Multivariable connected sums and multiple polylogarithms

We introduce the multivariable connected sum which is a generalization of Seki–Yamamoto’s connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating multivariable connected sums and for giving relations among special values of multiple polylogarithms. In particular, our class of relations contains Ohno’s relations for multiple polylogarithms.

A Note on the Summation of the Incomplete Gamma Function

We examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero distribution.

Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics

In this manuscript, several types of exact solutions including trigonometric, hyperbolic, exponential, and rational function are successfully constructed with the implementation of two modified mathematical methods, namely called extended simple equation and modified F-expansion methods on the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa and the combined sinh–cosh-Gordon equations. Diverse form of solitary wave solutions is achieved from exact solutions by passing the special values to the parameters. Some solution are plotted in the form of 3D and 2D by assigning the specific values to parameters under the constrain condition to the solutions. These approaches yield the new solutions that we think other researchers have missed in the field of nonlinear sciences. Hence the searched wave’s results are loyal to the researchers and also have imperious applications in applied sciences.

Valeurs particulières des Clitiques Datifs En Français et en Roumain (exemples Empruntés Aux Proverbes)

In this paper we want to make a contrastive presentation, in French and in Romanian, upon the way the unstressed pronominal forms having the function of complement in the Dative are used in proverbs. We also want to emphasize the similarities and the differences between the two languages – when we speak about the morpho-syntactic and the semantic levels. Such differences and similarities occur especially when it comes to the possession relationship. Most part of our study is dedicated to presenting some special values of the unstressed pronominal forms in the possessive Dative – including the variant of the Dative with an attributive function and the ethical Dative. We have done this research in order to establish to what extent the use of such constructions varies. We shall also emphasize the specific constructions in Romanian where the Dative has a neutral value and the analytic Dative is thought as a prepositional group in the colloquial language. In order to illustrate this phenomenon in a better way, we relied our study on a corpus of proverbs and adages which were selected from specialized collections and electronic versions of some dictionairies.

Series Solutions of Delay Integral Equations via a Modified Approach of Homotopy Analysis Method

In this paper, the series solutions of a non-linear delay integral equations are considered by a modified approach of homotopy analysis method (MAHAM). We split the function into infinite sums. The outcomes of the illustrated examples are included to confirm the accuracy and efficiency of the MAHAM. The exact solution can be obtained using special values of the convergence parameter.

Celestial diamonds: conformal multiplets in celestial CFT

We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

An integral transform and its application in the propagation of Lorentz-Gaussian beams

The aim of the present note is to derive an integral transform I = ∫ 0 ∞ x s + 1 e - β x 2 + γ x M k , v ( 2 ζ x 2 ) J μ ( χ x ) d x , I = \int_0^\infty {{x^{s + 1}}{e^{ - \beta x}}^{2 + \gamma x}{M_{k,v}}} \left( {2\zeta {x^2}} \right)J\mu \left( {\chi x} \right)dx, involving the product of the Whittaker function Mk, ν and the Bessel function of the first kind Jµ of order µ. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters k and ν of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details [13], [3]).