choquet type l 1 spaces of a vector capacity abstract given a set function with values in a banach space x we construct an integration theory for scalar functions with respect to by using duality on x and choquet scalar integrals our construction extends the classical bartle dunford schwartz integration for vector measures since just the minimal necessary conditions on are required several l 1 spaces of integrable functions associated to appear in such a way that the integration map can be defined in them we study the properties of these spaces and how they are related we show that the behavior of the l 1 spaces and the integration map can be improved in the case when x is an order continuous banach lattice providing new tools for non linear operator theory and information sciences

some properties of the variations of non additive set functions ii in this paper we continue the work of the preceding paper zhang fuzzy sets and systems to appear to introduce the concepts of the third kind of variations for non additive set functions the inclusion variations and discuss some properties of the variations in particular we investigate the inclusion variations of signed fuzzy measures which have closely to do with the uniqueness of jordan decomposition of non additive set functions we also show that these three kinds of variations inclusion variation disjoint variation and chain variation coincide when the considered set functions are additive finally we attempt to answer one of the open problems raised by pap null additive set functions kluwer academic publishers dordrecht 1995

encoding of dklr sequences using one weight set traditional schemes for encoding and decoding runlength constrained sequences using the enumeration principle require two sets of weighting coefficients a new enumeration is presented requiring only one set of coefficients

the exponential homomorphism for the second syntomic cohomology abstract let ok be a complete discrete valuation ring with perfect residue field f of characteristic p 3 and m a free filtered dieudonne module the second relative syntomic cohomology h2 ok f s m 2 with coefficients in m is an object related to arithmetic geometry such as the albanese kernel in this article we study h2 ok f s m 2 by constructing the exponential homomorphism we determine the structure of h2 ok f s m 2 under the assumption that m is of hodge witt type and that the absolute ramification index of ok is prime to p

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

optimal block type decodable encoders for constrained systems a constrained system is presented by a finite state labeled graph for such systems we focus on block type decodable encoders comprising three classes known as block block decodable and deterministic encoders franaszek 1968 gives a sufficient condition which guarantees the equality of the optimal rates of block decodable and deterministic encoders for the same block length we introduce another sufficient condition called the straight line condition which yields the same result run length limited rll d k and maximum transition run mtr j k constraints are shown to satisfy both conditions in general block type decodable encoders are constructed by choosing a subset of states of the graph to be used as encoder states such a subset is known as a set of principal states for each type of encoder and each block length a natural problem is to find a set of principal states which maximizes the code rate we show how to compute the asymptotically optimal sets of principal states for deterministic encoders and how they are related to the case of large but finite block lengths we give optimal sets of principal states for mtr j k block type decodable encoders for all codeword lengths finally we compare the code rate of nonreturn to zero inverted nrzi encoders to that of corresponding nonreturn to zero nrz and signed nrzi encoders

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

integral crystalline cohomology over very ramified valuation rings in this paper we intend to show how fontaine s comparison theory fol fo2 between crystalline and p adic etale cohomology can be extented to very ramified base rings so far it had been developed either for qp coefficients or zp coefficients if the base is unramified over the witt vectors see fa2 for example it states that for any p adic discrete valuation ring v there exists a ring b v with the following property if x denotes a smooth and proper v scheme the p adic etale cohomology of the generic fiber x xv k is related to the crystalline cohomology of x v0 vo defined below by an isomorphism

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

on the direct summand conjecture and its derived variant andre recently gave a beautiful proof of hochster s direct summand conjecture in commutative algebra using perfectoid spaces his two main results are a generalization of the almost purity theorem the perfectoid abhyankar lemma and a construction of certain faithfully flat extensions of perfectoid algebras where discriminants acquire all p power roots in this paper we explain a quicker proof of hochster s conjecture that circumvents the perfectoid abhyankar lemma instead we prove and use a quantitative form of scholze s hebbarkeitssatz the riemann extension theorem for perfectoid spaces the same idea also leads to a proof of a derived variant of the direct summand conjecture put forth by de jong

serre tate theory for shimura varieties of hodge type we study the formal neighbourhood of a point in the mu ordinary locus of an integral model of a hodge type shimura variety we show that this formal neighbourhood has a structure of a shifted cascade moreover we show that the cm points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization in terms of its endomorphisms analogous to the serre tate canonical lift of an ordinary abelian variety

mod points on shimura varieties of abelian type we show that the mod p points on a shimura variety of abelian type with hyperspecial level have the form predicted by the conjectures of kottwitz and langlands rapoport along the way we show that the isogeny class of a mod p point contains the reduction of a special point

optimal block codes for m ary runlength constrained channels in this work we consider the analysis and design of optimal block decodable m ary runlength limited rll codes we present two general construction methods one based on permutation codes due to datta and mclaughlin 1999 and the other a nonbinary generalization of the binary enumeration methods of patrovics and immink 1996 and gu and fuja 1994 the construction based on permutation codes is simple and asymptotically in block length optimal while the other construction is optimal in the sense that the resulting codes have the highest rate among all block decodable codes for any block length in the process we shall also extend a result due to zehavi and wolf 1988 on the capacity of binary d k constraints to m ary channels finally we present examples of template codes remarkably low complexity m d k block codes which achieve the optimal rate without the use of enumeration

a general error correcting code construction for run length limited binary channels a general method is presented for constructing a single error correcting run length limited code for the class of input restricted binary symmetric channels described by the parameters d k where d is the minimum and k the maximum number of consecutive zeros in any allowable channel input sequence upper and lower bounds on the rates of these codes are derived

on the null additivity and the autocontinuity of a fuzzy measure abstract in this paper further research on the null additivity and autocontinuity of fuzzy measures is made we prove that autocontinuity from below and autocontinuity from above of a fuzzy measure are equivalent when this fuzzy measure is finite furthermore if the space x is countable then the null additivity is equivalent to the autocontinuity

syntomic complexes and p adic nearby cycles we compute syntomic cohomology of semistable affinoids in terms of cohomology of varphi gamma modules which thanks to work of fontaine herr andreatta iovita and kedlaya liu is known to compute galois cohomology of these affinoids for a semistable scheme over a mixed characteristic local ring this implies a comparison isomorphism up to some universal constants between truncated sheaves of p adic nearby cycles and syntomic cohomology sheaves this generalizes the comparison results of kato kurihara and tsuji for small tate twists where no constants are necessary as well as the comparison result of tsuji that holds over the algebraic closure of the field as an application we combine this local comparison isomorphism with the theory of finite dimensional banach spaces and finiteness of etale cohomology of rigid analytic spaces proved by scholze to prove a semistable conjecture for formal schemes with semistable reduction

some properties of the variations of non additive set functions on t tribes the inclusion variation and chain variation on t tribes play an important role in t measures and fuzzy games theory where they were used for additive set functions on t tribe in this paper classical variation theory is extended to non additive set functions on ttribes after defining the inclusion variation disjoint and chain variation on t tribes we investigate some properties of these three variations in detail such as the null null additivity exhaustivity order continuity continuity from the left and so on an alternative proof of the jordan decomposition theorem is given thus some results pertaining to variations in classical measure theory are generalized in some case as for t measures on t tribe its different formal variations can be extended to ts measures on ts tribes

la filtration canonique des mathcal o modules p divisibles in this article we associate to g a truncated p divisible mathcal o module of given signature where mathcal o is a finite unramified extension of mathbb z p a filtration of g by sub mathcal o modules under the condition that its hasse mu invariant is smaller than an explicit bound this filtration generalise the one given when g is mu ordinary the construction of the filtration relies on a precise study of the crystalline periods of a p divisible mathcal o module we then apply this result to families of such groups in particular to strict neighbourhoods of the mu ordinary locus inside some pel shimura varieties

potentially semi stable deformation rings let k qp be a finite extension and gk gal k k the galois group of an alge braic closure k let f be a finite field of characteristic p and vf a finite dimensional f vector space equipped with a continuous action of gkthe study of the defor mation theory of galois representations was initiated by mazur ma who showed that if vf has no non trivial endomorphisms then it admits a universal deformation ring ryw after the work of wiles wi and the conjectures of fontaine mazur fm it became clear that for arithmetic applications it was important to understand cer tain quotients of ry corresponding to deformations satisfying certain conditions for example wiles uses deformations which arise from finite flat group schemes and the corresponding quotient of ryw was constructed by ramakrishna ra suppose that l k is a finite extension and let a b be integers it seems to be a kind of folklore conjecture that there should be a quotient of ry whose points in finite extensions of w f l p correspond to deformations of vf which become semi stable over l and have hodge tate weights in the interval a b this is closely related to the final conjecture of fo 3 special cases of this when vf is 2 dimensional are conjectured in the papers of fontaine mazur fm p 191 breuil conrad diamond taylor bcdt conj 1 1 1 and breuil m zard bm 2 2 2 4 the purpose of this paper is to prove such a result

the almost product structure of newton strata in the deformation space of a barsotti tate group with crystalline tate tensors in this paper we construct the almost product structure of the minimal newton stratum in deformation spaces of barsotti tate groups with crystalline tate tensors similar to oort s and mantovan s construction for shimura varieties of pel type it allows us to describe the geometry of the newton stratum in terms of the geometry of two simpler objects the central leaf and the isogeny leaf this yields the dimension and the closure relations of the newton strata in the deformation space in particular their nonemptiness shows that a generalisation of grothendieck s conjecture of deformations of barsotti tate groups with given newton polygon holds as an application we determine analogous geometric properties of the newton stratification of shimura varieties of hodge type and prove the equidimensionality of rapoport zink spaces of hodge type

further discussion on the hahn decomposition theorem for signed fuzzy measure abstract this paper gives a counterexample that the union of two negative sets is not a negative set for signed fuzzy measure showing that the proof of theorem 2 in liu 1993 is not valid furthermore we provide a proof for the hahn decomposition theorem when the space x is countable or the signed fuzzy measure possess the property d

on the hodge newton filtration for p divisible o modules the notions hodge newton decomposition and hodge newton filtration for f crystals are due to katz and generalize messing s result on the existence of the local etale filtration for p divisible groups recently some of katz s classical results have been generalized by kottwitz to the context of f crystals with additional structures and by moonen to ordinary p divisible groups in this paper we discuss further generalizations to the situation of crystals in characteristic p and of p divisible groups with additional structure by endomorphisms

lebesgue decomposition theorem for σ finite signed fuzzy measures further research on signed fuzzy measures is made lebesgue decomposition theorems for finite signed fuzzy measures and fuzzy measures are proved under the null null additive condition thus the relative result in classical measure theory is generalized

on central leaves of hodge type shimura varieties with parahoric level structure kisin and pappas publ math inst hautes etudes sci 2018 constructed integral models of hodge type shimura varieties with parahoric level structure at p 2 such that the formal neighbourhood of a mod p point can be interpreted as a deformation space of p divisible group with some tate cycles generalising faltings construction in this paper we study the central leaf and the closed newton stratum in the formal neighbourhoods of mod p points of kisin pappas integral models with parahoric level structure namely we obtain the dimension of central leaves and the almost product structure of newton strata in the case of hyperspecial level structure i e in the good reduction case our main results were already obtained by hamacher math z 287 3 4 1255 1277 2017 and we show that the result of this paper holds for ramified groups as well

on fuzzy measures defined by fuzzy integrals on definit une mesure floue comme une fonction ensemble sur 7b f qui est une algebre de sous ensembles de l ensemble x

dieudonne crystals and wach modules for p divisible groups let k be a perfect field of characteristic p 2 and k an extension of f fracw k contained in some f pr using crystalline dieudonne theory we provide a classification of p divisible groups over r ok t1 td in terms of finite height modules over s w k u t1 td when d 0 such a classification is a consequence of a special case of the theory of kisin ren in this setting our construction gives an independent proof of this result and moreover allows us to recover the dieudonne crystal of a p divisible group from the wach module associated to its tate module by berger breuil or by kisin ren

pseudo atoms atoms and a jordan type decomposition in effect algebras abstract the aim of this paper is to introduce and investigate the concept of pseudo atoms of a real valued function m defined on an effect algebra l a few examples of pseudo atoms and atoms are given in the context of null additive null null additive and pseudo null additive functions and also some fundamental results for pseudo atoms under the assumption of null null additivity are established the notions of total variation m positive variation m and negative variation m of a real valued function m on l are studied elaborately and it is proved for a modular measure m which is of bounded total variation defined on a d lattice l that m is pseudo atomic or atomic if and only if its total variation m is pseudo atomic or atomic finally a jordan type decomposition theorem for an extended real valued function m of bounded total variation defined on an effect algebra l is proved and some properties on decomposed parts of m such as continuity from below pseudo atomicity or atomicity and being measure are discussed a characterization for the function m to be of bounded total variation is established here and used in proving above mentioned jordan type decomposition theorem

finite state codes a class of codes called finite state fs codes is defined and investigated the codes which generalize both block and convolutional codes are defined by their encoders which are finite state machines with parallel inputs and outputs a family of upper bounds on the free distance of a given fs code is derived a general construction for fs codes is given and it is shown that in many cases the fs codes constructed in this way have a free distance that is the largest possible catastrophic error propagation cep for fs codes is also discussed it is found that to avoid cep one must solve the graph theoretic problem of finding a uniquely decodable edge labeling of the state diagram

on the hodge newton filtration for p divisible groups of hodge type a p divisible group or more generally an f crystal is said to be hodge newton reducible if its newton polygon and hodge polygon have a nontrivial contact point katz proved that hodge newton reducible f crystals admit a canonical filtration called the hodge newton filtration the notion of hodge newton reducibility plays an important role in the deformation theory of p divisible groups the key property is that the hodge newton filtration of a p divisible group over a field of characteristic p can be uniquely lifted to a filtration of its deformation we generalize katz s result to f crystals that arise from an unramified local shimura datum of hodge type as an application we give a generalization of serre tate deformation theory for local shimura data of hodge type

an enumerative method for runlength limited codes permutation codes permutation codes introduced by slepian 1965 were shown to perform well on an additive white gaussian noise awgn channel unfortunately these codes required large lookup tables making them quite complex to implement even though the maximum likelihood decoder is very simple in this correspondence we present an enumeration scheme which encodes and decodes permutation codes with low complexity we concentrate on the use of permutation codes for constructing high rate codes that satisfy runlength limited constraints wolf 1990 showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless runlength limited constrained channel wolf however gave no efficient encoders decoder our code construction is enumerative but unlike other enumerative codes has storage requirements that are a function of the runlength parameters d and k instead of the block length n in addition these codes have error detection and correction capabilities finally we use this approach to construct 0 g i codes whereby all odd numbered occurrences of double adjacent errors are detected as an example a 99 2 efficient rate 498 528 0 6 3 code is presented

a finer tate duality theorem for local galois symbols abstract let k be a finite extension of q p let a b be abelian varieties over k with good reduction for any integer m 1 we consider the galois symbol k k a b m h 2 k a m b m where k k a b is the somekawa k group attached to a b this map is a generalization of the galois symbol k 2 m k m h 2 k m 2 of the bloch kato conjecture where k 2 m k is the milnor k group of k in this paper we give a geometric description of the image of this generalized galois symbol by looking at the tate duality pairing h 2 k a m b m hom g k a m b m z m where b is the dual abelian variety of b under this perfect pairing we compute the exact annihilator of the image of the galois symbol in terms of an object of integral p adic hodge theory in this way we generalize a result of tate for h 1 moreover our result has applications to zero cycles on abelian varieties

a new approach to constructing optimal block codes for runlength limited channels the paper describes a technique for constructing fixed length block codes for d k constrained channels the codes described are of the simplest variety codes for which the encoder restricted to any particular channel state is a one to one mapping and which is not permitted to look ahead to future messages such codes can be decoded with no memory and no anticipation and are thus an example of what schouhamer immink 1992 has referred to as block decodable for a given blocklength n and given values of d k the procedure constructs a code with the highest possible rate among all such block codes and it does so without the iterative search that is typically used i e franaszek s recursive elimination algorithm the technique used is similar to beenker and immink s 1983 construction 2 in that every message is associated with a d k l r sequence of length n d however the values used in the present approach are l k d and r k 1 as opposed to beenker and schouhamer immink s values of l r k d thus the present approach demonstrates that construction 2 is optimal for d 1 but is suboptimal for d 1 furthermore the structure of the present codes permits enumerative coding techniques to simplify encoding and decoding

on a conjecture of rapoport and zink in their book rapoport and zink constructed rigid analytic period spaces mathcal f wa for fontaine s filtered isocrystals and period morphisms from pel moduli spaces of p divisible groups to some of these period spaces they conjectured the existence of an etale bijective morphism mathcal f a to mathcal f wa of rigid analytic spaces and of a universal local system of p vector spaces on mathcal f a such a local system would give rise to a tower of etale covering spaces breve mathcal e widetilde k of mathcal f a equipped with a hecke action and an action of the automorphism group j p of the isocrystal with extra structure

l adic etale cohomology of shimura varieties of hodge type with non trivial coefficients let mathsf g mathsf x be a shimura datum of hodge type let p be an odd prime such that mathsf g mathbb q p splits after a tamely ramified extension and p not mid pi 1 mathsf g mathrm der under some mild additional assumptions that are satisfied if the associated shimura variety is proper and mathsf g mathbb q p is either unramified or residually split we prove the generalisation of mantovan s formula for the l adic cohomology of the associated shimura variety on the way we derive some new results about the geometry of the newton stratification of the reduction modulo p of the kisin pappas integral model

a motivic conjecture of milne let k be an algebraically closed field of characteristic p 0 let w k be the ring of witt vectors with coefficients ink we prove a motivic conjecture of milne that relates thecohomology with zp coefficients to the crystalline cohomology with integral coefficients in the wider context ofp divisible groups endowed with families of crystalline tensors over a finite discrete valuation ring extension of w k the result extends work of faltings as a main new tool we construct global deformations of p divisible groups endowed with crystalline tensors over certain regular formally smooth schemes over w k