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Abstract In this work, we aim at disentangling the theoretical contribution through mathematical modeling approach to advance the understanding of rabies dynamics and control in livestock population. A fractional order model of rabies, using Atangana–Baleanu fractional operator is created. The analysis of suggested system and its application are both conducted. The capacity of proposed model to forecast the disease can help researchers and livestock health care agencies to take preventive actions.

Introduction: Congenital absence of teeth is a common developmental dental anomaly in humans that affects the occlusal development and the beauty of the smile in particular and the face in general, especially if the injury is in the frontal area. Aim: This study aimed to investigate the prevalence and distribution of hypodontia of permanent teeth in a Syrian population. Materials and Methods: Four hundred and sixty panoramic X-rays of children in North Syria, whose ages ranged from approximately 6–12 years, were taken at the dental clinics of the hospital of Syrian University for Science and Technology, Aleppo, Syria. The prevalence and distribution of hypodontia were recorded, and descriptive statistics were performed. A Chi-square test was used to determine the difference between genders (α =0.05). Results and Discussion: The prevalence of hypodontia was 7.8% (females 9.6% and males 6.5%). The most frequently missing teeth were the mandibular second premolar, maxillary lateral incisors, and mandibular central incisors. Missing was significantly more frequent in the mandible compared to the maxilla (P < 0.05). Conclusions: The number of cases of congenital absence of permanent teeth is impressive. These conditions can cause many dental problems, so careful examination and proper investigation are required to diagnose them and prevent subsequent problems.

AbstractA subset Δ of non-negative integers [Formula: see text] is called a numerical semigroup if it is a submonoid of [Formula: see text] and has a finite complement in [Formula: see text]. A graph [Formula: see text] is called a [Formula: see text]-graph if there exists a numerical semigroup Δ with multiplicity α and embedding dimension β such that [Formula: see text] and [Formula: see text]. In this article, we compute the [Formula: see text]-graphs for irreducible and Arf numerical semigroups having a metric dimension of 2. It is proved that if Δ be an irreducible and arf numerical semigroup then there are exactly 2 and 8 non-isomorphic [Formula: see text]-graphs respectively, whose metric dimension is 2.

Abstract 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 $$C_{10}H_{20}$$ 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.

Abstract 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 ( $$\mathcal{A}\mathcal{B}\mathcal{C}$$ A B C ), the geometric-arithmetic index ( $$\mathcal{G}\mathcal{A}$$ G A ), the arithmetic–geometric index ( $$\mathcal{A}\mathcal{G}$$ A G ) and the forgotten index ( $$\mathcal{F}$$ 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 $$\mathcal{A}\mathcal{B}\mathcal{C}$$ A B C , $$\mathcal{G}\mathcal{A}$$ G A , $$\mathcal{A}\mathcal{G}$$ A G , and $$\mathcal{F}$$ F indices of random cyclooctane chains.

Abstract Almond pruning biomass is an important agricultural residue that has been scarcely studied for the co-production of sugars and solid biofuels. In this work, the production of monosaccharides from almond prunings was optimised by a two-step process scheme: pretreatment with dilute sulphuric acid (0.025 M, at 185.9–214.1 ℃ for 0.8–9.2 min) followed by enzyme saccharification of the pretreated cellulose. The application of a response surface methodology enabled the mathematical modelling of the process, establishing pretreatment conditions to maximise both the amount of sugar in the acid prehydrolysate (23.4 kg/100 kg raw material, at 195.7 ℃ for 3.5 min) and the enzymatic digestibility of the pretreated cellulose (45.4%, at 210.0 ℃ for 8.0 min). The highest overall sugar yield (36.8 kg/100 kg raw material, equivalent to 64.3% of all sugars in the feedstock) was obtained with a pretreatment carried out at 197.0 ℃ for 4.0 min. Under these conditions, moreover, the final solids showed better properties for thermochemical utilisation (22.0 MJ/kg heating value, 0.87% ash content, and 72.1 mg/g moisture adsorption capacity) compared to those of the original prunings. Graphical Abstract

Cyclooctane is classified as a cycloalkane, characterized by the chemical formula C8H16. 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.

Superlattices are periodic arrangements of two or more different materials on a nanoscale. Ge-Sb-Te (Germanium-Antimony-Tellurium) superlattices are a type of material used in phase-change memory (PCM) technology. PCM is a non-volatile memory technology that relies on the reversible phase transition between amorphous and crystalline states in certain materials. This phase-change property, combined with the non-volatile nature of the material, makes it suitable for applications like phase-change memory in electronic devices. Topological and entropy indices are the mathematical tools that are helpful to estimate the physico-chemical characteristics of chemical compounds. In this article, we have calculated some reduced reverse degree-based topological indices and entropy indices for Ge-Sb-Te superlattice. Ravi et al. [32] examined the statistically significant relationship of reduced reverse degree-based topological indices with physico-chemical characteristics of drug structures and proposed regression models using entropy indices. In this context, our computed results can be helpful in predicting the physico-chemical characteristics of Ge-Sb-Te superlattices.

The investigation into the flow of sodium alginate-alumina/copper hybrid nanofluids toward a power law form stretching/shrinking sheet while taking into account the effect of suction was carried out numerically. Sodium alginate-alumina/copper hybrid nanofluids have been of great interest in recent years due to their potential applications in various fields. Hybrid nanofluid is currently being used to enhance the efficiency of heat transmission rates. The primary objective of this research is to analyze the influence that certain characteristics, such as those pertaining to magnetic M, shrinking parameter ϵ, thermal radiation R, and thermal slip factor βT parameters, have on temperature and velocity profiles. Furthermore, as part of this investigation, the local skin friction as well as the Nusselt number according to the copper solid volume fraction φCu against shrinkage ϵ and suction γ effect were explored. In order to convert the nonlinear partial differential equation into a system of ordinary differential equations, appropriate similarity variables have to be incorporated into the transformation process. Ordinary differential equations are resolved with the help of the MATLAB bvp4c solver program, which is used in the conclusion phase. The study identified two approaches to shrinking ϵ sheet and suction γ zone with varying parameter values for copper volume fractions φCu. No solution was obtained in the range of when ϵ

A numerical study was carried out on dual solutions of rotating stretching/shrinking surfaces to explore the influence of convective boundary conditions, viscous dissipation, thermal radiation, and heat sources/sinks on 3-D hybrid nanofluid flow. Hybrid nanofluids have great potential for a variety of applications due to their unique properties and versatility. It is improved the effectiveness of heat transfer rates. The main objective of this study is to investigate the influence that certain parameters on the temperature and velocities profiles against the parameters, including the volume fraction of copper, suction effect, viscous dissipation, thermal radiation, Biot number and rotating parameter. Further, the impact of the suction effect and shrinking sheet on reduced heat transfer and skin friction is also considered against the volume fraction of copper. The nonlinear partial differential equations are transformed into a collection of ordinary differential equations by including linear similarity variables. The generated combination of higher order nonlinear ODEs is solved via a boundary value algorithm called bvp4c, which executes on the MATLAB computing tool. The findings confirmed the existence of two branches (dual solution) with varied quantities of copper volume fraction according to the shrinking surface and suction effect. Additionally, as the Biot number, Eckert number, thermal radiation, and copper volume fraction all increase in strength, the rate at which heat flows in both solutions also increases. However, the heat transfer rate declined as increased the suction effect. Besides, when a positive and negative increment is applied to the rotational parameter, both solutions suffer an increase in both velocities. In summary, unique solutions are obtained S

In this work, we investigated the transmission of cholera infection through mathematical modelling. We calculated the contact number by applying the technique of next generation matrix method to find about infection dissemination as well as control in the population. Two types of constant solutions: infection free as well as infection present have been calculated. Stability of both constant solutions has been discussed. To control the dissemination of disease, we formulated an optimal control problem. Strategies, which are used to control this disease, have been composed on the consequences of sensitivity analysis. In order to gain better insight into the comparative results of analytical and numerical outcomes, the problem was revisited, and found that numerical results support our analytical findings. Our results conclude that pre-exposure vaccination can substantially reduce the risk of cholera.

This study employs the Tiwari and Das model to numerically evaluate the heat-transfer properties of a magnetized Casson sodium alginate-copper/alumina hybrid nanofluid flow over a permeable moving surface, taking into account the effects of viscous dissipation. Sodium alginate-alumina/copper hybrid nanofluids have garnered significant attention in modern society because of their potential uses in a variety of different industries. The key goal of the study is to examine the effect of the Casson parameter and copper solid volume fraction for skin friction coefficient and Nusselt number against velocity ratio parameter. Additionally, in the present study, velocity and temperature profiles for velocity ratio parameter, suction effect, magnetic parameter, Eckert number, and Prandtl number are also included. Using the bvp4c technique, the PDEs are converted into a set of non-linear ODEs with the use of suitable similarity variables. Dual approaches for controlling parameter using varied Casson fluid parameter and copper solid volume fraction quantities have been identified. Unique solutions, no solutions, and dual solutions exist in specific ranges of parameters. Consequently, beyond the critical values, no solution exists. The rate of heat transfer strengthened as the capacity of the Eckert number augmented. The temperature profile also diminished when the Prandtl number improved. The appearance of the boundary layer separation extension resulted from incorporating the copper solid volume fraction. Finally, stability analysis reveals that the first solution is stable, and the second solution is unstable.

Dyes are well known major pollutants in wastewater discharged by various textile industries which are toxic to human beings and aquatic life. It is necessary to remove these colorants from water with low-cost yet effective method by which these pollutants can be removed from the water bodies. Current study has been designed to develop cost-effective material for the removal of dyes in wastewater along with the application of composite to inhibit the growth of Gram negative (GN) and Gram positive (GP) bacterium. Nanocomposite (Ag-NiO2@PVA) of silver and nickel was synthesized by the chemical reduction method and polyvinyl alcohol (PVA) was used as a stabilizing medium. Nanocomposite (NC) was characterized employing different techniques including XRD, SEM, and FTIR which not only confirmed its synthesis but also provided their structure and morphology. The hexagonal close packed nanocomposite was tested for the catalytic degradation of different azo and anthraquinone dyes including methylene blue (MB), methyl orange (MO) and eosin yellow (EY). The degradation of MO, MB and EY was recorded in 20, 16 and 20 min with percentage removal 89.26, 95.88 and 96.56 % respectively. Antibacterial potential of the nanocomposite was assessed against different GN and GP bacterial strains namely Bacillus subtilis, Staphylococcus aureus and Escherichia coli and the as-synthesized Ag-NiO2@PVA exhibited strong zone of inhibition against all types of bacterial strains mentioned herein. Nanocomposite was recovered and analyzed after dye degradation as well as the antibacterial studies have confirmed stability and recyclability of the nanocomposite. Results of the current study strongly recommend the composite for wastewater treatment applications i.e., removal of different dyes and pathogens. Silver and nickel based nanocomposite can be synthesized and modified followed by the stabilization with PVA for different applications in material sciences.

Cavitation in hydro turbines causes component deterioration that requires continuous and costly maintenance in the hydroelectric power generation stations. The Tarbela Dam Hydel Project (TDHP) in Pakistan is facing a cavitation problem in the Francis Turbine components, such as the runner and draft tube. Simulation work has been performed to examine and quantify the cavitation rate as a function of the suction head (SH) and flow velocity (FV) by utilizing a homogeneous cavitation model. The result shows that pressure fluctuation is maximum for overcrowded conditions and minimum for rated load conditions. Moreover, a higher cavitation rate is found for the part and overcrowded conditions compared to the rated load condition. Additionally, the cavitation rate becomes 50% higher when the SH increases from 5.54 to 12.34 m. Moreover, SEM results have verified the CFD results that higher FV and SH enhance the cavitation rate. Furthermore, the numerical work is validated by simplified hydrofoil geometry. The computational fluid dynamics results presented a good arrangement with the experimental data.

Suspending particles of tiny solid in a fluid used to transport energy can enhance its thermal conductivity and heat transport properties. Our main goal of this examination is to study the radiative unsteady two-dimensional (2D) flow on a continuously diminishing, horizontal sheet. with suction for the hybrid water-based nanofluid and an aligned field of magnetic, including the combined suction, magnetic, and velocity slip conditions effect. The Tiwari & Das model of nanofluid equations is used, which takes into consideration the solid volume percentage. Equations of similarity are derived by employing the transformations of similarity, and the associated equations have been simplified numerically by employing the bvp4c method in MATLAB software for a variety of values of the nanoparticle volume fraction, the unsteadiness, and the wall mass suction in water. It is discovered that, within the given the unsteadiness parameter range, two solutions exist. Moreover, it is found that the fluid velocity slows down in 1st solution as volume fraction of copper nanoparticles rises but speeds up in the second solution at first before slowing down again. Using a temporal stability analysis, it is found that only one of the dual branches is stable over the long run, while the other is unstable.

The present study aims to resolve the existing research gaps on olive pomace (OP) hydrochars application as a fuel by evaluating its molecular structures (FTIR and solid NMR analysis), identifying influential characteristics (Pearson correlation analysis), process optimization (response surface methodology), slagging–fouling risks (empirical indices), and combustion performance (TG-DSC analysis). The response surfaces plot for hydrothermal carbonization (HTC) of OP slurry performed in a pressure reactor under varied temperatures (180–250 °C) and residence times (2–30 min) revealed 250 °C for 30 min to be optimal conditions for producing hydrochar fuel with a higher heating value (32.20 MJ·Kg−1) and energy densification ratio (1.40). However, in terms of process efficiency and cost-effectiveness, the optimal HTC conditions for producing the hydrochar with the highest energy yield of 87.9% were 202.7 °C and 2.0 min. The molecular structure of hydrochar was mainly comprised of aromatic rings with methyl groups, alpha-C atoms of esters, and ether bond linkages of lignin fractions. The slagging and fouling risks of hydrochars were comparatively lower than those of raw OP, as indicated by low slagging and fouling indices. The Pearson correlation analysis emphasized that the enrichment of acid-insoluble lignin and extractive contents, carbon densification, and reduced ash content were the main pivotal factors for hydrochar to exhibit better biofuel characteristics for energy applications.

Hansenula polymorpha is a non-conventional and thermo-tolerant yeast that is well-known for its use in the industrial production of recombinant proteins. However, research to evaluate this yeast’s potential for the high-temperature fermentation of sugar to produce alcohols for biofuel applications is limited. The present work investigated a wild-type H. polymorpha strain (DSM 70277) for the production of ethanol at a temperature of 40 °C under limited oxygen presence by using a batch fermentation reactor. Fermentation experiments were performed using three types of sugar (glucose, fructose, xylose) as substrates with two initial inoculum concentrations (1.1 g·L−1 and 5.0 g·L−1). The maximum specific growth rates of H. polymorpha yeast were 0.121–0.159 h−1 for fructose, 0.140–0.175 h−1 for glucose, and 0.003–0.009 h−1 for xylose. The biomass volumetric productivity was 0.270–0.473 g·L−1h−1 (fructose), 0.185–0.483 g·L−1h−1 (glucose), and 0.001–0.069 g·L−1h−1 (xylose). The overall yield of ethanol from glucose (0.470 g·g−1) was higher than that from fructose (0.434 g·g−1) and xylose (0.071 g·g−1). The H. polymorpha yeast exhibited different behavior and efficacy regarding the use of glucose, fructose, and xylose as substrates for producing ethanol. The present knowledge could be applied to improve the fermentation process for valorization of waste biomass to produce bioethanol.

The Weibull algorithm is one of the most accurate tools for forecasting and estimating wind energy potential. Two main parameters of the Weibull algorithm are the ‘Weibull shape’ and ‘Weibull scale’ factors. There are six different numerical methods to estimate the two Weibull parameters. These six methods are the empirical method of Justus (method 1), the empirical method of Lysen (method 2), the maximum likelihood method (method 3), the modified maximum likelihood method (method 4), the energy pattern factor method (method 5) and the graphical method (method 6). Many commercial wind energy software programs use the Weibull algorithm, and these six methods are used to calculate the potential wind energy at a given site. However, their accuracy is rarely discussed, particularly regarding wind data height. For this purpose, wind data measured for a long period (six years) at real sites are introduced. The wind data sites are categorized into three levels, i.e., low, medium, and high, based on wind data measurement height. The analysis shows that methods 1 and 2 are the most accurate methods among all six methods at low and medium heights. The number of errors increases with the height of these two methods. Methods 3 and 4 are the most suitable options for larger heights, as these scenarios have minimal error. The present study’s findings can be used in various fields, e.g., wind energy forecasting and wind farm planning.

The battery pack is at the heart of electric vehicles, and lithium-ion cells are preferred because of their high power density, long life, high energy density, and viability for usage in relatively high and low temperatures. Lithium-ion batteries are negatively affected by overvoltage, undervoltage, thermal runaway, and cell voltage imbalance. The minimisation of cell imbalance is particularly important because it causes uneven power dissipation by each cell and, hence, temperature distribution that adversely impacts the battery lifetime. Several papers in the literature proposed advanced cell-balancing techniques to increase the effectiveness of basic cell-balancing approaches, reduce power losses, and reduce the number of components in balancing circuits. The new developments and optimisations over the last few years have been particularly intense due to the increased interest in battery technologies for several end-use applications. This paper reviews and discusses recent cell-balancing techniques or methods, covering their operating principles and the optimised utilisation of electrical components.

Here in, heat transfer characteristics of a magnetized Casson sodium alginate-alumina/copper hybrid nanofluid flowing through the permeable moving plane are investigated considering the effects of thermal radiation and Joule heating with Tiwari and Das model. The primary objective of the present study is to investigate the influence of the velocity ratio parameter on the solid volume fraction and the Casson parameter. In addition, the velocity and temperature profiles used in the current study illustrate the effects of the velocity ratio parameter R, solid volume fraction, suction effect, magnetic field, Joule heating, and thermal radiation. To apply the three-stage Lobatto IIIa with boundary value problems (bvp4c) approach to implement the appropriate similarity variables to transform the partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). It has been determined that there are two branch solutions for the velocity ratio parameter against using the Casson parameter and copper volume fraction values. Non-unique branch at R Rci. As the Eckert number and radiation grew, the rate of heat transmission surged. The increase of Casson hybrid nanofluid parameter values caused to drop the skin friction in both upper and lower branch.

The classification and the geometry of corank one map germs from $ ({\mathbb{C}}^2, 0) \rightarrow ({\mathbb{C}}^3, 0) $ have been studied by Mond [1,2]. In this paper we characterize the classification of map germs of corank at most $ 1 $, in terms of certain invariants. Moreover, by using this characterization, we develop an algorithm to compute the type of map germs with out computing the normal form. Also, we give its implementation in the computer algebra system SINGULAR [15].

The aim of the study is to examine how lesson study activities affect primary school preservice teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 primary school preservice teachers. The data were obtained from the observation form, video recordings, reflection reports and field notes in order to reveal how the lesson study model affected the noticing development of preservice teachers. In addition to these, the "video exam" at the end of the Teaching Practicum-II course also constituted one of the data collection tools. Descriptive analysis was used in the study. The data obtained were analyzed by adapting the theoretical framework of "Levels of Noticing of Students' Mathematical Thinking" developed by van Es (2011) as "Levels of Noticing of Students' Misconceptions" in order to reveal preservice teachers' noticing of students' mathematical thinking. As a result of the research, it was concluded that noticing skills of the lesson study group preservice teachers were mostly at the level of reasoning and justifying their reasons (level 3) and offering alternative pedagogical solution suggestions based on comments (level 4). It was concluded that the noticing skills of the comparison group preservice teachers were mostly descriptive (level 1) and at the level of identifying important events but being insufficient to expand their interpretations (level 2).

Objective: This study aimed to present an amniotic band syndrome case who underwent intrauterine fetoscopic surgery. Case(s): On ultrasound examination, edema was detected at the distal of the right upper extremity. The constrictive amniotic band tangling around the extremity at the upper part of the right elbow and around the umbilical cord was detected during the fetoscopic examination. The amniotic band was released by using endoscopic scissors and grasper. It was observed that the right hand was at the flexion position and was able to return to the neutral position on neonatal examination. Conclusion: Releasing amniotic band with fetoscopic surgery in amniotic band syndrome cases is an efficient method to prevent progressive destruction in the extremities and the procedure-related complications seem to be acceptable.

In this paper, we present generalized Jensen-Mercer inequality for a generalized h-convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h-convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature.

This study aimed to investigate students' reflections on using smartphones to enhance vocabulary learning. The sample consisted of 64 college students enrolled in required English as a Foreign Language (EFL) reading course. A twenty-two-item questionnaire was developed to elicit students' reflections on their experiences in terms of three aspects; engagement, vocabulary learning strategies, and attitudes towards smartphone use. The study also explored the effect of previous experiences of smartphones use on the students' reflections. Results showed that students' engagement was generally high, their vocabulary learning strategies had changed, and that their attitudes towards using smartphones to develop their vocabulary were positive. The study also found that there were differences between those who have experience in using smartphones and those who did not, in favour of those with experience. It is recommended that teachers encourage their students to use smartphones to enhance their English language abilities, especially their vocabulary.

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.

We present new Mercer variants of Hermite-Hadamard (HH) type inequalities via Atangana-Baleanu (AB) fractional integral operators pertaining non-local and non-singular kernels. We establish trapezoidal type identities for fractional operator involving non-singular kernel and give Jensen-Mercer (JM) variants of Hermite-Hadamard type inequalities for differentiable mapping Υ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.

Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3–Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%–10% copper nanoparticles and 1%–500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f″(0) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport −θ′(0) decreases. As heat generation/absorption increases 1%–500%, −θ′(0) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S≥Sci in assisting flow case, while no fluid flow is possible when S

Topological indices provide a mathematical language for capturing molecular structure, symmetry, and predicting properties. Dendrimers are microscopic bilaterally symmetrical molecules with a well-defined homogeneous nanoparticles structure, often consisting of a symmetric center, inner shell, and outer shell. In this work, first we compute some degree-based topological indices of Porphyrin (DnPn),Poly (Propyl) Ether Imine(PETIM), Zinc porphyrin (DPZn), and Polyamidoamine (PAMAM) dendrimers. Then, we use multi-criteria decision making (MCDM) techniques to establish the weighted evaluation of dendrimer classes based on certain topological indices. For weighted analysis we correlate the properties of benzene derivatives with topological invariants. Finally, based on the multi-criteria decision making techniques namely TOPSIS, SAW and MOORA method, we have ranked the dendrimer structures based on their properties.

Wind power is a significant and urging sustainable power source asset to petroleum derivatives. Wind machines, for example, H-Darrieus vertical pivot wind turbines (VAWTs) have increased much notoriety in research network throughout the most recent couple of decades because of their applications at destinations having moderately low wind speed. Be that as it may, it is noticed that such wind turbines have low effectiveness. The point of this examination is to plan rotor cutting edges which could create most extreme power yield and execution. Different plan factors, for instance, harmony length, pitch edge, rotor distance across, cutting edge length and pitch point are explored to upgrade the presentation of VAWT. Rotor cutting edges are manufactured using the NACA-0030 structure and tried in wind burrow office and contrast its outcomes and DSM 523 profile. Numerical simulations are performed to get best geometry and stream conduct for achieving greatest power. It is seen that for higher tip-speed-proportion (TSR), shorter harmony length and bigger distance across the rotor (i.e., lower robustness) yields higher effectiveness in NACA 0030. Nevertheless, for lower TSR, the more drawn out agreement length and slighter distance across rotor (i.e., higher strength) gives better implementation. The pitch point is - 2° for TSR = 3 and - 3° for TSR = 2.5. The most extreme power yield of the wind turbine is acquired for the sharp edge profile NACA 0030. Besides, instantaneous control coefficient, power coefficient (CP) is the greatest reason for azimuthal edge of 245° and least esteem for 180°.