on a conjecture of gluck let mathbf f g and b g respectively denote the fitting subgroup and the largest degree of an irreducible complex character of a finite group g a well known conjecture of d gluck claims that if g is solvable then g mathbf f g le b g 2 we confirm this conjecture in the case where mathbf f g is coprime to 6 we also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure

a fast expected time algorithm for the 2 d point pattern matching problem point set pattern matching is an integral part ofmany pattern recognition problems we study a randomized algorithm f or the alignment approach to model based recognition under certain mild assumptions we show that ifour scene is a set of n points and our model is a set of min points our algorithm has expected running time o n log m 3 2 for 5nding an occurrence of the model in the scene this is signi5cantly faster than any existing algorithms in the literature we then describe some experimental results on randomly generated data using a practical version ofour algorithm these results agree well with the theoretical analysis 2004 pattern recognition society published by elsevier ltd all rights reserved

ant colony optimization based binary search for efficient point pattern matching in images abstract point pattern matching ppm is a task to pair up the points in two images of a same scene there are many existing approaches in literature for point pattern matching however the drawback lies in the high complexity of the algorithms to overcome this drawback an ant colony optimization based binary search point pattern matching acobsppm algorithm is proposed according to this approach the edges of the image are stored in the form of point patterns to match an incoming image with the stored images the ant agent chooses a point value in the incoming image point pattern and employs a binary search method to find a match with the point values in the stored image point pattern chosen for comparison once a match occurs the ant agent finds a match for the next point value in the incoming image point pattern by searching between the matching position and maximum number of point values in the stored image point pattern the stored image point pattern having the maximum number of matches is the image matching with the incoming image experimental results are shown to prove that acobsppm algorithm is efficient when compared to the existing point pattern matching approaches in terms of time complexity and precision accuracy

stability properties of solutions of linear second order differential equations with random coefficients abstract the equation x a 2 t x 0 a t a k 0 if t k 1 t t k k n is considered where a k k 1 is given and t k k 1 is a random sequence sufficient conditions are proved which guarantee either stability or instability for the zero solution stability means that all solutions almost surely tend to zero as t by instability we mean that the sequence of the expected values of the amplitudes of every solution tends to infinity as k it turns out that a k k implies stability for all absolutely continuous distributions and for the overwhelming majority of the singular distributions the instability theorem is applied to the problem of random swinging when a k k 1 is periodic with two different terms meissner s equation and t k t k 1 k 1 are independent identically distributed random variables the application gives conditions for stochastic parametric resonance

improving explicit bounds for the solutions of second order linear differential equations this paper improves the algorithm for the construction of explicit bounds for the solutions of second order linear differential equations of the type p x y x q x y x 0 p x q x 0 x x 0 described in a recent paper of the authors the main improvements come from the introduction of new functionals devised by trevisan and from the application of an enhanced version of the mean value theorem for integrals when some functions of the integrand are monotonic

quadratic rational solvable groups abstract a finite group g is quadratic rational if all its irreducible characters are either rational or quadratic if g is a quadratic rational solvable group we show that the prime divisors of g lie in 2 3 5 7 13 and no prime can be removed from this list more generally if g is solvable and the field q generated by the values of over q satisfies q q k for all irr g then the set of prime divisors of g is bounded in terms of k also we prove that the degree of the field generated by the values of all characters of a semi rational solvable group see chillag and dolfi 2010 1 or a quadratic rational solvable group over q is bounded giving a positive answer to a question by d chillag and s dolfi

accurate continuous numerical solutions of time dependent mixed partial differential problems in this paper a separation of variables method for the solution of time dependent problems of the type u t t c t u x x 0 0 subject to u 0 t u p t 0 and u x 0 x u t x 0 g x is developed first an exact series solution of the problem is given given an admissible error e 0 and a bounded domain d t x t 0 x p 0 t t a continuous numerical solution is constructed so that the approximation error is uniformly upper bounded by e in d t

new bounds for the solutions of second order linear differential equations this paper presents a new method to construct explicit bounds for the solutions of second order linear differential equations of the type p x y x q x y x 0 p x q x 0 x x 0 which complements the method described in recent papers of the authors the method lies in the use of beesack s version of opial s inequality some results on asymptotics of the solution for the case p x 1 are also included

fuchsian groups finite simple groups and representation varieties let be a fuchsian group of genus at least 2 at least 3 if is non oriented we study the spaces of homomorphisms from to finite simple groups g and derive a number of applications concerning random generation and representation varieties precise asymptotic estimates for hom g are given implying in particular that as the rank of g tends to infinity this is of the form g 1 o 1 where is the measure of we then prove that a randomly chosen homomorphism from to g is surjective with probability tending to 1 as g combining our results with lang weil estimates from algebraic geometry we obtain the dimensions of the representation varieties text hom gamma bar g where bar g is gl n k or a simple algebraic group over k an algebraically closed field of arbitrary characteristic a key ingredient of our approach is character theory involving the study of the zeta function g s 1 s where the sum is over all irreducible complex characters of g

upper bound on the characters of the symmetric groups let c be a conjugacy class in the symmetric group s n and be a partition of n let f be the degree of the irreducible representation s c the character of s at c and r c the normalized character c f we prove that there exist constants b 0 and 1 q 0 such that for n 4 for every conjugacy class c in s n and every irreducible representation s of s n r c max q 1 n 1 n b supp c where supp c is the number of non fixed digits under the action of a permutation in c 1 is the size of the largest part in and 1 is the number of parts in the proof is obtained by enumeration of rim hook tableaux the hook formula and probabilistic arguments combinatorial algebraic and statistical applications follow this result in particular we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes

some characterizations of the weil representations of the symplectic and unitary groups abstract let g be a finite symplectic or unitary group we characterize the weil representations of g via their restriction to a standard subgroup then we complete the determination of complex representations of g with specific minimal polynomials of certain elements by showing that they coincide with the weil representations

fast algorithm for point pattern matching invariant to translations rotations and scale changes abstract based on 2 d cluster approach a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters scaling s and rotation on a two parameter space s experiments are conducted both on real and synthetic data the experimental results show that the proposed matching algorithm can handle translation rotation and scaling differences under noisy or distorted condition the computational time is just about 0 5 s for 50 to 50 point matching on sun 4 workstation

on first order neutral differential equations of euler form with unbounded delays abstract in this paper we investigate the first order neutral differential equation of euler form with variable unbounded delay d d t x t cx t 1 t i 1 n p i x i t 0 t t 0 0 where 0 c 1 0 1 0 i 1 and p i 0 are constants i 1 2 n some necessary and sufficient as well as explicit sufficient conditions for the oscillation of all solutions are established several relevant results in the literature are improved

labeled point pattern matching by delaunay triangulation and maximal cliques abstract in many problems of pattern recognition objects in an image may be efficiently represented by a set of labeled points this paper describes a method for matching labeled point patterns with one of the prototypes the delaunay triangulation is used to partition a point pattern into a set of triangles and the largest maximal clique of the consistency graph for each triangle is used to obtain the largest set of mutually consistent point pairs the proposed method is invariant under affine transformation of point patterns and allows for additions and deletions of points and some random perturbations in their relative locations the method is applied to the matching of constellations

approximate geometric pattern matching under rigid motions we present techniques for matching point sets in two and three dimensions under rigid body transformations we prove bounds on the worst case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst case bounds

explicit bounds for the solutions of second order linear differential equations this paper deals with the construction of explicit bounds for solutions of second order linear differential equations of the type p x y x q x y x 0 p x q x 0 x x 0 the construction is based on the study of the evolution of two complementary functionals involving y x in the sequence of zeroes of y x and y x based on that both a theoretical bound and an algorithm to explicitly calculate that bound are presented an illustrative example shows that the bounds proposed here improve previous results

mixed problems for separated variable coefficient wave equations analytic numerical solutions with a priori error bounds this paper deals with the construction of accurate analytic numerical solutions of mixed problems related to the separated variable dependent wave equation utt b t a x uxx 0 0 based on the study of the growth of eigenfunctions of the underlying sturm liouville problems an exact theoretical series solution is firstly obtained explicit bounds allow truncation of the series solution so that the error of the truncated approximation is less than e1 in a bounded domain d x t 0 x l 0 t d since the approximation involves only a finite number of exact eigenvalues i2 1 i n0 the admissible error for the approximated eigenvalues i2 1 i n0 is determined in order to construct an analytical numerical solution of the mixed problem involving only approximated eigenvalues i2 so that the total error is less than e uniformly in d uniqueness of solutions is also treated

character degrees and random walks in finite groups of lie type for a finite group h let irr h denote the set of irreducible characters of h and define the zeta function zeta h t sum chi in irr h chi 1 t for real t 0 we study the asymptotic behaviour of zeta h t for finite simple groups h of lie type and also of a corresponding zeta function defined in terms of conjugacy classes applications are given to the study of random walks on simple groups and on base sizes of primitive permutation groups

on character tables of wreath products the theory of characters of wreath products of finite groups is very well known the basic fact is that any invariant irreducible character of the base group is extendible to the wreath product and an extension can be computed explicitly in this paper we shall study the character table of a wreath product as a whole rather than single characters we shall prove that the character table of a wreath product g a is determined uniquely by the permutation group a and the character table of g this result provides a powerful tool for increasing the derived length of a group while keeping its character table under control we shall employ it in section 4 to construct pairs g h of groups with identical character tables and derived lengths n and n 1 for any given natural number n 2

labeled point pattern matching by fuzzy relaxation abstract a method of matching labeled point patterns is described on the basis of a fuzzy relaxation the method is applicable to labeled point patterns which differ by geometrical transformations such as translation rotation and scale change in this method the point pairs are considered to be the pattern primitives the pattern primitives are geometrically transformed in the process of relaxation so as to minimize a measure of mismatch between the primitive pairs the compatible primitive pairs between the two labeled point patterns are established after only a few iterations of relaxation and the corresponding points are obtained from the primitive pairs as an example the method is applied to the matching of constellations

upper bounds for the number of conjugacy classes of a finite group abstract for a finite group g let k g denote the number of conjugacy classes of g we prove that a simple group of lie type of untwisted rank l over the field of q elements has at most 6 q l conjugacy classes using this estimate we show that for completely reducible subgroups g of gl n q we have k g q 10 n confirming a conjecture of kovacs and robinson for finite groups g with f g a p group we prove that k g cp a where p a is the order of a sylow p subgroup of g and c is a constant for groups with o p g 1 we obtain that k g g p this latter result confirms a conjecture of iranzo navarro and monasor we also improve various earlier results concerning conjugacy classes of permutation groups and linear groups as a by product we show that any finite group g has a soluble subgroup s and a nilpotent subgroup n such that k g s and k g n 3

fuchsian groups coverings of riemann surfaces subgroup growth random quotients and random walks abstract fuchsian groups acting as isometries of the hyperbolic plane occur naturally in geometry combinatorial group theory and other contexts we use character theoretic and probabilistic methods to study the spaces of homomorphisms from fuchsian groups to symmetric groups we obtain a wide variety of applications ranging from counting branched coverings of riemann surfaces to subgroup growth and random finite quotients of fuchsian groups as well as random walks on symmetric groups in particular we show that in some sense almost all homomorphisms from a fuchsian group to alternating groups an are surjective and this implies higman s conjecture that every fuchsian group surjects onto all large enough alternating groups as a very special case we obtain a random hurwitz generation of an namely random generation by two elements of orders 2 and 3 whose product has order 7 we also establish the analogue of higman s conjecture for symmetric groups we apply these results to branched coverings of riemann surfaces showing that under some assumptions on the ramification types their monodromy group is almost always sn or an another application concerns subgroup growth we show that a fuchsian group has n o 1 index n subgroups where is the measure of and derive similar estimates for so called eisenstein numbers of coverings of riemann surfaces a final application concerns random walks on alternating and symmetric groups we give necessary and sufficient conditions for a collection of almost homogeneous conjugacy classes in an to have product equal to an almost uniformly pointwise our methods involve some new asymptotic results for degrees and values of irreducible characters of symmetric groups

asymptotic behaviour of the solutions of second order functional differential equations abstract this paper presents integral criteria to determine the asymptotic behaviour of the solutions of second order nonlinear differential equations of the type y x q x f y x 0 with q x 0 and f y odd and positive for y 0 as x tends to it also compares them with the results obtained by chanturia 1975 in 11 for the same problem

complex group algebras of finite groups brauer s problem 1 abstract brauer s problem 1 asks the following what are the possible complex group algebras of finite groups it seems that with the present knowledge of representation theory it is not possible to settle this question the goal of this paper is to present a partial solution to this problem we conjecture that if the complex group algebra of a finite group does not have more than a fixed number m of isomorphic summands then its dimension is bounded in terms of m we prove that this is true for every finite group if it is true for the symmetric groups the problem for symmetric groups reduces to an explicitly stated question in number theory or combinatorics

the existence of positive solutions to neutral differential equations abstract in this paper we shall consider a class of neutral differential equations of the form x t r t r t x t q t x t 0 t t 0 where 0 0 q t c t0 r r t c t0 0 with r t nondecreasing on t0 we shall show that all positive solutions of can be classified into four types a b c and d and we shall obtain sufficient and necessary conditions for the existence of a type b type and d type positive solutions of respectively a sufficient condition for the existence of c type positive solutions of is also given finally we shall offer a sharp oscillation result for all solutions of our results generalize and improve those established in b yang and b g zhang funkcial ekvac 39 1996 347 362

asymptotic stability and asymptotic solutions of second order differential equations abstract we improve simplify and extend on quasi linear case some results on asymptotical stability of ordinary second order differential equations with complex valued coefficients obtained in our previous paper g r hovhannisyan asymptotic stability for second order differential equations with complex coefficients electron j differential equations 2004 85 2004 1 20 to prove asymptotic stability of second order differential equations we establish stability estimates using integral representations of solutions via asymptotic solutions and error estimates several examples are discussed

automatic solution of sturm liouville problems using the pruess method abstract we develop algorithms based on coefficient approximation for the automatic solution of regular and singular sturm liouville problems

oscillation criteria for odd order neutral equations abstract in this paper four main results are obtained for oscillation of all solutions of the odd order neutral differential equation formula where p i t 0 i 0 i r r i 1 2 m and p 0 theorem 1 shows that if in addition to the above 0 p i x x n 1 and for some 0 1 all solutions of the first order delay equation formula are oscillatory then all solutions of are oscillatory in particular when m 1 and p 1 t p 1 0 then p 1 n 1 1 p n e n n 1 n 1 implies that all solutions of are oscillatory in such case theorem 4 1 due to gopalsamy et al czech math j 42 1992 313 323 reduces to p 1 n 1 1 p n which in view of the known inequality 1 e n n 1 n 1 j math anal appl 139 1989 311 318 graef et al j math anal appl 155 1991 562 571 and ladas et al proc amer math soc 113 1991 123 133 have been generalized in theorems 2 3 and 4 respectively

parameterized point pattern matching and its application to recognition of object families the problem of recognizing and localizing objects that can vary in parameterized ways is considered to achieve this goal a concept of parameterized point pattern is introduced to model parameterized families of such objects and a parameterized point pattern matching algorithm is proposed a parameterized point pattern is a very flexible concept that can be used to model a large class of parameterized objects such as a pair of scissors with rotating blades the proposed matching algorithm is formulated as a tree search procedure and it generates all maximum matchings satisfying a condition called delta boundedness several pruning methods based on the condition of delta boundedness and their efficient computing techniques are given the proposed matching algorithm is applied to a real shape matching problem in order to check the validity of the approach

an upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation this paper presents an upper bound for the distance between a zero and a critical point of a solution of the second order linear differential equation p x y q x y x 0 with p x q x 0 it also compares it with previous results

cross characteristic representations of even characteristic symplectic groups we classify the small irreducible representations of sp 2n q with q even in odd characteristic this improves even the known results for complex representations the smallest representation for this group is much larger than in the case when q is odd this makes the problem much more difficult