Search Results (401)

This article presents a newly defined subclass of univalent functions that are starlike with respect to a boundary point, closely related to the Robertson class and specifically associated with a vertical strip domain. Additionally, this study derives generalized coefficient estimates for these classes, as well as for the Robertson class linked to the Nephroid domain and the Lemniscate of Bernoulli. Full article

Here in this paper, we establish the basic inclusion relations among the harmonic class $\mathbb{HF}(\sigma ,\eta )$ with the classes $S_{\mathcal{HF}}^{*}$ of starlike harmonic functions and $K_{\mathcal{HF}}$ of convex harmonic functions defined in open symmetric unit disk U. Moreover, we investigate inclusion connections for the harmonic classes $\mathcal{T}{\mathfrak{N}}_{\mathbb{HF}}\left(\varrho \right)$ and $\mathcal{T}{\mathfrak{Q}}_{\mathbb{HF}}\left(\varrho \right)$ of harmonic functions by applying the operator $\mathrm{\Lambda }$ associated with the Bessel function. Furthermore, several special cases of the main results are obtained for the particular case $\sigma =0$. Full article

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to $1+\mathrm{s}\mathrm{i}\mathrm{n}z$. Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a particular focus on the second- and third-order Hankel determinants. To illustrate the non-emptiness of the proposed class, we consider the function $\sqrt{1+tanhz}$, which maps the unit disk onto a bean-shaped domain. This function satisfies the required subordination condition and hence serves as an explicit member of the class. A graphical depiction of the image domain is provided to highlight its geometric characteristics. The results obtained in this work confirm that the class under study is non-trivial and possesses rich geometric structure, making it suitable for further development in the theory of geometric function classes and coefficient estimation problems. Full article

Phylogeographic studies in Antarctica allow us to understand the demographic events of populations during glacial periods. In this study, the polyplacophoran Tonicina zschaui was analyzed in several localities on the West Antarctic Coast using the mitochondrial gene cytochrome oxidase subunit I (COI). Two genetically distinct populations were identified: one in the Weddell Sea and another across the Antarctic Peninsula and South Shetland Islands. Genetic diversity was generally low to moderate, suggesting limited gene flow and the influence of historical climatic events. Star-like haplotype networks and demographic analyses indicate population contractions during the Last Glaciation followed by postglacial expansion, especially in the Antarctic Peninsula–South Shetland Islands population. Several sites in this region were identified as potential glacial refugia, exhibiting proportionally elevated genetic diversity and exclusive haplotypes. Conversely, the small Weddell Sea population displayed signs of long-term isolation, limited expansion, and low diversity, likely due to stronger environmental constraints and genetic drift. Ocean currents such as the Antarctic Coastal Current, the Antarctic Peninsula Coastal Current and the Weddell Gyre appear to restrict larval dispersal, reinforcing genetic discontinuities. These findings support the hypothesis of glacial survival in localized refugia and postglacial recolonization, a pattern observed in other Antarctic marine invertebrates. Full article

To meet the supergravity requirements of a black hole without a singularity, we propose some possible finite-sized core structures to avoid the confusing singularity problem. This research first studies the Coulomb repulsion between electrons at a distance of 10⁻¹⁵ m, where the inverse square of the distance is still workable, revealing that the energy of the entire observable universe is required to form a charged region with a radius of 50 m, including 1.4 × 10³¹ Coulomb electrons. Therefore, the existence of a singularity at the center of a black hole becomes physically unreasonable in this case. To avoid the singularity problem, we propose a finite-sized black hole core in which the inner core is composed of the vast majority of neutrons and a very small amount of ⁵⁶Fe. Under the conditions of a total charge of 1.648824 × 10²⁰ C and a total mass equivalent to the Sun, a finite-sized black hole is constructed through this finite-sized core model. We use this non-rotating but charged, compact, star-like structure, surrounded by counter-rotating and co-rotating electrons, to construct a Kerr–Newman black hole with a finite-sized core structure. Based on this model, we can obtain the same spacetime as that of a traditional Kerr–Newman black hole. Full article

Spilostethus pandurus is a phytophagous insect widely distributed across Asia, Europe, and Africa, yet its genetic variation remains poorly understood. This study presents the first comprehensive analysis of the genetic diversity and structure of S. pandurus in Thailand using mitochondrial cytochrome c oxidase subunit 1 (CO1) sequences from 202 individuals across 27 localities. A total of 58 haplotypes were identified, with high haplotype and nucleotide diversity observed, suggesting substantial genetic variation. The haplotype network revealed a star-like topology, indicating recent population expansion or ongoing gene flow. Neutrality tests and mismatch distribution analyses showed no strong signal of recent demographic expansion. Phylogenetic analysis confirmed that all Thai specimens clustered within a well-supported S. pandurus clade along with sequences from India, Namibia, and Europe. Analysis of Molecular Variance (AMOVA) revealed significant genetic differentiation among four continental groups, indicating that geographic isolation and restricted gene flow have shaped genetic divergence at a broad biogeographic scale. Further research using highly polymorphic nuclear markers is recommended to better resolve the population structure and evolutionary history of S. pandurus in Thailand and beyond. Full article

In this investigation, we introduce a new meromorphic operator defined by meromorphic univalent functions. A new class of meromorphic functions is introduced by this operator, which can generate several distinct subclasses depending on the values of its parameters. Within the framework of this class of functions, we obtain several significant algebraic and geometric properties, including coefficient estimates, distortion theorems, the radius of starlikeness, convex combination closure, extreme point characterization, and neighborhood structure. Our findings are sharp, offering accurate and significant insights into the mathematical structure and behavior of these functions. In addition, we present several applications of these results in fluid mechanics, like identifying stagnation points in vortex flows, predicting velocity decline in source/sink systems, and determining stability thresholds that protect crucial streamlines from perturbations, which demonstrates that the introduced operator and class characterize critical properties of 2D potential flows. Full article

This work investigates the behavior of the coefficients of analytic functions within certain subclasses characterized by inherent symmetric structures. By leveraging deep connections with functions exhibiting positive real part properties, the approach introduces a modern analytical framework that links the studied coefficients to those of auxiliary functions with regulated behavior. This connection allows for the derivation of sharp estimates and facilitates computational treatment. The proposed method builds upon certain classical and modern coefficient inequalities. The study focuses on obtaining precise bounds for specific determinant expressions associated with initial, inverse, and inverse logarithmic coefficients, all within a subclass of starlike functions exhibiting internal symmetry aligned with a recently introduced canonical structure. This symmetric perspective reveals how geometric properties can lead to refined quantitative outcomes that enhance contemporary analytic theory. Full article

Cystic echinococcosis is a zoonosis caused by the cestode Echinococcus granulosus sensu stricto. Population genetic studies and phylogeographic patterns are essential to understanding the transmission dynamics of this parasite under varying environmental conditions. In this study, the genetic diversity of E. granulosus s.s. was evaluated using 46 hydatid cyst samples obtained from sheep, goats, cattle, and humans across three regions of Chile: Coquimbo, La Araucanía, and Magallanes. Mitochondrial cox1 gene sequences were analyzed and compared with reference sequences reported from South America, Europe, Africa, Asia, and Oceania. In Chile, the EG01 haplotype was the predominant haplotype. A total of four haplotypes were identified, with low haplotype diversity (Hd = 0.461 ± 0.00637) and low nucleotide diversity (π = 0.00181 ± 0.00036). The haplotype network displayed a star-like configuration, with the EG01 genotype at the center, suggesting a potentially ancestral or widely distributed lineage. In Coquimbo (Tajima’s D = −0.93302, p = 0.061; Fu’s Fs = −0.003, p = 0.502) and Magallanes (Tajima’s D = −0.17406, p = 0.386; Fu’s Fs = −0.121, p = 0.414), both neutrality tests were non-significant, indicating no strong evidence for recent population expansion or selection. Star-like haplotype network patterns were also observed in populations from Europe, the Middle East, Asia, Africa, and Oceania, with the EG01 genotype occupying the central position. The population genetic structure of Echinococcus granulosus s.s. in Chile demonstrates considerable complexity, with EG01 as the predominant haplotype. Further comprehensive studies are required to assess the intraspecific genetic variability of E. granulosus s.s. throughout Chile and to determine whether this variability influences the key biological traits of the parasite. This structure may prove even more complex when longer fragments are analyzed, which could allow for the detection of finer-scale microdiversity among isolates from different hosts. We recommended that future cystic echinococcosis control programs take into account the genetic variability of E. granulosus s.s. strains circulating in each endemic region, to better understand their epidemiological, immunological, and possibly pathological differences. Full article

The concept of coefficient estimates on univalent functions is one of the interesting aspects explored recently by many researchers. Motivated by this direction, in this present work, we obtain the upper bounds of initial inverse coefficients and logarithmic coefficients and the upper bounds of differences between these successive coefficients related to concave univalent functions. Further, we also calculate the upper bounds of third-order Hankel, Toeplitz, and Vandermonde determinants in terms of specified coefficients connected to concave univalent functions. Full article

This paper introduces a novel class of analytic functions that integrates q-calculus, Janowski-type functions, and (a, b)-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions that lay the groundwork for subsequent research. Building on a new conceptual framework, we also define analogous neighborhoods for the classes ${\overline{\mathcal{F}}}_q^{a,b}(F,H)$ and investigate related neighborhood properties. These developments provide a deeper understanding of the structural and analytical behavior of these functions, opening up avenues for future study. Full article

In the present paper, we present certain geometric properties, such as starlikeness, convexity of order $\eta (0\le \eta <1)$, and close-to-convexity, in an open unit disk of the normalized form of Ramanujan-type entire functions. As a consequence, a specific range of parameters is derived such that this function belongs to Hardy spaces ${\mathcal{H}}^{\infty }$ and ${\mathcal{H}}^r.$ Finally, as an application, we present the monotonicity property of the Ramanujan-type entire function using the method of subordination factor sequences. Full article

A function that is holomorphic in a set E, in the complex plane, is called p-valent in E if, for every complex number, w, the equation f (z) = w has, at most, p roots in E. In this paper, we established some sufficient conditions for holomorphic functions in the unit disk |z| < 1 to be at most p-valent in the unit disk or p-valent or p-valent starlike in the unit disk. Full article

The $N_k$-index (k-distance degree index) of a connected graph G was first introduced by Naji and Soner as a generalization of the distance degree concept, as $N_k\left(G\right)={\displaystyle \sum _{k=1}^{d\left(G\right)}}\left({\displaystyle \sum _{v\in V\left(G\right)}}{d}_k\left(v\right)\right)k$, where the distance between u and v in G is denoted by $d(u,v)$, the diameter of a graph G is denoted by $d\left(G\right)$, and the degree of a vertex v at distance k is denoted by $d_k\left(v\right)=\{u,v\in V\left(G\right)d(u,v)=k\}$. In this paper, we extend the study of the $N_k$-index of graphs. We introduced some graph transformations and their impact on the $N_k$-index of graph and proved that the star graph has the minimum, and the path graph has the maximum $N_k$-index among the set of all trees on n vertices. We also show that among all trees with fixed maximum-degree $\Delta$, the broom graph $B_{n,\Delta }$ (consisting of a star $S_{\Delta +1}$ and a pendant path of length $n-\Delta -1$ attached to any arbitrary pendant path of star) is a unique tree which maximizes the $N_k$-index. Further, we also defined and proved a graph with maximum $N_k$-index for a given number of n vertices, maximum-degree $\Delta$, and perfect matching among trees. We characterize the starlike trees which minimize the $N_k$-index and propose a unique tree which minimizes the $N_k$-index with diameter d and n vertices among trees. Full article