factorizing a finite group into conjugates of a subgroup abstract for every non nilpotent finite group g there exists at least one proper subgroup m such that g is the setwise product of a finite number of conjugates of m we define cp g to be the smallest number k such that g is a product in some order of k pairwise conjugated proper subgroups of g we prove that if g is non solvable then cp g 36 while if g is solvable then cp g can attain any integer value bigger than 2 while on the other hand cp g 4 log 2 g

successive iteration of positive solution for a discontinuous third order boundary value problem in this paper we obtain a successively iterative scheme of positive solution for the nonlinear third order two point boundary value problem u q u f t u 0 u 0 a u 1 b u 0 c where f is a caratheodory function f and q satisfy some additional monotone conditions the iterative scheme starts off with zero function and is therefore useful for computation purpose the main tool is monotone iterative technique on banach space moreover the iterative scheme is independent of the existence of lower and upper solutions

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

imprimitive permutations in primitive groups abstract the goal of this paper is to study primitive groups that are contained in the union of maximal in the symmetric group imprimitive groups the study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups however this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult fortunately the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem in this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact in addition we introduce some algorithms to handle permutations provide the corresponding gap implementation solve some open problems and propose a large list of open problems

singular perturbation approximation of linear hyperbolic systems of balance laws this technical note deals with a class of linear hyperbolic systems of balance laws with multiple time scales the scale of time constants is modeled by a perturbation parameter this parameter is introduced in both dynamics and boundary conditions the solution of the full system is approximated by that of the reduced subsystem when the perturbation parameter is small enough lyapunov technique is used to prove it the main result is illustrated by an academic example moreover the boundary control synthesis to a gas flow transport model is shown based on singular perturbation approach

normal coverings and pairwise generation of finite alternating and symmetric groups abstract the normal covering number g of a finite non cyclic group g is the least number of proper subgroups such that each element of g lies in some conjugate of one of these subgroups we prove that there is a positive constant c such that for g a symmetric group sym n or an alternating group alt n g c n this improves results of the first two authors who had earlier proved that a n g 2 n 3 for some positive constant a where is the euler totient function bounds are also obtained for the maximum size g of a set x of conjugacy classes of g sym n or alt n such that any pair of elements from distinct classes in x generates g namely c n g 2 n 3

stability analysis of coupled linear ode hyperbolic pde systems with two time scales abstract this paper is concerned with a class of coupled ode pde systems with two time scales the fast constant time scale is modeled by a small positive perturbation parameter first we state a general sufficient stability condition for such systems this condition is also sufficient for the stability of the reduced and boundary layer subsystems however counterexamples illustrate that the converse is not true next we study the stability of such systems by taking into account the fact that the perturbation parameter is sufficiently small for linear ode coupled with fast hyperbolic pde systems the stability of both subsystems implies the stability of the full system on the other hand a counterexample shows that the full system can be unstable even though the two subsystems are stable for a pde coupled with fast ode system numerical simulations on academic examples are proposed moreover an application to boundary control of a gas flow transport system is used to illustrate the theoretical result

finite time stabilization of 2 times2 hyperbolic systems on tree shaped networks we investigate the finite time boundary stabilization of a one dimensional first order quasilinear hyperbolic system of diagonal form on 0 1 the dynamics of both boundary controls are governed by a finite time stable ode the solutions of the closed loop system issuing from small initial data in lip 0 1 are shown to exist for all times and to reach the null equilibrium state in finite time when only one boundary feedback law is available a finite time stabilization is shown to occur roughly in a twice longer time the above feedback strategy is then applied to the saint venant system for the regulation of water flows in a network of canals

brief paper lyapunov exponential stability of 1 d linear hyperbolic systems of balance laws explicit boundary dissipative conditions are given for the exponential stability in l 2 norm of one dimensional linear hyperbolic systems of balance laws email protected email protected email protected x 0 over a finite interval when the matrix m is marginally diagonally stable the result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised saint venant exner equations

uniform asymptotic stability of non linear singularly perturbed general and large scale systems new general advantageous criteria are established for uniform asymptotic stability of singularly perturbed general and large scale systems possibly containing non differentiable non linearities which often appear in control systems for systems with multiple time scales caused by several small parameters or for large scale systems an essential order reduction of aggregation matrices is achieved the results are conceptually and numerically applied to the absolute stability analysis of singularly perturbed lurie postnikov systems

primitive permutation groups as products of point stabilizers we prove that there exists a universal constant c such that any finite primitive permutation group of degree n with a non trivial point stabilizer is a product of no more than clog n point stabilizers

positive solutions of nonlinear singular third order two point boundary value problem abstract in this paper we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third order two point boundary value problem u t a t f u t 0 0 t 1 u 0 u 0 u 1 0 where is a positive parameter under various assumptions on a and f we establish intervals of the parameter which yield the existence of at least one at least two and infinitely many positive solutions of the boundary value problem by using krasnoselskii s fixed point theorem of cone expansion compression type

covers and normal covers of finite groups for a finite non cyclic group g let g be the smallest integer k such that g contains k proper subgroups h1 hk with the property that every element of g is contained in h g i for some i 2 1 k and g 2 g we prove that if g is a noncyclic permutation group of degree n then g n 2 2 we then investigate the structure of the groups g with g g where g is the size of a minimal cover of g and of those with g 2

singular perturbation approximation by means of a h 2 lyapunov function for linear hyperbolic systems abstract a linear hyperbolic system of two conservation laws with two time scales is considered in this paper the fast time scale is modeled by a small perturbation parameter by formally setting the perturbation parameter to zero the full system is decomposed into two subsystems the reduced subsystem representing the slow dynamics and the boundary layer subsystem standing for the fast dynamics the solution of the full system can be approximated by the solution of the reduced subsystem this result is obtained by using a h 2 lyapunov function the estimate of the errors is the order of the perturbation parameter for all initial conditions belonging to h 2 and satisfying suitable compatibility conditions moreover for a particular subset of initial conditions more precise estimates are obtained the main result is illustrated by means of numerical simulations

tikhonov theorem for linear hyperbolic systems abstract a class of linear hyperbolic systems of conservation laws with multiple time scales which are modeled by a perturbation parameter is considered in this paper by setting the perturbation parameter to zero two subsystems the reduced subsystem standing for the slow dynamics and the boundary layer subsystem representing the fast dynamics are computed it is first proved that the exponential stability of the full system implies the stability of both subsystems secondly a counterexample is given to indicate that the stability of the two subsystems does not ensure the full system s stability moreover a new tikhonov theorem for this class of infinite dimensional systems is stated the solution of the full system can be approximated by that of the reduced subsystem and this is proved by lyapunov techniques an application to boundary feedback stabilization of gas transport model is used to illustrate the results

finite primitive permutation groups containing a permutation having at most four cycles we classify the finite primitive groups containing a permutation with at most four cycles including fixed points in its disjoint cycle representation

on the maximum orders of elements of finite almost simple groups and primitive permutation groups we determine upper bounds for the maximum order of an element of a finite almost simple group with socle t in terms of the minimum index m t of a maximal subgroup of t for t not an alternating group we prove that with finitely many excep tions the maximum element order is at most m t moreover apart from an explicit list of groups the bound can be reduced to m t 4 these results are applied to determine all primitive permutation groups on a set of size n that contain permutations of order greater than or equal to n 4 we note again that this result gives upper bounds for meo aut t in terms of m t and for meo g in terms of m g since m t m g moreover equality in the up per bound meo aut t m t holds when t psld q for all but two pairs d q see table 3 and theorem 2 16 theorem 2 16 and table 3 provide good estimates for

existence of solution for discontinuous third order boundary value problems abstract in this paper we obtain existence results for the problem u q u f t u with boundary conditions u a a u b b u a c and u a u b u a u b u a c we assume f a caratheodory function q l r 0 such that 1 q l loc r 0 and suppose the existence of lower and upper solutions the existence of solution for the first considered conditions is obtained as a consequence of the fixed points theorems we obtain the solution of the second problem as a limit of solutions of the first case for the first problem the monotone method is developed

rapid boundary stabilization of the wave equation the boundary stabilization of the wave equation in bounded domains is studied it is shown that a particular choice of the feedback leads to fast energy decay explicit decay rate estimates are obt

boundary feedback control of linear hyperbolic systems application to the saint venant exner equations distributed parameter systems modeled by hyperbolic partial differential equations are considered in this paper the dynamic models include a source term and heterodirectional velocities a boundary control problem is introduced and it is first shown that it is well posed in the sense of tucsnak and weiss under appropriate assumptions coupling the boundary conditions and the source term then a sufficient exponential stability condition is derived using operator theory this condition is written in terms of linear matrix inequalities that are numerically tractable and that allow an optimization program connections with another classical stability condition are given this approach is applied to the saint venant exner equation describing the dynamics of the water level of the water flow and of the sediment inside of a channel the effect of the friction and of the slope are taken into account in the application model

extremal solutions for third order nonlinear problems with upper and lower solutions in reversed order abstract this paper deals with the existence of extremal solutions for the third order nonlinear boundary value problem u t f t u t t a b u a a u a b u b c in the presence of a pair of lower and upper solutions in reversed order here r r is an increasing homeomorphism f a b r r is a carathedory function and a b c r the proof follows from monotone iterative techniques which are based on suitable anti maximum principles for adequate operators to deduce such results we study some related problems coupled with boundary value conditions of the form p 0 u a q 0 u a a p 1 u b q 1 u b b u a c and u a a u a b u b c

extremality and comparison results for discontinuous third order functional initial boundary value problems extremality and comparison results are derived for third order functional initial boundary value problems differential equations of problems may involve discontinuous nonlinearities

singular perturbation analysis of a coupled system involving the wave equation this article considers a system coupling an ordinary differential equation with a wave equation through its boundary data the existence of a small parameter in the wave equation as a factor multiplying the time derivative suggests the idea of applying a singular perturbation method to get the stability of the full system by analyzing the stability of some appropriate subsystems given by the method however for infinite dimensional systems it is known that in some cases this method does not work indeed one cannot be sure of the stability of the full system even if the given subsystems are stable in this article we prove that the singular perturbation method works for the system under study using this strategy we get the stability of the system and a tikhonov theorem which is the first of this kind for systems involving the wave equation simulations are performed to show the applicability of our results

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

extremality and comparison results for discontinuous implicit third order functional initial boundary value problems extremality results are derived for implicit third order functional initial boundary value problems differential equations initial conditions and boundary conditions of problems may involve discontinuous nonlinearities

uniqueness comparison and existence results for third order initial boundary value problems abstract we derive maximum principles for a nonlinear third order differential operator and prove uniqueness comparison and existence results for different types of third order initial boundary value problems including existence results for functional problems