generalized symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear generalized symmetric dual variational problems involving vector valued functions which unify the wolfe and mond weir models for a special case our problems become the symmetric dual pair of d s kim and w j lee 1998 j math anal appl 218 34 48 under invexity assumptions we establish weak strong and converse duality theorems for our variational problems by using the concept of efficiency also we give the static case of our multiobjective generalized symmetric duality results several known results are obtained as special cases

on twisted forms and relative algebraic k theory this paper introduces a new approach to the study of certain aspects of galois module theory by combining ideas arising from the study of the galois structure of torsors of finite group schemes with techniques coming from relative algebraic k theory

complexity of metric temporal logics with counting and the pnueli modalities the common metric temporal logics for continuous time were shown to be insufficient when it was proved in hirshfeld and rabinovich 1999 2007 7 12 that they cannot express a modality suggested by pnueli moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modality the temporal logic with counting modalities tlc is the extension of until since temporal logic tl u s by counting modalities c n x and email protected n email protected n for each n the modality c n x says that x will be true at least at n points in the next unit of time and its dual email protected n x says that x has happened n times in the last unit of time in hirshfeld and rabinovich 2006 11 it was proved that this temporal logic is expressively complete for a natural decidable metric predicate logic in particular the pnueli modalities pn k x 1 x k there is an increasing sequence t 1 t k of points in the unit interval ahead such that x i holds at t i are definable in tlc in this paper we investigate the complexity of the satisfiability problem for tlc and show that the problem is pspace complete when the index of c n is coded in unary and expspace complete when the index is coded in binary we also show that the satisfiability problem for the until since temporal logic extended by the pnueli modalities is pspace complete

quantitative temporal logics over the reals pspace and below in many cases the addition of metric operators to qualitative temporal logics tls increases the complexity of satisfiability by at least one exponential while common qualitative tls are complete for np or pspace their metric extensions are often expspace complete or even undecidable in this paper we exhibit several metric extensions of qualitative tls of the real line that are at most pspace complete and analyze the transition from np to pspace for such logics our first result is that the logic obtained by extending since until logic of the real line with the operators sometime within n time units in the past future is still pspace complete in contrast to existing results we also capture the case where n is coded in binary and the finite variability assumption is not made to establish containment in pspace we use a novel reduction technique that can also be used to prove tight upper complexity bounds for many other metric tls in which the numerical parameters to metric operators are coded in binary we then consider metric tls of the reals that do not offer any qualitative temporal operators in such languages the complexity turns out to depend on whether binary or unary coding of parameters is assumed satisfiability is still pspace complete under binary coding but only np complete under unary coding

minimax mixed integer symmetric duality for multiobjective variational problems abstract a mond weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated applying the separability and generalized f convexity on the functions involved weak strong and converse duality theorems are established self duality theorem is proved a close relationship between these variational problems and static symmetric dual minimax mixed integer multiobjective programming problems is also presented

symmetric duality for multiobjective fractional variational problems with generalized invexity the concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems weak strong and converse duality theorems are proved under generalized invexity assumptions a close relationship between these problems and multiobjective fractional symmetric dual problems is also presented

invariance under stuttering in a temporal logic of actions we show that some simple and useful stutter invariant properties definable in the language of lamport s simple temporal logic of actions stla are not definable in stla and present a natural extension of stla that allows one to express all stutter invariant properties definable in the language of stla

duality for multiobjective variational problems abstract wolfe and mond weir type duals for multiobjective variational problems are formulated under convexity assumptions on the functions involved weak and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems a close relationship between these variational problems and nonlinear multiobjective programming problems is also indicated

symmetric duality for multiobjective variational problems abstract a mond weir type symmetric dual for a multiobjective variational problem is formulated weak and strong duality theorems under generalized convexity assumptions are proved for properly efficient solutions under an additional condition on the kernel function that occurs in the formulation of the problems a self duality theorem is proved a close relationship between these variational problems and symmetric dual nonlinear multiobjective programming problems is also incorporated

invariants de classes exemples de non annulation en dimension superieure the so called class invariant homomorphism measures the galois module structure of torsors under a finite flat group scheme g which lie in the image of a coboundary map associated to an isogeny between neron models of abelian varieties with kernel g when the varieties are elliptic curves with semi stable reduction and the order of g is coprime to 6 it is known that the homomorphism vanishes on torsion points in this paper using weil restrictions of elliptic curves we give the construction for any prime number p 2 of an abelian variety a of dimension p endowed with an isogeny with kernel p whose coboundary map is surjective in the case when a has rank zero and the p part of the picard group of the base is non trivial we obtain examples where does not vanish on torsion points

axioms for real time logics this paper presents a complete axiomatization of two decidable propositional real time linear temporal logics event clock logic eventclocktl and metric interval temporal logic with past metricintervaltl the completeness proof consists of an effective proof building procedure for eventclocktl from this result we obtain a complete axiomatization of metricintervaltl by providing axioms translating metricintervaltl formulae into eventclocktl formulae the two logics being equally expressive our proof is structured to yield axiomatizations also for interesting fragments of these logics such as the linear temporal logic of the real numbers tlr

on arithmetic class invariants let f be a number field with ring of integers of and let s be a finite set of places of f assume that s contains the set s of archimedean places of f and write sf for the set of finite places contained in s let os or o when there is no danger of confusion denote the ring of sf integers of f write f for an algebraic closure of f let y be any scheme over spec o suppose thatg is a finite flat commutative group scheme over y of exponent n and let g denote the cartier dual of g let x y be ag torsor and write 0 g y for the trivialg torsor thenox is anog comodule and so it is also anogd module see 12 as an ogd module ox is locally free of rank one and it therefore gives a line bundle m over g set l m m 1 0 then the map h y g pic g l

a note on elliptic curves and galois module structure in global function fields in this paper we study the galois module structure of certain kummer orders obtained by dividing torsion points on an elliptic curve defined over a global function field we prove that such kummer orders are globally free as galois modules this is the analogue over function fields of a conjecture first stated by m j taylor for cm elliptic curves defined over number fields

symmetric duality for multiobjective fractional variational problems involving cones in this paper a pair of multiobjective fractional variational symmetric dual problems over cones is formulated weak strong and converse duality theorems are established under generalized f convexity assumptions moreover self duality theorem is also discussed

taming past ltl and flat counter systems reachability and ltl model checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in np the best known complexity upper bound for the latter problem is made of a tower of several exponentials herein we show that this problem is only np complete even if ltl admits past time operators and arithmetical constraints on counters as far as past time operators are concerned their addition to ltl immediately leads to complications and hence an np upper bound cannot be deduced by translating formulae into ltl and studying the problem only for this latter logic we also provide other complexity results obtained by restricting further the class of flat counter systems

the galois module structure of certain arithmetic principal homogeneous spaces in this paper we obtain galois module results for rings of integers of certain abelian extensions of cyclotomic extensions and of division fields for elliptic curves with complex multiplication in the cyclotomic case we consider the rings of integers of non ramified extensions and in the elliptic case we are concerned with extensions arising from the selmer group of the curve in each case we can describe those rings of integers which are free galois modules by means of l function congruences this then is a further instance of how galois module structure is dominated by l functions with the classic case being the tame theory see f t3 where it is the root numbers of the sympletic characters of the galois group which determine the galois module structure in broad terms the results of this paper arise from marrying the algebraic results in tl and certain powerful results from iwasawa theory both cyclotomic and elliptic for aesthetic reasons as well as for the sake of brevity we introduce notation which will simultaneously cover both the cyclotomic and the elliptic case we begin by defining the notation for

an until hierarchy and other applications of an ehrenfeucht fraisse game for temporal logic we prove there is a strict hierarchy of expressive power according to the until depth of linear temporal logic ltl formulas for each k there is a natural property based on quantitative fairness that is not expressible with k nestings of until operators regardless of the number of applications of other operators but is expressible by a formula with until depth k 1 our proof uses a new ehrenfeucht fra sse ef game designed specifically for ltl these properties can all be expressed in first order logic with quantifier depth and size o logk and we use them to observe some interesting relationships between ltl and first order expressibility we note that our until hierarchy proof for ltl carries over to the branching time logics ctl and ctl we then use the ef game in a novel way to effectively characterize 1 the ltl properties expressible without until as well as 2 those expressible without both until and next by playing the game on finite automata we prove that the automata recognizing languages expressible in each of the two fragments have distinctive structural properties the characterization for the first fragment was originally proved by cohen perrin and pin using sophisticated semigroup theoretic techniques they asked whether such a characterization exists for the second fragment the technique we develop is general and can potentially be applied in other contexts

definability with bounded number of bound variables abstract a theory satisfies the k variable property if every first order formula is equivalent to a formula with at most k bound variables possibly reused gabbay has shown that a model of temporal logic satisfies the k variable property for some k if and only if there exists a finite basis for the temporal connectives over that model we give a model theoretic method for establishing the k variable property involving a restricted ehrenfeucht fraisse game in which each player has only k pebbles we use the method to unify and simplify results in the literature for linear orders we also establish new k variable properties for various theories of bounded degree trees and in each case obtain tight upper and lower bounds on k this gives the first finite basis theorems for branching time models of temporal logic

the class group pairing and p descent on elliptic curves we give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field then we relate it to the descent relative to a suitable cyclic isogeny this allows us to connect the resulting selmer group with the logarithmic class group of the base these constructions are explicit and suitable for computer experimentation from a conceptual point of view the questions that arise here are analogues of visibility questions in the sense of cremona and mazur

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

reasoning in a restricted temporal logic abstract we consider rtl a linear time propositional temporal logic whose only modalities are the formula eventually operator and its dual formula always although less expressive than the full temporal logic rtl is the fragment of temporal logic that is used most often and in many verification systems indeed many properties of distributed systems discussed in the literature are rtl properties another advantage of rtl over the full temporal logic is in the decidability procedure while deciding satisfiability of a formula in full temporal logic is a pspace complete procedure doing so for an rtl formula is in np we characterize the class of regular languages that are definable in rtl and show simple translations between regular sets and rtl formulae that define them we explore the applications of rtl in reasoning about communication systems finally we relate variants of rtl when interpreted over a real line segments to several fragments of interval modal logic and show that the satisfiability problem for rtl when interpreted over a real line is np complete