Exploring expected values of topological indices of random cyclodecane chains for chemical insights.

Chemical graph theory has made a significant contribution to understand the chemical compound properties in the modern era of chemical science. At present, calculation of the topological indices is one of most important area of research in the field of chemical graph theory. Cyclodecane is a cyclic hydrocarbon with the chemical formula C 10 H 20 . It consists of a ring of ten carbon atoms bonded together in a cyclical structure. Cyclodecane chains can be part of larger molecules or polymers, where multiple cyclodecane rings are connected together. These molecules can have various applications in chemistry, materials science, and pharmaceuticals. This article aims to determine expected values of some connectivity based topological indices of random cyclodecane chains, containing saturated hydrocarbons with at least two rings. It also compares these descriptors using explicit formulae, numerical tables and present graphical profiles of these comparisons.

Multicriteria decision making attributes and estimation of physicochemical properties of kidney cancer drugs via topological descriptors.

Based on topological descriptors, QSPR analysis is an incredibly helpful statistical method for examining many physical and chemical properties of compounds without demanding costly and time-consuming laboratory tests. Firstly, we discuss and provide research on kidney cancer drugs using topological indices and done partition of the edges of kidney cancer drugs which are based on the degree. Secondly, we examine the attributes of nineteen drugs casodex, eligard, mitoxanrone, rubraca, and zoladex, etc and among others, using linear QSPR model. The study in the article not only demonstrates a good correlation between TIs and physical characteristics with the QSPR model being the most suitable for predicting complexity, enthalpy, molar refractivity, and other factors and a best-fit model is attained in this study. This theoretical approach might benefit chemists and professionals in the pharmaceutical industry to forecast the characteristics of kidney cancer therapies. This leads towards new opportunities to paved the way for drug discovery and the formation of efficient and suitable treatment options in therapeutic targeting. We also employed multicriteria decision making techniques like COPRAS and PROMETHEE-II for ranking of said disease treatment drugs and physicochemical characteristics.

Analyzing the expected values of neighborhood degree-based topological indices in random cyclooctane chains.

Cyclooctane is classified as a cycloalkane, characterized by the chemical formula C 8 H 16. It consists of a closed ring structure composed of eight carbon atoms and sixteen hydrogen atoms. A cyclooctane chain typically refers to a series of cyclooctane molecules linked together. Cyclooctane and its derivatives find various applications in chemistry, materials science, and industry. Topological indices are numerical values associated with the molecular graph of a chemical compound, predicting certain physical or chemical properties. In this study, we calculated the expected values of degree-based and neighborhood degree-based topological descriptors for random cyclooctane chains. A comparison of these topological indices' expected values is presented at the end.

The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature.

It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature.

Computation of expected values of some connectivity based topological descriptors of random cyclooctane chains.

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.

Analysis of two layered peristaltic-ciliary transport of Jeffrey fluid and in vitro preimplantation embryo development.

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 ([Formula: see text]) and estradiol ([Formula: see text]) 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, [Formula: see text], AMH, and TSH.

QSPR analysis of distance-based structural indices for drug compounds in tuberculosis treatment.

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.

An estimation of physiochemical properties of bladder cancer drugs via degree-based chemical bonding topological descriptors.

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.

A paradigmatic approach to the molecular descriptor computation for some antiviral drugs.

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.

Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure.

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.

Computational Studies on Diverse Characterizations of Molecular Descriptors for Graphyne Nanoribbon Structures.

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.

Computation of Entropy Measures for Metal-Organic Frameworks.

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.

Some Study of Semigroups of h-Bi-Ideals of Semirings.

Semigroups are generalizations of groups and rings. In the semigroup theory, there are certain kinds of band decompositions which are useful in the study of the structure of semigroups. This research will open up new horizons in the field of mathematics by aiming to use semigroup of h-bi-ideal of semiring with semilattice additive reduct. With the course of this research, it will prove that subsemigroup, the set of all right h-bi-ideals, and set of all left h-bi-ideals are bands for h-regular semiring. Moreover, it will be demonstrated that if semigroup of all h-bi-ideals (B(H), ∗) is semilattice, then H is h-Clifford. This research will also explore the classification of minimal h-bi-ideal.

A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information.

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an illustrative application is provided for its better demonstration, which is subjected to the selection of a suitable company of virtual reality devices. Finally, a comparison of the initiated method is explored with some existing models, including intuitionistic fuzzy soft expert sets.

An Efficient Computational Technique for Fractal Vehicular Traffic Flow.

In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors.

This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and ß -conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and ß -conformable attractors are provided to illustrate the effectiveness of the proposed method.