conservation laws for conformally invariant variational problems we succeed in writing 2 dimensional conformally invariant non linear elliptic pde harmonic map equation prescribed mean curvature equations etc in divergence form these divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for weakly harmonic maps into homogeneous spaces from this form we can recover without the use of moving frame all the classical regularity results known for 2 dimensional conformally invariant non linear elliptic pde see hel it enables us also to establish new results in particular we solve a conjecture by e heinz asserting that the solutions to the prescribed bounded mean curvature equation in arbitrary manifolds are continuous and we solve a conjecture by s hildebrandt hil1 claiming that critical points of continuously differentiable elliptic conformally invariant lagrangian in two dimensions are continuous

completing biprefix codes a subset x of the free monoid a is called a biprefix code if it is both a prefix code and a suffix code we prove in this note that any finite biprefix code is contained in a miximal biprefix code which is recognizable by a finite automation

fluctuations around classical solutions for gauge theories in lagrangian and hamiltonian approach we analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both lagrangian and hamiltonian formalisms we prove that a fluctuations theory described by a quadratic lagrangian has the same constraint structure and number of physical degrees of freedom as the original non perturbed theory assuming the non degenerate solution has been chosen we show that the number of noether gauge symmetries is the same in both theories but that the gauge algebra in the fluctuations theory becomes abelianized we also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it we illustrate these results with examples

finite maximal solid codes solid codes a special class of bifix codes were introduced recently in the connection with formal languages however they have a much earlier history and more important motivation in information transmission dating back to the 1960s in this paper they are studied as an independent subject in the theory of variable length codes it is shown that every finite solid code is contained in a finite maximal one based on further analysis of the structure of finite maximal solid codes an algorithm is proposed to construct all of them starting from the most simple and evident ones

on maximal codes with a finite interpreting delay the notion of codes with a finite interpreting delay f i d was introduced in guesnet theoret inform appl 34 2000 47 59 in this paper we are interested in the notion of maximality for f i d codes we characterize the maximal f i d codes in terms of completeness we also present an embedding procedure keeping thinness rationality and the delay

the jacobian determinant revisited this paper is devoted to the study of the jacobian determinant of a map g from a smooth bounded open subset of rn into rn n 2 more generally could be a smooth bounded open subset of an n dimensional manifold starting with the seminal work of c b morrey 27 y reshetnyak 32 and j ball 1 it has been known that one can define the distributional jacobian determinant det g under fairly weak assumption on g in particular it is defined for all maps g w 1 n2 n 1 and also for all

on the maximality of languages with combined types of code properties we consider the decision problem of whether or not a given regular language is maximal with respect to certain combined types of code properties in the recent past there have been a few formal methods for defining code properties such as the trajectory based type of codes and the transducer based type of codes that allow one to decide the maximality problem including the case where maximality is tested with respect to combined properties within these formal methods the property of deciphering delay 1 also known as decoding delay 1 is not known to be definable with these methods but it is known that the maximality of this property alone is decidable for regular languages here we consider the problem of deciding maximality of a regular language with respect to deciphering delay 1 and a transducer based property such as suffix code overlap free language and error detection properties

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

state splitting for variable length graphs corresp the state splitting algorithm of adler coppersmith and hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths this has the potential to improve modulation code construction techniques although the ideas of state splitting come from dynamical systems completely graph theoretic terms are used

constraint rescaling in refined algebraic quantisation momentum constraint we investigate refined algebraic quantisation within a family of classically equivalent constrained hamiltonian systems that are related to each other by rescaling a momentum type constraint the quantum constraint is implemented by a rigging map that is motivated by group averaging but has a resolution finer than what can be peeled off from the formally divergent contributions to the averaging integral three cases emerge depending on the asymptotics of the rescaling function i quantisation is equivalent to that with identity scaling ii quantisation fails owing to nonexistence of self adjoint extensions of the constraint operator iii a quantisation ambiguity arises from the self adjoint extension of the constraint operator and the resolution of this purely quantum mechanical ambiguity determines the superselection structure of the physical hilbert space prospects of generalising the analysis to systems with several constraints are discussed

precircular codes and periodic biinfinite words the aim of decoding or factorizing in a single way biinfinite words with a finitary language leads us to consider two distinct notions of factorization for biinfinite words for one of these notions requiring singleness of decoding periodic biinfinite words leads us to study circular codes the other notion leads us to define the new notion of precircular codes precircular codes are defined and analyzed the family of precircular codes is compared to the family of circular codes and to the family of almost circular codes the structure of two element precircular codes is determined codes and precircular codes are characterized by their way of acting upon periodic biinfinite words

on regularity theory for n p harmonic maps into manifolds abstract in this paper we continue the investigation started in the paper da lio and schikorra 2014 of the regularity of the so called weak n p harmonic maps in the critical case these are critical points of the following nonlocal energy l s u r n s 2 u x p d x where u h s p r n n and n r n is a closed k dimensional smooth manifold and s n p we prove holder continuity for such critical points for p 2 for p 2 we obtain the same under an additional lorentz space assumption the regularity theory is in the two cases based on regularity results for nonlocal schrodinger systems with an antisymmetric potential

codes unambiguous automata and sofic systems we study the relationship between codes and unambiguous automata inside a sofic system we show that a recognizable set is a code in a sofic system if and only if a particular automaton associated to the set and the shift is unambiguous we discuss an example of a finite complete code in a sofic system in connection with the factorization conjecture

sharp commutator estimates via harmonic extensions abstract we give an alternative proof of several sharp commutator estimates involving riesz transforms riesz potentials and fractional laplacians our methods only involve harmonic extensions to the upper half space integration by parts and trace space characterizations the commutators we investigate are jacobians more generally coifman rochberg weiss commutators chanillo s commutator with the riesz potential coifman mcintosh meyer kato ponce vega type commutators the fractional leibniz rule and the da lio riviere three term commutators we also give a new limiting l 1 estimate for a double commutator of coifman rochberg weiss type and several intermediate estimates the beauty of our method is that all those commutator estimates which are originally proven by various specific methods or by general para product arguments can be obtained purely from integration by parts and trace theorems another interesting feature is that in all these cases the cancellation effect responsible for the commutator estimate simply follows from the product rule for classical derivatives and can be traced in a precise way

fractional div curl quantities and applications to nonlocal geometric equations abstract we investigate a fractional notion of gradient and divergence operator we generalize the div curl estimate by coifman lions meyer semmes to fractional div curl quantities obtaining in particular a nonlocal version of wente s lemma we demonstrate how these quantities appear naturally in nonlocal geometric equations which can be used to obtain a theory for fractional harmonic maps analogous to the local theory firstly regarding fractional harmonic maps into spheres we obtain a conservation law analogous to shatah s conservation law and give a new regularity proof analogous to helein s for harmonic maps into spheres secondly we prove regularity for solutions to critical systems with nonlocal antisymmetric potentials on the right hand side since the half harmonic map equation into general target manifolds has this form as a corollary we obtain a new proof of the regularity of half harmonic maps into general target manifolds following closely riviere s celebrated argument in the local case lastly the fractional div curl quantities provide also a new simpler proof for holder continuity of w s n s harmonic maps into spheres and we extend this to an argument for w s n s harmonic maps into homogeneous targets this is an analogue of strzelecki s and toro wang s proof for n harmonic maps into spheres and homogeneous target manifolds respectively

traces of weighted sobolev spaces old and new abstract we give short simple proofs of uspenski s results characterizing besov spaces as trace spaces of weighted sobolev spaces we generalize uspenski s results and prove the optimality of these generalizations we next show how classical results on the functional calculus in the besov spaces can be obtained as straightforward consequences of the theory of weighted sobolev spaces

on generators of rational ω power languages un language parfait est un langage l de la forme l r ou r est un langage de mots finis appele generateur de l etant donne un langage rationel r nous etudions la relation d inclusion dans la famille des generateurs de r 1 1 nous montrons d abord que les generateurs maximaux pour l inclusion sont rationnels constructibles et en nombre fini de plus tout generateur de r est inclus dans l un d entre eux 2 2 nous montrons ensuite que l on peut tester si un generateur est minimal pour l inclusion an power language is an language l of the form l r for some language r called generator of l for a given rational language r we study the relation of inclusion in the family of the generators of r 1 1 we first prove that the maximal generators with respect to the inclusion are rational constructible and finite in number moreover any generator of r is included in one of them 2 2 then we prove that one can test whether a generator is minimal for the inclusion

a syntactic congruence for rational ω languages buchi has proved that if l is a rational language then there exists a finite congruence for which l is saturated in the following sense u v l 0 u v l here we define the syntactic congruence of l which is the largest congruence having this property

completing circular codes in regular submonoids let m be an arbitrary submonoid of the free monoid a and let x m be a variable length code for short a code x is weakly m complete iff any word in m is a factor of some word in x j neraud c selmi free monoid theory maximality and completeness in arbitrary submonoids internat j algebra comput 13 5 2003 507 516 given a regular submonoid m and given an arbitrary code x m we are interested in the existence of a weakly m complete code x that contains x actually in j neraud completing a code in a regular submonoid in acts of mcu 2004 lect notes comput sci 3354 2005 281 291 j neraud completing a code in a submonoid of finite rank fund inform 74 2006 549 562 by presenting a general formula we have established that in any case such a code x exists in the present paper we prove that any regular circular code x m may be embedded into a weakly m complete one iff the minimal automaton with behavior m has a synchronizing word as a consequence of our result an extension of the famous theorem of schutzenberger is stated for regular circular codes in the framework of regular submonoids we study also the behaviour of the subclass of uniformly synchronous codes in connection with these questions

the fractional calderon problem low regularity and stability abstract the calderon problem for the fractional schrodinger equation was introduced in the work ghosh et al to appear which gave a global uniqueness result also in the partial data case this article improves this result in two ways first we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds second we show that the results are valid for potentials in scale invariant l p or negative order sobolev spaces a key point is a quantitative approximation property for solutions of fractional equations obtained by combining a careful propagation of smallness analysis for the caffarelli silvestre extension and a duality argument

locally complete sets and finite decomposable codes we are interested in the concept of locally complete set a subset x of the free monoid is locally complete if a code y a exists with y a x y and such that both the sets of xand y have the same sets of factors our contribution is based on the three following results a characterization of local completeness for very thin sets in terms of morphic images a polynomial time algorithm for deciding whether a finite code is locally complete a polynomial time algorithm for deciding whether a finite maximal code is decomposable

the method of poles a coding method for constrained channels a method for solving coding problems involving channels restricted by finite state constraints is presented the method was introduced by p a franaszek 1969 and is based on the computation of a set of principal states it is proved that state independent decoding is guaranteed the main result is that the transducer constructed using the method is a local automaton in its output the method is also related to recent work in symbolic dynamics by r l adler 1987 b marcus 1985 and others typical applications are coding methods for magnetic storage

codes circulaires automates locaux et entropie abstract the theory of codes and finite automata is applied to prove the existence of codes suitable for coding arbitrary sequences into a constrained system of sequences called system of finite type the techniques are different from those used by adler coppersmith hassner and marcus in earlier work on the same problem

on maximal synchronous codes in this paper we are interested in maximal synchronous codes more precisely we prove that we can embed any synchronous code in a maximal one moreover we establish that for synchronous codes the notion of maximality in the family of synchronous codes is equivalent to the notion of maximality in the family of codes

an application of hajo s factorizations to variable length codes we give a new characterization of some factorizations of finite cyclic groups described by hajos as a consequence we prove that the embedding problem for a particular class of codes is decidable in particular we link this problem for codes c a b ba to schutzenberger s factorization conjecture via hajos factorizations

dynamical structure of irregular constrained systems hamiltonian systems with functionally dependent constraints irregular systems for which the standard dirac procedure is not directly applicable are discussed they are classified according to their behavior in the vicinity of the constraint surface into two fundamental types if the irregular constraints are multilinear type i then it is possible to regularize the system so that the hamiltonian and lagrangian descriptions are equivalent when the constraints are power of a linear function type ii regularization is not always possible and the hamiltonian and lagrangian descriptions may be dynamically inequivalent it is shown that the inequivalence between the two formalisms can occur if the kinetic energy is an indefinite quadratic form in the velocities it is also shown that a system of type i can evolve in time from a regular configuration into an irregular one without any catastrophic changes irregularities have important consequences in the linearized approximation to nonlinear theories

regularity of n 2 harmonic maps into spheres we prove holder continuity for n 2 harmonic maps from arbitrary subsets of rn into a sphere this extends a recent one dimensional result by f da lio and t riviere to arbitrary dimensions the proof relies on compensation effects which we quantify adapting an approach for wente s inequality by l tartar instead of besov space arguments which were used in the one dimensional case moreover fractional analogues of hodge decomposition and higher order poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied this work was the author s phd thesis written in march 2010

equivalence between the lagrangian and hamiltonian formalism for constrained systems the equivalence between the lagrangian and hamiltonian formalism is studied for constraint systems a procedure to construct the lagrangian constraints from the hamiltonian constraints is given those hamiltonian constraints that are first class with respect to the hamiltonian constraints produce lagrangian constraints that are fl projectable

finitely generated bi l languages abstract in this paper we are interested in the bi infinite words and mainly in the bi infinite power of languages of finite words with the aim of deciding whether given a rational language r r is finitely generated i e whether r r for some finite set f we study the notions of bilimit and biadherence the stated results become then efficient tools for solving the initial decision problem

completion of recognizable bifix codes in 1982 perrin obtained a method to embed a finite bifix code into a recognizable complete bifix code it is unknown whether any recognizable bifix code is contained in a recognizable complete bifix code this open problem is positively solved in this paper we show that any recognizable bifix code is contained in a recognizable complete bifix code and an embedding method is obtained

completing prefix codes in submonoids let m be a submonoid of the free monoid a and let x m be a variable length code for short a code x is weakly m complete if any word in m is a factor of some word in x j neraud c selmi free monoid theory maximality and completeness in arbitrary submonoids internat j algorithms comput 13 5 2003 507 516 given a code x m we are interested in the construction of a weakly m complete code that contains x if it exists in the case where m and x are regular sets the existence of such a code has been established j neraud completing a code in a regular submonoid of the free monoid in acts of mcu 2004 lecture notes in computer sciences vol 3354 springer berlin 2005 pp 281 291 j neraud on the completion of codes in submonoids with finite rank fund inform to appear actually this result lays upon a method of construction that preserves the regularity of sets as well known any regular or finite code may be embedded into a regular finite prefix code that is complete in a instance a regular submonoid m of a and a regular or finite prefix code x m question does a weakly m complete regular finite prefix code containing x exist

nonlinear commutators for the fractional p laplacian and applications we prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p laplacian this implies that solutions to certain degenerate nonlocal equations are higher differentiable also weakly fractional p harmonic functions which a priori are less regular than variational solutions are in fact classical as an application we show that sequences of uniformly bounded frac n s harmonic maps converge strongly outside at most finitely many points

lifting degree and distributional jacobian revisited let g i 0 1 s1 if g vmo we may write g ei for some vmo this is unique modulo 2 see 13 and the earlier work 14 there is no control of bmo in terms of g bmo since we always have g bmo 2 and bmo can be arbitrarily large recall however that when g bmo is sufficiently small there is a linear estimate bmo c g bmo see 13 theorem 4 14 and remark 0 2 below we are going to establish that a norm slightly stronger than g bmo does control bmo consider for 1 p 0 s 1 the fractional sobolev space ws p i equipped with its standard seminorm

on energy critical half wave maps into mathbb s 2 s 2 we consider the energy critical half wave maps equation begin aligned partial t mathbf u mathbf u wedge nabla mathbf u 0 end aligned for mathbf u 0 t times mathbb r rightarrow mathbb s 2 we give a complete classification of all traveling solitary waves with finite energy the proof is based on a geometric characterization of these solutions as minimal surfaces with not necessarily free boundary on mathbb s 2 in particular we discover an explicit lorentz boost symmetry which is implemented by the conformal mobius group on the target mathbb s 2 applied to half harmonic maps from mathbb r to mathbb s 2 complementing our classification result we carry out a detailed analysis of the linearized operator l around half harmonic maps mathbf q with arbitrary degree m geqslant 1 and consisting of m identical blaschke factors here we explicitly determine the nullspace including the zero energy resonances in particular we prove the nondegeneracy of mathbf q moreover we give a full description of the spectrum of l by finding all its l 2 eigenvalues and proving their simplicity furthermore we prove a coercivity estimate for l and we rule out embedded eigenvalues inside the essential spectrum our spectral analysis is based on a reformulation in terms of certain jacobi operators tridiagonal infinite matrices obtained from a conformal transformation of the spectral problem posed on mathbb r to the unit circle mathbb s finally we construct a unitary map which can be seen as a gauge transform tailored for a future stability and blowup analysis close to half harmonic maps our spectral results also have potential applications to the half harmonic map heat flow which is the parabolic counterpart of the half wave maps equation

completion of codes with finite bi decoding delays let a be a free monoid generated by a set a and let x a be a code with property p the embedding of x into a complete code y a with the same property p is called the completion of x the method of completion of rational bifix codes and codes with finite decoding delays have been investigated by a number of authors in this paper we provide a general method of construction for completing the codes with finite bi decoding delays as a consequence the completion method of rational bifix codes and codes with finite decoding delays is extended and applied to codes with finite bi decoding delays

sub criticality of non local schrodinger systems with antisymmetric potentials and applications to half harmonic maps abstract we consider non local linear schrodinger type critical systems of the type 1 1 4 v v in r where is antisymmetric potential in l 2 r so m v is an r m valued map and v denotes the matrix multiplication we show that every solution v l 2 r r m of 1 is in fact in l loc p r r m for every 2 p in other words we prove that the system 1 which is a priori only critical in l 2 happens to have a subcritical behavior for antisymmetric potentials as an application we obtain the c loc 0 regularity of weak 1 2 harmonic maps into c 2 compact sub manifolds without boundary

codes and local constraints etude du probleme de l existance et de la construction de codes dont les elements des mots satisfont certaines contraintes concernant les sequences de lettres qu ils peuvent contenir l equivalence entre les notions de maximalite et de completude pour ces codes est etudiee

the difficulty of symplectic analysis with second class systems using the basic concepts of the chain by chain method we show that the symplectic analysis which was claimed to be equivalent to the usual dirac method fails when second class constraints are present we propose a modification in symplectic analysis that solves the problem

completing comma free codes we prove that for every regular comma free code there exists a maximal comma free code containing it which is still regular and moreover we can effectively locate such a completion in particular we can decide whether a given regular comma free code is maximal

boundary equations and regularity theory for geometric variational systems with neumann data we study boundary regularity of maps from two dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which at the boundary intersect perpendicularly with a support manifold for example harmonic maps or h surfaces with a partially free boundary condition in the interior it is known by the celebrated work of riviere that these maps satisfy a system with an antisymmetric potential from which one can derive the interior regularity of the solution avoiding a reflection argument we show that these maps satisfy along the boundary a system of equations which also exhibits a nonlocal antisymmetric potential that combines information from the interior potential and the geometric neumann boundary condition we then proceed to show boundary regularity for solutions to such systems