely large radial strains e r they attain their upper bound for r a then the shearing strains r at r a increase infinitely as well in contradistinction to the limit carrying capacity the decohesive carrying capacity depends essentially on poisson s ratio v interaction curves corresponding to dcc are shown in the plane of external loadings a comparison with the condition of discontinuous bifurcation under uniform stresses and strains is given and full agreement is found though in the case under consideration the state of stress is evidently non uniform diagrams of stress and strain distribution at the moment of decohesion are also presented

on a class of 6j coefficients with one multiplicity index for groups sp 2n so 2n and so 2n 1 an important class of 6j symbols for the groups sp 2n so 2n and so 2n 1 with one nontrivial multiplicity index is investigated an appropriate choice of a basis in the multiplicity space is made and the so called canonical form for 6j symbols is obtained their expressions depending on the roots of an nth order equation and explicit expressions for some simple class of representations are obtained

uniqueness and localization i associative and non associative elastoplasticity abstract localization of deformation into a planar band in the incremental response of elasto plastic material is studied in the case of small strains and rotations the critical hardening modulus for localization is given in an explicit form uncoupled from the band normal for an arbitrary rate independent non associative plasticity loss of uniqueness of the response is investigated in terms of positiveness of the second order work density criteria for loss of second order work positiveness and localization are compared for plane stress and plane strain in these cases for the associative flow rule the threshold for the second order work positiveness coincides with the threshold for shear band formation this coincidence may not however occur if localization into splitting mode is attained

analytical and numerical tests for loss of material stability material instability occurs when ellipticity is lost for symmetric constitutive equations prior to loss of ellipticity it is possible that the second order work of hill or drucker becomes negative there are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second order work is not positive the instant that the second order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations the loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated an analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane numerical solutions are given for several sample problems for all cases the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost

simultaneity and reality of u n and su n 3jm and 6j symbols a simple proof is given of the simultaneous existence of a real set of 3jm and 6j symbols for the unitary groups u n and su n including the case of mixed tensor representations we observe that simultaneity is incompatible with the conventional permutation symmetries for u n with n 3 the relevance of these results to the schur weyl duality of u n with the symmetric groups sl is discussed

comments on loss of strong ellipticity in elastoplasticity the loss of strong ellipticity is analyzed for a rate independent infinitesimal elastoplastic model this local stability condition corresponds to the loss of positive definiteness of the symmetric part of the acoustic tensor first in the case of multisurface plasticity some expressions for the plastic hardening moduli are obtained for various bifurcation criteria next explicit expressions for the critical plastic hardening modulus and the critical orientation are obtained in the case of single surface plasticity hill type comparison solid the analysis is based on a geometric method linear isotropic elasticity and a general nonassociative flow rule are assumed however the principal axes of the second order tensors of the plastic potential and yield surfaces gradients are coaxial it is shown that similar to the loss of ellipticity the direction of the critical orientation is identical to one of the principal directions except in the particular case where the gradient of the plastic potential and yield surfaces each have a double eigenvalue in particular explicit expression for the plastic hardening modulus using the same geometric method is also presented for the raniecki type comparison solid as an illustrative example the critical orientation for the loss of strong ellipticity and the classical shear band localization loss of ellipticity are compared for axially symmetric compression and tension

efficient architectures for two dimensional discrete wavelet transform using lifting scheme novel architectures for 1 d and 2 d discrete wavelet transform dwt by using lifting schemes are presented in this paper an embedded decimation technique is exploited to optimize the architecture for 1 d dwt which is designed to receive an input and generate an output with the low and high frequency components of original data being available alternately based on this 1 d dwt architecture an efficient line based architecture for 2 d dwt is further proposed by employing parallel and pipeline techniques which is mainly composed of two horizontal filter modules and one vertical filter module working in parallel and pipeline fashion with 100 hardware utilization this 2 d architecture is called fast architecture fa that can perform j levels of decomposition for n n image in approximately 2n2 1 4 j 3 internal clock cycles moreover another efficient generic line based 2 d architecture is proposed by exploiting the parallelism among four subband transforms in lifting based 2 d dwt which can perform j levels of decomposition for n n image in approximately n2 1 4 j 3 internal clock cycles hence it is called high speed architecture the throughput rate of the latter is increased by two times when comparing with the former 2 d architecture but only less additional hardware cost is added compared with the works reported in previous literature the proposed architectures for 2 d dwt are efficient alternatives in tradeoff among hardware cost throughput rate output latency and control complexity etc

negative dimensional groups in quantum physics the author shows that an explicit definition of negative dimensional classical groups in terms of their action on grassmann representation spaces together with weyl s character formula for the grassmann tensorial representations of such groups leads to a framework in which some surprising negative dimensional properties of group theoretic invariants arise naturally as an application he shows that the spectra of the grassmann harmonic oscillator and of grassmann angular momentum are related to their bosonic counterparts by a simple analytic continuation in the dimension

on failure indicators in multidissipative materials abstract multi dissipative constitutive descriptions of irreversible material degradation result in tangent operators that are made up of multiple rank one updates of the elasticity tensors multisurface elastoplasticity plastic yielding combined with elastic degradation and multicrack models are representative examples the spectral properties of these tangent operators determine failure conditions at the material level in terms of loss of uniqueness and discontinuous bifurcation of the incremental response these failure properties are analysed herein by studying the eigensolution of the sum of n rank one m m matrices and the eigensolution of n rank one updates of the m m identity matrix whereby the tangent material tensors are written in matrix form analytical eigensolutions are presented and interpreted mechanically in terms of continuous and discontinuous failure indicators in the light of these spectral properties the failure indicators of single dissipative materials are revisited and explicit results are presented for double dissipative models in the form of plasticity combined with elastic damage in particular it is shown that the activation and interaction of two dissipation processes may destabilize the tangent operators beyond the state resulting from a single active mechanism

bounds and approximations for elastodynamic wave speeds in tetragonal media this paper presents an analytical study of elastodynamic waves propagating along an arbitrary direction in anisotropic materials with tetragonal symmetry upper and lower bounds are developed on the wave speeds through an additive decomposition of the acoustic tensor into an associated hexagonal counterpart and a rank one modification the eigenproperties of which can be determined analytically the bounds are obtained by applying the minimax property of eigenvalues linear approximations of the wave speeds are obtained from a first order expansion of the eigenvalues of the acoustic tensor with respect to a tetragonality index about the value of that index for which tetragonal symmetry degenerates to hexagonal symmetry a numerical example shows that the linear approximations agree remarkably well with the exact values of the wave speeds

on the axioms of plasticity abstract in the present paper some propositions usually considered as independent axioms in plasticity theory including ii yushin s postulate are obtained as consequences of a general axiomatic structure of continuum damage mechanics this fact indicates that continuum damage mechanics and plasticity theory have common conceptual foundations notwithstanding that their phenomenological manifestations are different for many aspects the formal framework used is able to consider different plasticity constitutive models and some of the non classical situations discussed recently in technical literature on the basic concepts of plasticity theory as the loss of convexity of the yield surface and the violation of ii yushin s postulate in non associative plasticity a comparative analysis with other proposals on foundations of plasticity in technical literature is developed

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

algebraic formulas for some nontrivial un 6j symbols and umn um un 3jm symbols we give tables of algebraic formulas for some nontrivial 6j symbols and 3jm symbols of the unitary groups the tables demonstrate that the building up method can be used successfully to obtain the rank dependence of unitary group j and jm symbols to emphasize the rank dependent nature of this calculation we have employed the composite young tableaux notation or back to back notation to label the unitary group irreps in using this notation the transpose conjugate symmetry of the corresponding composite young diagram leads to a new symmetry of the unitary group 6j and 3jm symbols the transposition of the groups um and un gives rise to a further symmetry of the 3jm symbols of umn um un

algebraic expressions for some multiplicity free 6j symbols and isoscalar factors for g2 generalized 6j symbols for g2 in which all four triangular conditions involve the seven dimensional irreducible representation irrep 10 are multiplicity free algebraic expressions depending on the highest weights of the accompanying irreps are found by using generalizations of the racah wigner algebra a rule is given for generalizing the so 3 phase factors the results are applied to finding algebraic expressions for a class of isoscalar factors for so 7 g2

efficient architectures for 1 d and 2 d lifting based wavelet transforms the lifting scheme reduces the computational complexity of the discrete wavelet transform dwt by factoring the wavelet filters into cascades of simple lifting steps that process the input samples in pairs we propose four compact and efficient hardware architectures for implementing lifting based dwts namely one dimensional 1 d and two dimensional 2 d versions of what we call recursive and dual scan architectures the 1 d recursive architecture exploits interdependencies among the wavelet coefficients by interleaving on alternate clock cycles using the same datapath hardware the calculation of higher order coefficients along with that of the first stage coefficients the resulting hardware utilization exceeds 90 in the typical case of a five stage 1 d dwt operating on 1024 samples the 1 d dual scan architecture achieves 100 datapath hardware utilization by processing two independent data streams together using shared functional blocks the recursive and dual scan architectures can be readily extended to the 2 d case the 2 d recursive architecture is roughly 25 faster than conventional implementations and it requires a buffer that stores only a few rows of the data array instead of a fixed fraction typically 25 or more of the entire array the 2 d dual scan architecture processes the column and row transforms simultaneously and the memory buffer size is comparable to existing architectures