pinecone/core-2020-05-10-deduplication huggingface dataset:
A land information system for Turkey - a key to the country's sustainable development

This paper describes the development by the General Directorate of
Rural Services (GDRS) of a land information system for Turkey,
namely the National Soil and Water Information System. It is of
great significance for the modern state of Turkey as, prior to its
establishment in 1999 under the Turkish Agricultural Research
Project, there was no definitive, national technological information
resource underpinning land and water resource management. The
system will underpin the operational and research responsibilities
of the Directorate in combating some of the pressing contemporary
environmental concerns in Turkey, including wind and water
erosion, waterlogging, sodicity and salination of the soil resource.
The complex process of compiling the first national digital soil map
will be among the initial tasks, as well as establishing a national
infrastructure for distributing the information amongst GDRS
managers and scientists. With the proposed accession of the
Turkish Republic to the European Union, alignment of the National
Soil and Water Information System with European standards and
protocols will prove to be an important facet of its ongoing
development
Alteration and Contamination of Archaeological Ceramics: the Perturbation Problem

Alteration and contamination processes modify the chemical composition of ceramic artefacts. This is not restricted solely to the affected elements, but also affects general concentrations. This is due to the compositional nature of chemical data, enclosed by the restriction of unit sum. Since it is impossible to know prior to data treatment whether the original compositions have been changed by such processes, the methodological approach used in provenance studies must be robust enough to handle materials that might have been altered or contaminated. The ability of the logratio transformation proposed by Aitchison to handle compositional data is studied and compared with that of present data treatments. The logaratio transformation appears to offer the most robust approac
An Imperial Legacy? An Exploration of the environmental impact of ancient metal mining and smelting in southern Jordan

Pyatt, B. Gilmore, G. Grattan, J. Hunt, C. McLaren, S. An imperial legacy? An exploration of the environmental impact of ancient metal mining and smelting in southern Jordan. Journal of Archaeological Science. 2000. 27 pp 771-778Extensive wastes from the copper mining and smelting activities of the Nabatean, Roman and Byzantine periods in the Wadi Faynan in the southern Jordanian desert continue to exert a profound influence upon the environment, mainly through processes of bioaccumulation. It is suggested that in antiquity both producers and consumers (plants and animals) would have similarly been subjected to enhanced bioaccumulation of potentially toxic heavy metals such as lead and copper, whose consequences are explored in this account.Peer reviewe
Radiocarbon Chronologies and Extinction Dynamics of the Late Quaternary Mammalian Megafauna of the Taimyr Peninsula, Russian Federation

This paper presents 75 new radiocarbon dates based on late Quaternary mammal remains recovered from eastern Taimyr Peninsula and adjacent parts of the northern Siberian lowlands, Russian Federation, including specimens of woolly mammoth (Mammuthus primigenius), steppe bison (Bison priscus), muskox (Ovibos moschatus), moose (Alces alces), reindeer (Rangifer tarandus), horse (Equus caballus) and wolf (Canis lupus). New evidence permits reanalysis of megafaunal extinction dynamics in the Asian high Arctic periphery. Increasingly, radiometric records of individual species show evidence of a gap at or near the Pleistocene/Holocene boundary (PHB). In the past, the PHB gap was regarded as significant only when actually terminal, i.e., when it marked the apparent ‘‘last’’ occurrence of a species (e.g., current ‘‘last’’ occurrence date for woolly mammoth in mainland Eurasia is 9600 yr BP). However, for high Arctic populations of horses and muskoxen the gap marks an interruption rather than extinction, because their radiocarbon records resume, nearly simultaneously, much later in the Holocene. Taphonomic effects, ΔC14 flux, and biased sampling are unlikely explanations for these hiatuses. A possible explanation is that the gap is the signature of an event, of unknown nature, that prompted the nearly simultaneous crash of many megafaunal populations in the high Arctic and possibly elsewhere in Eurasia.
On Projective Dimension of Spline Modules

AbstractLet a regionΩof the euclidean spaceRd(d⩾1) be decomposed as a polyhedral complex □, and letSr(□) denote the set of all multivariatecr-splines on □. Then, with pointwise operations, the setSr(□) turns out to be a finitely generated torsion free module over the ringR=R[x1, …,xd] of polynomials indvariables. In this paper, the results of Billera and Rose on the freeness of thisR-module on triangulated regions are extended to the projective dimension of this module and on arbitrary polygonal subdivisions. Possible relationships between the projective dimensions of the spline modules on subcomplexes have been established. Examples illustrating the theorems and counterexamples limiting the possibilities have been presented. In particular, an example showing that freeness of the spline moduleSr(□) is not a local concept for general polyhedral complexes, as against the triangulated ones, has been constructed
Orthogonal Matrix Polynomials: Zeros and Blumenthal's Theorem

AbstractIn this paper, we establish a quadrature formula and some basic properties of the zeros of a sequence (Pn)nof orthogonal matrix polynomials on the real line with respect to a positive definite matrix of measures. Using these results, we show how to get an orthogonalizing matrix of measures for a sequence (Pn)nsatisfying a matrix three-term recurrence relation. We prove Blumenthal's theorem for orthogonal matrix polynomials describing the support of the orthogonalizing matrix of measures in case the matrix recurrence coefficients associated with these matrix polynomials tend to matrix limits having the same entries on every diagonal
Extremal Problems for the Vector-Valued 〈L1/H01, H∞〉 Duality

AbstractLetXbe a complex Banach space andL1(X)≔L1(T; X) the Bochner space on the circle T. TheX-valued Hardy space H01(X)≔[f∈L1(X):f(n)=0 ∀n⩽0] is proximinal inL1(X) ifHhas ARNP and is contractively complemented inX″. It is semi-Chebyshev ifXis strictly convex. WithH∞(X′) the dual space ofL1(X)/H01(X), extremal kernels and functions for this duality are studied. Proximinality fails forX≔L1/H01; this is equivalent to the assertion that forΛ≔N×Z∪Z×N,LΛ1(T2) is not proximinal inL1(T2). A class of subsetsΛ⊂Z2is described for which this non-proximinality holds
Random Approximations and Fixed Point Theorems

AbstractAs an application of our random variational inequality proved in this paper, the random versions of Fan's best approximation theorem for both single-valued and set-valued mappings are given. These results, in turn, are used to derive some random fixed point theorems for both nonself single-valued and set-valued mappings in normed spaces. Our random fixed point theorems are closely related to, but not comparable with results given by Engl, Lin, Reich, Seghal and Waters, Tan and Yuan, and Xu
A Pincherle Theorem for Matrix Continued Fractions

AbstractPincherle theorems equate convergence of a continued fraction to existence of a recessive solution of the associated linear system. Matrix continued fractions have recently been used in the study of singular potentials in high energy physics. The matrix continued fractions and discrete Riccati equations previously studied by the author, which were motivated by discrete control theory, had symplectic coefficient matrices. However, the matrix continued fractions employed by Znojil do not have symplectic structure. The previous definition of a recessive solution is modified to allow extension of the Pincherle theorem to include a wider class of continued fractions
Optimal Approximation of Periodic Analytic Functions with Integrable Boundary Values

AbstractLetS=[z∈C: |Im(z)|<β] be a strip in the complex plane.Hq, 1⩽q<∞, denotes the space of functions, which are analytic and 2π-periodic inS, real-valued on the real axis, and possessq-integrable boundary values. Letμbe a positive measure on [0, 2π] andLp(μ) be the corresponding Lebesgue space of periodic real-valued functions on the real axis. The even dimensional Kolmogorov, Gel'fand, and linear widths of the unit ball ofHqinLp(μ) are determined exactly, when 1⩽p⩽q<∞ or when=q<p<∞ andβis sufficiently large. It is shown that all threen-widths coincide and a characterization of the widths in terms of Blaschke products is established
Multivariate Differences, Polynomials, and Splines

AbstractWe generalize the univariate divided difference to a multivariate setting by considering linear combinations of point evaluations that annihilate the null space of certain differential operators. The relationship between such a linear functional and polynomial interpolation resembles that between the divided difference and Lagrange interpolation. Applying the functional to the shifted multivariate truncated power produces a compactly supported spline by which the functional can be represented as an integral. Examples include, but are not limited to, the tensor product B-spline and the box spline
Unified Representations of Nonlinear Splines

AbstractGolomb and Jerome's framework is modified and extended. The new framework is more general since it also handles interpolants which are not allowed to “slide” at the nodes. The space of interpolants of variable length is shown to be a smooth manifold. If the length is fixed, and there are no nodes, then the space of interpolants is a manifold. When there is at least one node, and at least one node is not on the line segment between the endpoints, then the space of interpolants of fixed length is a smooth manifold. Sufficient conditions are given which ensure the space of interpolants continues to be a smooth manifold in the presence of additional constraints such as clamping and pinning. A new fundamental finite-dimensional equation is derived. When it is solved it yields all nonlinear splines, and every nonlinear spline appears in this way. An important feature is that the same symbolic equation is used for all possible combinations of the constraints considered. It is shown how to take the solutions of the fundamental equation and use them to express the corresponding nonlinear splines in terms of a pair of elliptic functions. An inequality is derived that specifies which elliptic function appears along each section of the spline. The nonlinear splines are in a unified way shown to beC2for all possible combinations of the constraints considered
On the Existence of Unbiased Monte Carlo Estimators

AbstractFor many typical instances where Monte Carlo methods are applied attempts were made to find unbiased estimators, since for them the Monte Carlo error reduces to the statistical error. These problems usually take values in the scalar field. If we study vector valued Monte Carlo methods, then we are confronted with the question of whether there can exist unbiased estimators. This problem is apparently new. Below it is settled precisely. Partial answers are given, indicating relations to several classes of linear operators in Banach spaces
Quantitative Approximation Theorems for Elliptic Operators

AbstractLetL(D) be an elliptic linear partial differential operator with constant coefficients and only highest order terms. For compact setsK⊂RNwhose complements are John domains we prove a quantitative Runge theorem: if a functionfsatisfiesL(D)f=0 on a fixed neighborhood ofK, we estimate the sup-norm distance fromfto the polynomial solutions of degree at mostn. The proof utilizes a two-constants theorem for solutions to elliptic equations. We then deduce versions of Jackson and Bernstein theorems for elliptic operators
On a Conjecture Concerning Monotonicity of Zeros of Ultraspherical Polynomials

AbstractLetCλn,n=0, ;1, …, λ>−1/2 be the ultraspherical (Gegenbauer) polynomials, orthogonal on (−1, 1) with respect to the weight (1−x2)λ−1/2. Denote byζn, k(λ),k=1, …, [n/2] the positive zeros ofCλnenumerated in decreasing order. The problem of finding the “extremal” functionffor which the productsf(λ)ζn, k(λ) are increasing functions ofλis of recent interest. Ismail, Letessier, and Askey conjectured thatf(λ)=(λ+1)1/2is the function to solve this problem. We prove the conjecture for sufficiently largenand some related results
Whittaker–Kotelnikov–Shannon Sampling Theorem and Aliasing Error

AbstractLetBσ, p, 1⩽p⩽∞, be the set of all functions fromLp(R) which can be continued to entire functions of exponential type ⩽σ. The well known Whittaker–Kotelnikov–Shannon sampling theorem states that everyf∈Bσ, 2can be represented as[formula]in normL2(R). We prove that it is also true for allf∈Bσ, p, 1<p<∞, in normLp(R). From this, we further prove that iff(x)=O(Ψ(x)), whereΨ(x)∈Lp(R),Ψ(x)⩾0 is even and non-increasing on [0, ∞), andf(x) is Riemann integrable on every finite interval, then the aliasing error off, i.e.,f(x)−∑k∈Zf(kπ/σ)sinσ(x−kπ/σ)[σ(x−kπ/σ)]−1, converges to zero inLp(R), 1<p<∞, whenσ→+∞. Iff∈Lrp(R),r∈N, we also determine the error bound of its aliasing error
Newman's Inequality for Müntz Polynomials on Positive Intervals

AbstractThe principal result of this paper is the following Markov-type inequality for Müntz polynomials.Theorem(Newman's Inequality on [a, b]⊂(0, ∞)).Let Λ:=(λj)∞j=0be an increasing sequence of nonnegative real numbers. Suppose λ0=0and there exists a δ>0so that λj⩾δj for each j. Suppose0<a<b. Then there exists a constant c(a, b, δ)depending only on a, b, and δ so that[formula]for every P∈Mn(Λ), where Mn(Λ)denotes the linear span of{xλ0, xλ1, …, xλn}overR. When [a, b]=[0, 1] and with ‖P′‖[a, b]replaced with ‖xP′(x)‖[a, b]this was proved by Newman. Note that the interval [0, 1] plays a special role in the study of Müntz spacesMn(Λ). A linear transformationy=αx+βdoes not preserve membership inMn(Λ) in general (unlessβ=0). So the analogue of Newman's Inequality on [a, b] fora>0 does not seem to be obtainable in any straightforward fashion from the [0, b] cas
Orthogonal Polynomials on Arcs of the Unit Circle, I

AbstractLetEl=∪lj=1[ϕ2j−1, ϕ2j]⊆[0, 2π], R(ϕ)=∏2lj=1sin((ϕ−ϕj)/2) and[formula]forϕ∈(ϕ2j−1, ϕ2j). Furthermore let V, W be arbitrary real trigonometric polynomials such that R=VW and let A(ϕ) be a real trigonometric polynomial which has no zero inEl. First we derive an explicit representation of the Caratheodory function associated withf(ϕ; W)=W(ϕ)/A(ϕ)r(ϕ) onEl. With the help of this result the polynomialsPn(z), which are orthogonal on the set of arcsΓEl:={eiϕ:emsp14;ϕ∈El} with respect tof(ϕ; W), are completely characterized by a quadratic equation. (In fact a more general case including Dirac-mass points is considered.) This characterization is the basis of all of our further investigations on polynomials orthogonal on several arcs as the description of that measures which generate orthogonal polynomials with periodic or asymptotically periodic reflection coefficients, the explicit representation of the orthogonality measure of the associated polynomials, the asymptotic representation of polynomials orthogonal onΓEl, etc
Simultaneous Approximation and Quasi-Interpolants

AbstractIt is shown that the shift-invariant spaceS(ϕ) generated byϕ∈Wm2(Rs) provides simultaneous approximation orderk, withk>m, iffS(Dαϕ) provides approximation orderk−min theL2(Rs)-norm to all functions inDαWk2(Rs) for each |α|=m. Without appealing to the argument of polynomial reproduction, an explicit formula is presented for construction of quasi-interpolant of semi-discrete convolution type that achieves the approximation order provided byS(ϕ). The traditional condition that the symbol ∑α∈Zsϕ(α)eαdoes not vanish on [−π…π]sis reduced to that it does not vanish on a neighborhood of the origin
Best Interpolatory Approximation in Normed Linear Spaces

AbstractA theory of best approximation with interpolatory contraints from a finite-dimensional subspaceMof a normed linear spaceXis developed. In particular, to eachx∈X, best approximations are sought from a subsetM(x) ofMwhichdependson the elementxbeing approximated. It is shown that this “parametric approximation” problem can be essentially reduced to the “usual” one involving a certainfixedsubspaceM0ofM. More detailed results can be obtained when (1)Xis a Hilbert space, or (2)Mis an “interpolating subspace” ofX(in the sense of [1])
Extension and Completion of Wynn's Theory on Convergence of Columns of the Epsilon Table

AbstractLet {Sn}∞n=0be such thatSn∽S+∑∞j=1ajλnjasn→∞, with 1>|λ1|>|λ2|>…, such that limj→∞λj=0. A well-known result by Wynn states that when the Shanks transformation or its equivalentε-algorithm is applied to {Sn}∞n=0, thenε(n)2k−S∽ak+1[∏ki=1(λk+1−λi)/(1−λi)]2λnk+1asn→∞. In the present work we extend this result (i) by allowing some of theλjto have the same modulus and (ii) by replacing the constantsajby some polynomialsPj(n) inn. Sequences {Sn}∞n=0with these characteristics arise frequently, e.g., in fixed point iterative solution of linear systems and in trapezoidal rule approximation of finite range integrals with logarithmic endpoint singularities and their multidimensional analogues. The results of this work are obtained by exploiting the connection between the Shanks transformation and Padé approximants and by using some recent results of the author on Padé approximants for meromorphic functions
Null Spaces of Differential Operators, Polar Forms, and Splines

AbstractIn this article we consider a class of functions, called D-polynomials, which are contained in the null space of certain second order differential operators with constant coefficients. The class of splines generated by these D-polynomials strictly contains the polynomial, trigonometric, and hyperbolic splines. The main objective of this paper is to present a unified theory of this class of splines via the concept of a polar form. By systematically employing polar forms, we extend essentially all of the well-known results concerning polynomial splines. Among other topics, we introduce a Schoenberg operator and define control curves for these splines. We also examine the knot insertion and subdivision algorithms and prove that the subdivision schemes converge quadratically
Polynomial Approximation on Varying Sets

AbstractLet {γm}m=1∞be a sequence of positive numbers, and letf:Rd→Cbe a function such that for someC=Cf<∞ and everyξ∈Rdthere exist polynomialsPm(x)=Pm(x; ξ), degPm≤m,m=0, 1, ..., satisfying inequalities[formula]In this paper the authors study smoothness, quasianalytic and analytic properties offin terms of the sequence {γm}m=1∞. The results are new even for the case thatPmare Taylor polynomials. Using them, the authors prove a Cartwright-type theorem on entire functions of exponential type bounded on some discrete subset of the real hyperplane and construct such a weight-functionϕ:Rd→R,d>1, that algebraic polynomials are dense inCϕ|A0(A) for every affine subspaceA⊂Rdof dimension less thand, but are not dense in the spaceCϕ0(Rd)
Conjugate Jacobi Series and Conjugate Functions

AbstractConjugate Jacobi series is introduced, according to the viewpoint of Muckenhoupt and Stein, in the sense that the Jacobi harmonic function and the conjugate harmonic function satisfy the generalized Cauchy–Riemann equations. The integral form of Jacobi conjugate functions is also introduced, which is identifiable with the conjugate Jacobi series in some sense. TheL1weak-boundedness andLpboundedness for 1<p<∞ of the conjugacy mapping are proved. The convergence of the Abel means of conjugate Jacobi series is also considered
On the Approximation of Continuous Functions by Fourier–Legendre Sums

AbstractLet {Xn}∞0be the orthonormal system of Legendre polynomials on [−1, 1]. Forf∈C[−1, 1] letSn(f) (n+1∈N) be thenth partial sum of the Fourier–Legendre series of the functionf. Some refinements of the classical inequality[formula]involving best approximation inLp-norms are discussed. For a class of examples we obtain better order estimates than those that can be derived from (1). Furthermore, we show that the results are best possible in a certain sense. It turns out that only in two particular cases (p=43andp=4) there is no proof of optimality of the results. In conclusion, we give without proof a generalization of the main theorem to the ultraspherical case
On the Convergence of General Order Multivariate Padé-Type Approximants

AbstractIn previous papers the convergence of sequences of “rectangular” multivariate Padé-type approximants was studied. In other publications definitions of “triangular” multivariate Padé-type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Padé approximants
On Sobolev Orthogonality for the Generalized Laguerre Polynomials

AbstractThe orthogonality of the generalized Laguerre polynomials, {L(α)n(x)}n⩾0, is a well known fact when the parameterαis a real number but not a negative integer. In fact, for −1<α, they are orthogonal on the interval [0, +∞) with respect to the weight functionρ(x)=xαe−x, and forα<−1, but not an integer, they are orthogonal with respect to a non-positive definite linear functional. In this work we will show that, for every value of the real parameterα, the generalized Laguerre polynomials are orthogonal with respect to a non-diagonal Sobolev inner product, that is, an inner product involving derivatives
Almost Optimal Differentiation Using Noisy Data

AbstractWe study differentiation of functionsfbased on noisy dataf(ti)+εi. We recoverf(k)either at a single point or on the interval [0, 1] inL2-norm. Under stochastic assumptions onfandεi, we determine the order of the errors of the best linear methods which use n noisy function values. Polynomial interpolation for the pointwise problem and smoothing splines for the problem inL2-norm are shown to be almost optimal. The analysis involves worst case estimates in reproducing kernel Hilbert spaces and a Landau inequality
On Positive and Copositive Polynomial and Spline Approximation inLp[−1, 1], 0<p<∞

AbstractFor a functionf∈Lp[−1, 1], 0<p<∞, with finitely many sign changes, we construct a sequence of polynomialsPn∈Πnwhich are copositive withfand such that ‖f−Pn‖p⩽Cωϕ(f, (n+1)−1)p, whereωϕ(f, t)pdenotes the Ditzian–Totik modulus of continuity inLpmetric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, thenωϕcannot be replaced byω2if 1<p<∞. In fact, we show that even for positive approximation and all 0<p<∞ the same conclusion is true. Also, some results for (co)positive spline approximation, exact in the same sense, are obtained