new good quasi cyclic ternary and quaternary linear codes let n k d q codes be linear codes of length n dimension k and minimum hamming distance d over gf q the following quasi cyclic codes are constructed in this paper 44 11 20 3 55 11 26 3 66 11 32 3 48 12 21 3 60 12 28 3 56 13 24 3 65 13 29 3 56 14 23 3 60 15 23 3 64 16 25 3 36 9 19 4 90 9 55 4 99 9 61 4 30 10 14 4 50 10 27 4 55 10 30 4 33 11 15 4 44 11 22 4 55 11 29 4 36 12 16 4 48 12 23 4 60 12 31 4 all of these codes have established or exceed the respective lower bounds on the minimum distance given by brouwer

multiple solutions to some degenerate quasilinear equation with variable exponents via perturbation method abstract in this paper we prove the existence of signed and sign changing solutions to some degenerate quasilinear and elliptic equation containing a gradient term and involving a variable exponent our main idea is to make use of the perturbation method together with invariant sets of descending flow the fact that the exponent is not constant plays an important role

axiomatizations for probabilistic finite state behaviors we study a process calculus which combines both nondeterministic and probabilistic behavior in the style of segala and lynch s probabilistic automata we consider various strong and weak behavioral equivalences and we provide complete axiomatizations for finite state processes restricted to guarded recursion in case of the weak equivalences we conjecture that in the general case of unguarded recursion the natural weak equivalences are undecidable this is the first work to our knowledge that provides a complete axiomatization for weak equivalences in the presence of recursion and both nondeterministic and probabilistic choice

existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in rn abstract mountain pass in a suitable orlicz space is employed to prove the existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in r n these equations contain strongly singular nonlinearities which include derivatives of the second order such equations have been studied as models of several physical phenomena the nonlinearity here corresponds to the superfluid film equation in plasma physics

quasilinear elliptic equations with critical growth via perturbation method abstract we consider a class of quasilinear schrodinger equations which include the modified nonlinear schrodinger equations a new perturbation approach is used to treat the critical exponent case giving new existence results

a tutorial on empa a theory of concurrent processes with nondeterminism priorities probabilities and time we give an overview of empa a process algebra for modeling and analyzing concurrent systems where nondeterminism priorities probabilities and time are present aiming at a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory

optimal quaternary linear codes of dimension five let d sub q n k be the maximum possible minimum hamming distance of a q ary n k d code for given values of n and k it is proved that d sub 4 33 5 22 d sub 4 49 5 34 d sub 4 131 5 96 d sub 4 142 5 104 d sub 4 147 5 108 d sub 4 152 5 112 d sub 4 158 5 116 d sub 4 176 5 spl ges 129 d sub 4 180 5 spl ges 132 d sub 4 190 5 spl ges 140 d sub 4 195 5 144 d sub 4 200 5 148 d sub 4 205 5 152 d sub 4 216 5 160 d sub 4 227 5 168 d sub 4 232 5 172 d sub 4 237 5 176 d sub 4 240 5 178 d sub 4 242 5 180 and d sub 4 247 5 184 a survey of the results of recent work on bounds for quaternary linear codes in dimensions four and five is made and a table with lower and upper bounds for d sub 4 n 5 is presented

consta abelian codes over galois rings we study n length consta abelian codes a generalization of the well known abelian codes and constacyclic codes over galois rings of characteristic p sup a where n and p are coprime a twisted discrete fourier transform dft is used to generalize transform domain results of abelian and constacyclic codes to consta abelian codes further we characterize consta abelian codes invariant under two kinds of monomials whose underlying permutations are effected by i multiplying the coordinates with a unit in the appropriate mixed radix representation of the coordinate positions and ii shifting the coordinates by t positions all the codes studied here belong to the class of quasi twisted codes which are known to contain some good codes we show that the dual of a consta abelian code invariant under the two monomials is also a consta abelian code closed under both monomials

infinitely many sign changing solutions for a quasilinear elliptic equation in r n abstract in this paper by using the methods of perturbation and invariant sets of descending flow we obtain the existence of infinitely many sign changing solutions of a quasilinear elliptic equation in r n

bisimulation and cocongruence for probabilistic systems we introduce a new notion of bisimulation called event bisimulation on labelled markov processes and compare it with the now standard notion of probabilistic bisimulation originally due to larsen and skou event bisimulation uses a sub algebra as the basic carrier of information rather than an equivalence relation the resulting notion is thus based on measurable subsets rather than on points hence the name event bisimulation applies smoothly for general measure spaces bisimulation on the other hand is known only to work satisfactorily for analytic spaces we prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary bisimulation these complexities only arise when we show that on analytic spaces the two concepts coincide we show that the concept of event bisimulation arises naturally from taking the cocongruence point of view for probabilistic systems we show that the theory can be given a pleasing categorical treatment in line with general coalgebraic principles as an easy application of these ideas we develop a notion of almost sure bisimulation the theory comes almost for free once we modify giry s monad appropriately

new quasi twisted quaternary linear codes let n k d sub q codes be linear codes of length n dimension k and minimum hamming distance d over gf q in this article 31 new quaternary q 4 codes are constructed which improve the respective lower bounds on minimum distance in brouwer s tables

sign changing solutions for schrodinger equations with indefinite supperlinear nonlinearities abstract in this paper we obtain existence of ground state solutions and ground state sign changing solutions for the following schrodinger equation u v x u k x u p 2 u in r n u 0 as x where n 3 2 p 2 2 n n 2 v x and k x are sign changing functions satisfying very mild assumptions the proofs rely on a new perturbed method which we design in this paper

some ternary and quaternary codes and associated sphere packings tables of good ternary and quaternary codes are presented and they are used in the construction of dense sphere packings results include 1 tables of the best ternary and quaternary constacyclic codes including cyclic codes up to block length 50 2 a class of optimal n 2 codes over gf q 3 the u v w mod 2u v mod u construction a new ternary code construction technique that can be used to construct the ternary reed muller codes and others and 4 tables of linear ternary and quaternary codes obtained by modifying and combining various codes here and in the literature packings are generated in even dimensions up to 100 using these codes and a sphere packing construction in dimensions 36 and 60 new record densities appear to have been achieved

multiple constant sign and nodal solutions for nonlinear elliptic equations with the p laplacian we consider a nonlinear elliptic equation driven by the p laplacian with dirichlet boundary conditions using variational techniques combined with the method of upper lower solutions and suitable truncation arguments we establish the existence of at least five nontrivial solutions two positive two negative and a nodal sign changing solution our framework of analysis incorporates both coercive and p superlinear problems also the result on multiple constant sign solutions incorporates the case of concave convex nonlinearities

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

efficient approximation of optimal control for continuous time markov games we study the time bounded reachability problem for continuous time markov decision processes ctmdps and games ctmgs existing techniques for this problem use discretisation techniques to partition time into discrete intervals of size e and optimal control is approximated for each interval separately current techniques provide an accuracy of o e 2 on each interval which leads to an infeasibly large number of intervals we propose a sequence of approximations that achieve accuracies of o e 3 o e 4 and o e 5 that allow us to drastically reduce the number of intervals that are considered for ctmdps the performance of the resulting algorithms is comparable to the heuristic approach given by buchholz and schulz while also being theoretically justified all of our results generalise to ctmgs where our results yield the first practically implementable algorithms for this problem we also provide memoryless strategies for both players that achieve similar error bounds

on the semantics of markov automata markov automata describe systems in terms of events which may be nondeterministic may occur probabilistically or may be subject to time delays we define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems a generalisation of reduction barbed congruence the well known touchstone equivalence for a large variety of process description languages

sign changing solutions for a class of kirchhoff type problem in bounded domains abstract we are interested in the existence of least energy sign changing solutions for a class of kirchhoff type problem in bounded domains because the so called nonlocal term b u 2 d x u is involving in the equation the variational functional of the equation has totally different properties from the case of b 0 combining constraint variational method and quantitative deformation lemma we prove that the problem possesses one least energy sign changing solution u b moreover we show that the energy of u b is strictly larger than the ground state energy finally we regard b as a parameter and give a convergence property of u b as b 0

infinitely many sign changing solutions for a schrodinger equation in rn abstract in this paper we consider a schrodinger equation u a x 1 u f u applying principle of symmetric criticality and the invariant set method under some assumptions on a and f we obtain an unbounded sequence of radial sign changing solutions for the above equation in r n when 0 large enough as n 4 or n 6 0 given using fountain theorem and the principle of symmetric criticality we prove that there exists an unbounded sequence of non radial sign changing solutions for the above equation in r n

weak bisimulation is sound and complete for pctl abstract we investigate weak bisimulation of probabilistic systems in the presence of nondeterminism i e labelled concurrent markov chains lcmc with silent transitions we develop an approach based on allowing convex combinations of computations similar to segala and lynch s use of randomized schedulers the definition of weak bisimulation destroys the additivity property of the probability distributions yielding instead capacities the mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values our analysis leads to three new developments we identify a characterization of image finiteness for countable state systems and present a new definition of weak bisimulation for these lcmcs we prove that our definition coincides with that of philippou lee and sokolsky for finite state systems we show that bisimilar states have matching computations the notion of matching involves convex combinations of transitions we study a minor variant of the probabilistic logic pctl the variation arises from an extra path formula to address action labels we show that bisimulation is sound and complete for this variant of pctl this is an extended complete version of a paper that was presented at concur 2002

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

infinitely many sign changing solutions to some quasilinear equation involving exponential term abstract in this paper we prove the existence of infinitely many sign changing solutions to some quasilinear and elliptic equation whose divergence part contains exponential term our main idea consists of the use of the perturbation method together with invariant sets of descending flow in the framework of classical critical point theory

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

new optimal quaternary linear codes of dimension 5 in this correspondence new optimal quaternary linear codes of dimension 5 are presented which extend previously known results these codes belong to the class of quasi twisted qt codes and have been obtained using a greedy local search algorithm other codes are also given which provide a lower bound on the maximum possible minimum distance the generator polynomials for these codes are tabulated and the minimum distances of known qt codes are given

multiplicity of solutions for quasilinear elliptic equations in rn in the present paper we study some quasilinear elliptic problem for which we prove the existence of infinitely many weak solutions on rn all the coefficient involved the unknown function so the using of a nonsmooth critical point theory approach

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9