Search Results (27)

Morphological changes during body development measurements are crucial in understanding growth rates, allometric relationships, and sexual dimorphism. Recent advances in drone technology provide a new perspective enabling an indirect, non-invasive morphological assessment of free-ranging cetaceans. In this study, 10 body parameters were measured and examined with drone-based aerial photogrammetry across 82 individual fin whales (Balaenoptera physalus) along the Catalan coast of the Northwestern Mediterranean Sea, between 2021 and 2023. The growth pattern of each body parameter relative to the total length was determined as negative allometry. The developmental changes depicted that the head region at first decreases proportionally until the animal reaches approximately 14 m in length. Then, it remains constant until 18 m, subsequently followed by a relative increase. The difference in the growth rates among the sexes leads to a proportional shift between females and males approximately between 15 and 17 m in length. Overall, males exhibit a more rapid body elongation, along with moderate development of the other body parameters, while females display the contrary. The morphological parameters reveal insights into the population status dynamics and provide information on the reproductive status. These parameters are critical for the proper conservation and management of the local population of the species. Full article

Recent advancements in geospatial technologies have significantly expanded the volume and diversity of geospatial data, unlocking new and innovative applications that require novel Geographic Information Systems (GIS). (Discrete) Global Grid Systems (DGGSs) have emerged as a promising solution to further enhance modern geospatial capabilities. Current DGGSs employ a simple, low-resolution polyhedral approximation of the Earth for efficient operations, but require a projection between the Earth’s surface and the polyhedral faces. Equal-area DGGSs are desirable for their low distortion, but they fall short of this promise due to the inefficiency of equal-area projections. On the other hand, efficiency-first DGGSs need to better address distortion. We introduce a novel mesh-based DGGS (MBD) which generalizes efficient operations over watertight triangular meshes with spherical topology. Unlike traditional approaches that rely on Platonic or Catalan solids, our mesh-based method leverages high-resolution spherical meshes to offer greater flexibility and accuracy. MBD allows high-resolution polyhedra (HRP) to be used as the base polyhedron of a DGGS, significantly reducing distortion. To address the operational challenges, we introduce a new hash encoding method and an efficient barycentric indexing method (BIM). MBD extends Atlas of Connectivity Maps to the BIM to provide efficient spatial and hierarchical traversal. We introduce several new base polyhedra with lower areal and angular distortion, and we experimentally validate their properties and demonstrate their efficiency. Our experimentation shows that we achieve constant-time operations for high-resolution MBD, and we recommend polyhedra to be used as the base polyhedron for low-distortion DGGSs, compact faces, and efficient operations. Full article

Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichlet’s beta function, and Riemann’s zeta function, as well as $\pi$ in the denominator. Full article

Eight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series $\mathfrak{W}$ is introduced and shown to be expressible in terms of the trilogarithm function. Several remarkable integral values and difficult infinite series identities are shown as consequences. Full article

A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we present several closed forms of series involving zeta functions by using formulas for series associated with the zeta functions detailed in the aforementioned paper. Another closed form of series involving Riemann zeta functions is provided by utilizing a known identity for a series of rational functions in the series index, expressed in terms of Gamma functions. Furthermore, we demonstrate a myriad of applications and relationships of series involving the zeta functions and the extended parametric linear Euler sums. These include connections with Wallis’s infinite product formula for $\pi$, Mathieu series, Mellin transforms, determinants of Laplacians, certain integrals expressed in terms of Euler sums, representations and evaluations of some integrals, and certain parametric Euler sum identities. The use of Mathematica for various approximation values and certain integral formulas is elaborated upon. Symmetry naturally occurs in Euler sums. Full article

Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is to provide certain reduction, transformation and summation formulae for the general Kampé de Fériet function and Srivastava’s general triple hypergeometric series, where the parameters and the variables are suitably specified. The identities presented in the theorems and additional comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. Symmetry occurs naturally in ${}_{p+1}{F}_p$, the Kampé de Fériet function and the Srivastava’s function $F^{\left(3\right)}[x,y,z]$, which are three of the most important functions discussed in this study. Full article

This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the Riemann Zeta function and fundamental mathematical constants, including Catalan’s constant. This representation of Catalan’s constant suggests it could be rational. Full article

We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as $\pi$, $ln2$ and the Catalan constant G. Full article

In the fields of science and engineering, tasks involving repeated integrals appear on occasion. The authors’ study on repeated integrals of a class of exponential and logarithmic functions is presented in this publication. The paper includes several examples that demonstrate the evaluation of the analytical parts of the multi-dimensional integral derived. All the results in this work are new. Full article

The objective of the present paper is to obtain a quadruple infinite integral. This integral involves the product of the Struve and parabolic cylinder functions and expresses it in terms of the Hurwitz–Lerch Zeta function. Almost all Hurwitz-Lerch Zeta functions have an asymmetrical zero distributionSpecial cases in terms fundamental constants and other special functions are produced. All the results in the work are new. Full article

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. Full article

In this paper, we have derived and evaluated a quadruple integral whose kernel involves the logarithm and product of Bessel functions of the first kind. A new quadruple integral representation of Catalan’s G and Apéry’s $\zeta \left(3\right)$ constants are produced. Some special cases of the result in terms of fundamental constants are evaluated. All the results in this work are new. Full article

A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic, exponential, quotient radical, and polynomial functions. Special cases are derived in terms of fundamental constants; results are summarized in a table. All results in this work are new. Full article