production rate of the coarse grained gibbs entropy and the kolmogorov sinai entropy a real connection we discuss the connection between the kolmogorov sinai entropy hks and the production rate of the coarse grained gibbs entropy rg detailed numerical computations show that the often accepted identification of the two quantities does not hold in systems with intermittent behavior and or very different characteristic times and in systems presenting pseudochaos the basic reason for this is in the asymptotic with respect to time nature of hks while rg is a quantity related to short time features of a system

principal series of finite subgroups of su 3 we attempt to give a complete description of the exceptional finite subgroups 36 3 72 3 and 216 3 of su 3 with the aim to make them amenable to model building for fermion masses and mixing the information on these groups which we derive contains conjugacy classes proper normal subgroups irreducible representations character tables and tensor products of their three dimensional irreducible representations we show that for these three exceptional groups usage of their principal series i e ascending chains of normal subgroups greatly facilitates the computations and illuminates the relationship between the groups as a preparation and testing ground for the usage of principal series we study first the dihedral like groups 27 and 54 because both are members of the principal series of the three groups discussed in the paper

a holonomic systems approach to special functions identities abstract we observe that many special functions are solutions of so called holonomic systems bernstein s deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps this is partially substantiated by an algorithm that proves terminating hypergeometric series identities and that is given both in english and in maple

comments on the classification of the finite subgroups of su 3 many finite subgroups of su 3 are commonly used in particle physics the classification of the finite subgroups of su 3 began with the work of h f blichfeldt at the beginning of the 20th century in blichfeldt s work the two series c and d of finite subgroups of su 3 are defined while the group series 3n2 and 6n2 which are subseries of c and d respectively have been intensively studied there is not much knowledge about the group series c and d in this work we show that c and d have the structures and respectively furthermore we show that while the c groups can be interpreted as irreducible representations of 3n2 the d groups can in general not be interpreted as irreducible representations of 6n2

summation transformation and expansion formulas for bibasic series etude des extensions a deux bases de la formule de transformation d euler et de la formule de developpement de fields wimp etablissement d une formule de transformation a quatre bases independantes d une formule d inversion de lagrange et de quelques formules de sommation de degres 2 3 et 4

cocharacter sequences are holonomic abstract let c n n 0 be a codimension sequence of a characteristic zero p i algebra then the c n satisfy a linear homogenous recurrence relation whose coefficients are rational functions of n

simple finite non abelian flavor groups the recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two and three dimensional irreducible representations this paper details the mathematics of the two finite simple groups with such representations the icosahedral group a5 a subgroup of so 3 and psl2 7 a subgroup of su 3

on the characterization of the su 3 subgroups of type c and d we investigate the two classes of finite subgroups of su 3 that are called type c and d in the book of miller blichfeldt and dickson we present two theorems which fully determine the form of the generators in a suitable basis after exploring further properties of these groups we are able to construct a complete list of infinite series in which these groups are arranged for type c there are infinitely many series whereas for type d there are only two explicit examples of these series are presented which illustrate the general results

finite size lyapunov exponent review on applications in dynamical systems the growth of infinitesimal perturbations is well characterized by the lyapunov exponents in many situations of interest however important phenomena involve finite amplitude perturbations which are ruled by nonlinear dynamics out of tangent space and thus cannot be captured by the standard lyapunov exponents we review the application of the finite size lyapunov exponent fsle for the characterization of non infinitesimal perturbations in a variety of systems in particular we illustrate their usage in the context of predictability of systems with multiple spatio temporal scales of geophysical relevance in the characterization of nonlinear instabilities and in some aspects of transport in fluid flows we also discuss the application of the fsle to more general aspects such as chaos noise detection and coarse grained descriptions of signals this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

on the parametrization of certain finite groups and their representations we discuss a convenient way of parametrizing certain finite groups they comprise groups with abelian normal subgroups and central extensions thereof they include the groups dn t o and their double groups as well as the su 3 subgroups tn 3n2 6n2 72 216 36 and their z3 extensions the method allows for a rapid calculation of representations and coupling coefficients in particular it solves the multiplicity problem of nonsimply reducible groups we illustrate the method treating the hessian group 216 and its central extension

pi algebras and their cocharacters abstract all pi algebras r satisfy identities of the form f x y x 1 y 1 x 2 y 2 y n 1 x n theorem a the existence of these identities imply also that cocharacters x n r lie in a hook shaped strip of width depending on the degree of the minimal identity of r theorem c this extends a characterization of rings satisfying a capelli identity theorem b

on the finite subgroups of u 3 of order smaller than 512 we use the smallgroups library to find the finite subgroups of u 3 of order smaller than 512 which possess a faithful three dimensional irreducible representation from the resulting list of groups we extract those groups that cannot be written as direct products with cyclic groups these groups are the basic building blocks for models based on finite subgroups of u 3 all resulting finite subgroups of su 3 can be identified using the well known list of finite subgroups of su 3 derived by miller blichfeldt and dickson at the beginning of the 20th century furthermore we prove a theorem which allows us to construct infinite series of finite subgroups of u 3 from a special type of finite subgroups of u 3 this theorem is used to construct some new series of finite subgroups of u 3 the first members of these series can be found in the derived list of finite subgroups of u 3 of order smaller than 512 in the last part of this work we analyze some interesting finite subgroups of u 3 especially the group which is closely related to the important su 3 subgroup s4

generation of universal linear optics by any beam splitter universal quantum computers have proved difficult to build as one response researchers have proposed limited models of quantum computation which might be easier to realize three examples are the one clean qubit model of knill and laflamme 15 the commuting hamiltonians model of bremner jozsa and shepherd 3 and the boson sampling model of aaronson and arkhipov 1 none of these models are known or believed to be capable of universal quantum computation or depending on modeling details even universal classical computation but all of them can perform certain estimation or sampling tasks for which no polynomial time classical algorithm is known one obvious way to define a limited model of quantum computation is to restrict the set of allowed gates however almost every gate set is universal 17 and so are most natural gate sets for example controlled not together with any real one qubit gate that does not square to the identity is universal 21 as a result very few nontrivial examples of non universal gate sets are known all known non universal gate sets on o 1 qubits such as the clifford group 8 are efficiently classically simulable if the input and measurement outcomes both belong to an appropriately chosen qubit basis1 as a result it is tempting to conjecture that there does not exist such an intermediate gate set or more precisely that any gate set on o 1 qubits is either efficiently classical simulable with appropriate input and output states or else universal for quantum computing strikingly this dichotomy conjecture remains open even for the special case of 1and 2 qubit gates we regard proving or disproving the conjecture as an important open problem for quantum computing theory in this paper we prove a related conjecture in the quantum linear optics model in quantum optics the hilbert space is not built up as a tensor product of qubits instead it s built up as a direct sum of optical modes an optical gate is then just a unitary transformation that acts nontrivially ono 1 of the modes and as the identity on the rest whenever we have a k mode gate we assume that we can apply it to any subset of k modes in any order as often as desired the most common optical gates considered are beamsplitters which act on two modes and correspond to a 2 2 unitary matrix with determinant 1 2 and phaseshifters which act on one mode and simply apply a phase ei note that any unitary transformation acting on the one photon hilbert space automatically gets lifted by homomorphism to a unitary transformation acting on the hilbert space of n photons furthermore every element of the n photon linear optical group that is every n photon unitary transformation achievable using linear optics arises in this way see 1 sec iii for details of course if n 2 then there are also n photon unitaries that cannot be achieved linearoptically that is the n photon linear optical group is a proper subgroup of the full unitary group on the n photon hilbert space

sister celine s technique and its generalizations abstract sister celine fasenmyer s technique for obtaining pure recurrence relations for hypergeometric polynomials is formalized and generalized in various directions applications include algorithms for verifying any given binomial coefficients identity and any identities involving sums and integrals of products of special functions this is shown to lead to a new approach to the theory of special functions which allows a natural definition of special functions of several variables

slow relaxation in weakly open rational polygons the interplay between the regular piecewise linear and irregular vertex angle boundary effects in nonintegrable rational polygonal billiards of m equal sides is discussed decay dynamics in polygons of perimeter p m and small opening delta is analyzed through the late time survival probability s m approximately equal t delta two distinct slow relaxation channels are established the primary universal channel exhibits relaxation of regular sliding orbits with delta 1 the secondary channel is given by delta 1 and becomes open when m p m delta it originates from vertex order disorder dual effects and is due to relaxation of chaoticlike excitations

on generating series of finitely presented operads abstract given an operad p with a finite grobner basis of relations we study the generating functions for the dimensions of its graded components p n under moderate assumptions on the relations we prove that the exponential generating function for the sequence dim p n is differential algebraic and in fact algebraic if p is a symmetrization of a non symmetric operad if in addition the growth of the dimensions of p n is bounded by an exponent of n or a polynomial of n in the non symmetric case then moreover the ordinary generating function for the above sequence dim p n is rational we give a number of examples of calculations and discuss conjectures about the above generating functions for more general classes of operads

the flavor group δ 6n2 many non abelian finite subgroups of su 3 have been used to explain the flavor structure of the standard model in order to systematize and classify successful models a detailed knowledge of their mathematical structure is necessary in this paper we shall therefore look closely at the series of finite non abelian groups known as 6n2 its smallest members being s3 n 1 and s4 n 2 for arbitrary n we determine the conjugacy classes the irreducible representations the kronecker products as well as the clebsch gordan coefficients

the freedman group a physical interpretation for the su 3 subgroup d 18 1 1 2 1 1 of order 648 we study a subgroup fr 162 4 of su 3 of order 648 which is an extension of d 9 1 1 2 1 1 and whose generators arise from anyonic systems we show that this group is isomorphic to a semi direct product with respect to conjugation and we give a presentation of the group we show that the group d 18 1 1 2 1 1 from the series d in the existing classification for finite su 3 subgroups is also isomorphic to a semi direct product with respect to conjugation we next exhibit the isomorphism between both groups we prove that fr 162 4 is not isomorphic to the exceptional su 3 subgroup 216 3 of the same order 648 we further prove that the only su 3 finite subgroups from the 1916 classification by blichfeldt or its extended version in which fr 162 4 may be isomorphic belong to the d series finally we show that fr 162 4 and d 18 1 1 2 1 1 are both conjugate under the orthogonal matrix which we provide

finite flavour groups of fermions we present an overview of the theory of finite groups with regard to their application as flavour symmetries in particle physics in a general part we discuss useful theorems concerning group structure conjugacy classes representations and character tables in a specialized part we attempt to give a fairly comprehensive review of finite subgroups of so 3 and su 3 in which we apply and illustrate the general theory moreover we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of u 3 and finite subgroups of su 3 although in this review we give a detailed description of a wide range of finite groups the main focus is on the methods which allow the exploration of their different aspects

finite subgroups of su 3 we present a new class of finite subgroups of su 3 of the form zm s zn semidirect product we also apply the methods used to investigate semidirect products to the known su 3 subgroups 3n2 and 6n2 and give analytic formulae for representations characters and clebsch gordan coefficients

representations and clebsch gordan coefficients of z metacyclic groups we investigate finite groups of the form zmszn and give all irreducible representations and clebsch gordan coefficients in analytic form two subclasses are considered which seem to be inportant for applications the m metacyclic groups which are important for spin systems and the k metacyclic groups which are the smallest finite groups that have an irreducible representation of dimension p 1 where p is prime

some comments on finite subgroups of su 3 a recently published set of finite subgroups of su 3 is shown to contain some groups which are not subgroups of su 3 the others are subgroups of one of the dihedral like family of su 3 subgroups of order 3n2 some comments are made also on the structure of other finite subgroups previously listed