small groups of finite morley rank with involutions by analogy with thompson s classification of nonsolvable finite n groups we classify groups of finite morley rank with solvable local subgroups of even and mixed type we also consider several aspects reminiscent of small groups of finite morley rank of odd type

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

global stabilization and convergence of nonlinear systems with uncertain exogenous dynamics in this note a class of nonlinear uncertain systems are considered and uncertainties in the systems are assumed to be generated by exogenous dynamics robust control is designed by employing nonlinear observers to estimate the uncertainties it is shown that if a partial knowledge of the exogenous system is available and its known dynamics meet certain conditions or if input channel of the plant has certain properties global stability and global estimation convergence can be achieved in the latter case the results on stability and convergence hold even if exogenous dynamics are completely unknown but bounded by some known function

solvable groups of finite morley rank abstract we prove the following theorem the commutator subgroup of a solvable connected group of finite morley rank is nilpotent

global stabilization of nonlinear systems with a class of unmatched uncertainties abstract global and asymptotic stabilization of uncertain dynamical systems which violate the matching conditions is investigated a class of unmatched uncertainties called equivalently matched uncertainties is defined a robust controller is proposed to stabilize the uncertain system asymptotically in the large provided that the nominal system is uniformly asymptotically stable and that the unmatched uncertainties are equivalently matched the required information about uncertain dynamics in the system is merely that the uncertainties are bounded in euclidean norm by known functions of the system state

multilevel monte carlo for stochastic differential equations with small noise we consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by brownian motions in the commonly occurring small noise regime we consider i standard monte carlo methods combined with numerical discretization algorithms tailored to the small noise setting and ii a multilevel monte carlo method combined with a standard euler maruyama implementation under the assumptions we make on the underlying model the multilevel method combined with euler maruyama is often found to be the most efficient option moreover under a wide range of scalings the multilevel method is found to give the same asymptotic complexity that would arise in the idealized case where we have access to exact samples of the required distribution at a cost of o 1 per sample a key step in our analysis is to analyze the variance between two coupled paths directly as opposed to their l 2 distance careful simulations are provided to illustrate the asymptotic results

groups of finite morley rank with a generically sharply multiply transitive action abstract we prove that if g is a group of finite morley rank that acts definably and generically sharply n transitively on a connected abelian group v of morley rank n with no involutions then there is an algebraically closed field f of characteristic 2 such that v has the structure of a vector space of dimension n over f and g acts on v as the group gl n f in its natural action on f n

lie rank in groups of finite morley rank with solvable local subgroups we prove a general dichotomy theorem for groups of finite morley rank with solvable local subgroups and of prufer p rank at least 2 leading either to some p strong embedding or to the prufer p rank being exactly 2

groupes de rang de morley fini de type pair avec un sous groupe faiblement inclus resume we show that a minimal counterexample to the cherlin zil ber conjecture of even type and with a weakly embedded subgroup is isomorphic to psl 2 k where k is an algebraically closed field of characteristic 2

cascaded feedback linearization and its application to stabilization of nonholonomic systems in this paper a new cascaded feedback linearization problem is formulated and a set of conditions on the cascaded feedback linearizability are established for a class of two input affine nonlinear systems the proposed cascaded feedback linearization method enlarges the classes of nonlinear systems which can be dealt with using the feedback linearization technique in particular the proposed design can be applied to address the feedback stabilization problem for a few classes of nonlinear systems which have uncontrollable linearization and do not satisfy the standard feedback linearization conditions as an illustrative application the proposed cascade feedback linearization concept is used to solve the feedback stabilization problem of nonholonomic systems within the framework of continuously differentiable state feedback control simulation results are provided to illustrate the proposed method

analytical approach to an integrate and fire model with spike triggered adaptation the calculation of the steady state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale the theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron i a membrane potential distribution with a convex shape ii a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation and iii a maximized variability associated with the adaptation current at a finite adaptation time scale

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

the classical involution theorem for groups of finite morley rank abstract this paper gives a partial answer to the cherlin zil ber conjecture which states that every infinite simple group of finite morley rank is isomorphic to an algebraic group over an algebraically closed field the classification of the generic case of tame groups of odd type follows from the main result of this work which is an analogue of aschbacher s classical involution theorem for finite simple groups

signalizers and balance in groups of finite morley rank abstract there is a longstanding conjecture due to gregory cherlin and boris zilber that all simple groups of finite morley rank are simple algebraic groups the most successful approach to this conjecture has been borovik s program analyzing a minimal counterexample or simple k group we show that a simple k group of finite morley rank and odd type is either algebraic of else has prufer rank at most two this result signifies a switch from the general methods used to handle large groups to the specilized methods which must be used to identify psl 2 psl 3 psp 4 and g 2

tame minimal simple groups of finite morley rank abstract we consider tame minimal simple groups of finite morley rank and of odd type we show that the prufer 2 rank of such a group is bounded by 2 we also find all potential nonalgebraic configurations there are essentially four of them and we delineate them with some precision

on solvable groups of finite morley rank we investigate solvable groups of finite morley rank we find conditions on g for g to split in g in particular if g is abelian and z g 1 we prove that g g t for some t and the ring z t anng is intepretable in g we exploit the methods used in proving these results to find more information about solvable groups

structure des groupes lineaires definissables dans un corps de rang de morley fini we generalize several properties of linear algebraic groups to the case of the linear groups which are defined in a field of finite morley rank we show three structure theorems and the conjugacy of the borels of the carter subgroups of the maximal tori in conclusion we generalize the results to fields of morley rank n without subgroups of finite rank in contrary to the case of finite morley rank there are known examples of such fields with definable non algebraic subgroups of gln k

cosets genericity and the weyl group abstract in a connected group of finite morley rank in which generically elements belong to connected nilpotent subgroups proper normalizing cosets of definable subgroups are not generous we explain why this is true and what consequences this has for the abstract theory of weyl groups in groups of finite morley rank

groups of mixed type the cherlin zil ber conjecture states that an infinite simple group of finite morley rank is an algebraic group over an algebraically closed field the proofs of the following three conjectures would provide a proof of the cherlin zil ber conjecture conjecture 1 there exist no nonsolvable connected groups of finite morley rank all of whose proper definable connected subgroups are nilpotent such groups are called bad groups 2 conjecture 2 there exists no structure k q a of finite morley rank where k is an algebraically closed field and a is an infinite proper definable subgroup of the multiplicative group of k such structures are called bad fields

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

optimal range of a nonlocal kernel for stochastic resonance in extended systems abstract here we study stochastic resonance sr in a spatially extended system described by a reaction diffusion equation for a scalar activator like field including a nonlocal contribution we assume that such a contribution arises from an effective adiabatic elimination of an auxiliary inhibitor like field our aim is to study the role played by the range of the nonlocal kernel on the sr phenomena we have found that increasing the nonlocal coupling reduces the system s response and that similar to the so called system size sr there is an optimal value of the kernel s range yielding a maximum in the system s response

on groups of finite morley rank with weakly embedded subgroups the present paper is a contribution to the classification of tame stable groups of finite morley rank a group of finite morley rank is called tame if it involves no bad groups and no bad fields in the sense of 1 see also 1 it is conjectured that an infinite simple tame group of finite morley rank is isomorphic to an algebraic group over an algebraically closed field it is known that a minimal counterexample is either of even type meaning that the sylow 2 subgroups are of bounded exponent or of odd type meaning that the sylow 2 subgroups are finite extensions of divisible abelian groups we deal here with tame simple groups of even type having a weakly embedded subgroup a notion related to the notion of strongly embedded subgroup in the finite case but having no exact analog in that case in 10 the classication of simple tame groups with a strongly embedded subgroup was derived in an inductive framework as follows

groupes de type mixte resume we show that a minimal counterexample to the cherlin zil ber conjecture tame or not cannot be of mixed type

minimal connected simple groups of finite morley rank with strongly embedded subgroups let g be a simple k group of finite morley rank of odd type which is not algebraic then g has prufer 2 rank at most two this improves on an earlier result of the second and third authors for the tame case in the critical case g is minimal connected simple of odd type with a proper definable strongly embedded subgroup the bulk of the analysis relies on the first author s theory of 0 unipotence and the related 0 sylow subgroup theory as well as the so called bender method adapted to this context

a signalizer functor theorem for groups of finite morley rank there is a longstanding conjecture due to gregory cherlin and boris zilber that all simple groups of finite morley rank are simple algebraic groups towards this end the development of the theory of groups of finite morley rank has achieved a good theory of sylow 2 subgroups it is now common practice to divide the cherlin zilber conjecture into different cases depending on the nature of the connected component of the sylow 2 subgroup known as the sylow 2 subgroup we shall be working with groups whose sylow 2 subgroup is divisible or odd type groups to date the main theorem in the area of odd type groups is borovik s trichotomy theorem the trichotomy here is a case division of the minimal counterexamples within odd type more technically borovik s result represents a major success at transferring signalizer functors and their applications from finite group theory to the finite morley rank setting the major difference between the two settings is the absence of a solvable signalizer functor theorem this forced borovik to work only with nilpotent signalizer functors and the trichotomy theorem ends up depending on the assumption of tameness to assure that the necessary signalizer functors are nilpotent the present paper shows that one may obtain a connected nilpotent signalizer functor from any sufficiently non trivial solvable signalizer functor this result plugs seamlessly into borovik s work to eliminate the assumption of tameness from his trichotomy theorem in the meantime a new approach to the trichotomy theorem has been developed by borovik 7 based on the generic identification theorem of berkman and borovik 5 borovik uses his original signalizer functor arguments and incorporates the result of the present paper the paper is organized as follows the first section will develop a limited characteristic zero notion of unipotence to complement the usual p unipotence theory the section on centralizers and generation which follows will establish some background needed in the rest of the paper in section 4 we prove our main result on signalizer functors and in section 5 we discuss some applications with borovik s kind permission we include a proof of the nilpotent signalizer functor theorem as an appendix the results of section 3 are based in part on a section of an unpublished version of 3

non solvable groups of morley rank 3 abstract we prove the following theorem let g be a connected centerless non solvable group of morley rank 3 whose proper definable subgroups have rank 1 then g has no involutions and for all x g cg x is connected our method permits us to deduce that son r is not stable for n 3

exact nonequilibrium potential for the fitzhugh nagumo model in the excitable and bistable regimes we obtain an analytically exact nonequilibrium potential for the space independent fitzhugh nagumo model valid in the excitable and bistable regimes in the limit of small noise this potential allows us to characterize the nature of the barrier in the excitable regime and after subjecting the system to a modulated weak signal that rocks the potential inducing the phenomenon of stochastic resonance to calculate the signalto noise ratio in the bistable regime s1063 651x 98 08506 7

groups in supersimple and pseudofinite theories we consider groups g interpretable in a supersimple nite rank theory t such that t eq eliminates 9 1 it is shown that g has a denable soluble radical if g has rank 2 then if g is pseudonite it is soluble by nite and partial results are obtained under weaker hypotheses such as functional unimodularity of the theory a classication is obtained when t is pseudonite and g has a denable and denably

noise driven synchronization of a fitzhugh nagumo ring with phase repulsive coupling a perspective from the system s nonequilibrium potential abstract we study a one dimensional array of n autonomous units with excitable fitzhugh nagumo dynamics coupled in phase repulsive way to form a ring and submitted to a common subthreshold harmonic signal and independent gaussian white noises with a common intensity by varying two macroscopic regimes are observed for some value of noise intensity a transition from the rest state to an activated one with almost half of the neurons excited forming an activated inhibited activated structure along the ring takes place for larger values of the inverse transition is also observed and both states alternate in a synchronized way with the signal moreover measures of activation and coherent behavior become maximal for intermediate values of the origin of these collective effects is explained in terms of the system s nonequilibrium potential in particular the levels of noise for activation and synchronization are theoretically estimated