Rational Equivalence Research Articles

Homogeneous localizations of some quantum enveloping superalgebras

Under suitable conditions the skewfield of fractions of a superalgebra which is a noetherian domain is canonically provided with a structure of superalgebra. This gives rise to a notion of rational equivalence in the category of superalgebras. We study from the point of view of this rational equivalence some low dimensional examples of quantum enveloping algebras of Lie superalgebras.

Standard conjectures for abelian fourfolds

Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type for A. By combining this result with a theorem of Clozel we deduce that numerical equivalence on A coincides with l-adic homological equivalence on A for infinitely many l. The approach consists in reformulating this question into a p-adic problem and then using p-adic Hodge Theory to solve it.

A proposal for perception measurement on a linguistic scale coded with unconventional fuzzy numbers

The aim of this paper is to formulate a new proposal for perception measurement on a linguistic scale coded with fuzzy numbers. Additionally, an attempt is made to show the assessment process of the adequacy of a linguistic scale. The basis for the proposal is the discussion of issues related to the ambiguity of the results of measurements made by means of a subjective type of measurement scales. The proposed assessment technique is relevant when the results of the measurement based on a linguistic scale are coded with numerical equivalents in the form of e.g. unconventional fuzzy numbers. The issue the subjective perception of the products’ quality illustrates the objectivity level of measurement results. Subjective perception is measured with a specially designed IT tool allowing the respondent to determine all the characteristics of the resulting fuzzy numbers. The scale adequacy assessment tool is based on the Item Response Theory, and particulary so on the model devised by Georg Rasch. The measurement of socio-economic phenomena, including material and subjective wellbeing of households, the quality of households’ durable goods, and the assessment of the quality of goods available on the market requires special tools. It seems that one of the most useful and powerful tools for the measurement of socio-economic phenomena is a linguistic scale. The problematic issue in the analysis presented in the paper is coding verbal terms with their numerical equivalents.

Rational equivalence of cusps

We prove that two cusps of the same dimension in the Baily-Borel compactification of some classical series of modular varieties are linearly dependent in the rational Chow group of the compactification. This gives a higher dimensional analogue of the Manin-Drinfeld theorem. As a consequence, we obtain a higher dimensional generalization of modular units as higher Chow cycles on the modular variety.

Rational equivalence and Lagrangian tori on K3 surfaces

Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L \subset X to the skyscraper sheaf of a point y \in Y . We show there are Lagrangian tori with vanishing Maslov class in X whose class in the Grothendieck group of the Fukaya category is not generated by Lagrangian spheres. This is mirror to a statement about the “Beauville–Voisin subring” in the Chow groups of Y , and fits into a conjectural relationship between Lagrangian cobordism and rational equivalence of algebraic cycles.

Pressure-Induced Metallization of Diamond at Room Temperature

We use four different methods for testing the hypothesis of putative numerical equivalence between the hardness of diamond and the critical pressure of diamond metallization. In modeling crystal distortion by uniaxial compression, the initial calculations of external pressure give the lower limit for the critical pressure: Pm(1) = 213 GPa. This value is compared to semi-empirical findings obtained within Penn’s model for dielectrics, which is Pm(2) = 187.67 GPa. An experimental value for the Vickers hardness, which is HV(1) = 92 GPa, is compared using a semi-empirical approach. A theoretical value for diamond’s hardness calculated within the Penn’s model is HV(2) = 92.22 GPa.

On a conjecture of Voisin on the gonality of very general abelian varieties

We study orbits for rational equivalence of zero-cycles on very general abelian varieties by adapting a method of Voisin to powers of abelian varieties. We deduce that, for k at least 3, a very general abelian variety of dimension at least 2k−2 has covering gonality greater than k. This settles a conjecture of Voisin. We also discuss how upper bounds for the dimension of orbits for rational equivalence can be used to provide new lower bounds on other measures of irrationality. In particular, we obtain a strengthening of the Alzati-Pirola bound on the degree of irrationality of abelian varieties.

Kilisli Divan Şairlerinin Şiirlerinde Tarihin İzleri

Harflerin rakamsal karşılıkları yani ebced hesabı ile tarih düşürme geleneği, önemli bir olayı tarihe kaydetmek amacıyla Arap, Fars ve Türk edebiyatlarında sıklıkla kullanılan bir gelenektir. Belâgat kitaplarında her ne kadar bedi‘ sanatlar arasında sayılsa da tarih düşürme aslında beceri ve hüner gerektiren teknik bir olaydır. Şairler, tarih düşürmeyi şairliğin bir gereği olarak görmüşler, sanatlarını, hünerlerini ve ustalıklarını gösterebilmek için bu gelenekten faydalanmışlardır. Sanatlarını ve ustalıklarını gösterirken de içinde bulundukları topluma dair önemli gördükleri olayları bu gelenek vasıtası ile tarihe not olarak düşmüşlerdir. Fakrî Dede, Hâkî, Kâ’il, Rûhî, Mehmed Emin Vahid Paşa, Celal Paşa, Zihnî, Bekir Vahîd Efendi, Lütfullah Hâzım, Hâmî, Şeyh Abdullah Sermest gibi şairler yetiştirmiş olan Kilis, Osmanlı coğrafyasının önemli kültür merkezlerinden biri olmuştur. Çalışmamızda Kilis’te yetişen şairlerden Ebubekir Vahid Efendi, Hâmî, Lutfullah Hâzım ve Zihnî’nin divan ya da divançelerinde yer alan tarih manzumeleri esas alınacaktır. Bu tarih manzumeleri muhtevalarına göre vefat yahut velâdet hakkında düşürülen tarihler, inşa yahut tecdid hakkında düşürülen tarihler, doğal afetler hakkında düşürülen tarihler, zafer münasebetiyle düşürülen tarihler, padişahın tahta geçişi münasebetiyle düşürülen tarihler ve diğer konular hakkında düşürülen tarihler şeklinde tasnif edilerek çeşitli yönleriyle açıklanmaya çalışılacaktır.

Torus actions on rationally elliptic manifolds

An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed (simply connected) rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up to equivariant rational homotopy equivalence.

Художественный реаликон как категория переводоведения

В статье анализируется специфика передачи при переводе лингвокультурных реалий (артефактов и ментефактов) на материале повести И. А. Бунина «Суходол» и ее переводов на французский язык. Реалии представляют собой одну из эстетических доминант произведений И. А. Бунина и делают произведения русского писателя особенно трудными для перевода. Цель данного исследования – проследить особенности ревербализации лингвокультурных реалий при переводе. Методологической базой исследования является теория межъязыковой реноминации и лингвистическая теория реалии. В процессе исследования использовался метод сопоставительного анализа текста оригинала и перевода. Авторы выдвигают и обосновывают гипотезу о том, что в художественном тексте с высоким уровнем национального колорита реалии образуют в своей совокупности художественный реаликон – единый идейно-эстетический комплекс, отображающий индивидуально-авторскую картину мира писателя. Элементы реаликона имеют полевую структуру, в которой можно выделить ядро и периферию. Наибольшие изменения при переводе претерпевает ядро реаликона, поскольку место в нем сохраняют лишь немногочисленные русские L-реалии, а также некоторые французские R-реалии, реноминирующие ключевые концепты повести. Ближняя периферия образована С-реалиями, передаваемыми при помощи экспликации или сопровождающимися переводческим метатекстом. Дальнюю периферию образуют многочисленные R-реалии, функциональные эквиваленты и гиперонимы, а также С-реалии, передаваемые с помощью французских эквивалентов или путем дословного перевода, что полностью стирает национальный колорит текста оригинала. Таким образом, проведенное исследование позволяет выявить сходства и различия в реаликонах как фрагментах художественных картин мира, отображенных в ИТ и ПТ, а также определить и обосновать количественно и качественно доминирующую стратегию передачи национального колорита.

TOWARDS AN INTERSECTION CHOW COHOMOLOGY THEORY FOR GIT QUOTIENTS

We study the Fulton-MacPherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are etale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore natural extensions of GIT quotients. Our main result is that, with ℚ-coefficients, every operational class can be represented by a topologically strong cycle on the corresponding stack. Moreover, this cycle is unique modulo rational equivalence on the stack. Our methods also allow us to prove that if X is the good moduli space of a properly stable, smooth, Artin stack then the natural map Pic(X)ℚ, L ↦ c1(L) is an isomorphism.

Étale monodromy and rational equivalence for -cycles on cubic hypersurfaces in

Let be an uncountable algebraically closed field of characteristic , and let be a smooth projective connected variety of dimension , embedded into over . Let be a hyperplane section of , and let and be the groups of algebraically trivial algebraic cycles of codimension and modulo rational equivalence on and , respectively. Assume that, whenever is smooth, the group is regularly parametrized by an abelian variety and coincides with the subgroup of degree classes in the Chow group . We prove that the kernel of the push-forward homomorphism from to is the union of a countable collection of shifts of a certain abelian subvariety inside . For a very general hyperplane section either or coincides with an abelian subvariety in whose tangent space is the group of vanishing cycles . Then we apply these general results to sections of a smooth cubic fourfold in . Bibliography: 33 titles.

Nonlinearity In Similar Structures: On (3a−1)(3b−1) = (5c−1)(5d−1), And gu=fv.

Liptai, Nemeth, et. al. (2020) conjectured (and supposedly proved) that in the diophantine equation (3a−1)(3b−1)=(5c−1)(5d−1) in positive integers a≤b, and c≤d, the only solution to the title equation is (a,b,c,d)=(1,2,1,1). This article proves that the Liptai, Nemeth, et. al. (2020) conjecture and results are wrong, and that there is more than one solution for the equation (3a−1)(3b−1)=(5c−1)(5d−1). This article introduces “Existence Conditions” and new theories of “Rational Equivalence”, and a new theorem pertaining to the equation gu=fv.

On log motives

We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and homological equivalence coincide, and that it is also equivalent to that the latter is a Tannakian category. We discuss various realizations, formulate Tate and Hodge conjectures, and verify them in curve case.

Rational Inattention Via Ignorance Equivalence

Rational Inattention Via Ignorance Equivalence

Distinguished cycles on varieties with motive of abelian type and the Section Property

A remarkable result of Peter O’Sullivan asserts that the algebra epimorphism from the rational Chow ring of an abelian variety to its rational Chow ring modulo numerical equivalence admits a (canonical) section. Motivated by Beauville’s splitting principle, we formulate a conjectural Section Property which predicts that for smooth projective holomorphic symplectic varieties there exists such a section of algebra whose image contains all the Chern classes of the variety. In this paper, we investigate this property for (not necessarily symplectic) varieties with a Chow motive of abelian type. We introduce the notion of a symmetrically distinguished abelian motive and use it to provide a sufficient condition for a smooth projective variety to admit such a section. We then give a series of examples of varieties for which our theory works. For instance, we prove the existence of such a section for arbitrary products of varieties with Chow groups of finite rank, abelian varieties, hyperelliptic curves, Fermat cubic hypersurfaces, Hilbert schemes of points on an abelian surface or a Kummer surface or a K3 surface with Picard number at least 19, and generalized Kummer varieties. The latter cases provide evidence for the conjectural Section Property and exemplify the mantra that the motives of holomorphic symplectic varieties should behave as the motives of abelian varieties, as algebra objects.

Numeric equivalents for alpha acuities: salvation for EMR research disasters

Numeric equivalents for alpha acuities: salvation for EMR research disasters

The progressive 6-year-old conserver: Numerical saliency and sensitivity as core mechanisms of numerical abstraction in a Piaget-like estimation task

In Piaget’s theory of number development, children do not possess a true concept of number until they are able to reason on numerical quantity regardless of changes in other nonnumerical magnitudes, such as length. Recent studies have echoed this result by arguing that abstracting number from nonnumerical dimensions of magnitude is a developmental milestone and a strong predictor of mathematics achievement. However, the mechanisms supporting such abstraction remain largely underspecified. We aimed to study how identification of the numerical equivalence in a Piaget-like estimation task by 6-year-old children is affected by (a) the degree of interference between number and nonnumerical magnitudes and (b) children’s spontaneous orientation to numerosity. Six-year-old children first performed a card sorting task assessing their spontaneous orientation towards numerosity, spacing, or item size in a set of dots. Then, they completed a Piaget-like same/different numerical estimation task using two rows of dots in which the length ratio between the two rows varied systematically. Children were less likely to accept the numerical equivalence in the Piaget-like estimation task (a) as the difference in spacing between the dots increased and (b) as the children were more spontaneously oriented towards spacing over number in the card sorting task. Our results suggest that abstracting number depends on its saliency, which varies both as a function of the context (i.e., length ratio between the two rows) and of individual differences in children’s sensitivity to the numerical aspects of their environment. These factors could be at the root of the observed development of performance in the seminal number-conservation task, which appears as a progressive abstraction of number rather than a conceptual shift, as Piaget hypothesized.

Chow ring and gonality of general abelian varieties

We study the (covering) gonality of abelian varieties and their orbits of zero-cycles for rational equivalence. We show that any orbit for rational equivalence of zero-cycles of degree k has dimension at most k-1. Building on the work of Pirola, we show that very general abelian varieties of dimension g have (covering) gonality at least f(g), where f(g) grows like log g. This answers a question asked by Bastianelli, De Poi, Ein, Lazarsfeld and B. Ullery. We also obtain results on the Chow ring of very general abelian varieties A of dimension g, e.g., if g≥2k-1, the set of divisors D∈ Pic 0 (A) such that D k =0 in CH k (A) is at most countable.

A numerical equivalence result for generalized method of moments

This note shows when a GMM estimator has an alternative representation as a 2SLS estimator after data filtering. The result exploits a weaker condition than the conditions earlier invariance to transformation results use and applies to panel and system estimation.