the induction coefficient of induced representation theory its algebra and an analytic expression the induction coefficient is defined as the element of a matrix reducing the induced representation into irreducible constituents the authors give the algebra of these coefficients and a closed analytic expression in terms of matrix elements of coset representatives the consequences of this choice are derived and the importance of some of these results for the racah wigner coupling algebra of the symmetric and unitary groups noted

the racah wigner approach to harmonic oscillations of the cluster of nodes of a cube the racah wigner approach is applied to demonstrate various group theoretic labelling schemes for modes of oscillations and elasticity parameters of the cluster of nodes of a cube it is shown that there exists a fundamental basis in the configuration space closed under the action of the group oh the geometric symmetry group of the equilibrium it provides a transparent interpretation of all basic invariants the fibre bundle and tensor product structure of invariant bilinear forms over the configuration space yields three classification schemes for elasticity parameters in a way that resembles racah recoupling of several angular momenta

naor yung paradigm with shared randomness and applications abstract the naor yung paradigm 63 allows to generically boost security under chosen plaintext attacks cpa to security against chosen ciphertext attacks cca for public key encryption pke schemes the main idea is to encrypt the plaintext twice under independent public keys and to append a non interactive zero knowledge nizk proof that the two ciphertexts indeed encrypt the same message later work by camenisch chandran and shoup 32 and naor and segev 28 30 established that the very same technique can also be used in the settings of key dependent message kdm and key leakage attacks respectively in this paper we study the conditions under which the two ciphertexts in the naor yung construction can share the same random coins we find that this is possible provided that the underlying pke scheme meets an additional simple property the motivation for re using the same random coins is that this allows to design much more efficient nizk proofs we showcase such an improvement in the random oracle model under standard complexity assumptions including decisional diffie hellman quadratic residuosity and subset sum the length of the resulting ciphertexts is reduced by 50 yielding truly efficient pke schemes achieving cca security under kdm and key leakage attacks as an additional contribution we design the first pke scheme whose cpa security under kdm attacks can be directly reduced to low density instances of the subset sum assumption our pke scheme supports key dependent messages computed via any affine function of the secret key

symmetry properties of direct sum systems an interpretation of double coset decompositions of groups is given in terms of the construction of systems from similar disjoint subsystems a natural labelling scheme is developed for the direct product states of systems of this type providing an extension of the concept of unique labelling an application of the decoupling transformation to finite direct sum systems is investigated

the random oracle methodology revisited we take a critical look at the relationship between the security of cryptographic schemes in the random oracle model and the security of the schemes that result from implementing the random oracle by so called cryptographic hash functions the main result of this article is a negative one there exist signature and encryption schemes that are secure in the random oracle model but for which any implementation of the random oracle results in insecure schemes in the process of devising the above schemes we consider possible definitions for the notion of a good implementation of a random oracle pointing out limitations and challenges

mixed and componentwise condition numbers of nonsymmetric algebraic riccati equation abstract in this paper the mixed and componentwise condition numbers of nonsymmetric algebraic riccati equation are considered the explicit expressions of two kinds of condition numbers are derived in the uniform manner and the upper bounds are proposed some simple numerical experiments show that the mixed and componentwise condition numbers can be sharp

norm estimations for the moore penrose inverse of multiplicative perturbations of matrices abstract let b be a multiplicative perturbation of a c m n given by b d 1 a d 2 where d 1 c m m and d 2 c n n are both nonsingular new norm upper bounds for b a f and b a 2 are derived where a and b are the moore penrose inverses of a and b respectively the main results of meng and zheng 2015 10 are improved in the cases of the frobenius norm and the spectral norm

condition numbers of the generalized sylvester equation this note is devoted to the perturbation analysis for the generalized sylvester equations ax yb dx ye c f which have some important applications in control and system theory expressions and upper bounds for normwise mixed and componentwise condition numbers are presented the results are illustrated by numerical examples

representations and computations of 2 3 we investigate full rank representations of 2 3 and 2 4 inverses with prescribed rank as well as with prescribed range and null space in an indefinite inner product space in certain particular cases we obtain new results or generalizations related with 2 3 and 2 4 inverses in a hilbert unitary space direct and iterative methods for computing 2 3 and 2 4 inverses in an indefinite inner product space are developed numerical examples with different metric matrices are presented

brief paper perturbation analysis and condition numbers of symmetric algebraic riccati equations this paper is devoted to the perturbation analysis of symmetric algebraic riccati equations based on our perturbation analysis the upper bounds for the normwise mixed and componentwise condition numbers are presented the results are demonstrated by our preliminary numerical experiments

the notion of security for probabilistic cryptosystems three very different formal definitions of security for public key cryptosystems have been proposed two by goldwasser and micali and one by yao we prove all of them to be equivalent this equivalence provides evidence that the right formalization of the notion of security has been reached

structure and representations of the hyperoctahedral group in this paper the main properties of the symmetry group of the n dimensional cube are reviewed and formulated with respect to possible applications in lattice theories the connection between the hyperoctahedral group wn and the orthogonal group o n is investigated by means of the canonical representation

on mixed and componentwise condition numbers for moore penrose inverse and linear least squares problems classical condition numbers are normwise they measure the size of both input perturbations and output errors using some norms to take into account the relative of each data component and in particular a possible data sparseness componentwise condition numbers have been increasingly considered these are mostly of two kinds mixed and componentwise in this paper we give explicit expressions computable from the data for the mixed and componentwise condition numbers for the computation of the moore penrose inverse as well as for the computation of solutions and residues of linear least squares problems in both cases the data matrices have full column row rank

on lattices learning with errors random linear codes and cryptography our main result is a reduction from worst case lattice problems such as gapsvp and sivp to a certain learning problem this learning problem is a natural extension of the learning from parity with error problem to higher moduli it can also be viewed as the problem of decoding from a random linear code this we believe gives a strong indication that these problems are hard our reduction however is quantum hence an efficient solution to the learning problem implies a quantum algorithm for gapsvp and sivp a main open question is whether this reduction can be made classical i e nonquantum we also present a classical public key cryptosystem whose security is based on the hardness of the learning problem by the main result its security is also based on the worst case quantum hardness of gapsvp and sivp the new cryptosystem is much more efficient than previous lattice based cryptosystems the public key is of size o n2 and encrypting a message increases its size by a factor of o n in previous cryptosystems these values are o n4 and o n2 respectively in fact under the assumption that all parties share a random bit string of length o n2 the size of the public key can be reduced to o n

branching rules for the weyl group w dn reduction theorems for the decomposition of induced and irreducible characters of w dn in terms of induced and irreducible characters of w dn 1 respectively are given

linear estimation in krein spaces i theory the authors develop a self contained theory for linear estimation in krein spaces the derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between krein space projection and the recursive computation of the stationary points of certain second order or quadratic forms the authors use the innovations process to obtain a general recursive linear estimation algorithm when specialized to a state space structure the algorithm yields a krein space generalization of the celebrated kalman filter with applications in several areas such as h sup spl infin filtering and control game problems risk sensitive control and adaptive filtering

combinatorial enumeration and group representations it is shown that in addition to the number of distinct equivalence classes the representation characters of a labelling can also be derived using standard combinatorial methods these characters provide additional information on the structure of the equivalence classes which is relevant in physical applications

branching processes in the annni model the mean field equations of the simple cubic annni model are studied on finite lattices the results are consistent with the sequence of distinct commensurate phases 2k 13 k 1 2 3 springing from the multiphase point found using low temperature series expansions moreover evidence for new structure combination branching processes is presented which generate phases of type 2l3 m 2l 13 n or 23l m 23l 1 n where l m and n are integers

the condition numbers for weighted moore penrose inverse and weighted linear least squares problem condition numbers play an important role in numerical analysis classical normise condition numbers are used to measure the size of both input perturbations and output errors in this paper we study the weighted normwise relative condition numbers for the weighted moore penrose inverse and the weighted linear least squares wls problems in the case of the full column rank matrix the bounds or formulas for the weighted condition numbers are presented the obtained results can be viewed as extensions of the earlier works studied by others

on the relations between irreducible representations of the hyperoctahedral group and o 4 and so 4 in this paper we describe the relations between the irreducible representations of the hyperoctahedral group in four dimensions and irreducible low dimensional representations of the orthogonal groups o 4 and so 4

on mixed and componentwise condition numbers for indefinite least squares problem in this paper we mainly consider the mixed and componentwise condition numbers for the indefinite least squares problem without constraints or with least squares constraints the explicit expressions and the easily computable upper bounds for these condition numbers are presented two numerical examples are given to test these results and illustrate their superiority compared with the corresponding normwise condition numbers furthermore we also provide the mixed and componentwise condition numbers for the moore penrose inverse in indefinite inner product spaces

the unique labelling of states via mackey s theorem a new approach to finding unique labels for many electron states in multicentre systems is described and a particular example eight electrons in s states on eight centres is worked out in detail this approach is shown to provide a labelling with a more direct physical interpretation than has previously been found

unique labelling of many electron states in multicentre systems general methods of generating complete sets of states for l or 2n electrons in s states on n centres are described it is shown that a unique labelling of these states can always be obtained using a fictitious sn symmetry of the n centres explicit descriptions of eight seven and four electrons on eight centres are derived and the problem of determining a unique labelling for these states on rigid eight centre structures with cubic and lower symmetry is solved

a pseudorandom generator from any one way function pseudorandom generators are fundamental to many theoretical and applied aspects of computing we show how to construct a pseudorandom generator from any one way function since it is easy to construct a one way function from a pseudorandom generator this result shows that there is a pseudorandom generator if and only if there is a one way function

structure and representations of the symmetry group of the four dimensional cube in this paper we give explicitly the description of the structure the characters and the complete system of irreducible representations of the hyperoctahedral group in four dimensions which we call w4 from the german wurfel in a second step we do the same for the subgroup sw4 which is formed by all pure rotations contained in w4

on the symmetry of logic embedding logical operations in non dissipative physical processes requires the use of reversible logic following feynman s 1986 approach the sixteen distinct truth tables of classical logic are shown to be contained in the 8 reversible logic operations covered by the symmetric group s8 which permute the eight values of three logical variables small subgroups of s8 are shown to cover respectively reversible logic reversible switching and reversible arithmetic a new universal primitive is found which generates a covering group of reversible logic it is shown that the octahedral group in four dimensions covers both reversible logic and switching and hence that the orthogonal group o 4 provides a covering group for quantum gates

unique labelling of symmetry coordinates and cyclic regions in crystals earlier work on unique labelling schemes in oh symmetry is extended to include 48 atom shells and the symmetry coordinates of shells subject to periodicity conditions a new approach to labelling is introduced based on the concept of cyclic regions in a crystal these are described by finite factor groups of the crystallographic space group which contain the isogonal group as a subgroup some examples are worked out in detail

the global symmetries of spin systems defined on abelian groups ii we consider the classification problem of the global symmetry groups of spin systems defined on abelian groups its implications on the generating functional the transfer matrix the hamiltonian formalism and factorization properties of spin systems are discussed the duality properties of spin systems defined on semidirect products of abelian groups are revisited in the first of this series of three papers we list the groups for systems defined on zp p prime z2 z2 and z2 z2 z2 manifolds they are direct or wreath products of m metacyclic groups and symmetric groups

structured mixed and componentwise condition numbers of some structured matrices structured matrices such as cauchy vandermonde toeplitz hankel and circulant matrices are considered in this paper we apply a kronecker product based technique to deduce the structured mixed and componentwise condition numbers for the matrix inversion and for the corresponding linear systems