the motivic nearby fiber and degeneration of stable rationality we prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities our proof is based on motivic specialization techniques and the criterion of larsen and lunts for stable rationality in the grothendieck ring of varieties

towards the hierarchical verification of reactive systems the hierarchical design approach for action based systems that is known as action refinement has been studied in the literature extensively in a paper of m huhn published in concur 1996 a refinement operator on a linear time logic is presented that mimics precisely a semantic action refinement on synchronisation structures we present here an alternative approach where our starting point is a process algebraic setting with a syntactic action refinement we present a refinement operator on the modal mu calculus that conforms with the process algebraic refinement in the following sense provided some reasonable conditions are met the transition system induced by a process term p satisfies a modal mu calculus specification if and only if the system which is induced by a refinement of p satisfies a particular refinement of alleviating these conditions we show that each of the two implications in the equivalence assertion above can be separately proven valid for a particular fragment of the modal mu calculus we demonstrate that the obtained results can indeed be used as a hierarchical verification technique as a further application of our results we explain how they can be employed as an abstraction technique in order to enhance model checking techniques

deciding parity games in quasi polynomial time it is shown that the parity game can be solved in quasi polynomial time the parameterized parity game with n nodes and m distinct values a k a colors or priorities is proven to be in th

an improved algorithm for the evaluation of fixpoint expressions many automated finite state verification procedures can be viewed as fixpoint computations over a finite lattice typically the powerset of the set of system states hence fixpoint calculi such as the propositional calculus have proven useful both as ways to describe verification algorithms and as specification formalisms in their own right we consider the problem of evaluating expressions in a fixpoint calculus over a given model a naive algorithm for this task may require time n q where n is the maximum length of a chain in the lattice and q is the depth of fixpoint nesting in 1986 emerson and lei presented a method requiring about n d steps where d is the number of alternations between least and greatest fixpoints more recent algorithms have reduced the exponent by one or two but the complexity has remained at about nd in this paper we present a new algorithm that makes extensive use of monotonicity considerations to solve the problem in about nd 2 steps thus the time required by our method is only about the square root of the time required by the earlier algorithms

geometric criteria for tame ramification we prove an a campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field k as a first application we relate the orders of the tame monodromy eigenvalues on the l adic cohomology of a k curve to the geometry of a relatively minimal sncd model and we show that the semi stable reduction theorem and saito s criterion for cohomological tameness are immediate consequences of this result as a second application we compute the error term in the trace formula for smooth and proper k varieties we see that the validity of the trace formula would imply a partial generalization of saito s criterion to arbitrary dimension

hypersurfaces that are not stably rational a fundamental problem of algebraic geometry is to determine which varieties are rational that is isomorphic to projective space after removing lower dimensional subvarieties from both sides in particular we want to know which smooth hypersurfaces in projective space are rational an easy case is that smooth complex hypersurfaces of degree at least n 2 in p are not covered by rational curves and hence are not rational by far the most general result on rationality of hypersurfaces is kollar s theorem that for d at least 2d n 3 3e a very general complex hypersurface of degree d in p is not ruled and therefore not rational 13 theorem v 5 14 very little is known about rationality in lower degrees except for cubic 3 folds and quintic 4 folds 4 19 chapter 3 a rational variety is also stably rational meaning that some product of the variety with projective space is rational many techniques for proving non rationality give no information about stable rationality voisin made a breakthrough in 2013 by showing that a very general quartic double solid a double cover of p ramified over a quartic surface is not stably rational 23 these fano 3 folds were known to be non rational over the complex numbers but stable rationality was an open question voisin s method was to show that the chow group of zero cycles is not universally trivial that is the chow group becomes nontrivial over some extension of the base field by degenerating the variety to a nodal 3 fold which has a resolution of singularities x with nonzero torsion in h3 x z colliot thelene and pirutka simplified and generalized voisin s degeneration method they deduced that very general quartic 3 folds are not stably rational 6 this was striking in that non rationality of smooth quartic 3 folds was the original triumph of iskovskikh manin s work on birational rigidity while stable rationality of these varieties was unknown 11 beauville applied the method to prove that very general sextic double solids quartic double 4 folds and quartic double 5 folds are not stably rational 1 2 in this paper we show that a wide class of hypersurfaces in all dimensions are not stably rational namely for all d 2d n 2 3e and n 3 a very general complex hypersurface of degree d in p is not stably rational theorem 2 1 the theorem covers all the degrees in which kollar proved non rationality in fact we get a bit more since kollar assumed d 2d n 3 3e for example very general quartic 4 folds are not stably rational whereas it was not even known whether these varieties are rational the method applies to some smooth hypersurfaces over q in each even degree section 3 gives some examples over q which are not stably rational over c the idea is that the most powerful results are obtained by degenerating a smooth complex variety to a singular variety in positive characteristic rather than to a sin

inequalities of wealth distribution in a conservative economy abstract we analyze a conservative market model for the competition among economic agents in a society with conserved total wealth a minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare after a transient the system self organizes into a critical state where the wealth distribution have a minimum threshold with almost no agent below this poverty line also very few extremely rich agents are stable in time above the poverty line the distribution follows an exponential behavior the local solution exhibits a low gini index while the mean field solution of the model generates a wealth distribution similar to welfare states like sweden

income distribution an adaptive heterogeneous model abstract in this communication an adaptive process is introduced into a many agent model for closed economic system in order to establish general features of income distribution in this new version agents are able to modify their exchange parameter i of resources through an adaptive process the conclusions indicate that assuming an instantaneous learning behavior of all agents a distribution for income is reproduced while a frozen behavior establishes a pareto s distribution for income with an exponent 0 94 0 02 a third case occurs when a heterogeneous inertia behavior is introduced leading us to a distribution at the low income regime and a power law decay for the large income values with an exponent 2 05 0 05 this method enables investigation of the resources flux in the economic environment and produces also bounding values for the gini index comparable with data evidences

toroidal varieties and the weak factorization theorem we develop the theory of stratified toroidal varieties which gives together with the theory of birational cobordisms 73 a proof of the weak factorization conjecture for birational maps in characteristic zero a birational map between complete nonsingular varieties over an algebraically closed field k of characteristic zero is a composite of blow ups and blow downs with smooth centers

rationally isotropic quadratic spaces are locally isotropic let r be a regular local ring k its field of fractions and v a quadratic space over r assume that r contains a field of characteristic zero we show that if v r k is isotropic over k then v is isotropic over r this solves the characteristic zero case of a question raised by j l colliot thelene in 3 the proof is based on a variant of a moving lemma from 7 a purity theorem for quadratic spaces is proved as well it generalizes in the charactersitic zero case the main purity result from 9 and it is used to prove the main result in 2

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

statistical model with a standard γ distribution we study a statistical model consisting of n basic units which interact with each other by exchanging a physical entity according to a given microscopic random law depending on a parameter ensuremath lambda we focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard gamma distribution the model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity ensuremath lambda alternatively from the nature of the equilibrium distribution we show that the model can also be interpreted as a perfect gas at an effective temperature t ensuremath lambda where particles exchange energy in a space with an effective dimension d ensuremath lambda

the alternation hierarchy in fixpoint logic with chop is strict too fixpoint logic with chop extends the modal calculus with a sequential composition operator which results in an increase in expressive power we develop a game theoretic characterisation of its model checking problem and use these games to show that the alternation hierarchy in this logic is strict the structure of this result follows the lines of arnold s proof showing that the alternation hierarchy in the modal calculus is strict over the class of binary trees

evolution of consumption distribution and model of wealth distribution in china between 1995 and 2012 abstract we study the evolution of the distribution of consumption of individuals in the majority population in china during the period 1995 2012 and find that its probability density functions pdfs obey the rule p c x k x e x 2 2 2 we also find i that the pdfs and the individual income distribution appear to be identical ii that the peaks of the pdfs of the individual consumption distribution are consistently on the low side of the pdfs of the income distribution and iii that the average of the marginal propensity to consume mpc is large m p c 0 77 indicating that in the majority population individual consumption is low and strongly dependent on income the long right tail of the pdfs of consumption indicates that few people in china are participating in the high consumption economy and that consumption inequality is high after comparing the pdfs of consumption with the pdfs of income we obtain the pdfs of residual wealth during the period 1995 2012 which exhibit a gaussian distribution we use an agent based kinetic wealth exchange model kwem to simulate this evolutional process and find that this gaussian distribution indicates a strong propensity to save rather than spend this may be due to an anticipation of such large potential outlays as housing education and health care in the context of an inadequate welfare support system

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial