nils-herrmann/clean_scirepeval huggingface dataset:
Combining Functions for Certainty Degrees in Consulting Systems
Consulting systems are rule-based systems of Artificial Intelligence working with propositions that may be uncertain, i.e. may have a truth-value different from “true” and “false”. The work of a consulting system consists, roughly, in propagation of uncertain knowledge throughout the net of rules according to some combining functions. It is shown that the notion of an ordered Abelian group is central for the definition of these combining functions. Various particular groups, both Archimedean and non-Archimedean, are considered for use in consulting systems. Practical experiments with them are also described.

title: Fuzzy Logic and Arithmetical Hierarchy, II
abstract: A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.

title: SYSTEMS OF CONDITIONAL BELIEFS IN DEMPSTER-SHAFER THEORY AND EXPERT SYSTEMS
abstract: Various notions of soundness for systems of conditional beliefs are introduced and interrelated (the term “belief” being used in the sense of Dempster-Shafer theory). An application to the analysis of the use of Dempster-Shafer theory in classical (rule-based, MYCIN-like) expert systems is sketched. Some open problems are formulated.

title: Metamathematics of Fuzzy Logic
abstract: Preface. 1. Preliminaries. 2. Many-Valued Propositional Calculi. 3. Lukasiewicz Propositional Logic. 4. Product Logic, Godel Logic. 5. Many-Valued Predicate Logics. 6. Complexity and Undecidability. 7. On Approximate Inference. 8. Generalized Quantifiers and Modalities. 9. Miscellanea. 10. Historical Remarks.

title: GETTING BELIEF FUNCTIONS FROM KRIPKE MODELS

title: A simple dynamic logic
abstract: A system of dynamic predicate logic is presented. It allows nonstandard modelling of time, which makes recursive axiomatization possible, and is essentially one-sorted (the same elements code data and time), which makes the system reasonably simple and transparent. The system is subjected to usual mathematical considerations; in particular, it is shown to be equivalent to the three-sorted system due to Andreka, Nemeti and Sain (1982). A conservation result for the latter system is obtained as a by-product.

title: Polynomial algebras on classical banach spaces
abstract: For the classical Banach spacesX = ℓp,C(K) we identify alln such that every polynomial of degreen + 1 onX is uniformly approximable on the unit ball by elements of the algebra generated by all polynomials of degree up ton onX.

title: Dual renormings of Banach spaces
abstract: We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.
Epistemic Entrenchment and Arithmetical Hierarchy
If the underlying theory is sufficiently rich (e.g. like first-order arithmetic), then no epistemic entrenchment preorder of sentences is recursively enumerable. Consequently, the set of all defeasible proofs (determined by such a fixed preorder) is not recursively enumerable and hence, a fortiori, nonrecursive. On the other hand there is a satisfactorily rich epistemic entrenchment preorder

title: SYSTEMS OF CONDITIONAL BELIEFS IN DEMPSTER-SHAFER THEORY AND EXPERT SYSTEMS
abstract: Various notions of soundness for systems of conditional beliefs are introduced and interrelated (the term “belief” being used in the sense of Dempster-Shafer theory). An application to the analysis of the use of Dempster-Shafer theory in classical (rule-based, MYCIN-like) expert systems is sketched. Some open problems are formulated.

title: Fuzzy Logic and Arithmetical Hierarchy, II
abstract: A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.

title: A simple dynamic logic
abstract: A system of dynamic predicate logic is presented. It allows nonstandard modelling of time, which makes recursive axiomatization possible, and is essentially one-sorted (the same elements code data and time), which makes the system reasonably simple and transparent. The system is subjected to usual mathematical considerations; in particular, it is shown to be equivalent to the three-sorted system due to Andreka, Nemeti and Sain (1982). A conservation result for the latter system is obtained as a by-product.

title: GETTING BELIEF FUNCTIONS FROM KRIPKE MODELS

title: Metamathematics of Fuzzy Logic
abstract: Preface. 1. Preliminaries. 2. Many-Valued Propositional Calculi. 3. Lukasiewicz Propositional Logic. 4. Product Logic, Godel Logic. 5. Many-Valued Predicate Logics. 6. Complexity and Undecidability. 7. On Approximate Inference. 8. Generalized Quantifiers and Modalities. 9. Miscellanea. 10. Historical Remarks.

title: Dual renormings of Banach spaces
abstract: We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.

title: Polynomial algebras on classical banach spaces
abstract: For the classical Banach spacesX = ℓp,C(K) we identify alln such that every polynomial of degreen + 1 onX is uniformly approximable on the unit ball by elements of the algebra generated by all polynomials of degree up ton onX.
Über Teilerfunktionen in Dirichletschen Reihen

title: Mittelwerteigenschaften der Riemannschen Zeta-Funktion

title: Optimal rates of convergence in the CLT for quadratic forms
abstract: We prove optimal convergence rates in the central limit theorem for sums in R k . Assuming a fourth moment, we obtain a Berry-Esseen type bound of O(N - 1) for the probability of hitting a ball provided that k ≥ 5. The proof still requires a technical assumption related to the independence of coordinates of sums.
Asymptotic expansions for bivariate von Mises functionals
SummaryA Berry-Essen result and asymptotic expansions are derived for the distribution of bivariate von Mises functionals under moment and smoothness conditions.The results apply to the Cramér-von Mises ω2 — statistic as well as to the Central Limit Theorem in Hilbert space, yielding a convergence rate O(n−1+ɛ) for every ɛ>0 on centered ellipsoids.

title: Asymptotic Distribution of Quadratic Forms
abstract: We consider quadratic forms Q n = Σ a jh X j X k , 1 ≤j ¬= k ≤ n where X j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q n and the distribution of the same quadratic forms with X j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well as to nonstationary AR(1) processes.

title: The Berry-Esseen bound for student's statistic
abstract: We prove the Berry-Esseen bound for the Student t-statistic. Under the assumption of a third moment this bound coincides (up to an absolute constant) with the classical Berry-Esseen bound for the mean. In general the distribution of the Student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean, and sometimes faster. For example, rates of convergence can be proved if the underlying distribution is in the domain of attraction of the normal law.

title: Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces
abstract: Let X,X1,X2,… be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space ℝd. Assume that EX=0 and that X is not concentrated in a proper subspace of ℝd. Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms ℚ[SN] of the normalized sums SN=N−1/2(X1+⋯+XN) and show that
provided that d≥9 and the fourth moment of X exists. The bound ?(N−1) is optimal and improves, e.g., the well-known bound ?(N−d/(d+1)) due to Esseen (1945). The result extends to the case of random vectors taking values in a Hilbert space. Furthermore, we provide explicit bounds for ΔN and for the concentration function of the random variable ℚ[SN].

title: On the Rate of Convergence in the Central Limit Theorem in Banach Spaces
abstract: On demontre un resultat et on l'utilise pour demontrer que le taux de convergence dans le theoreme limite fonctionnel pour des processus empiriques est d'ordre O )n −1/2 )

title: Berry-Esseen bounds for statistics of weakly dependent samples
abstract: We prove Berry-Esseen bounds for a general class of asymptotically normal statistics which are functions of N weakly dependent random variables under easily verifiable conditions. In particular, we show, for some 6 > 0, the validity of the bound o(N-'/~ log6 N) for U-statistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order statistics.

title: Über Teilerfunktionen in Dirichletschen Reihen
Asymptotic Distribution of Quadratic Forms
We consider quadratic forms Q n = Σ a jh X j X k , 1 ≤j ¬= k ≤ n where X j are i.i.d. random variables with finite third moment. We obtain optimal bounds for the Kolmogorov distance between the distribution of Q n and the distribution of the same quadratic forms with X j replaced by corresponding Gaussian random variables. These bounds are applied to Toeplitz and random matrices as well as to nonstationary AR(1) processes.

title: Berry-Esseen bounds for statistics of weakly dependent samples
abstract: We prove Berry-Esseen bounds for a general class of asymptotically normal statistics which are functions of N weakly dependent random variables under easily verifiable conditions. In particular, we show, for some 6 > 0, the validity of the bound o(N-'/~ log6 N) for U-statistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order statistics.

title: On Minimal Moment Assumptions in Berry–Esséen Theorems for U-Statistics
abstract: The rate of convergence for asymptotically normal U-statistics is of order $O(n^{ - {1 / 2}} )$ provided that \[ {\bf E}\left| {{\bf E}\left\{ {h\left( {X_1 ,X_2 } \right)\left| {X_1 } \right.} \right\}} \right|^3 0$. In this paper we extend the result for statistics of higher orders and with possible nonnormal limit distributions.

title: The Berry-Esseen bound for student's statistic
abstract: We prove the Berry-Esseen bound for the Student t-statistic. Under the assumption of a third moment this bound coincides (up to an absolute constant) with the classical Berry-Esseen bound for the mean. In general the distribution of the Student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean, and sometimes faster. For example, rates of convergence can be proved if the underlying distribution is in the domain of attraction of the normal law.

title: Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces
abstract: Let X,X1,X2,… be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space ℝd. Assume that EX=0 and that X is not concentrated in a proper subspace of ℝd. Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms ℚ[SN] of the normalized sums SN=N−1/2(X1+⋯+XN) and show that
provided that d≥9 and the fourth moment of X exists. The bound ?(N−1) is optimal and improves, e.g., the well-known bound ?(N−d/(d+1)) due to Esseen (1945). The result extends to the case of random vectors taking values in a Hilbert space. Furthermore, we provide explicit bounds for ΔN and for the concentration function of the random variable ℚ[SN].

title: On the Rate of Convergence in the Central Limit Theorem in Banach Spaces
abstract: On demontre un resultat et on l'utilise pour demontrer que le taux de convergence dans le theoreme limite fonctionnel pour des processus empiriques est d'ordre O )n −1/2 )

title: Über Teilerfunktionen in Dirichletschen Reihen
On the Approximation of Fixed Points of Nonlinear Compact Operators
Certain methods for the approximate solution of $x - Kx = 0$, where K is a compact operator, lead to a family of operator equations $x - K_n x = 0$, $n \geqq 1$, where $K_n $,$n \geqq 1$, are collectively compact and converge pointwise to K. In this paper a new and simplified proof of the existence and uniqueness of a solution of $x - K_n x = 0$ in a neighborhood of an isolated solution of $x - Kx = 0$ is given.

title: Symmetric graphs with projective subconstituents
abstract: Let P be an undirected graph and G a subgroup of aut(r) acting transitively on the vertex set of P. Let x be an arbitrary vertex of P. We denote by P(x) the set of vertices adjacent to x and by G(x)F(x) the permutation group induced by the stabilizer G (x) of x in G on P(x); G (x)r(X) is called the subconstituent of the pair (P, G). For each i E N let Gi(x) = {a E G(x)Ia E G(y) if a (x, y) 1 then s 3. In , it was shown that s 3. We prove the following partial result:

title: On finite Moufang polygons
abstract: We show that a finite generalized polygon Γ is Moufang with respect to a groupG if and only if for every flag {x, y} of Γ, the subgroupG1(x, y) ofG fixing every element incident with one ofx, y acts transitively on the set of apartments containing the elementsu, x, y, w, whereu≠y (resp.w≠x) is an arbitrary element incident withx (resp.y).

title: The nonexistence of certain Moufang polygons
abstract: Let F=(V, E) be an arbitrary undirected graph, finite or infinite, V the vertex set of F, E the edge set, and let G be an arbitrary subgroup of aut(F). For each x e V we denote by F(x) the set of vertices adjacent to x, by G(x) the stabilizer of x in G and, for each ieN, by Gi(x ) the subgroup  for all y e V with O(x,y)<i} where O(x,y) denotes the distance between x and y. An s-path (for seN) is an (s+ 1)-tuple (x 0 . . . . . x~) of vertices such that xi~F(x i_ 1) if 1 < i N s and xi+xi_ 2 if 2=<i<s. Let

title: Graphs which are locally Grassmann

title: A Geometric Characterization of Certain Groups of Lie Type
abstract: Let r be an undirected graph with vertex set V(r) and edge set E(r) and let G be a subgroup of Aut (r). For each {x, y} E E(r), we denote by G{x, y} the stabilizer of {x, y} in G (which mayor may not contain elements exchanging the vertices x and y). For each x E V(r) we denote by r(x) the set of vertices adjacent to x, by G(x) the stabilizer of x in G and, for each i E N, by Gi(x) the subgroup {a E Gla E G(u) for all u E V(r) with a(x, u) "'" i} where a(x, u) denotes the distance from x to u. An s-path (for sEN) is an (s + I)-tuple (xo, Xl. .•• , xs ) of vertices such that Xi E r(Xi-l) if 1"", i "'" s and Xi ¥Xi-Z if 2"", i "'" s. Let G(xo, ... , xs ) = G(xo) n··· n G(xs ) and Gi(xo, ... , xs ) = Gi(xo) n· .. n Gi(xs ) for each s-path (xo, ... , xs ) and each i E N. If H is any group acting on a set X, we denote by H X the permutation group on X induced by H. . In  we proved the following result.

title: On a theorem of Goldschmidt
Multigrid methods for variation problems: The V-cycle☆
In an earlier paper, we developed a convergence theory for a class of multigrid methods applied to differential boundary value problems, where the differential operator is self-adjoint and positive definite. The multigrid structure assumed a variational setting (although it applies to finite differences as well as finite elements) and incorporated the so-called W-cycle process. In the present paper, we extend this theory to include some results on the corresponding V-cycle multigrid algorithm.

title: Multigrid Methods for Variational Problems: General Theory for the V-Cycle
abstract: In two earlier papers [ (1982), pp. 924–929; 21 (1984), ], we developed an algebraic convergence theory for a class of multigrid methods applied to positive definite self-adjoint linear operator equations. The purpose of the present paper is to extend these results by eliminating an earlier approximation order restriction, developing additional rate estimates and allowing for very general relaxation schemes, including those that are nonstationary and nonsymmetric. These results apply to most well-known iterative methods and preconditioners.

title: MULTIGRID METHODS FOR VARIATIONAL PROBLEMS: FURTHER RESULTS*
abstract: In an earlier paper [ (1982), pp. 924–929], we developed a convergence theory for a class of multigrid methods applied to positive definite self-adjoint differential boundary value problems, where the multigrid process used W-cycling and Richardson’s iteration. In the present paper, we extend this theory to include V-cycling and more general relaxation schemes such as Jacobi and (arbitrarily ordered) Gauss-Seidel.

title: A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems
abstract: The objective of this paper is the development of a mesh refinement technique for applying Newton’s method to the solution of nonlinear two-point boundary value problems. The process represents a significant improvement on an earlier approach both in its general applicability and in its numerical performance. This is demonstrated by several reported numerical examples.
MULTIGRID METHODS FOR VARIATIONAL PROBLEMS: FURTHER RESULTS*
In an earlier paper [ (1982), pp. 924–929], we developed a convergence theory for a class of multigrid methods applied to positive definite self-adjoint differential boundary value problems, where the multigrid process used W-cycling and Richardson’s iteration. In the present paper, we extend this theory to include V-cycling and more general relaxation schemes such as Jacobi and (arbitrarily ordered) Gauss-Seidel.

title: Multigrid Methods for Variational Problems: General Theory for the V-Cycle
abstract: In two earlier papers [ (1982), pp. 924–929; 21 (1984), ], we developed an algebraic convergence theory for a class of multigrid methods applied to positive definite self-adjoint linear operator equations. The purpose of the present paper is to extend these results by eliminating an earlier approximation order restriction, developing additional rate estimates and allowing for very general relaxation schemes, including those that are nonstationary and nonsymmetric. These results apply to most well-known iterative methods and preconditioners.

title: A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems
abstract: The objective of this paper is the development of a mesh refinement technique for applying Newton’s method to the solution of nonlinear two-point boundary value problems. The process represents a significant improvement on an earlier approach both in its general applicability and in its numerical performance. This is demonstrated by several reported numerical examples.
The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift
Mixtures of polyisocyanates are prepared in one step by reacting phosgene with a slurry of selected polyamines in an inert solvent.

title: Uniformization of attracting basins for exponential maps
abstract: Soit la famille exponentielle complexe Eλ(Z)=λ exp(Z). Il y a un ensemble ouvert de valeurs de λ dans le plan complexe pour lesquelles Eλ a un point fixe attractif unique; Ωλ est le bassin d'attraction pour ces valeurs. On considere l'uniformisation Φλ de Ωλ et on etudie la dynamique induite par Φλ sur le disque unite

title: Fixed points of polynomial maps. Part II. Fixed point portraits
abstract: — Douady, Hubbard and Branner have introduced the concept of a "limb" in the Mandelbrot set. A quadratic map f(z) = z + c belongs to the p/q-limb if and only if there exist q external rays of its Julia set which land at a common fixed point of/, and which are permuted by/with combinatorial rotation number ^^Q/Z, p / q ^ O . ( This note will make a similar analysis of higher degree polynomials by introducing the concept of the "fixed point portrait" of a monic polynomial map.

title: A finiteness theorem for a dynamical class of entire functions

title: On the shape of the unit sphere in Q(Δ)
abstract: We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points

title: Fixed points of polynomial maps. I. Rotation subsets of the circles
abstract: — We give a combinatorial analysis of rational rotation subsets of the circle. These are invariant subsets that have well-defined rational rotation numbers under the standard self-covering maps of S. This analysis has applications to the classification of dynamical systems generated by polynomials in one complex variable.

title: Volatility of the short rate in the rational lognormal model
abstract: A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.
Fixed points of polynomial maps. I. Rotation subsets of the circles
— We give a combinatorial analysis of rational rotation subsets of the circle. These are invariant subsets that have well-defined rational rotation numbers under the standard self-covering maps of S. This analysis has applications to the classification of dynamical systems generated by polynomials in one complex variable.

title: A finiteness theorem for a dynamical class of entire functions

title: On the shape of the unit sphere in Q(Δ)
abstract: We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points

title: Fixed points of polynomial maps. Part II. Fixed point portraits
abstract: — Douady, Hubbard and Branner have introduced the concept of a "limb" in the Mandelbrot set. A quadratic map f(z) = z + c belongs to the p/q-limb if and only if there exist q external rays of its Julia set which land at a common fixed point of/, and which are permuted by/with combinatorial rotation number ^^Q/Z, p / q ^ O . ( This note will make a similar analysis of higher degree polynomials by introducing the concept of the "fixed point portrait" of a monic polynomial map.

title: Volatility of the short rate in the rational lognormal model
abstract: A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.