least squares design of variable maximally linear fir differentiators in this correspondence the design of variable maximally linear vml fir differentiators by least squares method is proposed the vml differentiator is designed such that its maximally flat frequency is adjustable the used transfer function is formulated in a variable frame and the farrow structure can be applied for the implementation of vml fir differentiators for comparison the non variable optimal design of maximally linear fir differentiators is also proposed the experiments show that the variable design indeed possesses the flat characteristics as the independent optimal design

the derived category of an exact category there is some confusion in the literature regarding the derived category of an exact category 8 thomason gives a satisfactory treatment of the bounded derived category in ct 1 11 6 see also appendix a the result is that provided all weakly split epimorphisms in 8 are admissible the bounded derived category may be defined as usual although thomason does not say it the categories d 6 d d may also be defined in the same way the definition of the unbounded derived category is more difficult and is very poorly treated in the literature for instance in bbd this derived category is only defined provided every morphism in 6 admits a kernel see bbd 1 1 41 this is very unsatisfactory since very few exact categories satisfy the condition in this article we will show that d b may be defined whenever 6 is saturated karoubian in thomason s terminology an exact category is saturated if every idempotent splits i e 6 contains all direct summands of its objects for the purpose of comparing with thomason s result the bounded derived category is defined for more 8 s all that is required to define db is that whenever an idempotent e a a factors as a f ba a with fog lb then e is split thomason calls such idempotents weakly split and we will honor his notation we will show here that these constructions are in some sense best possible remark 1 8 for d 6 remarks 1 9 and 1 10 for d d d b db 6 there are two reasons why i wrote this note one is to correct the misconceptions in the literature but more importantly the proof of the key result lemma 1 2 depends on an important characterization of tpaisse subcategories due to rickard and this article is intended to highlight rickard s criterion a full triangulated subcategory y of a triangulated

p adic multiple zeta values ii tannakian interpretations we establish a tannakian formalism of p adic multiple polylogarithms and p adic multiple zeta values introduced in our previous paper via a comparison isomorphism between a de rham fundamental torsor and a rigid fundamental torsor of the projective line minus three points and also discuss its hodge and e tale analogues as an application we give a way to erase log poles of p adic multiple polylogarithms and introduce overconvergent p adic multiple polylogarithms which might be p adic multiple analogue of zagier s single valued complex polylogarithms

from discrete visco elasticity to continuum rate independent plasticity rigorous results we show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco elastic crystal lattice with quenched disorder the constitutive structure changes as a result of two concurrent limiting procedures the vanishing viscosity limit and the discrete to continuum limit in the course of these limits a non convex elastic problem transforms into a convex elastic problem while the quadratic rate dependent dissipation of visco elastic lattice transforms into a singular rate independent dissipation of an ideally plastic solid in order to emphasize our ideas we employ in our proofs the simplest prototypical system mimicking the phenomenology of transformational plasticity in shape memory alloys the approach however is sufficiently general that it can be used for similar reductions in the cases of more general plasticity and damage models

on integrality of p adic iterated integrals abstract the purpose of this paper is to prove integrality for certain p adic iterated coleman integrals as underlying geometry we will take the complement of a divisor d x with good reduction where x is the projective line or an elliptic curve over the witt vectors of a perfect characteristic p field as a corollary we prove a lower bound for the valuations of p adic multiple zeta values

on the design of fir digital differentiators which are maximally linear at the frequency pi p p in positive integers digital differentiators dds which are maximally linear at the spot frequency omega pi p p in positive integers are proposed for operation over a narrow band of frequencies the suggested dds besides giving zero phase error over the entire band of frequencies pi

coleman integration using the tannakian formalism we use a new idea to construct a theory of iterated coleman functions on overconvergent spaces with good reduction in any dimension a coleman function in this theory consists of a unipotent differential equation a functional on the underlying bundle and a solution to the equation on a residue class the new idea is to use the theory of tannakian categories and the action of frobenius to analytically continue solutions of the differential equation to all residue classes

p adic multiple zeta values i our main aim in this paper is to give a foundation of the theory of p adic multiple zeta values we introduce one variable p adic multiple polylogarithms by coleman s p adic iterated integration theory we define p adic multiple zeta values to be special values of p adic multiple polylogarithms we consider the formal p adic kz equation and introduce the p adic drinfel d associator by using certain two fundamental solutions of the p adic kz equation we show that our p adic multiple polylogarithms appear as coefficients of a certain fundamental solution of the p adic kz equation and our p adic multiple zeta values appear as coefficients of the p adic drinfel d associator we show various properties of p adic multiple zeta values which are sometimes analogous to the complex case and are sometimes peculiar to the p adic case via the p adic kz equation

consequences of denseness of dirac young measures 1 introductiona fundamental property of the set of dirac young measures is itsdenseness in the set of all young measures when the underlying measurespace is nonatomic e g see 11 theorem iv 2 6 6 in what would wx appear to be its most general form this result was stated for a completelyregular suslin space of control points 3 moreover a simple observation wxstemming directly from the proof of the result states that such densenessof the dirac young measures is maintained under a finite number ofcertain integral functional inequalities 3 corollary 3 for this reason awxrecent characterization of

on tannakian duality over valuation rings in this paper we generalize the tannakian theory which gives a correspondence between groupoids and tannakian categories over a field k to the case where k is a valuation ring we give a general theorem how to reconstruct groupoids in arbitrary categories from their category of representations and we show that this theorem can be applied to groupoids over dedekind rings we also give a partial answer how to see whether a category is the representation category of a groupoid over a valuation ring

young measure solutions for a viscoelastically damped wave equation with nonmonotone stress strain relation we study the viscoelastically damped wave equation with a nonmonotone stress strain relation this system describes the dynamics of phase transitions which is closely related to the creation of microstructures in order to analyze the dynamic behavior of microstructures we consider highly oscillatory initial states two questions are addressed in this work how do oscillations propagate in space and time what can be said about the long time behavior an appropriate tool to deal with oscillations are young measures they describe the local distribution or one point statistics of a sequence of fast fluctuating functions we demonstrate that highly oscillatory initial states generate in a unique fashion an evolution in the space of young measures and we derive the determining equations further on we prove a generalized dissipation identity for young measure solutions as a consequence it is shown that every low energy solution converges to a young measure equilibrium as t this is a generalization of g friesecke s j b mcleod s fm96 convergence result for classical solutions to the case of young measure solutions

syntomic regulators and special values of p adic l functions in this paper p adic analogs of the lichtenbaum conjectures are proven for abelian number fields f and odd prime numbers p which generalize leopoldt s p adic class number formula and express special values of p adic l functions in terms of orders of k groups and higher p adic regulators the approach uses syntomic regulator maps which are the p adic equivalent of the beilinson regulator maps they can be compared with etale regulators via the fontaine messing map and computations of bloch kato in the case that p is unramified in f lead to results about generalized coates wiles homomorphisms and cyclotomic characters

linear phase low pass iir digital differentiators a novel approach to designing approximately linear phase infinite impulse response iir digital filters in the passband region is introduced the proposed approach yields digital iir filters whose numerators represent linear phase finite impulse response fir filters as an example low pass iir differentiators are introduced the range and high frequency suppression of the proposed low pass differentiators are comparable to those obtained by higher order fir low pass differentiators in addition the differentiators exhibit almost linear phases in the passband regions

torsion points on curves and p adic abelian integrals theorem a let f c j be an albanese morphism defined over a number field k of a s mooth curve of genus g into its jacobian suppose j has potential complex multiplication let s denote the set of primes p of k satisfying i p does not divide 2 or 3 ii k q is unramified at p iii c has good ordinary reduction over k then the set t of torsion points of a defined over an algebraic closure of k which lie on the image of c is defined over an extension of k unramified above s moreover to pg

cardinal exponential splines part ii think analog act digital by interpreting the green function reproduction property of exponential splines in signal processing terms we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts the link is that the latter are the b spline coefficients of the former which happen to be exponential splines motivated by this observation we introduce an extended family of cardinal splines the generalized e splines to generalize the concept for all convolution operators with rational transfer functions we construct the corresponding compactly supported b spline basis functions which are characterized by their poles and zeros thereby establishing an interesting connection with analog filter design techniques we investigate the properties of these new b splines and present the corresponding signal processing calculus which allows us to perform continuous time operations such as convolution differential operators and modulation by simple application of the discrete version of these operators in the b spline domain in particular we show how the formalism can be used to obtain exact discrete implementations of analog filters finally we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real world analog to digital a to d and d to a conversion systems