Contiguous Relations Research Articles

Hume’s Dialogues: a natural explanation of natural religion?

ABSTRACT Hume’s Dialogues concerning Natural Religion (1779) describes a philosophical discussion on the validity of the argument from design. What Hume investigates, however, is not the rational grounds of religion, but human nature and its attraction to the idea of design. I argue that the key to understanding Hume’s Dialogues is his conception of the imagination as described in the Treatise. Hume characterizes the human imagination or mind as self-indulgent, with a strong drive to unite perceptions in relations of resemblance, contiguity or causality, often adding fictional constructions to create an easy transition between ideas. Natural religion is a prime example, as the whole universe is united in orderly means-to-ends relations and provided with a familiar cause: something resembling the human mind. This reading of the Dialogues, however, does not warrant the conclusion that Hume provides a reductionist natural explanation of natural religion. Knowing human nature helps to understand religion’s attraction and the attraction of religion helps to understand humans, because it is paradigmatic of who we are. To connect perceptions, construct wholes and create meaning out of chaos is an essential feature of human nature, and a source of great pleasure.

Investigation of Extended k-Hypergeometric Functions and Associated Fractional Integrals

Hypergeometric functions have many applications in various areas of mathematical analysis, probability theory, physics, and engineering. Very recently, Hidan et al. (Math. Probl. Eng., ID 5535962, 2021) introduced the (p, k)-extended hypergeometric functions and their various applications. In this line of research, we present an expansion of the k-Gauss hypergeometric functions and investigate its several properties, including, its convergence properties, derivative formulas, integral representations, contiguous function relations, differential equations, and fractional integral operators. Furthermore, the current results contain several of the familiar special functions as particular cases, and this extension may enrich the theory of special functions.

Investigation of the k-Analogue of Gauss Hypergeometric Functions Constructed by the Hadamard Product

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted to the study of the k-analogue of Gauss hypergeometric functions by the Hadamard product. We give a definition of the Hadamard product of k-Gauss hypergeometric functions (HPkGHF) associated with the fourth numerator and two denominator parameters. In addition, convergence properties are derived from this function. We also discuss interesting properties such as derivative formulae, integral representations, and integral transforms including beta transform and Laplace transform. Furthermore, we investigate some contiguous function relations and differential equations connecting the HPkGHF. The current results are more general than previous ones. Moreover, the proposed results are useful in the theory of k-special functions where the hypergeometric function naturally occurs.

“I am an atypical mother”: Motherhood and maternal language in Giovanna Cristina Vivinetto’s poetry

In her debut book Dolore minimo, Giovanna Cristina Vivinetto engages in a reflection on motherhood to recount an autobiographical story of gender self-determination and male to female transition. This article explores Vivinetto’s poetry as the retelling of transformative moments in two mother–daughter relationships, which generate a reshaping of life and language. In the book, these two storylines intersect, blur, and even overlap, creating a poetic discourse in which the maternal acts simultaneously as powerful catalyzer and producer of meanings. In discussing how, in Dolore minimo, the relationship of two atypical mothers becomes the creative site of a new possible symbolic order, my analysis engages an atypical approach: it reads Vivinetto’s queer representation of motherhood via the theorization developed by the women of Diotima—including, in particular, Luisa Muraro, Chiara Zamboni, Diana Sartori, and Ida Dominijanni. These feminist thinkers have been generally criticized for reinforcing binary understandings of sex and gender, based on an essentialist view of the category of woman. Yet, what if the feminism forwarded by Diotima, by positioning the feminine as a creative producer and first-person narrator of change, could still offer a productive avenue for dialogue? The article begins with a discussion of Diotima’s key theorizations, which lays the groundwork for interpreting the maternal poetics of Dolore minimo. The subsequent sections examine in more depth how Vivinetto’s poetry has reinvented the figure of the mother as a teacher and learner of new words, and how, through this reinvention, she has crafted a maternal language that knits together new relations of contiguity and change. Ultimately, by redeploying the figure of the mother beyond cisgender norms, Vivinetto’s poetry is revealing the inexhaustible vitality of this character.

New recurrence relations for Wilson polynomials via a system of Jacobi type orthogonal functions

In this paper, we will find an orthogonal basis in term of explicit Jacobi polynomials, of the corresponding weighted L2-space on the whole of the real numbers, which is mapped onto another orthogonal basis involving Wilson polynomials by the Jacobi-Dunkl transform. Next we give a tridiagonalization of the Jacobi-Dunkl Laplacian for the Jacobi type functions. This tridiagonalization leads to a new result, which can be viewed as contiguous relations for Wilson polynomials.

Further study on the conformable fractional Gauss hypergeometric function

<abstract> This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points $ x = 1 $ and $ x = \infty $. Next, various generating functions of the CFGHF are established. We also develop some differential forms for the CFGHF. Subsequently, differential operators and contiguous relations are reported. Furthermore, we introduce the conformable fractional integral representation and the fractional Laplace transform of CFGHF. As an application, and after making a suitable change of the independent variable, we provide general solutions of some known conformable fractional differential equations, which could be written by means of the CFGHF. </abstract>

Q-Difference Systems for the Jackson Integral of Symmetric Selberg Type

We provide an explicit expression for the first order q-difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of q-analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system we use a set of the symmetric polynomials introduced by Matsuo in his study of the q-KZ equation. Our main result is an explicit expression for the coefficient matrix of the q-difference system in terms of its Gauss matrix decomposition. We introduce a class of symmetric polynomials called interpolation polynomials, which includes Matsuo's polynomials. By repeated use of three-term relations among the interpolation polynomials we compute the coefficient matrix.

Two integral transformations related to ζ(2)

We prove two integral transformations that relate different constructions of rational approximations to ζ(2). The first one relates a double integral over the unit square and a Barnes-type integral. The second one relates two Barnes-type integrals and was discovered and proved by W. Zudilin using an automated proof method. Here we offer a proof based on more classical means such as contiguous relations, the second Barnes lemma and the duplication formula for the gamma function.

Transformations of the Hypergeometric 4F3 with One Unit Shift: A Group Theoretic Study

We study the group of transformations of 4F3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known transformations to generate a subgroup whose structure is then thoroughly studied. Using some known results for 3F2 transformation groups, we show that this subgroup is isomorphic to the direct product of the symmetric group of degree 5 and 5-dimensional integer lattice. We investigate the relation between two-term 4F3 transformations from our group and three-term 3F2 transformations and present a method for computing the coefficients of the contiguous relations for 3F2 functions evaluated at unity. We further furnish a class of summation formulas associated with the elements of our group. In the appendix to this paper, we give a collection of Wolfram Mathematica® routines facilitating the group calculations.

Cruzamentos entre palavra e imagem em três momentos da arte brasileira

Este artigo aborda o cruzamento entre palavra e visualidade em três momentos da arte brasileira: Concretismo, Neoconcretismo e Nova Objetividade Brasileira. De um primeiro momento em que se busca a identidade entre palavra e imagem de modo predominantemente óptico passa-se a outro em que essa identidade está na dimensão simbólica da palavra identificada com o corpo e o espaço, tornando-se háptica, e chega-se a um terceiro em que palavra e imagem instauram uma relação de contiguidade, metonímica, que mobiliza o contexto que as inscreve numa rede de significações e relações de poder. É traçada, a partir do conceito de “participação semântica” (1967), de Hélio Oiticica, uma mudança de paradigma na relação entre palavra e imagem.

On basic Horn hypergeometric functions mathbf{H}_{3} and mathbf{H}_{4}

The purpose of this work is to demonstrate several interesting contiguous function relations and q-differential formulas for basic Horn hypergeometric functions mathbf{H}_{3} and mathbf{H}_{4}. Some properties of our main results are also constructed.

Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators

The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras and . It is shown that the q-para Racah polynomials corresponding to a non-conventional truncation of the Askey–Wilson polynomials form a basis for a finite-dimensional representation of . The first order Heun operators defined by a degree raising condition on polynomials are shown to form a five-dimensional vector space that encompasses . The most general quadratic expression in the five basis operators and such that it raises degrees by no more than one is identified with the Heun–Askey–Wilson operator.

New methods for conformal correlation functions

The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with spinor in- dices only and standard projection operators, allows a unified treatment of all quasi-primary operators irrespective of their Lorentz group irreducible representations. This unified treatment works at the level of the operator product expansion and hence applies to all correlation functions. A very useful differential operator appearing in the operator product expansion is established and its action on appropriate products of embedding space coordinates is explicitly computed. This computation leads to tensorial generalizations of the usual Exton function for all correlation functions. Several important identities and contiguous relations are also demonstrated for these new tensorial functions. From the operator product expansion all correlation functions for all quasi-primary operators, irrespective of their Lorentz group irreducible representations, can be computed recursively in a systematic way. The resulting answer can be expressed in terms of tensor structures that carry all the Lorentz group information and linear combinations of the new tensorial functions. Finally, a summary of the well-defined rules allowing the computation of all correlation functions constructively is presented.

Quasi-orthogonality and zeros of some [formula omitted] and [formula omitted] polynomials

We state and prove the q-extension of a result due to Johnston and Jordaan (cf. Johnston and Jordaan (2015)) and make use of this result, the orthogonality of q-Laguerre, little q-Jacobi, q-Meixner and Al-Salam–Carlitz I polynomials as well as contiguous relations satisfied by the polynomials, to establish the quasi-orthogonality of certain 2ϕ2 and 3ϕ2 polynomials. The location and interlacing properties of the real zeros of these quasi-orthogonal polynomials are studied. Interlacing properties of the zeros of q-Laguerre quasi-orthogonal polynomials Ln(δ)(z;q) when −2<δ<−1 with those of Ln−1(δ+1)(z;q) and Ln(δ+1)(z;q) are also considered.

English

English

Certain Integral Representations, Transformation Formulas and Summation Formulas Related to Humbert Matrix Functions

The main objective of this work is to present some important results and formulas in the theory of Humbert matrix functions by using the concepts of matrix functional calculus. We define Humbert matrix functions assuming that not all the matrices involved are commuting. We show that these two variable Humbert matrix functions follow naturally as confluent cases of Appell matrix functions. We determine their regions of convergence, integral representations, transformation formulas, summation formulas, contiguous relations and matrix differential equations satisfied by them.

Hypergeometric integrals associated with hypersphere arrangements and Cayley-Menger determinants

The $n$-dimensional hypergeometric integrals associated with a hypersphere arrangement $S$ are formulated by the pairing of $n$-dimensional twisted cohomology $H_\nabla^n (X, \Omega^\cdot (*S))$ and its dual. Under the condition of general position we present an explicit representation of the standard form by a special (NBC) basis of the twisted cohomology (contiguity relation in positive direction), the variational formula of the corresponding integral in terms of special invariant $1$-forms $\theta_J$ written by Calyley-Menger minor determinants, and a connection relation of the unique twisted $n$-cycle identified with the unbounded chamber to a special basis of twisted $n$-cycles identified with bounded chambers. Gauss-Manin connections are formulated and are explicitly presented in two simplest cases. In the appendix contiguity relation in negative direction is presented in terms of Cayley-Menger determinants.

Vector Space of Feynman Integrals and Multivariate Intersection Numbers.

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for the construction of multivariate intersection numbers relevant to Feynman integrals, and show for the first time how they can be used to solve the problem of integral reduction to a basis of master integrals by projections, and to directly derive functional equations fulfilled by the latter. We apply it to the decomposition of a few Feynman integrals at one and two loops, as first steps toward potential applications to generic multiloop integrals. The proposed method can be more generally employed for the derivation of contiguity relations for special functions admitting multifold integral representations.

Cross Sectional and Longitudinal Fuzzy Clustering of the NUTS and Positioning of the Italian Regions with Respect to the Regional Competitiveness Index (RCI) Indicators with Contiguity Constraints

In socio-economical clustering often the empirical information is represented by time-varying data generated by indicators observed over time on a set of subnational (regional) units. Usually among these units may exist contiguity relations, spatial but not only. In this paper we propose a fuzzy clustering model of multivariate time-varying data, the longitudinal fuzzy C-Medoids clustering with contiguity constraints. The temporal aspect is dealt with by using appropriate measures of dissimilarity between time trajectories. The contiguity among units is dealt with adding a contiguity matrix as a penalization term in the clustering model. The cross sectional fuzzy C-Medoids clustering with contiguity constraints is obtained considering one instant of time. The model is applied to the classification of the European NUTS on the basis of the observed dynamics of the Basic, Efficiency and Innovation subindexes of the Regional Competitiveness Index (RCI) 2013 and 2016. The positioning of the Italian regions is analyzed through the values of the medoids of the clusters and shows the peculiarities of the regions with respect to the subindexes either in single times or in the dynamic. Two contiguity constraints, one based on the European Western, Southern, Central and Northern geographic areas and one on the level of GDP—taken into account in the computation of the RCI—are also introduced in the models.

Decision and time from a Humean point of view

Until recently, little attention has been paid to the consequences of Hume’s theory of action for intertemporal decision. Yet in view of the recurring discussion concerning situations of conflicting choice between a close and a remote objective, which runs from Book 2 of the Treatise, to the second Enquiry, to the Dissertation, intertemporal decision appears, at least in part, to be an outcome of the role of the natural relation of contiguity in the formation of the structure of desires, and thus different from the structure of pleasure. This paper shows, and expresses formally, that Hume’s approach provides alternative conditions which explain time-consistency on the one hand, and dynamic time-inconsistency on the other, when the link between contiguity and the ’violence’ of the passions is taken into account. The possibility of time-inconsistency is acknowledged by Hume as giving rise to general aversion, therefore constitutes a key argument in explaining the origin of government.