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Taking into account the most recent improvements in graph theory and algebra, we can associate graphs of some mathematical structures with certifiable, widely known applications. This paper seeks to explore the connections established through edge labeling among Latin squares derived from Moufang quasigroups, which are constructed using additive abelian and multiplicative groups, along with their substructures and complete bipartite graphs. The algebraic characteristics of quasigroups exhibiting the antiautomorphic inverse property have been extensively examined in this study. These characteristics encompass identities associated with fixed element maps. To analyze the behavior of these groups under holomorphism, we utilize similar conditions. [ABSTRACT FROM AUTHOR]

A relatively new and rapidly expanding area of mathematics research is the study of graphs' spectral properties. Spectral graph theory plays a very important role in understanding certifiable applications such as cryptography, combinatorial design, and coding theory. Nonassociative algebras, loop groups, and quasigroups are the generalizations of associative algebra. Many studies have focused on the spectral properties of simple graphs connected to associative algebras like finite groups and rings, but the same research direction remains unexplored for loop groups and quasigroups. Eigenvalue analysis, subgraph counting, matrix representation, and the combinatorial approach are key techniques and methods in our work. The main purpose of this paper is to characterize finite quasigroups with the help of relatively prime graphs. Moreover, we investigate the structural and spectral properties of these graphs associated with finite quasigroups in the forms of star graphs, eigenvalues, connectivity, girth, clique, and chromatic number. [ABSTRACT FROM AUTHOR]

Expansive soils pose significant challenges in civil engineering due to their susceptibility to volumetric changes, leading to structural instability and damage in infrastructure. This study evaluates the performance and microstructural characteristics of industrial solid waste materials (Class F‐fly ash and ground granulated blast‐furnace slag) as additives for stabilizing expansive soils. Tests, including moisture density, unconfined compressive strength, Atterberg limits, compressibility index (Cc), cation exchange capacity, direct shear test, and California bearing ratio, were conducted on the treated expansive soil. Scanning electron microscopy and energy dispersive X‐ray spectroscopy (EDX) were used to analyze the changes in the soil matrix due to the incorporation of the waste materials. The results demonstrate improved engineering properties of expansive soil treated with these additives. The analysis confirms enhancements in particle arrangement, reduced porosity/pore sizes, and improved bonding between soil particles, indicating the formation of calcium silicate hydrate and calcium aluminate hydrate. This research suggests that these waste materials can be eco‐friendly and cost‐effective alternatives for stabilizing expansive soils in construction projects. [ABSTRACT FROM AUTHOR]

Many real‐world applications can be modelled as graphs or networks, including social networks and biological networks. The theory of algebraic combinatorics provides tools to analyze the functioning of these networks, and it also contributes to the understanding of complex systems and their dynamics. Algebraic methods help uncover hidden patterns and properties that may not be immediately apparent in a visual representation of a graph. In this paper, we introduce left and right inverse graphs associated with finite loop structures and two mappings, P‐edge labeling and V‐edge labeling, of Latin squares. Moreover, this work includes some structural and graphical results of the commutator subloop, nucleus, and loop isotopes of inverse property quasigroups. [ABSTRACT FROM AUTHOR]

The present study aimed to develop ready-to-drink (RTD) beverage using the choongan (Caralluma tuberculata L.) extract and further to evaluate antioxidant potential and mineral estimation of the prepared RTD. The stem of Caralluma tuberculata was used to further isolate and purify the powder. Then, C. tuberculata powder was utilized in the formulation of beverages. All the treatments observed a decreasing trend for acidity, total soluble solids, total phenols, total antioxidant activity, total flavonoids, DPPH radical scavenging activity, and viscosity during storage whilst pH showed an increasing trend. It was observed that Caralluma RTD contained increasing trend of phytochemicals by increasing contents of the Caralluma extract. The same trend was also observed regarding all the mineral contents investigated in the present study. The treatment T4 (Caralluma RTD having 1.5 g C. tuberculata powder) showed the maximum values regarding phytochemicals as well as minerals. The microbial counts (log10 CFU/mL) for all the treatments increased during storage. Even though T4 showed promising results regarding phytochemicals and minerals, T1 showed the maximum sensory score even after 21 days of storage. [ABSTRACT FROM AUTHOR]

In mathematical chemistry, the algebraic polynomial serves as essential for calculating the most accurate expressions of distance-based, degree-distance-based, and degree-based topological indices. The chemical reactivity of molecules, which includes their tendency to engage in particular chemical processes or go through particular reactions, can be predicted using topological indices. Considerable effort has been put into examining the many topological descriptors of simple graphs using ring structures and well-known groups instead of nonassociative algebras, quasigroups, and loops. Both finite quasigroups and loops are the generalizations of groups. In this article, we calculate topological descriptors and some well-known polynomials, M -polynomial, Hosoya's polynomial, Schultz's polynomial, and modified Schultz polynomial of finite relatively prime graphs of most orders connected with two classes of quasigroups and go through their graphical aspects. [ABSTRACT FROM AUTHOR]

Wave problem arises in various phenomena of science and engineering. This study proposes an efficient and appropriate scheme to produce the approximate solutions of multidimensional problems arising in wave propagation. We use a new iterative strategy (NIS) to minimize the computational cost and less time than other approaches studied in the literature. Since the variational iteration method (VIM) has some assumptions and restrictions of variables during the construction of the recurrence relation, we present a Sawi integral transform for the construction of the recurrence to overcome this difficulty. The series solution for this recurrence relation is determined using the homotopy perturbation strategy (HPS) in the form of convergence that provides the precise solution after a few iterations. This NIS does not require any discretization in the findings of results and derives the algebraic equations. Some numerical models and graphical representations are illustrated to verify the performance of this scheme. [ABSTRACT FROM AUTHOR]

The present study investigates the impact of traditional and novel cooking techniques on the nutritional and bioactive profile of Brassica oleracea, commonly known as kale. As a member of the Brassica family, kale is well known for its high nutritional value and possible health benefits. However, it is crucial to remember that the cooking techniques can significantly impact the nutritional profile of kale. Various cooking methods were applied to kale samples through controlled experiments. Traditional techniques like boiling and steaming were compared with innovative approaches such as microwave cooking and vacuum cooking. Soluble solids, which include sugars and other compounds, were used as indicators of nutritional change. Additionally, the levels of vital bioactive components, such as vitamins, antioxidants, and phytochemicals, were analyzed to assess the overall impact of cooking methods. Preliminary findings suggest that the choice of cooking method plays a pivotal role in determining the extent of nutritional and bioactive alterations in kale. Traditional methods, such as boiling, exhibited substantial losses of soluble solids and certain heat-sensitive nutrients. In contrast, novel methods like vacuum cooking displayed better preservation of soluble solids and bioactive compounds. The study sheds light on the complex relationship between cooking techniques and the nutritional integrity of kale. By exploring various methods, this review paper contributes to understanding how culinary practices can be optimized to enhance the retention of vital nutrients and beneficial bioactive components in kale. These findings hold practical implications for individuals seeking to maximize the health benefits of kale consumption while enjoying its culinary versatility. [ABSTRACT FROM AUTHOR]

Kinnow peel oil has been reported to possess antimicrobial and antioxidant activities due to presence of many bioactive compounds. Therefore, the experiments reported in this research paper aimed to investigate the shelf stability and antioxidant potential of Cheddar cheese coated with Kinnow peel oil at various concentrations (0.2%, 0.4%, and 0.6%). The physicochemical characteristics, microbial counts, antioxidant potential, and sensory acceptability of Cheddar cheese were evaluated during ripening (up to 9 months, 4°C). The titratable acidity (%), pH, moisture (%), fat (%), protein contents (%), and soluble nitrogen (SN, %) of Cheddar cheese investigated in the present study showed significant p < 0.05 variations among treatments during ripening. The maximum plate counts (8.36 Log cfu·g−1) were observed in control cheese (T0) ripened for 3 months whereas T3 (9 months ripened) showed the minimum counts (5.04 Log cfu·g−1) among all the treatments. The maximum (3.76 Log cfu·g−1) yeast and mold counts were observed in T0 cheese ripened for 9 month whereas the respective samples of T3 showed the lowest values (2.89 Log cfu·g−1) among all the treatments. The surfaces of Cheddar cheese coated with 0.6% Kinnow peel (T3) did not show any visible signs of yeast and molds. The maximum (366.56 mg GAE/100 g) total phenolic contents were observed in T3 ripened for 6 months. The maximum values (1995.02 mM TE/100 g) of DPPH radical scavenging activity were observed in T3 ripened for 6 months. Similarly, T3 obtained the highest sensory scores among all the treatments. Hence, it was concluded that Kinnow peel oil significantly improved antioxidant potential, sensory perception, and shelf stability of Cheddar cheese. [ABSTRACT FROM AUTHOR]

In this paper, we present an idea of a new iterative procedure (NIP) to examine the approximate solution of the nonlinear fractional Drinfeld–Sokolov–Wilson (DSW) equation. We first use Mohand transform (MT) to the problem and obtain a recurrence relation without any assumption or restrictive variable. This relation is now very easy to handle and suitable for the study of the homotopy perturbation method (HPM). We observe that HPM produces the iterations in the form of convergence series that becomes very close to the precise solution. The fractional derivative is considered in the Caputo sense. We also demonstrate the graphical solution to show that NIP is a very simple, straightforward, and efficient tool for nonlinear problems of fractional derivatives. [ABSTRACT FROM AUTHOR]

Optimal graph embeddings represent graphs in a lower dimensional space in a way that preserves the structure and properties of the original graph. These techniques have wide applications in fields such as machine learning, data mining, and network analysis. Do we have small (if possible minimal) k -connected graphs with the property that for any j vertices there is a longest path avoiding all of them? This question of Zamfirescu (1972) was the first variant of Gallai's question (1966): Do all longest paths in a connected graph share a common vertex? Several good examples answering Zamfirescu's question are known. In 2001, he asked to investigate the family of geometrical lattices with respect to this property. In 2017, Chang and Yuan proved the existence of such graphs in Archimedean tiling. Here, we prove that the graphs presented by Chang and Yuan are not optimal by constructing such graphs of sufficiently smaller orders. The problem of finding nonconcurrent longest paths in Archimedean tessellations refers to finding paths in a lattice such that the paths do not overlap or intersect with each other and are as long as possible. The complexity of embedding graph is still unknown. This problem can be challenging because it requires finding paths that are both long and do not intersect, which can be difficult due to the constraints of the lattice structure. [ABSTRACT FROM AUTHOR]

Due to the rapid development of image data and the necessity to analyze it to extract meaningful information, heterogeneous systems have gained prominence. One of the most critical aspects of distributed systems is load balancing. When it comes to the distribution of workload in a balanced manner in a cluster, some heterogeneous systems are used for image processing. When workloads are allocated in these systems, the computational power of the processors is not considered. As a result, in these heterogeneous systems for image processing applications, an uneven workload distribution issue is found. A workload distribution programming framework is presented and discussed in this paper. The proposed strategy consists of two parts. As a first step, image data is split into optimal split sizes and distributed across nodes, then the image data is distributed across CPU and GPU in a second step for processing. A heterogeneous environment is created by combining the CPU and GPU. The OpenCL Java bindings are used to set up both the CPU and GPU to run the program. To assess the performance of the suggested technique, certain tests are carried out and compared to current platforms. For image processing applications in heterogeneous clusters, the proposed workload distribution approach distributed image data efficiently. The results of the proposed solution (Hadoop + GPU) show that using an effective workload allocation mechanism in heterogeneous systems reduces average execution time while improving overall application performance. [ABSTRACT FROM AUTHOR]

In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the model are calculated by applying fractional calculus theory and the homotopy perturbation method. A comparison is given for fractional and fuzzy results, and the numerical findings validate the fuzzy fractional case. Using MATLAB software, the results are simulated for various fractional orders, corresponding to the provided data. The simulations demonstrate the model's appropriateness. [ABSTRACT FROM AUTHOR]

This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He's fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). Numerical results are derived in a rapid converge series form to improve the accuracy of the scheme greatly. Graphical representations and error distribution show that the two-scale approach is a very convenient tool. [ABSTRACT FROM AUTHOR]

Trigonella foenum-graecum and Zingiber officinale are used as traditional medicinal plants for the treatment of infectious and inflammatory diseases. However, a comparative analysis and bioactivities of T. foenum-graecum and Z. officinale lack some necessary information for therapeutic purposes. This study was designed to evaluate the biochemical characterizations and biological efficacy of T. foenum-graecum and Z. officinale as antioxidant, antidiabetic, antiamnesic, and cytotoxic agents. Antioxidant activity was determined by DPPH free radical scavenging assay. Antidiabetic potentials were evaluated by glycation, alpha-amylase, and acetylcholinesterase inhibition assays. We performed biochemical characterization through analyses of high-performance liquid chromatography (HPLC) and FTIR (Fourier transform infrared spectroscopy). Results revealed that total phenolic contents (TPCs) (g GAE/100 g) of T. foenum-graecum and Z. officinale were 5.74 ± 0.81 g and 6.15 ± 0.06 g, respectively, and total flavonoid contents (TFCs) varied from 1.51 ± 0.58 g CE/100 g to 17.54 ± 0.58. DPPH scavenging potentials of T. foenum-graecum and Z. officinale extract were 50.27% and 88.82%, respectively. Antiglycation potentials of T. foenum-graecum and Z. officinale showed a maximum activity at 16–29% and 96%. Alpha-amylase and alpha-glucosidase inhibition ranged from 9.43–24.95 and 10.52–27.89 and 54.97%, respectively. All the test samples of T. foenum-graecum and Z. officinale showed acetylcholinesterase inhibition potential at 0.37–46.88%. HPLC analysis of T. foenum-graecum revealed the presence of quercetin, gallic acid, caffeic acid, vanillic acid, syringic acid, and cumeric acid, while Z. officinale revealed the quercetin, gallic acid, vanillic acid, benzoic acid, chlorogenic acid, p.Coumaric acid, ferulic acid, and cinnamic acid. FTIR analysis revealed the presence of aldehydes, ketones, aromatic compounds, amines, and carbonyl groups in T. foenum-graecum, while alcohol, alkane, alkene, ketone, amine, and ether are bioactives present in the methanolic extract of Z. officinale. It was concluded that a comparative analysis of T. foenum-graecum and Z. officinale showed that Z. officinale showed higher therapeutic effects. [ABSTRACT FROM AUTHOR]

Topological indices are empirical features of graphs that characterize the topology of the graph and, for the most part, are graph independent. An important branch of graph theory is chemical graph theory. In chemical graph theory, the atoms corresponds vertices and edges corresponds covalent bonds. A topological index is a numeric number that represents the topology of underline structure. In this article, we examined the topological properties of prism octahedron network of dimension m and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to utilize the distance between the vertices of a prism octahedron network. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to introduce a new scheme for the approximate solution of 1D, 2D, and 3D wave equations. The recurrence relation is very important to deal with the approximate solution of differential problems. We construct a scheme with the help of the Laplace-Carson integral transform ( L c IT) and the homotopy perturbation method (HPM), called Laplace-Carson homotopy integral transform method ( L c HITM). L c IT produces the recurrence relation and destructs the restriction of variables whereas HPM gives the successive iteration of the relation using the initial conditions. The convergence analysis is provided to study the wave equation with multiple dimensions. Some numerical examples are considered to show the efficiency of this scheme. Graphical representation and plot distribution between the approximate and the exact solution predict the high rate of convergence of this approach. [ABSTRACT FROM AUTHOR]

In this study, ice creams were produced from cow and buffalo milk using 15% sugar, 13% fat, 11% milk solids not fat, and 0.5% cremodan (TS 39.5%). Triglycerides from C26 to C36 were significantly higher in buffalo milk ice cream than cow milk ice cream. Milk type and storage both affected the fatty acid composition of ice cream samples. Concentrations of unsaturated fatty acids in cow and buffalo milk ice cream samples were 24.4% and 29.9%, respectively. Total antioxidant capacity of buffalo milk ice cream was 18% higher than cow milk ice cream. Concentrations of vitamin A and E were significantly higher in buffalo milk ice cream samples. Buffalo milk ice cream had lower peroxide value and higher oxidative stability than cow milk ice cream. Induction period of cow and buffalo milk ice cream was 8.55 h and 10.79 h with no difference in sensory properties of both types of ice creams. Practical applications: Buffalo milk is widely used for the production of several value‐added dairy products and is the major source of milk in some Asian countries. However, due to limited research work, buffalo milk processing industry could not develop, and buffalo milk based dairy products are not available in markets of these countries. This research work can be helpful for the dairy industries to produce ice cream from buffalo milk at commercial level. [ABSTRACT FROM AUTHOR]

Withania coagulans is a shrub that has milk‐clotting activity. Its coagulation efficiency at different concentrations and incubation temperatures was measured for Mozzarella cheese from curd formation to its application on the pizza top. Curd made at higher W. coagulans concentration (1%) has less coagulation time (1272.99 ± 96.68 s), viscosity (148.58 ± 9.25 Pa s), pH (5.89 ± 0.05), and yield (7.87 ± 0.53%) as compared to rest of samples. Increasing temperature (39°C) also decreased coagulation time (1599.19 ± 380.06 s), viscosity (146.56 ± 15.51 Pa s), pH (6.01 ± 0.17), and yield (8.87 ± 0.48%) of curd. W. coagulans at 0.2% concentration showed caseinolytic activity (78.83 ± 1.97%) very close to rennet (84.12 ± 2.3%). High W. coagulans and temperature conditions lead to the grainy texture that results in the loss of proteins, fats, and moisture from the cheese. Highest protein (21.89 ± 0.8%; 23.39 ± 2.15%), fat (17.64 ± 0.62%; 18.50 ± 0.32%), and moisture (43.55 ± 8.01%; 50.00 ± 6.13%) were observed in Mozzarella cheese at 0.2% W. coagulans concentration and 33°C temperature, respectively. This study showed that 0.2% extract of W. coagulans can be used to clot the milk for cheese production at 33°C. Novelty impact statement: The interest in plant‐based coagulant consumption has been growing because of the rennet shortage and religious matters of some vegetarian people. A plant‐based coagulant from Withania coagulans has been reported for its milk‐clotting activity, but its behavior for Mozzarella cheese production from curd formation to its application on pizza topping needs detailed study for its use on an industrial scale. In this study, W. coagulans behavior was studied during curd formation. Its caseinolytic and proteolytic activities in comparison to rennet were studied. Mozzarella cheese physicochemical and functional characteristics on pizza topping were also described in this research. [ABSTRACT FROM AUTHOR]

Present study was conducted to investigate the functional properties of multigrain cookies with the addition of mango waste as a source of bioactive compounds. Purposely, fortified cookies were prepared using mango peel and kernel powder in 2%, 4%, and 6% ratio in simple wheat flour along with 10% oat and 10% barley flour. The prepared cookies were analyzed for proximate, antioxidant, physical, and sensory characteristics. The results revealed that mango peel powder had high content of antioxidant and crude fiber, whereas mango kernel powder had a high content of moisture (6.62 ± 0.15%), ash (2.17 ± 0.13%), protein (8.17 ± 0.05%), and fat (1.67 ± 0.02%) as compared with mango peel powder. However, 4% mango peel and 2% mango kernel powder did not impact the texture or color of the cookies while substituting up to 6% resulted in color differences that were disliked. In cookies, phenolic and flavonoid content increased due to addition of mango peel and mango kernel that boosted their antioxidant activity. The sensory evaluation revealed that substituting up to 4% mango peel and 2% mango kernel powder resulted in cookies with acceptable mango taste and flavor; however, cookies prepared with the addition of 2% peel powder and 2% kernel powder resulted in highest sensory score and showed better results for physicochemical as well as antioxidant analysis. It is concluded that 2% mango peel and kernel were found to play a vital impact in improving the nutritional characteristics of fortified cookies. Practical applications: It is observed that the waste from fruit and vegetables is a rich source of biologically active compounds such as flavonoids and phenolic compounds, having strong antioxidant potential. Current study is conducted to not only validate the nutritional characterization and sensory evaluation of multigrain mango peel and kernel cookies but also enhance significance of fruit waste by its utilizing in different food products especially in baked products. [ABSTRACT FROM AUTHOR]

The current study is aimed at examining the overall effects of steroids on the tissues of organisms and pharmacotherapeutics and pharmaco-histokinetics of several steroids, including Bromocriptine as mesylate and estradiol valerate in common quails (Coturnix coturnix). A total of 100 birds were used for pharmaco-histokinetics. The research was carried out in two separate trials, one during the fall season and the other during the spring season. Each experiment lasted for five, ten, fifteen, and twenty days. Each study group used 20 birds while basing their experiments on a control group of 5. At the stretch of five, ten, fifteen, and twenty days in each season, therapeutic dosages were administered to a sum of two groups representing two separate steroid trial groups. Each steroid was administered to each bird in a therapeutic dose, which was three drops administered twice daily. Clinical symptoms include despondency, sluggishness, and variations in weight and temperature that almost all treated birds display. However, only in trials conducted in the fall was a sizable degree of body enlargement in one treated bird noticed. The winter testing showed a mortality rate. Four birds have died in the twenty-day group. One bird died when treated with estradiol valerate, and three birds died treated with Bromocriptine as mesylate. Both the male and female birds showed signs of having lost some of their body weight. The treated birds' kidney, stomach, hearts, and livers exhibited some edema. In comparison, almost all birds show enteritis, which indicates that steroids mainly affect the intestine. There were apparent differences in the histological analysis of heart and skeletal muscle and some treated birds with the control group. The kidney, liver, and intestine show the major histopathological change in all treated birds. [ABSTRACT FROM AUTHOR]

This paper presents the concept of a new strategy that examines the analytical solution of the Harry Dym equation (HDEq) with fractional derivative in the Caputo sense. This new approach is called the Mohand homotopy perturbation transform scheme (MHPTS) which is constructed on the basis of the Mohand transform (MT) and the homotopy perturbation method (HPM). The implementation of MT produces the recurrence relation without any assumption and hypothesis theory whereas HPM is additionally used to overcome the nonlinearity in differential problems. Our primary focus is to handle the error analysis in the recurrence relation and generates the solution in the order of series. These obtained results yield the exact solution very rapidly due to its fast convergence. Some graphical representations are demonstrated to show the high efficiency and performance of this approach. [ABSTRACT FROM AUTHOR]

Abnormal uric acid level result in the development of hyperuricemia and hallmark of various diseases, including renal injury, gout, cardiovascular disorders, and non‐alcoholic fatty liver. This study was designed to explore the anti‐inflammatory potential of stevia residue extract (STR) against hyperuricemia‐associated renal injury in mice. The results revealed that STR at dosages of 150 and 300 mg/kg bw and allopurinol markedly modulated serum uric acid, blood urea nitrogen, and creatinine in hyperuricemic mice. Serum and renal cytokine levels (IL‐18, IL‐6, IL‐1Β, and TNF‐α) were also restored by STR treatments. Furthermore, mRNA and immunohistochemistry (IHC) analysis revealed that STR ameliorates UA (uric acid)‐associated renal inflammation, fibrosis, and EMT (epithelial‐mesenchymal transition) via MMPS (matrix metalloproteinases), inhibiting NF‐κB/NLRP3 activation by the AMPK/SIRT1 pathway and modulating the JAK2‐STAT3 and Nrf2 signaling pathways. In summary, the present study provided experimental evidence that STR is an ideal candidate for the treatment of hyperuricemia‐mediated renal inflammation. Practical applications: The higher uric acid results in hyperuricemia and gout. The available options for the treatment of hyperuricemia and gout are the use of allopurinol, and colchicine drugs, etc. These drugs possess several undesirable side effect. The polyphenolic compounds are abundantly present in plants, for example, stevia residue extract (STR) exert a positive effect on human health. From this study results, we can recommend that polyphenolic compounds enrich STR could be applied to develop treatment options for the treatment of hyperuricemia and gout. [ABSTRACT FROM AUTHOR]

Arthropods can be either large or too small to be seen from the microscope. Their legs are jointed and perform a specific function in the soil. Several arthropods have been identified to date. Therefore, it is essential to identify them in a different type of soil. An experiment to quantify the soil arthropods in the urban forests of D.G. Khan was conducted at the Zoology lab of Ghazi University on four tree plants, i.e., neem (Azadirachta indica), mango (Mangifera indica), guava (Psidium guajava), and phalsa (Grewia asiatica). Soil samples were taken from different areas and on different months. The diversity of arthropods was analyzed through the Shannon index. The results were all significant. The total number of arthropods found in the experiment was 5151, with the following distributions: millipedes were 132 in neem, 133 in guava, 113 in mango, and 121 in phalsa; centipedes were 136 in neem, 142 in guava, 118 in mango, and 132 in phalsa; springtails were 138 in neem, 130 in guava, 120 in mango, and 134 in phalsa. There were a total of 12 different species of arthropods found. Neem (Azadirachta indica) have mites, centipede, and ants; guava (Psidium guajava) have centipedes and ants. Mango (Mangifera indica) have millipedes, centipedes, mites, springtail, and ants, and phalsa (Grewia asiatica) have mites, ants, and centipedes. The study reveals that millipedes, centipedes, springtails, and ants were found abundantly in the urban forest area of D.G. Khan, resulting in increased organic matter decomposition and appropriate distribution of nutrients through the soil having beneficial effects on the terrestrial ecosystem. [ABSTRACT FROM AUTHOR]

Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters. [ABSTRACT FROM AUTHOR]

In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled with the homotopy perturbation method. This NIS is capable of reducing the linearization, perturbation, and restrictive assumptions that ruin the nature of the numerical problems. Some numerical examples are demonstrated to legitimate the accuracy and authenticity of this NIS. The computational results are obtained in the shape of a series that converges only after a few iterations. The comparison of the graphical representations shows that NIS is a very simple but also an effective approach for other numerical problems involving complex variables. [ABSTRACT FROM AUTHOR]

Longevity of probiotics is the main concern to confer positive health benefits to the host. Microencapsulation is one of the promising techniques to keep probiotics viable during storage and gastric transit. Immobilization can efficiently protect cells, making this technique potentially suitable for the industry for the delivery of probiotics to the gastrointestinal tract of humans through fermented dairy products. The objective of the study was to investigate the effect of single and double coating on the stability of Bifidobacterium bifidum in set type yoghurt. The encapsulation was carried out in two experimental plans. In the plan I, the B. bifidum was single coated with sodium alginate (SA) at 4%, 5%, and 6% and chitosan (CH) at 0.6%, 0.8%, and 1.0% concentrations. Based on their highest encapsulation efficiency (EE), single‐coated microbeads comprise of SA 6% and CH 0.8% were selected for double coating (plan II). Whey protein concentrate (WPC) at concentration of 5.0%, 7.5%, and 10% was used for double coating of SA 6% and CH 0.8% microbeads. The double‐coated beads with SA (6%), WPC (5%), and CH (0.8%) WPC (5%) further selected based on EE for yoghurt preparation. Different yoghurt treatments were prepared and stored (28 days) at 4 ± 2°C. All yoghurt samples were analyzed for physicochemical (pH, acidity), microbiological (viability of Streptococcus thermophilus, Lactobacillus delbrueckii subsp. bulgaricus, B. bifidum), and sensory characteristics. It was noted that EE of double‐coated microbeads was greater than 90% as compared to single coated. It was also observed that pH decreases up to 4.2 and the acidity increased with the storage time. The count of probiotic and yoghurt cultures was affected significantly during storage but the survival rate of encapsulated treatments was maintained more than the minimum recommendation (107 CFU/ml) till the end of the storage period. The sensory properties of yoghurt containing double‐coated microbeads also significantly vary from the sample containing free cells of B. bifidum. It is concluded that double coating with the polysaccharides–protein matrix can maintain viability (>106 CFU/ml) for 28 days with no prominent change in physicochemical and sensory attributes as compared to free cells. The whey and its products (whey protein isolate and concentrate) can be recommended as a coating material for probiotics in future studies. Novelty impact statement: The research study investigates the effect and comparison of single and double coating with different coating materials on the viability of Bifidobacterium bifidum in set type yoghurt. In this study, dairy industrial waste, that is, whey has been used along with sodium alginate and chitosan in different combinations. [ABSTRACT FROM AUTHOR]

In this paper, we propose an innovative approach to determine the approximate solution of the coupled time-fractional Keller-Segel (K-S) model. We use the fractional complex transform (FCT) to switch the model into its differential partner, and then, the homotopy perturbation method (HPM) is introduced to tackle its nonlinear elements using He's polynomials. This two-scale theory helps to define the physical meaning of the FCT for the solution of the K-S model. Some examples are illustrated to show that the proposed scheme presents the significant results. The considerable findings show that this strategy does not require any assumptions and also reduces the massive computations without imposing any constraints. This technique is also suitable in functional studies of fractal calculus due to its powerful and robust support for nonlinear problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations. We apply Yang transform homotopy perturbation method (Y T-HPM) to find the approximate solution of temperature distribution in the casting-mould heterogeneous system. The Y T-HPM is a combined form of Yang transform (Y T) and the homotopy perturbation method (HPM) using He's polynomials. Some examples are provided to demonstrate the superiority of the suggested technique. The significant findings reveal that Y T-HPM minimizes the enormous without imposing any assumptions. Due to its powerful and robust support for nonlinear problems, this approach presents a remarkable appearance in the functional studies of fractal calculus. [ABSTRACT FROM AUTHOR]

Date seed oil was cooled to −20°C, filtered to produce olein fraction (OF, yield 38%), olein was further cooled to −30°C to produce super olein fraction (SOF, yield 22%), kept in amber glass bottles at 25–30°C for 90 days. HPLC analysis showed that phenolic compounds were intensified in olein and super olein of date seed oil. In SOF, concentrations of chromatographic acid, quercetin, gallic acid, caffeic acid, chlorogenic acid, syringic acid, p‐coumeric acid, m‐coumeric acid, and ferulic acid were 26.11 mg/100 g, 245.61 mg/100 g, 23.72 mg/100 g, 115.19 mg/100 g, 133.42 mg/100 g, 18.74 mg/100 g, 83.25 mg/100 g, 53.47 mg/100 g, and 49.97 mg/100 g. The concentrations of C18:1 in date seed oil, olein, and super olein were 43.64%, 48.91%, and 55.37%, respectively. Total phenolic contents of date seed oil, olein, and super olein were 191, 295, and 343 mg GAE/100 g. At the end of storage, the peroxide value of date seed oil, olein, and super olein was 0.55, 0.71, and 0.85 (MeqO2/kg) with no difference in color, smell, and taste. Practical applications: Increased information on nutrition‐ and health‐associated disorders has a great influence on the development of functional foods. Unsaturated fatty acids, carotenoids, phytochemicals, and other bioactive compounds contained in vegetable oils have a large number of health benefits. Traditionally used vegetable oils are subjected to refining, bleaching, and deodorization to produce bland oils that lead to a complete elimination of almost all bioactive compounds. Date seed oil can be used in raw forms, and olein and super olein fractions of date seed oil were first time produced. Olein and super olein fractions had a higher concentration of unsaturated fatty acids, phenolic compounds than date seed oil with no difference in sensory characteristics. Olein and super olein fractions can be used in the development of the large number of functional foods. [ABSTRACT FROM AUTHOR]

The aim of this project is to fabricate a highly stable Fe3O4-OA-MWCNT composite and its colloidal suspension in polyalphaolefin (PAO) base fluid for heat transfer applications. The nanocomposite was produced in three mass ratios (0.5 : 1, 1 : 1, and 1.5 : 1) to explore the concentration effects on the stability of the nanocomposite. XRD analysis and FTIR spectroscopy were conducted to inspect the phase and composition of the synthesized nanocomposite. The crystallite sizes (3.75 nm, 7.74 nm, and 7.52 nm) and dislocation densities of each composite were calculated, and it was revealed that the samples with high concentration of iron oxide nanoparticles showed small defects in their lattices. Dispersion stability of ferrofluids was also examined by natural deposition method for 365 days. The ferrofluids displayed high stability for more than one year with no sign of sedimentation. Thermal conductivity of the nanofluid was also measured via. A transient plane source method and a linear trend with slight deviation were observed. [ABSTRACT FROM AUTHOR]

Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Q a ⊂ V G is considered to be an adjacency metric generator for G if u 1 , u 2 ∈ V \ Q a (supposing each pair); there must exist a vertex q ∈ Q a along with the condition that q is indeed adjacent to one of u 1 , u 2 . The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G , denoted by di m a G. In this work, we compute exact values of the adjacency metric dimension of circulant graph C n 1 , 2 , Möbius ladder, hexagonal Möbius ladder, and the ladder graph. [ABSTRACT FROM AUTHOR]

This article presents a new iterative method (NIM) for the investigation of the approximate solution of the Klein-Gordon and sine-Gordon equations. This approach is formulated on the combination of the Mohand transform and the homotopy perturbation method. Mohand transform (MT) is capable to handle the linear terms only, thus we introduce homotopy perturbation method (HPM) to tackle the nonlinear terms. This NIM derives the results in the form of a series solution. The proposed method emphasizes the stability of the derived solutions without any linearization, discretization, or hypothesis. Graphical representation and absolute error demonstrate the efficiency and authenticity of this scheme. Some numerical models are illustrated to show the compactness and reliability of this strategy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He's fractional complex transform (FCT). This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method (HPM) is employed to tackle the nonlinear terms in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering. [ABSTRACT FROM AUTHOR]

In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops. Also, there is a connection between bipartite graphs and mathematical structures, commutator subloop, associator subloop, and associative part, the nucleus of the loop, through edge labeling. [ABSTRACT FROM AUTHOR]

Drinking kills a significant proportion of individuals every year, particularly in low-income communities. An impulsive differential equation system is used to explore the effectiveness of activated charcoal in detoxifying the body after methanol poisoning. Our impression of activated charcoal is shaped by the fractional dynamics of the problem, which leads to speedy and low-cost first aid. The adsorption capacity of activated charcoal is investigated using impulsive differential equations. The ABC fractional operator's findings paint a more realistic image of first aid in public and primary health centers, which can assist to reduce methanol poisoning deaths. Numerical simulations are provided using generalized Adams–Bashforth–Moulton method (GABMM). [ABSTRACT FROM AUTHOR]

This study presents a modified simplest equation method (MSEM) to investigate some real and exact solutions of conformable time fractional Benjamin-Bona-Mahony (BBM) equation and Chan-Hilliard (CH) equation. We use traveling wave transformation to obtain the results in the form of series solution. Some calculations are performed through Mathematica software to analyze the accuracy of this approach. Graphical representations are reported for more significant results at different fractional-order which demonstrates that this approach is very simple, adequate, and legitimate. [ABSTRACT FROM AUTHOR]

We examined the thin-film flow problem of a third-grade fluid on an inclined plane under a fuzzy environment. The highly nonlinear flow governing differential equations (DEs) with the boundary conditions are fuzzified using the triangular fuzzy numbers (TFNs) developed by α -cut α ∈ 0,1 . The fuzzy perturbation (FPM) method is adopted to calculate the fuzzified form of the governing equations as well as the fuzzified boundary conditions. For the validation, the present work is in good agreement as compared to existing work in the literature under the crisp form. For various values of the fluid parameter λ , inclined parameter γ and fuzzy parameter α -cut is presented in graphical form. The α -cut controls TFNs, and the variability of uncertainty is investigated using a triangular membership function (MF). Using TFNs, the middle (crisp), left, and right values of the fuzzy velocity profile are used for fuzzy linear regression analysis. The outcome of this study and the fuzzy velocity profile have the maximum rate of flow as compared to the crisp velocity profile (mid values). [ABSTRACT FROM AUTHOR]

The metric dimension of a graph G is the selection of the minimum possible number of vertices such that each vertex of the graph G is distinctively defined by its vector of distances to the set of selected vertices. It was proved that the problem of determining the metric dimension of a graph is NP-hard. In this paper, the metric dimension of Toeplitz graphs with two and three generators is discussed and the exact values are found. Also, two conjectures about the exact metric dimension of Toeplitz graphs are given. [ABSTRACT FROM AUTHOR]

In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane Couette–Poiseuille flow of a third-grade non-Newtonian fluid between two horizontal parallel plates separated by a finite distance in a fuzzy environment are considered. The governing nonlinear differential equations (DEs) are converted into fuzzy differential equations (FDEs) and explain our approach with the help of the membership function (MF) of triangular fuzzy numbers (TFNs). Adomian decomposition method (ADM) is used to solve fundamental flow problems based on FDEs. In a crisp environment, the current findings are in good accord with their previous numerical and analytical results. Finally, the effect of the α -cut α ∈ 0,1 and other engineering constants on fuzzy velocity profile are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF. [ABSTRACT FROM AUTHOR]

Galactomannan from fenugreek and guar seeds were extracted, purified, and used in edible coatings, optimized via response surface methodology. The results showed that the emulsifying capacity and stability of fenugreek galactomannan (FG) and guar galactomannan (GG) increased with increase in the concentration of galactomannan up to 0.5–1%. The average optimized values of FG and GG in edible coatings were predicted to be 1.71% and 2.11% for weight loss, 0.72% and 2.14% for firmness, 1.02% and 1.44% for TSS, 0.83% and 1.36% for pH, 1.03% and 1.44% for acidity, respectively. Significant decrease in weight loss and maximum retention of firmness was observed in coated guava. The TSS increased up to a certain storage period in all treatments and decreased as the storage period progressed, whereas pH exhibited an increasing trend while a significant decrease in acidity was observed. The findings revealed that the shelf life of guava could considerably be improved by incorporating 1.24% galactomannan from GG and 1.01% from FG in the edible coating. [ABSTRACT FROM AUTHOR]

Given a finite commutative unital ring S having some non-zero elements x , y such that x. y = 0 , the elements of S that possess such property are called the zero divisors, denoted by Z S . We can associate a graph to S with the help of zero-divisor set Z S , denoted by ζ S (called the zero-divisor graph), to study the algebraic properties of the ring S. In this research work, we aim to produce some general bounds for the edge version of metric dimension regarding zero-divisor graphs of S. To do so, we will discuss the zero-divisor graphs for the ring of integers ℤ m modulo m , some quotient polynomial rings, and the ring of Gaussian integers ℤ m i modulo m. Then, we prove the general result for the bounds of edge metric dimension of zero-divisor graphs in terms of maximum degree and diameter of ζ S . In the end, we provide the commutative rings with the same metric dimension, edge metric dimension, and upper dimension. [ABSTRACT FROM AUTHOR]

The prime objective of the current study is to examine the effects of third-grade hybrid nanofluid with natural convection utilizing the ferro-particle Fe 3 O 4 and titanium dioxide TiO 2 and sodium alginate (SA) as a host fluid, flowing through vertical parallel plates, under the fuzzy atmosphere. The dimensionless highly nonlinear coupled ordinary differential equations are computed adopting the bvp4c numerical approach. This is an extremely effective technique with a low computational cost. For validation, it is found that as the volume fraction of Fe 3 O 4 + TiO 2 hybrid nanoparticles rises, so does the heat transfer rate. The current and existing results with their comparisons are shown in the form of the tables. The present findings are in good agreement with their previous numerical and analytical results in a crisp atmosphere. The nanoparticles volume fraction of Fe 3 O 4 and TiO 2 is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs) [0, 0.05, 0.1]. The TFNs are controlled by α − cut and the variability of the uncertainty is studied through triangular membership function (MF). [ABSTRACT FROM AUTHOR]

Let G = V G , E G be the connected graph. For any vertex i ∈ V G and a subset B ⊆ V G , the distance between i and B is d i ; B = min d i , j | j ∈ B . The ordered k -partition of V G is Π = B 1 , B 2 , ... , B k . The representation of vertex i with respect to Π is the k -vector, that is, r i | Π = d i , B 1 , d i , B 2 , ... , d i , B k . The partition Π is called the resolving (distinguishing) partition if r i | Π ≠ r j | Π , for all distinct i , j ∈ V G . The minimum cardinality of the resolving partition is called the partition dimension, denoted as pd G . In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets. [ABSTRACT FROM AUTHOR]

The present study especially concerns the investigation of the Couette flow and heat transfer with thermal radiation through an inclined channel. Single-wall carbon nanotube (SWCNT) and multiple-wall carbon nanotube (MWCNT) are nanoparticles embedded in the host fluid. The dimensionless highly nonlinear differential equations (DEs) are solved via numerical scheme bvp4c. The effects of the physical parameters on heat transfer are presented in the form of graphs. The results demonstrate that the heat transfer is enhanced by using solid particle frictions (SWCNT and MWCNT). The large estimation of a magnetic parameter declines the velocity component. The current and existing results with their comparisons are shown in the tabular form for the validation of our code. The current results are in good agreement with their existing results. Generally, fuzziness or uncertainty is inherent in modeling, analysis, and experimentation. Due to the uncertain environmental conditions, fuzziness broadly exists in various engineering heat transfer problems. In this work, the nanoparticles' volume fraction of the SWCNT and MWCNT is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs). The TFNs are controlled by the α − cut which has less computational effort for analyzing the fuzziness or uncertainties. Also, a comparison between the SWCNT and MWCNT through the membership function and the variability of the uncertainty is studied. [ABSTRACT FROM AUTHOR]

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]

In the present investigation, cheese milk was supplemented with vitamin A (retinol palmitate) at four different concentrations, i.e., 3,500, 4,000, 4,500, and 5,000 IU (T1, T2, T3, and T4), respectively. Treatment without supplementation of vitamin A was used as control. Prepared Cheddar cheese samples were stored at 4°C and further analyzed for vitamin A, organic acids, and fatty acids composition at different stages of ripening using high performance liquid chromatography and gas chromatography–mass spectrometry. Supplementation of vitamin A at all concentrations showed no significant effect on moisture, fat and protein contents of Cheddar cheese. After salting, recovery of vitamin A in control, T1, T2, T3, and T4 was 91.98%, 91.60%, 91.47%, 91.92%, and 91.56%, respectively. Storage period of 90 days significantly affected the fatty acids composition in control and all experimental samples. No significant difference was recorded in free fatty acids, peroxide value, and sensory characteristics in 90‐day‐old cheese samples. Practical applications: Effect of vitamin A supplementation on retention and stability of Cheddar cheese was first time investigated. These results suggest that vitamin A supplemented Cheddar cheese may be prepared by supplementing the cheese milk from 3,500 to 5,000 IU retinol palmitate with acceptable sensory properties. In modern world, the Cheddar cheese prepared with vitamin A supplementation may have huge market and can be widely used in many countries worldwide as indispensable part of wide range of fast foods and also a part of daily meals in some regions. [ABSTRACT FROM AUTHOR]