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The analysis of peristaltic-ciliary transport in the human female fallopian tube, specifically in relation to the growing embryo, is a matter of considerable physiological importance. This paper proposes a biomechanical model that incorporates a finite permeable tube consisting of two layers, where the Jeffrey fluid model characterizes the viscoelastic properties of the growing embryo and continuously secreting fluid. Jeffrey fluid entering with some negative pressure gradient forms the core fluid layer while continuously secreting Jeffrey fluid forms the peripheral fluid layer. The resulting partial differential equations are solved for closed-form solutions after employing the assumption of long wavelength. The analysis delineated that increasing the constant secretion velocity, Darcy number, and Reynolds number leads to a decrease in the appropriate residue time of the core fluid layer and a reduction in the size of the secreting fluid bolus in the peripheral fluid layer. Eventually, the boluses completely disappear when the constant secretion velocity exceeds 3.0 Progesterone ( P 4 ) and estradiol ( E 2 ) directly regulate the transportation of the growing embryo, while luteinizing hormone (LH) and follicle-stimulating hormone (FSH), prolactin, anti-mullerian hormone (AMH), and thyroid-stimulating hormone (TSH) have an indirect effects. Based on the number and size of blastomeres, the percentage of fragmentation, and the presence of multinucleated blastomeres two groups were formed in an in vitro experiment. Out of 50 patients, 26 (76.5%) were pregnant in a group of the good quality embryos, and only 8 (23.5%) were in a group of the bad quality embryos. The transport of growing embryo in the human fallopian tube and preimplantation development of human embryos in in vitro are constraint by baseline hormones FSH, LH, prolactin, E 2 , AMH, and TSH. [ABSTRACT FROM AUTHOR]

In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator D τ − λ L α , ζ m : A → A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator D τ − λ L α , ζ m together with a fuzzy set, and we next define a new class of analytic functions denoted by R ϝ ζ (m , α , δ). Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, R ϝ ζ (m , α , δ). The study includes examples that demonstrate the application of the fundamental theorems and corollaries. [ABSTRACT FROM AUTHOR]

The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of a spread in an arrangement; canonically labeling graphs; and inserting typical information in low-dimensional Euclidean spaces. In a graph G, the set S⊆V(G) of minimum vertices from which all other verticescan be uniquely determined by the distances to the vertices in S is called the resolving set. The cardinality of the resolving set is called the metric dimension. The set S is called fault-tolerant resolving set if S\{v} is still a resolving set of G. The minimum cardinality of such a set S is called fault-tolerant metric dimension of G. GeSbTe super lattice is the latest chemical compound to have electronic material that is capable of non-volatile storing phase change memories with minimum energy usage. In this work, we calculate the resolving set (fault tolerant resolving set) to find the metric dimension(fault-tolerant metric dimension) for the molecular structure of the GeSbTe lattice. The results may be useful in comparing network structure and categorizing the structure of the GeSbTe lattice. [ABSTRACT FROM AUTHOR]

In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king's graphs, and circular king's graphs. [ABSTRACT FROM AUTHOR]

This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coefficient bounds, Zalcman inequalities, and both Hankel and Toeplitz determinants for the new version of starlike functions are investigated. It is worth mentioning that most of the determined inequalities are sharp with the support of relevant extremal functions. [ABSTRACT FROM AUTHOR]

In this research, we define a few subclasses of analytic functions which are connected to sine functions and the cardioid domain in the unit disk. We investigate initial coefficient bounds, the Fekete–Szego problem and second and third Hankel determinants for the functions f belonging to these newly defined classes. We also define the class of m-fold symmetric functions related with the sine function and then investigate the bounds of the third Hankel determinant for twofold symmetric and threefold symmetric functions. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived. [ABSTRACT FROM AUTHOR]

In this paper, we study a new filtration class MF α , β μ , associated with the filtration of infinitesimal generators, by using the nonlinear fractional differential operator and study certain properties, like sharp Fekete–Szegö inequalities and filtration problems. [ABSTRACT FROM AUTHOR]

This article investigates inequalities for certain types of strongly convex functions by applying q-h-integrals. These inequalities provide the refinements of some well-known results that hold for (α , m) - and (ℏ - m) -convex and related functions. Inequalities for q-integrals are deducible by vanishing the parameter h. Some particular cases are discussed after proving the main results. [ABSTRACT FROM AUTHOR]

Materials made of graphyne, graphyne oxide, and graphyne quantum dots have drawn a lot of interest due to their potential uses in medicinal nanotechnology. Their remarkable physical, chemical, and mechanical qualities, which make them very desirable for a variety of prospective purposes in this area, are mostly to blame for this. In the subject of mathematical chemistry, molecular topology deals with the algebraic characterization of molecules. Molecular descriptors can examine a compound's properties and describe its molecular topology. By evaluating these indices, researchers can predict a molecule's behavior including its reactivity, solubility, and toxicity. Amidst the captivating realm of carbon allotropes, γ -graphyne has emerged as a mesmerizing tool, with exquisite attention due to its extraordinary electronic, optical, and mechanical attributes. Research into its possible applications across numerous scientific and technological fields has increased due to this motivated attention. The exploration of molecular descriptors for characterizing γ -graphyne is very attractive. As a result, it is crucial to investigate and predict γ -graphyne's molecular topology in order to comprehend its physicochemical characteristics fully. In this regard, various characterizations of γ -graphyne and zigzag γ -graphyne nanoribbons, by computing and comparing distance-degree-based topological indices, leap Zagreb indices, hyper leap Zagreb indices, leap gourava indices, and hyper leap gourava indices, are investigated. [ABSTRACT FROM AUTHOR]

The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function. We find certain inequalities, including the coefficient bounds, second Hankel determinants, and Fekete–Szegö inequalities, for this novel family of bi-univalent functions. It is worthy of note that almost all the results are sharp, and their corresponding extremal functions are presented. In addition, some special cases are demonstrated to show the validity of our findings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli's numbers of the second kind. Let φ B S (ξ) = ξ e ξ − 1 2 = ∑ n = 0 ∞ ξ n B n 2 n ! , where the coefficients of B n 2 are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions such that ξ ′ (ξ) (ξ) ≺ φ B S (ξ). We found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class. [ABSTRACT FROM AUTHOR]

Entropy is a thermodynamic function used in chemistry to determine the disorder and irregularities of molecules in a specific system or process. It does this by calculating the possible configurations for each molecule. It is applicable to numerous issues in biology, inorganic and organic chemistry, and other relevant fields. Metal–organic frameworks (MOFs) are a family of molecules that have piqued the curiosity of scientists in recent years. They are extensively researched due to their prospective applications and the increasing amount of information about them. Scientists are constantly discovering novel MOFs, which results in an increasing number of representations every year. Furthermore, new applications for MOFs continue to arise, illustrating the materials' adaptability. This article investigates the characterisation of the metal–organic framework of iron(III) tetra-p-tolyl porphyrin (FeTPyP) and CoBHT (CO) lattice. By constructing these structures with degree-based indices such as the K-Banhatti, redefined Zagreb, and the atom-bond sum connectivity indices, we also employ the information function to compute entropies. [ABSTRACT FROM AUTHOR]

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α , strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three. [ABSTRACT FROM AUTHOR]

This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function φ defined by φ (ζ) = (1 + ζ) λ , 0 < λ < 1 maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp. [ABSTRACT FROM AUTHOR]

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural formula, certain sharp radii results such as radius of starlikeness and convexity of order α. It also finds a radius for ratios of analytic functions associated with Euler numbers. [ABSTRACT FROM AUTHOR]

Motivated by the recent work on symmetric analytic functions by using the concept of Faber polynomials, this article introduces and studies two new subclasses of bi-close-to-convex and quasi-close-to-convex functions associated with Janowski functions. By using the Faber polynomial expansion method, it determines the general coefficient bounds for the functions belonging to these classes. It also finds initial coefficients of bi-close-to-convex and bi-quasi-convex functions by using Janowski functions. Some known consequences of the main results are also highlighted. [ABSTRACT FROM AUTHOR]

Nowadays, numeric paradigms have great significance in every field especially for solving the NDEs, PDEs, biochemical reactions etc. Here, we represent a realistic suicide substrate reaction specimen which can be represented by a system with four equations for the concentrations of the numerous molecules as functions of time. We present a technique to attain exact, approximate elucidations using the stochastic theory. This systematic technique provides more realistic numeric elucidations than other techniques which have been offered. Unfortunately, the numeric techniques like Euler–Maruyama, stochastic Euler, and stochastic RK4 fail for large step sizes. Stochastic nonstandard finite difference technique (SNSFD) has been fabricated for the suicide substrate reaction specimen and numeric tests are executed for diverse values of discretization parameter ' h '. The consequences are matched with a well-known numeric scheme. • The stochastic suicide substrate reaction model is considered. • The Euler–Maruyama, stochastic Euler, and stochastic RK4 methods are used. • The obtained results are given by figures. [ABSTRACT FROM AUTHOR]

The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrödinger equation. As a result, a number of novel traveling wave structures have been discovered. We also investigate the stability of solitary wave solutions for the governing model. Furthermore, the modulation instability is discussed by employing the standard linear-stability analysis. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behaviour. [ABSTRACT FROM AUTHOR]

Various operators of fractional calculus, as well as their quantum (or q -) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant. [ABSTRACT FROM AUTHOR]

This study we handled (1+1)-dimensional modified-mixed KDV (mmKdV) equation for unique soliton solutions. For this purpose Firstly, auto-Bäcklund and Cole-Hopf transformations are created through the homogeneous balance method. Various soliton-like solutions are given by the trigonometric, hyperbolic, and exponential function waves and that leads to the extraction of novel periodic, dark, and bright soliton solutions. Moreover, the bilinear form of the model is found by utilizing the logarithmic transformation. Density, 3-D, and 2-D graphics are displayed to illustrate the dynamics of the acquired solutions. It is determined that the approach employed to obtain analytic solutions to nonlinear partial differential equation is efficient and powerful. • This study examines a (1+1)-dimensional modified-mixed KDV (mmKdV) equation for unique soliton solutions. • Auto-Bäcklund transformation is created through the homogeneous balance method. • Various explicit precise solutions based on the acquired auto-Bäcklund transformation are investigated. • The bilinear form of the model is found by utilizing the logarithmic transformation. • Density, 3-D, and 2-D graphics are displayed to illustrate the dynamics of the acquired solutions. [ABSTRACT FROM AUTHOR]

Cyclooctane is a cycloalkane consisting of carbon and hydrogen atoms arranged in a closed ring structure. Cyclooctane chains can be found in various organic compounds and are significant in the field of organic chemistry due to their diverse reactivity and properties. The atom-bond connectivity index ( A B C ), the geometric-arithmetic index ( G A ), the arithmetic-geometric index ( A G ) and the forgotten index ( F ) are four well-studied molecular descriptors that have found applications in QSPR and QSAR studies. These topological descriptors have shown significant correlations with different physiochemical properties of octane isomers. In this work, the expected values of four degree based topological descriptors for random cyclooctane chains are calculated. An analytical comparison is given between the expected values of A B C , G A , A G , and F indices of random cyclooctane chains., (© 2024. The Author(s).)

Tuberculosis (TB) is one of the most contagious diseases that has a greater mortality rate than HIV/AIDS and the cases of TB are feared to rise as a repercussion of the COVID-19 pandemic. The pharmaceutical industry is constantly looking for ways to improve drug design processes in order to combat the growth of infections and cure newly identified syndromes or genetically based dysfunctions with the help of QSPR models. QSPR models are mathematical tools that establish relationships between a molecular structure and its physicochemical attributes using structural properties. Topological indices are such properties that are generated from the molecular graph without any empirically derived measurements. This work focuses on developing a QSPR model using distance-based topological indices for anti-tuberculosis medications and their diverse physicochemical features., Competing Interests: The authors declare that there is no conflict of interest regarding the publication of this article. All the authors of the paper have agreed to submit this paper., (© 2024 The Authors. Published by Elsevier Ltd.)

The use of topological descriptors remains a significant approach due to numerous advances in the field of drug design. Descriptors provide numerical representations of a molecule's chemical characteristics when used with QSPR models. The QSPR analysis for bladder medications is the main focus of this study. Linear regression model is developed for the computed indices values, the physicochemical properties of the bladder medications are examined.Communicated by Ramaswamy H. Sarma.

In theoretical chemistry, topological indices are commonly employed to model the physico-chemical properties of chemical compounds. Mathematicians frequently use Zagreb indices to calculate a chemical compound's strain energy, melting point, boiling temperature, distortion, and stability. The current global pandemic caused by the new SARS-CoV-2, also known as COVID-19, is a significant public health concern. Various therapy modalities are advised. The issue has become worse since there hasn't been enough counseling. Researchers are looking at compounds that might be used as SARS and MERS therapies based on earlier studies. In several quantitative structure-property-activity relationships (QSPR and QSAR) studies, a variety of physiochemical properties are successfully represented by topological indices, a sort of molecular descriptor that just specifies numerical values connected to a substance's molecular structure. This study investigates several irregularity-based topological indices for various antiviral medicines, depending on the degree of irregularity. In order to evaluate the effectiveness of the generated topological indices, a QSPR was also carried out using the indicated pharmaceuticals, the various topological indices, and the various physiochemical features of these antiviral medicines. The acquired results show a substantial association between the topological indices being studied by the curve-fitting approach and the physiochemical properties of possible antiviral medicines., Competing Interests: The authors declare that there is no conflict of interest regarding the publication of this article. All the authors of the paper have agreed to submit this paper. With best regards, (© 2023 The Author(s).)