henselian implies large in this note we show that the quotient field of a domain which is henselian with respect to a nontrivial ideal is a large field and give some applications of this fact using a specialization theorem for ramified covers of the line over generalized krull fields

ranks of elliptic curves this paper gives a general survey of ranks of elliptic curves over the field of rational numbers the rank is a measure of the size of the set of rational points the paper includes discussions of the birch and swinnertondyer conjecture the parity conjecture ranks in families of quadratic twists and ways to search for elliptic curves of large rank

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

a nonlinear correlation measure for multivariable data set abstract the paper states that the mutual information carried by the rank sequences that are obtained from the original two sequences is a good measure of nonlinear correlation based on that the nonlinear correlation information entropy ncie is proposed for measuring the general relationship of a multivariable data set ncie uses a number in the closed interval 0 1 to indicate the nonlinear correlation degree of the concerned multivariable data set with 0 and 1 denotes the weakest and the strongest relationship respectively data sets generated from an autoregressive model a nonlinear chaotic lorenz system and a logistic function as known correlation sequences are analyzed using the proposed ncie the results testify the suitableness and correctness of the proposed concepts as nonlinear correlation measure

a new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of banach space valued random elements abstract in this correspondence for an array x n k u n k v n n n of integrable random elements in a real separable banach space and an array a n k u n k v n n n of real numbers a new type of compact uniform integrability is introduced and it is used to obtain degenerate mean convergence theorems for the weighted sums k u n v n a n k x n k e x n k n n more specifically conditions are provided under which lim n e k u n v n a n k x n k e x n k 0

subfields of ample fields rational maps and definability abstract pop proved that a smooth curve c over an ample field k with c k has k many rational points we strengthen this result by showing that there are k many rational points that do not lie in a given proper subfield even after applying a rational map this has several consequences for example we gain insight into the structure of existentially definable i e diophantine subsets of ample fields

information and entropy in strange attractors a technique for analyzing time series data from experiments is presented that provides estimates of four basic characteristics of a system 1 the measure theoretic entropy 2 the accuracy of the measurements 3 the number of measurements necessary to specify a system state and 4 the best delay time t to use in order to construct phase space portraits by the method of delays these characteristics are obtained by separating the entropy of measurements into a part due to noise and parts due to deterministic effects for the technique to work the noise associated with each measurement must be independent of the noise associated with all other measurements an algorithm for implementing the analysis is presented with three examples

significance testing of information theoretic functionals abstract a transformation is derived such that under the transformation the mutual information of two unrelated variables is a normally distributed random variable with zero mean and unit variance it is demonstrated that the transformed mutual information can be used as a test statistic to test the statistical significance of the relationship between variables and provides an alternative to the method of surrogate data if the mutual information is regarded as a generalization of the linear correlation coefficient then this test statistic can be regarded as analogous to the fisher z test statistic

mathbb a 1 connected varieties of rank one over nonclosed fields in this paper we prove two results regarding the arithmetics of separably mathbb a 1 connected varieties of rank one first we prove that over a large field there is an mathbb a 1 curve through any rational point of the boundary if the boundary divisor is smooth and separably rationally connected secondly we generalize a theorem of hassett tschinkel for the zariski density of integral points over function fields of curves

embedding problems over large fields in this paper we study galois theoretic properties of a large class of fields a class which includes all fields satisfying a universal local global principle for the existence of rational points on varieties as applications we give a positive answer to a long standing conjecture which originates in an unpublished note of roquette and asserts that the absolute galois group of a countable hilbertian pac field is profinite free see f j problem 24 41 secondly we give new evidence for the conjecture of shafarevich which asserts that the absolute galois group of qab is profinite free finally one of the most interesting applications of the theory we develop here is the insight in the galois structure of the totally eg adic numbers

bounded multipliers of bounded a statistically convergent sequences abstract in this paper we provide an alternate proof of a result of kline it claims that the set of all a statistically convergent sequences cannot be given a locally convex fk topology where a is a nonnegative regular matrix whose rows spread we also study the bounded multiplier space of all bounded a statistically convergent sequences and using the n program we give an analogue of a result of fridy and miller for bounded multipliers

the boundedness of degree of fano varieties with picard number one contents 0 introduction 1 rational curves 1 1 deformation theory of morphisms 1 2 free rational curves 1 3 the invariant d m 2 special subvarieties in fano varieties of large degree 2 1 the statement 2 2 a siegel type lemma 2 3 multiplicity subspaces 2 4 the product theorem part i 2 5 the product theorem part ii 2 6 the proof 3 the covering lemma 4 collections of subsets 4 1 base change and push forward 4 2 an example 4 3 universally open morphisms 4 4 flat families 5 proof of theorem a

relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data commonly used dependence measures such as linear correlation cross correlogram or kendall s tau cannot capture the complete dependence structure in data unless the structure is restricted to linear periodic or monotonic mutual information mi has been frequently utilized for capturing the complete dependence structure including nonlinear dependence recently several methods have been proposed for the mi estimation such as kernel density estimators kde k nearest neighbors knn edgeworth approximation of differential entropy and adaptive partitioning of the xy plane however outstanding gaps in the current literature have precluded the ability to effectively automate these methods which in turn have caused limited adoptions by the application communities this study attempts to address a key gap in the literature specifically the evaluation of the above methods to choose the best method particularly in terms of their robustness for short and noisy data based on comparisons with the theoretical mi estimates which can be computed analytically as well with linear correlation and kendall s tau here we consider smaller data sizes such as 50 100 and 1 000 where this study considers 50 and 100 data points as very short and 1 000 as short we consider a broader class of functions specifically linear quadratic periodicmore and chaotic contaminated with artificial noise with varying noise to signal ratios the case studies presented here are motivated by domain consideration in the earth sciences where the data are short and noisy our results indicate kde as the best choice for very short data at relatively high noise to signal levels whereas the performance of knn is the best for short data at relatively low noise levels as well as for short data consistently across noise levels in addition the optimal smoothing parameter of a gaussian kernel appears to be the best choice for kde while three nearest neighbors appear optimal for knn thus in situations where the approximate data sizes are known in advance and exploratory data analysis and or domain knowledge can be used to provide a priori insights on the noise to signal ratios the results in the paper point to a way forward for automating the process of mi estimation less

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

weak approximation over function fields of curves over large or finite fields let k k c be the function field of a curve over a field k and let x be a smooth projective separably rationally connected k variety with x k neq emptyset under the assumption that x admits a smooth projective model pi mathcal x to c we prove the following weak approximation results 1 if k is a large field then x k is zariski dense 2 if k is an infinite algebraic extension of a finite field then x satisfies weak approximation at places of good reduction 3 if k is a nonarchimedean local field and r equivalence is trivial on one of the fibers mathcal x p over points of good reduction then there is a zariski dense subset w subseteq c k such that x satisfies weak approximation at places in w as applications of the methods we also obtain the following results over a finite field k 4 if k 10 then for a smooth cubic hypersurface x k the specialization map x k longrightarrow prod p in p mathcal x p kappa p at finitely many points of good reduction is surjective 5 if mathrm char k neq 2 3 and k 47 then a smooth cubic surface x over k satisfies weak approximation at any given place of good reduction

rational points of bounded height on general conic bundle surfaces a conjecture of manin predicts the asymptotic distribution of rational points of bounded height on fano varieties in this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved for example we obtain the conjectured lower bound of manin s conjecture for any del pezzo surface whose picard rank is sufficiently large or for arbitrary del pezzo surfaces after possibly an extension of the ground field of small degree

zero cycles on homogeneous varieties abstract in this paper we study the group a 0 x of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety x to do this we translate rational equivalence of 0 cycles on a projective variety into r equivalence on symmetric powers of the variety for certain homogeneous varieties we then relate these symmetric powers to moduli spaces of etale subalgebras of central simple algebras which we construct this allows us to show a 0 x 0 for certain classes of homogeneous varieties for groups of each of the classical types extending previous results of swan karpenko of merkurjev and of panin

galois theory over rings of arithmetic power series let r be a domain complete with respect to a norm which denes a non discrete topology on r we prove that the quotient eld of r is ample generalizing a theorem of pop we then consider the case where r is a ring of arithmetic power series which are holomorphic on the closed disc of radius 0 r 1 around the origin and apply the above result to prove that the absolute galois group of the quotient eld of r is semi free this strengthens a theorem of harbater who solved the inverse galois problem over these elds

construction de revetements de courbes pointees resume si k est un corps fertile large field chez f pop g un k schema en groupes fini etale et x un g torseur on construit un g revetement ramifie c p 1k ou c est lisse et geometriquement connexe sur k induisant en 0 p 1 k le torseur x lorsque k est de caracteristique nulle c est un resultat recent de colliot thelene on termine l article par des commentaires sur l utilisation du langage des champs algebriques dans ce type de probleme copyright 2001 academic press if k is a large field in the sense of f pop g a finite etale k group scheme and x a g torsor we construct a ramified g covering c p 1k where c is smooth and geometrically connected over k inducing at 0 p 1 k the given x when k has characteristic zero this was proved recently by colliot thelene we end with some comments on how the language of algebraic stacks can be used for such problems

statistical weighted b summability and its applications to approximation theorems in this paper which deals essentially with various summability concepts and summability techniques and shows how these concepts and techniques lead to a number of approximation results we have used the new concept of weighted a summability proposed by mohiuddine 2016 and introduced the notions of statistically weighted b summability and weighted b statistical convergence with respect to the weighted regular method we then prove a korovkin type approximation theorem for functions of two variables and also present an example via generalized meyer konig and zeller type operator to show that our proposed method is stronger than its classical and statistical versions furthermore the rate of convergence of approximating positive linear operators are estimated by means of the modulus of continuity and some voronovskaja type results are investigated computational and geometrical approaches to illustrate some of our results are also presented

quadratic families of elliptic curves and unirationality of degree 1 conic bundles we study families of elliptic curves whose coefficients are degree 2 polynomials in a variable t all such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers we prove that such conic bundles are unirational as a consequence one obtains that for infinitely many values of t the resulting elliptic curve has rank at least 1

matrix maps of statistically convergent sequences abstract let a and d be two nonnegative regular matrices and b be an arbitrary infinite matrix we give the sufficient necessary conditions under which the matrix map b sends a statistically convergent bounded sequences to d statistically convergent sequences these give nice additions to the work of fridy and khan we also provide the limit formula for such a map and evaluate the corresponding operator semi norm our results generalize many well known results

hierarchical structures in the gross domestic product per capita fluctuation in latin american countries abstract a description of relations between the yearly fluctuations of the gross domestic product gdp per capita of 19 latin american la countries is presented using either a linear pcc or a nonlinear correlation coefficient ncc various time windows have been examined to measure the weights giving rise to links used to built complex networks for which the countries are nodes the average overlap index aoi for la countries has been calculated for the two correlation coefficients showing that it is rather systematically higher than for the 25 eu countries the network structures are thereafter examined through a country elimination scheme based on the removal of the weakest links and raising the aoi threshold level the pcc and ncc schemes lead to different networks and clusters a principal component analysis is furthermore made for the two here above defined adjacency matrices resulting from the pcc and ncc methods to represent and analyze the country clustering structure and observe their coherence from such points of view it is concluded that both pcc and ncc schemes lead to similar clustering though have a different feeling for the sign of correlations moreover the 19 la countries seem to be less tied than the 25 eu

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

matrix characterization of a statistical convergence abstract the main objective of the paper is to characterize multipliers of summability fields of regular methods while relaxing the usual boundedness condition for this purpose we use the sequence spaces of a bounded sequences and a uniformly integrable sequences among the main results it is shown that the space of multipliers is closely related to the space of a statistically convergent sequences and that a statistical convergence over l is equivalent to a regular matrix method this observation eliminates the need for separate proofs of several a statistical convergence results

rational points of bounded height on fano varieties a prime pe7z let v be an algebraic variety defined over f and li a metrized line bundle on v i e a system l consisting of a line bundle l and a family of banach v adic metrics on l f for all v s satisfying well known conditions cf 1 chap vi then we can define a height function hl x f i r by the formula h x is x 1 where s is a local section of l non vanishing

rationally connected varieties over finite fields let x be a geometrically rational or more generally separably rationally connected variety over a finite field k we prove that if k is large enough then x contains many rational curves defined over k as a consequence we prove that r equivalence is trivial on x if k is large enough these results imply the following conjecture of j l colliot thelene let y be a rationally connected variety over a number field f for a prime p let y p denote the corresponding variety over the local field f p then for almost all primes p the chow group of 0 cycles on y p is trivial and r equivalence is trivial on y p

on statistical limit points and the consistency of statistical convergence abstract this article extends the concept of a statistical limit cluster point of a sequencex as introduced by fridy to at statistical limit cluster point wheretis a nonnegative regular matrix summability method these definitions are reformulated in the setting of n n it is shown that for a bounded sequencex the set oft statistical cluster points ofxforms a compact subset of r it is also shown that iftandrare two nonnegative regular summability matrices thent statistical convergence andr statistical convergence are consistent if and only if the support sets oftandrhave nonempty intersection

height zeta functions of equivariant compactifications of unipotent groups we prove manin s conjecture for bi equivariant compactifications of unipotent groups 2015 wiley periodicals inc

representation of ideal convergence as a union and intersection of matrix summability methods abstract we characterize ideals on n for which the ideal limit function is representable as an intersection union resp of matrix summability methods more specifically we characterize ideals i for which there is a family m of matrices such that a sequence x is i convergent to l x is a summable to l for every some resp a m we consider separately cases of all sequences and bounded sequences we also consider i convergence

on quadratic families of cm elliptic curves given a cm elliptic curve with weierstrass equation y 2 f x and a positive definite binary quadratic form q v v we show that there are infinitely many reduced integer pairs u v such that the twisted elliptic curve q u v y 2 f x has analytic rank and consequently mordell weil rank one in fact it follows that the number of such pairs with u v x is at least x 2 e for any e 0