nonlinear control of feedforward systems with bounded signals the stabilization problem for a class of nonlinear feedforward systems is solved using bounded control it is shown that when the lower subsystem of the cascade is input to state stable and the upper subsystem not exponentially unstable global asymptotic stability can be achieved via a simple static feedback having bounded amplitude that requires knowledge of the upper part of the state only this is made possible by invoking the bounded real lemma and a generalization of the small gain theorem thus stabilization is achieved with typical saturation functions saturations of constant sign or quantized control moreover the problem of asymptotic stabilization of a stable linear system with bounded outputs is solved by means of dynamic feedback finally a new class of stabilizing control laws for a chain of integrators with input saturation is proposed some robustness issues are also addressed and the theory is illustrated with examples on the stabilization of physical systems

broueʼs abelian defect group conjecture for the sporadic simple janko group j4 revisited abstract we show that the 3 block of the sporadic simple janko group j 4 with defect group c 3 c 3 and the principal 3 block of the alternating group a 8 are puig equivalent answering a question posed in our previous paper to accomplish this we apply computational techniques in particular an explicit version of the brauer construction

strategies for the renyi ulam game with fixed number of lies we consider the problem of finding the minimal number ll m of binary questions needed to find an unknown element of a set of cardinality m with a sequential strategy if at most l of the answers are lies obviously in the case l 0 log m questions are needed thus one more question is necessary if the number of elements is doubled we show that for every fixed l and sufficiently large m then ll 2m ll m 2 and moreover ll 3 2m ll m 1 these bounds are sharp in infinitely many cases as a consequence at most one question more than the information theoretic lower bound is needed to successfully find the unknown number one of our strategies uses the minimum amount of adaptiveness during the search process

broue s abelian defect group conjecture holds for the harada norton sporadic simple group hn abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent rickard equivalent this conjecture is called broue s abelian defect group conjecture we prove in this paper that broue s abelian defect group conjecture is true for a non principal 3 block a with an elementary abelian defect group p of order 9 of the harada norton simple group hn it then turns out that broue s abelian defect group conjecture holds for all primes p and for all p blocks of the harada norton simple group hn

bounded output feedback tracking control of fully actuated euler lagrange systems in this short note we deal with the problem of trajectory tracking control of fully actuated euler lagrange systems with unmeasurable velocities and bounded control inputs in order to avoid the use of velocity measurements we introduce a nonlinear dynamic extension for the plant which renders the closed loop system semi globally asymptotically stable hence we prove that by increasing some of the dynamic extension parameters it is possible to enlarge the domain of attraction and to maintain the control inputs bounded

eigenvalues of cartan matrices of principal 3 blocks of finite groups with abelian sylow 3 subgroups abstract let a be the principal 3 block of a finite group g with an abelian sylow 3 subgroup p let c a be the cartan matrix of a and we denote by c a the unique largest eigenvalue of c a the value c a is called the frobenius perron eigenvalue of c a we shall prove that c a is a rational number if and only if a and the principal 3 block of n g p are morita equivalent this generalizes earlier wada s theorem in 2007 where he proves it only for the case that the order of p is nine while we prove it for the case that p is an arbitrary finite abelian 3 group the result presented here uses the classification of finite simple groups

lyapunov based tracking control in the presence of uncertain nonlinear parameterizable friction modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research this interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem and compensating for the effects of friction in a controller has practical ramifications if the friction effects in the system can be accurately modeled there is an improved potential to design controllers that can cancel the effects whereas excessive steady state tracking errors oscillations and limit cycles can result from controllers that do not accurately compensate for friction a tracking controller is developed in this paper for a general euler lagrange system that contains a new continuously differentiable friction model with uncertain nonlinear parameterizable terms to achieve the semi global asymptotic tracking result a recently developed integral feedback compensation strategy is used to identify the friction effects online assuming exact model knowledge of the remaining dynamics a lyapunov based stability analysis is provided to conclude the tracking and friction identification results experimental results illustrate the tracking and friction identification performance of the developed controller

optimal two stage algorithms for group testing problems group testing refers to the situation in which one is given a set of objects cal o an unknown subset cal p subseteq cal o and the task of determining cal p by asking queries of the type does cal p intersect cal q where cal q is a subset of cal o group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing searching in storage systems multiple access communications and data compression among others group testing procedures have been recently applied in computational molecular biology where they are used for screening libraries of clones with hybridization probes and sequencing by hybridization motivated by particular features of group testing algorithms used in biological screening we study the efficiency of two stage group testing procedures our main result is the first optimal two stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem we also provide efficient algorithms for the case in which there is a bernoulli probability distribution on the possible sets cal p and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of inhibitory items in cal o our results depend on a combinatorial structure introduced in this paper we believe that it will prove useful in other contexts too

broue s conjecture holds for principal 3 blocks with elementary abelian defect group of order 9 abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a finite group g has an abelian sylow p subgroup p then the derived categories of the principal p blocks of g and of the normalizer ng p of p in g are equivalent we prove in this paper that broue inage kus conjecture holds for the principal 3 block of an arbitrary finite group g with an elementary abelian sylow 3 subgroup p of order 9 by using initiated works for the case where g is simple which are due to puig okuyama waki miyachi and the authors the result depends on the classification of finite simple groups

cellular algebras and cartan matrices abstract let a be a finite dimensional algebra over a field k and let c be the cartan matrix of a usually the eigenvalues of c being integers do not imply the semisimplicity of a however we prove that a cellular algebra a is semisimple if and only if det c 1 and all eigenvalues of c are integers moreover we use cartan matrices to classify the cellular algebras with the property that the determinant of the cartan matrix equals a given prime p and all eigenvalues are integers we also give a classification of cellular nakayama algebras with integral eigenvalues of their cartan matrices finally we show that if a is a cellular algebra then its trivial extension t a is also a cellular algebra in particular if a non simple connected cellular algebra a is quasi hereditary then the cartan matrix of t a has at least one non integral eigenvalue the main tool used in this paper is the well known perron frobenius theory on non negative matrices

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

equivariant splendid rickard equivalences abstract broue s conjecture says that if a finite group h has an abelian sylow p subgroup p then the principal blocks of h and n h p are splendidly rickard equivalent in this paper broue s conjecture is reduced to simple groups with a stability condition a structure theorem on finite groups with abelian sylow p subgroups due to kimmerle and sandling is used

eigenvalues of cartan matrices of principal 2 blocks with abelian defect groups abstract let g be a finite group with an abelian sylow 2 subgroup p let c b be the cartan matrix of the principal 2 block b of g we show that the frobenius perron eigenvalue b of c b is a rational integer if and only if b and its brauer correspondent block b of n g p are morita equivalent by using a classification of finite simple groups with an abelian sylow 2 subgroup in this case we can take the brauer character table b of b as a unimodular eigenvector matrix u b of c b over a complete discrete valuation ring r

broueʼs abelian defect group conjecture holds for the double cover of the higman sims sporadic simple group abstract in the representation theory of finite groups there is a well known and important conjecture due to broue saying that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent we prove in this paper that broue s abelian defect group conjecture and even rickard s splendid equivalence conjecture are true for the faithful 3 block a with an elementary abelian defect group p of order 9 of the double cover 2 hs of the higman sims sporadic simple group it then turns out that both conjectures hold for all primes p and for all p blocks of 2 hs

broueʼs abelian defect group conjecture holds for the sporadic simple conway group co3 in the representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block an of the normaliser ng p of p in g are derived equivalent rickard equivalent this conjecture is called strong version of broue s abelian defect group conjecture in this paper we prove that the strong version of broue s abelian defect group conjecture is true for the non principal 2 block a with an elementary abelian defect group p of order 8 of the sporadic simple conway group co3 this result completes the verification of the strong version of broue s abelian defect group conjecture for all primes p and for all p blocks of co3

trivial source modules in blocks with cyclic defect groups we shall present a method to get trivial source modules easily just by looking at values of ordinary characters at non identity p elements in finite groups instead of doing huge calculation the method is only for a case where defect groups are cyclic nevertheless it works well at least when we want to prove broue s abelian defect group conjecture for blocks which have elementary abelian defect groups of order p2

rise based adaptive control of a control affine uncertain nonlinear system with unknown state delays a continuous robust adaptive control method is designed for a class of uncertain nonlinear systems with unknown constant time delays in the states specifically a robust adaptive control method and a delay free gradient based desired compensation adaptation law dcal are utilized to compensate for unknown time delays linearly parameterizable uncertainties and additive bounded disturbances for a general nonlinear system despite these disturbances a lyapunov krasovskii based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory

optimal strategies against a liar abstract we consider the following scenario there are two individuals say q questioner and r responder involved in a search game player r chooses a number say x from the set s 1 m player q has to find out x by asking questions of type which one of the sets a 1 a 2 a q does x belong to where the sets a 1 a q constitute a partition of s player r answers i to indicate that the number x belongs to a i we are interested in the least number of questions player q has to ask in order to be always able to correctly guess the number x provided that r can lie at most e times the case e 0 obviously reduces to the classical q ary search and the necessary number of questions is log q m the case q 2 and e 1 has been widely studied and it is generally referred to as ulam s game in this paper we consider the general case of arbitrary q 2 under the assumption that player r is allowed to lie at most twice throughout the game we determine the minimum number of questions q needs to ask in order to successfully search for x in a set of cardinality m q i for any i 1 as a corollary we obtain a counterexample to a recently proposed conjecture of aigner for the case of an arbitrary number of lies we also exactly solve the problem when player r is allowed to lie a fixed but otherwise arbitrary number of times e and m q i with i not too large with respect to q for the general case of arbitrary m we give fairly tight upper and lower bounds on the number of the necessary questions

the principal 3 blocks of four and five dimensional projective special linear groups in non defining characteristic abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he has conjectured that for any prime p if a finite group g has an abelian sylow p subgroup p then the principal p blocks of g and the normalizer ng p of p in g are derived equivalent let q be a power of a prime such that q 2 or 5 mod 9 in this paper we show that broue s conjecture is true for p 3 and for g psl4 q and g psl5 q in these cases g has elementary abelian sylow 3 subgroups of order 9 what we prove here is the following in the case g psl4 q all the principal 3 blocks of g are morita even puig equivalent independently of infinitely many q in the case g psl5 q all the principal 3 blocks of g are morita even puig equivalent to the principal 3 block of ng p independently of infinitely many q

rouquier blocks in chevalley groups of type e abstract in finite chevalley groups of type e we shall find a rouquier like block algebra in non defining characteristic we construct a morita equivalence between this block and a principal block of a local subgroup as an application of the equivalence we shall determine some decomposition numbers in type e

least adaptive optimal search with unreliable tests we consider the basic problem of searching for an unknown m bit number by asking the minimum possible number of yes no questions when up to a finite number e of the answers may be erroneous in case the i 1 th question is adaptively asked after receiving the answer to the ith question the problem was posed by ulam and r enyi and is strictly related to berlekamp s theory of error correcting communication with noiseless feedback conversely in the fully non adaptive model when all questions are asked before knowing any answer the problem amounts to finding a shortest e error correcting code let qe m be the smallest integer q satisfying berlekamp s bound i 0e 2qm then at least qe m questions are necessary in the adaptive as well as in the non adaptive model in the fully adaptive case optimal searching strategies using exactly qe m questions always exist up to finitely many exceptional m s at the opposite non adaptive case searching strategies with exactly qe m questions or equivalently e error correcting codes with 2m codewords of length qe m are rather the exception already for e 2 and are generally not known to exist for e 2 in this paper for each e 1 and all sufficiently large m we exhibit searching strategies that use a first batch of m non adaptive questions and then only depending on the answers to these m questions a second batch of qe m m non adaptive questions these strategies are automatically optimal since even in the fully adaptive case qe m 1 questions do not suffice to find the unknown number and qe m questions generally do not suffice in the non adaptive case the results of our paper provide e fault tolerant searching strategies with minimum adaptiveness and minimum number of tests

splendid morita equivalences for principal 2 blocks with dihedral defect groups given a dihedral 2 group p of order at least 8 we classify the splendid morita equivalence classes of principal 2 blocks with defect groups isomorphic to p to this end we construct explicit stable equivalences of morita type induced by specific scott modules using brauer indecomposability and gluing methods we then determine when these stable equivalences are actually morita equivalences and hence automatically splendid morita equivalences finally we compute the generalised decomposition numbers in each case

lasalle yoshizawa corollaries for nonsmooth systems in this technical note two generalized corollaries to the lasalle yoshizawa theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right hand sides lyapunov based analysis methods that achieve asymptotic convergence when the candidate lyapunov derivative is upper bounded by a negative semi definite function in the presence of differential inclusions are presented a design example illustrates the utility of the corollaries

derived equivalent tame blocks abstract in this article we provide derived equivalences between several blocks of tame representation type based on erdmann s work on morita equivalence classes of tame blocks we obtain a classification of tame blocks up to derived equivalence as in erdmann s work in the case of two simple modules our classification is only complete up to scalars occurring in certain relations

the broue conjecture for the faithful 3 blocks of 4 m22 abstract we verify broue s conjecture for the faithful 3 blocks of defect 2 of the non split central extension of the sporadic simple mathieu group m 22 by a cyclic group of order 4 the proof is based on a strategy due to okuyama and rickard where a stable equivalence is lifted to a derived equivalence the stable equivalence in turn is provided by exploiting a result due to puig to handle this particular example next to theoretical investigations we apply a whole bunch of computational tools

vertices sources and green correspondents of the simple modules for the large mathieu groups we investigate the simple modules for the sporadic simple mathieu groups m22 m23 and m24 as well as those of the automorphism group the covering groups and the bicyclic extensions of m22 in characteristics 2 and 3 we determine the vertices and sources as well as the green correspondents of these simple modules we also find two 3 blocks with elementary abelian defect groups of order 9 in these groups which are morita equivalent to their brauer correspondents

eigenvalues and elementary divisors of cartan matrices of cyclic blocks with l b 5 and tame blocks abstract we give a conjecture on relation between eigenvalues and elementary divisors of the cartan matrix of a p block b of a finite group then we prove the conjecture is true for cyclic blocks with l b 5 and for tame blocks

saturated rise feedback control for a class of second order nonlinear systems a saturated controller is developed for a class of uncertain second order nonlinear systems which includes time varying and nonlinearly parameterized functions with bounded disturbances using a continuous control law with smooth saturation functions based on the robust integral of the sign of the error rise control methodology the developed controller is able to utilize the benefits of high gain control strategies while guaranteeing saturation limits are not surpassed the bounds on the control are known a priori and can be adjusted by changing the feedback gains the saturated controller yields asymptotic tracking despite model uncertainty and added disturbances in the dynamics experimental results using a two link robot manipulator demonstrate the performance of the developed controller

robust global stabilization of a class of uncertain feedforward nonlinear systems abstract the problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered the control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small with respect to previous works on the subject the design procedure is able to deal with uncertain possibly time varying parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system the small gain theorem for nonlinear systems which are input to state stable with restrictions is shown to be a key tool for designing a state feedback saturated control law

weakly adaptive comparison searching we consider schemes of discrete search in the set 1 n using only comparison queries i e those of the form x a for a 1 n such a scheme is called i adaptive if questions may be stated in i series so that answers are obtained after each series but not between particular questions in it we describe a worst case optimal algorithm of i adaptive search and determine its complexity the latter turns out to be i n1i where i may be a function of n we also consider the closely related version of continuous search with a given error bound

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

optimal comparison strategies in ulam s searching game with two errors abstract suppose x is an n bit integer by a comparison question we mean a question of the form does x satisfy either condition a x b or c x d we describe strategies to find x using the smallest possible number q n of comparison questions and allowing up to two of the answers to be erroneous as proved in this self contained paper with the exception of n 2 q n is the smallest number q satisfying berlekamp s inequality 2 q 2 n q 2 q 1 this result would disappear if we only allowed questions of the form does x satisfy the condition a x b since no strategy can find the unknown x 0 1 2n 1 with less than q n questions our result provides extremely simple optimal searching strategies for ulam s game with two lies the game of twenty questions where up to two of the answers may be erroneous

equivalent blocks of finite general linear groups in non describing characteristic abstract j chuang r kessar and j rickard have proved broue s abelian defect group conjecture for many symmetric groups we adapt the ideas of kessar and chuang towards finite general linear groups represented over non describing characteristic we then describe morita equivalences between certain p blocks of gl n q with defect group c p c p as q varies see theorem 2 here p and q are coprime this generalizes work of s koshitani and m hyoue who proved the same result for principal blocks of gl n q when p 3 1 in a different way

the derived categories of some blocks of symmetric groups and a conjecture of broue abstract a well known conjecture of broue in the representation theory of finite groups involves equivalences of derived categories of blocks the aim of this paper is to verify this conjecture for defect 2 blocks of symmetric groups actually we prove for these blocks a refinement of broue s conjecture due to rickard

asymptotic tracking for uncertain dynamic systems via a multilayer neural network feedforward and rise feedback control structure the use of a neural network nn as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade typical nn based controllers yield uniformly ultimately bounded uub stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances several researchers have proposed discontinuous feedback controllers e g variable structure or sliding mode controllers to reject the residual errors and yield asymptotic results the research in this paper describes how a recently developed continuous robust integral of the sign of the error rise feedback term can be incorporated with a nn based feedforward term to achieve semi global asymptotic tracking to achieve this result the typical stability analysis for the rise method is modified to enable the incorporation of the nn based feedforward terms and a projection algorithm is developed to guarantee bounded nn weight estimates

a counterexample to a conjecture of wada abstract wada conjectured in 2007 that the largest eigenvalue of the cartan matrix c of a block of a finite group is rational if and only if all eigenvalues of c are rational we provide a counterexample to this conjecture and discuss related questions

rationality of eigenvalues of cartan matrices in finite groups abstract we study the case in which eigenvalues and elementary divisors of a cartan matrix of a p block b of a finite group coincide in several cases we prove the coincidence occurs if and only if the perron frobenius eigenvalue of the cartan matrix is equal to the order of a defect group of b

eigenvector matrices of cartan matrices for finite groups abstract let c b be the cartan matrix of a p block b of a finite group g we show that there is a unimodular eigenvector matrix u b of c b over a discrete valuation ring r if all eigenvalues of c b are integers when b is a cyclic block a tame block a p block of a p solvable group or the principal 3 block with elementary abelian defect group of order 9

a robust extremum seeking scheme for dynamic systems with uncertainties and disturbances this paper studies a numerical optimization based extremum seeking scheme for systems with unmodeled dynamics and unknown disturbances without using dither signals the robust extremum seeking scheme is composed of a numerical gradient estimator a numerical optimizer and an extended state observer based state regulator a conjugate gradient method is adopted to achieve extremum seeking a nonlinear extended state observer based state regulator is proposed to regulate the states the robust extremum seeker is based on the numerical optimization based extremum seeking framework sufficient conditions are derived to ensure the convergence of the overall extremum seeking scheme the ultimate convergence bound is quantified for a class of strongly convex functions a numerical example is presented to verify the proposed method

ulam s searching game with a fixed number of lies abstract paul tries to find an unknown x from l to n by asking q yes no questions in response carole may lie up to k times for k fixed and n q sufficiently large necessary and sufficient conditions are given for paul to win

broue s abelian defect group conjecture for the held group and the sporadic suzuki group abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding p block b of ng p are derived equivalent we demonstrate in this paper that broue s conjecture holds for non principal 3 blocks a with elementary abelian defect group p of order 9 of the simple held group and the sporadic simple suzuki group

isometries and extra special sylow groups of order p3 abstract a new type of isometry between the sets of irreducible characters of blocks is introduced and a conjecture is stated using the classifications of finite simple groups and saturated fusion systems over an extra special group p of order p 3 and exponent p we check that the conjecture is affirmatively answered for the principal blocks of finite groups with sylow p subgroup p

perverse equivalences and broueʼs conjecture abstract we give a new approach to the construction of derived equivalences between blocks of finite groups based on perverse equivalences in the setting of broue s abelian defect group conjecture we provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with sylow subgroups elementary abelian of order 9 we also examine extensions to automorphism groups in a general setting

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

two batch search with lie cost we consider the problem of searching for an unknown number in the search space u 0 m 1 q ary questions can be asked and some of the answers may be wrong an arbitrary integer weighted bipartite graph gamma is given stipulating the cost gamma i j of each answer jnei when the correct answer is i i e the cost of a wrong answer correct answers are supposed to be cost less it is assumed that a maximum cost e for the sum of the cost of all wrong answers can be afforded by the responder during the whole search we provide tight upper and lower bounds for the largest size m m q e gamma n for which it is possible to find an unknown number x isinu with n q ary questions and maximum lie cost e our results improve the bounds of cicalese et al 2004 and ahlswede et al 2008 the questions in our strategies can be asked in two batches of nonadaptive questions finally we remark that our results can be further generalized to a wider class of error models including also unidirectional errors

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control