Numerical Properties Research Articles

Applications of conjunctive complex fuzzy subgroups to Sylow theory

<abstract><p>Sylow's theorems are fundamental theorems in classical group theory that are of paramount importance. The extension of these theorems into diverse fuzzy contexts emerges as a compelling area of exploration. This study introduces the novel concept of the conjunctive complex fuzzy conjugate element within the conjunctive complex fuzzy subgroup of a group, elucidating numerous crucial properties of this concept. Additionally, it propounds the notion of the conjunctive complex fuzzy <italic>p</italic>-subgroup within the conjunctive complex fuzzy subgroup (CCFSG) and delineates various indispensable characteristics associated with this construct. Additionally, the paper formulates the conjunctive complex fuzzy version of the Cauchy theorem for finite groups. Lastly, it defines the concept of the conjunctive complex fuzzy Sylow <italic>p</italic>-subgroup for a finite group and conducts a generalization of Sylow's theorems within a conjunctive complex fuzzy environment.</p></abstract>

Ionic Liquid-Catalyzed Multicomponent Synthesis of Isoxazole-5(4H)-ones: in vitro Activities and Principal Component Analysis

Heterocycles of the isoxazolone class stand out in the pharmaceutical field because they have numerous biological properties, such as antioxidant, antifungal and antibacterial properties. Thus, isoxazole derivatives have attracted the attention of organic researchers, and several procedures have been developed to obtain these compounds. The present study aimed to synthesize 17 derivatives of isoxazol-5(4H)-ones using a multicomponent reaction catalyzed by an acidic ionic liquid, which allowed yields from 20-96% of the products. To evaluate the bioactivity of the compounds, the synthesized derivatives were analyzed at various concentrations against bacteria and fungi; the derivatives, in general, showed a moderate activity of 125 μg mL-1 against the fungus Candida tropicalis (ATCC 13803) and four derivatives showed an inhibition of < 15.62 μg mL-1 for Gram-positive Staphylococcus epidermidis (ATCC 12228). Furthermore, the antioxidant potential of the derivatives was evaluated by measuring their ability to scavenge 2,2-diphenyl1-picryl-hydrazyl (DPPH) free radicals, resulting in a remarkable reduction percentage of up to 81.06%. To gain further insights into the structure-activity relationships, a principal component analysis was conducted to classify the compounds into active and inactive classes, providing a comprehensive understanding of their bioactivity profiles.

Dominacijski broj za ciklooktanske lance

Introduction/purpose: Chemical structures are conveniently represented by graphs where atoms are nodes (vertices) and chemical bonds are branches (lines) in the graph. A graphical representation of a molecule provides a lot of useful information about the chemical properties of the molecule. It is known that numerous physical and chemical properties of molecules are highly correlated with theoretical invariants of graphs, which we call topological indices. One such theoretical invariant is the dominance number. The aim of this research is to determine the k-dominance number for cyclooctane chains 𝐶𝑂𝐶𝑛 1 , 𝐶𝑂𝐶𝑛 2 , 𝐶𝑂𝐶𝑛 3 and 𝐶𝑂𝐶𝑛 4 , for k ∈ {1,2,3}, n ∈ 𝑁. Methods: The cyclooctane chain is a chain of octagons connected by a single line. The vertices of the octagon are treated as nodes of the graph, and the sides and the line connecting them, as branches in the graph. Using mathematical methods, k-dominance was determined on one octagon, k∈{1,2,3}. Then, by representing the cyclooctane chains 𝐶𝑂𝐶𝑛 1 , 𝐶𝑂𝐶𝑛 2 , 𝐶𝑂𝐶𝑛 3 and 𝐶𝑂𝐶𝑛 4 , in a convenient, isomorphic way, we determined their k-dominance number, k∈{ 1,2,3}. Results: Determining k-dominance, k∈{1,2,3}, for 4 cyclooctane chains 𝐶𝑂𝐶𝑛 1 , 𝐶𝑂𝐶𝑛 2 , 𝐶𝑂𝐶𝑛 3 and 𝐶𝑂𝐶𝑛 4 , we obtained 12 different formulas to calculate their k-dominance number. All formulas are composed of several alternative algebraic expressions, the selection of which is conditioned by the divisibility of the number n by the number 2, 3 or 4, depending on the type of cyclooctane chain and k-dominance to be determined. The results of the research are fully presented in the paper through mathematically proven theorems and graphical representations. Conclusion: The results show that the k-dominance numbers, k∈{1,2,3}, on cyclooctane chains 𝐶𝑂𝐶𝑛 1 , 𝐶𝑂𝐶𝑛 2 , 𝐶𝑂𝐶𝑛 3 and 𝐶𝑂𝐶𝑛 4 , are determined and explicitly expressed by mathematical expressions. They also indicate the possibility of their application in molecular graphs of cyclooctane rings, in computational chemistry, chemical and biological industry.

Giant intrinsic piezoelectricity in 2D hybrid organic-inorganic perovskites [C6H11NH3]2MX4 (M = Ge, Sn, Pb; X = Cl, Br, I).

2D-piezoelectric materials are attractive for micro-electromechanical systems (MEMS), medical implants and wearable devices because of their numerous exceptional properties. 2D-hybrid organic-inorganic perovskites (HOIPs) have attracted extensive research interest due to their merits of structural diversity, good mechanical flexibility, and ease of fabrication. The electronic energy band, charge density and the elastic properties of 2D-HOIP-[C6H11NH3]2MX4 (M = Ge, Sn, Pb; X = Cl, Br, I) were investigated using first-principles calculations. The excellent piezoelectricity of 2D-HOIP-[C6H11NH3]2MX4 has been analyzed in detail. More importantly, 2D-[C6H11NH3]2MX4 have giant intrinsic positive and negative out-of-plane piezoelectric coefficients under the effect of van der Waals interaction. The d31 and d32 of [C6H11NH3]2SnBr4 are 82.720 pm V-1 and -36.139 pm V-1, respectively, which are among the largest piezoelectric coefficients among all kinds of atomic-thick 2D materials reported. The high flexibility together with the giant out-of-plane piezoelectricity would endow these 2D-HOIP-[C6H11NH3]2MX4 with potential applications in ultrathin piezoelectric cantilever and diaphragm devices.

Recent progress in TiO2-biochar-based photocatalysts for water contaminants treatment: strategies to improve photocatalytic performance.

Toxic organic pollutants in wastewater have seriously damaged human health and ecosystems. Photocatalytic degradation is a potential and efficient tactic for wastewater treatment. Among the entire carbon family, biochar has been developed for the adsorption of pollutants due to its large specific surface area, porous skeleton structure, and abundant surface functional groups. Hence, combining adsorption and photocatalytic decomposition, TiO2-biochar photocatalysts have received considerable attention and have been extensively studied. Owing to biochar's adsorption, more active sites and strong interactions between contaminants and photocatalysts can be achieved. The synergistic effect of biochar and TiO2 nanomaterials substantially improves the photocatalytic capacity for pollutant degradation. TiO2-biochar composites have numerous attractive properties and advantages, culminating in infinite applications. This review discusses the characteristics and preparation techniques of biochar, presents in situ and ex situ synthesis approaches of TiO2-biochar nanocomposites, explains the benefits of TiO2-biochar-based compounds for photocatalytic degradation, and emphasizes the strategies for enhancing the photocatalytic efficiency of TiO2-biochar-based photocatalysts. Finally, the main difficulties and future advancements of TiO2-biochar-based photocatalysis are highlighted. The review gives an exhaustive overview of recent progress in TiO2-biochar-based photocatalysts for organic contaminants removal and is expected to encourage the development of robust TiO2-biochar-based photocatalysts for sewage remediation and other environmentally friendly uses.

Scalar Auxiliary Variable Techniques for Nonlinear Transverse String Vibration

The simulation of string vibration is of fundamental importance in musical acoustics. If the vibration amplitude is large then nonlinear phenomena, resulting from large deformations, cannot be neglected, and lead to perceptually salient features. Energy-conserving simulation algorithms found in the literature rely on tailored discretisation choices, making them model–specific. Recently, energy quadratisation–based techniques have been developed, under the assumption that the potential energy is single-signed. These methods allow for the solution of a variety of different nonlinear systems with the same time-stepping procedure, requiring only the evaluation of a specific nonlinear potential. Moreover, they possess an exact numerical energy conservation property, and permit efficient operation. Such methods were previously employed for solving nonlinear string models. In this paper, nonlinear models of transverse string vibration are first semi-discretised in space by means of both finite differences and modal methods. The resulting equations are solved through the use of the Scalar Auxiliary Variable (SAV) technique. Results are then compared against those obtained with model – specific numerical integrators in terms of Efficiency and accuracy.

Phytochemical and medicinal profiling of Russula vinosa Lindbl (RVL) using multiomics techniques

Russula vinosa Lindbl (RVL) is a multifunctional edible fungus that has recently gained widespread attention due to its numerous nutritious, delicious, and medicinal properties. However, little attention has been directed toward analyzing comprehensive phytochemical profiling and bioactivity in RVL. This study aimed to evaluate the phytochemical and medicinal profiling of RVL systematically. Herein, we characterized global RVL phytochemical profiling using the LC/GC-MS-based multiomics strategy through initial methodological optimization. A total of 633 metabolites were identified using untargeted multiomics, with fatty acids, amino acids, polyphenols, terpenoids, organic acids, sugars, and phospholipids as the primary metabolites. Polyphenols served as the main active components by quantitative analysis and antioxidant evaluation, impling that they may be related to antitumor effects. Moreover, based on phytochemical profiling, the potential gene targets and mechanisms of anticancer properties of RVL were explored through network pharmacology. The significance of this study lies in expanding our understanding of the phytochemical and bioactive components of RVL and providing references for its further utilization and exploitation. Therefore, RVL could be an excellent raw material for the food, nutraceutical, and pharmaceutical industries due to its richness in nutrients and bioactive ingredients.

Prediction of a two-dimensional high Curie temperature Weyl nodal line kagome semimetal.

Kagome lattices may have numerous exotic physical properties, such as stable ferromagnetism and topological states. Herein, combining the particle swarm structure search method with first-principles calculations, we identify a two-dimensional (2D) kagome Mo2Se3 crystal structure with space group P6/mmm. The results show that 2D kagome Mo2Se3 is a 100% spin-polarized topological nodal line semimetal and exhibits excellent ambient stability. The band crossing points form two nodal loops around the high-symmetry points Γ and K. On the other hand, Mo2Se3 shows intrinsic ferromagnetism with a large magnetic moment of 3.05 μB per Mo atom and magnetic anisotropy energy (MAE) of 4.78 meV. Monte Carlo simulations estimate that Mo2Se3 possesses a high Curie temperature of about 673 K. In addition, its ferromagnetic ground state can be well preserved under external strain, and the MAE can be improved by increasing the strain. More importantly, the position of each nodal line can be adjusted to the Fermi level through hole doping. This multifunctional 2D magnetic material that combines spin and topology has great potential in the field of nanoscale spintronic devices.

Comparative study on the effect of substrates on electrical properties of tin and chromium thin films

In thin film technology, substrate materials happen to be one of the deposition parameters that determine the physical properties of films. Hence, soda-lime glass and quartz continue to be the widely utilized substrate materials because of their high-frequency performance, price, and surface quality. For certain applications, various substrate materials that provide an acceptable compromise for the work at hand are required. Soda-lime glass and quartz have been chosen as the substrates for the tin and chromium thin films that will be produced via thermal evaporation in a vacuum. A comparative study on the electrical properties of chromium films was made in the light of Fuchs–Sondheimer and Mayadas–Shatzkes theories. Numerous physical properties, including resistivity of infinitely thick film, sticking coefficient, conduction electron mean free, etc., may be determined from resistivity-thickness data.

Lactobacillus reuteri's multifaceted role in mitigating ionizing radiation-induced injury in Drosophila melanogaster.

The numerous beneficial probiotic properties of Lactobacillus reuteri (L. reuteri) include decreasing metabolic syndrome, preventing disorders linked to oxidative stress, improving gut flora imbalances, controlling immunological function, and extending life span. Exposure to ionizing radiation is closely associated with several disorders. We examined the protective and salvaging effects of L. reuteri on ionizing radiation-induced injury to the intestinal tract, reproductive system, and nervous system of Drosophila melanogaster. We also examined its effects on lifespan, antioxidant capacity, progeny development, and behavioral aspects to assess the interaction between L. reuteri and ionizing radiation-induced injury. The findings demonstrated that L. reuteri improved the median survival time following irradiation and greatly extended its lifespan. In addition, it raised SOD activity, reduced ROS levels in intestinal epithelial cells, and increased the quantity of intestinal stem cells. Furthermore, L. reuteri enhanced the adult male flies' capacity to move. It also successfully safeguarded the generations' growth and development. L. reuteri dramatically enhanced expression of the AMPKα gene and regulated expression of its pathway-related gene, mTOR, as well as the autophagy-related genes Atg1 and Atg5 in female Drosophila exposed to irradiation. Notably, no prior reports have been made on the possible effects of L. reuteri on injuries caused by irradiation. As a result, our research offers important new information regarding L. reuteri's possible role as a shield against ionizing radiation-induced injury.

Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization

This contribution proposes a nonlinear and dissipative infinite-dimensional port-Hamiltonian (PH) model for the dynamics of geometrically exact strings. The mechanical model provides a description of large deformations including finite elastic and inelastic strains in a generalized Maxwell model. It is shown that the overall system results from a power-preserving interconnection of PH subsystems. By using a structure-preserving mixed finite element approach, a finite-dimensional PH model is derived. Eventually, midpoint discrete derivatives are employed to deduce an energy-consistent time-stepping method, which inherits discrete-time dissipativity for the irreversible system. An example simulation illustrates the numerical properties of the present approach.

Handy formulas for binomial moments

Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and simplified enough for intended applications. This paper introduces novel formulas for binomial moments in the form of polynomials in the variance rather than in the success probability. The obtained formulas are arguably better structured, simpler and superior in their numerical properties compared to prior works. In addition, the paper presents algorithms to derive these formulas along with working implementation in Python’s symbolic algebra package. The novel approach is a combinatorial argument coupled with clever algebraic simplifications which rely on symmetrization theory. As an interesting byproduct asymptotically sharp estimates for central binomial moments are established, improving upon previously known partial results.

Evaluation of secondary metabolites and antibacterial effect of Boerhavia diffusa roots with chromatographic studies

India has a vast diversity of medicinal herbs. Around 3,000 years ago, these herbs were acknowledged and used as medicinal plants helpful for treating people. New scientific research has established that some plants and herbs have presence of many active compounds and possess specific pharmacological properties.Boerhavia diffusa is one of the renowned medicinal plants used to treat large number of human ailments as mentioned in Ayurveda. The plant in whole or its peculiar parts (aerial parts and roots) have a numerous medicinal properties. It shows antibacterial, hepato-protective, antistress and also in treatment of stress, abdominal pain, inflammation and jaundice. Various phytochemical, Pharmacological, experimental and clinical investigations were done on Boerhavia diffusa by many scientists to clearly understand the ancient ayurvedic usage of punarnava. The evaluation of secondary metabolites and antibacterial activities of punarnava root extract were investigated on pathogens using the well diffusion method. HPTLC analysis of Boerhavia diffusa extracts were also carried out in different solvent.

Bioactivities of Nek Kara (Dillenia excelsa (Jack) Martelli ex. Gilg) leaves from forest medicinal plants of Kutai Ethnic

The utilization of traditional medicine and treatment within the community of Kutai Kartanegara, East Kalimantan, Indonesia is characterized by a wide range of practices. Medicinal plant extracts containing secondary metabolites, possessing diverse molecular structures and biological activities, exhibit promising potential for the development of medicines targeting various diseases. Phenolic compounds, present in plants, exhibit numerous biological effects, including antioxidant and antimicrobial properties. These secondary metabolite compounds play a crucial role in safeguarding against disease-induced damage. Nek Kara (Dillenia excelsa (Jack) Martelli ex. Gilg), a forest plant, has been traditionally employed by the local population for the treatment of diabetes. The objective of this study is to investigate the biological activities of the ethanol extract derived from Nek Kara leaves. The analysis encompasses the examination of phytochemical content, toxicity, as well as antioxidant and antimicrobial activities of the extract. The antioxidant activity is assessed through DPPH (1,1-diphenyl-2-picrylhydrazyl) scavenging activity using a spectrophotometer, while toxicity is determined via the BSLT (Brine Shrimp Lethality Test). The antimicrobial activity is evaluated using the diffusion method. The findings reveal the presence of phytochemical content, such as alkaloids, flavonoids, tannins, and steroids, within the ethanol extract derived from Nek Kara leaves. The BSLT results indicate the absence of toxic bioactivities in the ethanol extract. Furthermore, the Nek Kara leaf extract demonstrates potent antioxidant activity and exhibits inhibitory effects on the growth of bacterial and fungal colonies.

CONTENT OF MACRO- AND MICROELEMENTS IN CHEESES PRODUCED WITH THE ADDITION OF DIFFERENT SPICES

<p>Cheese is a dairy product used directly for human consumption or indirectly as an ingredient of other foods or ready meals. Being an extremely valued product, cheese is a concentrated source of proteins, vitamins and minerals, especially calcium, phosphorus and magnesium. Various spices are used to enhance the taste of food, which also have numerous medicinal properties. The aim of this study was to examine the effect of the addition of different spices on the mineral composition of cheeses, obtained by heat-acid coagulation of milk. There were six different samples of cheese produced in the milk processing plant (mini cheese factory). The first sample was taken as a control one, with no addition of spices, and the other five were produced with 0.5% addition of different spices (oregano, basil, parsley, rosemary, and chives). The total ash content and the content of macro- and microelements were determined in the tested cheese samples. It was established that the addition of different spices has a statistically significant (p<0.05) effect on the content of macro- and microelements in the produced cheeses. The total content of macro-elements ranged from 612.55 mg/100g to 811.81 mg/100g, of which sodium had the largest share (from 293.61 mg/100g to 389.20 mg/100g), as well as calcium (from 74.13 mg/ 100g to 278.12 mg/100g). The total content of microelements in the tested spice-containing cheeses ranged from 7.317 mg/100g to 9.360 mg/100g, of which the most abundant was zinc, the content of which was between 5.903 mg/100g and 7.351 mg/100g.</p>

Information Retrieval Evaluation Measures Defined on Some Axiomatic Models of Preferences

Information retrieval (IR) evaluation measures are essential for capturing the relevance of documents to topics and determining the task performance efficiency of retrieval systems. The study of IR evaluation measures through their formal properties enables a better understanding of their suitability for a specific task. Some works have modeled the effectiveness of retrieval measures with axioms, heuristics, or desirable properties, leading to order relationships on the set where they are defined. Each of these ordering structures constitutes an axiomatic model of preferences (AMP), which can be considered as an “ideal” scenario of retrieval. Based on lattice theory and on the representational theory of measurement, this work formally explores numeric, metric, and scale properties of some effectiveness measures defined on AMPs. In some of these scenarios, retrieval measures are completely determined from the scores of a subset of document rankings: join-irreducible elements. All the possible metrics and pseudometrics, defined on these structures are expressed in terms of the join-irreducible elements. The deduced scale properties of the precision, recall, F -measure, RBP , DCG , and AP confirm some recent results in the IR field.

Assessment of the Anti-Amyloidogenic Properties of Essential Oils and Their Constituents in Cells Using a Whole-Cell Recombinant Biosensor.

Essential oils exhibit numerous medicinal properties, including antimicrobial, anti-inflammatory and antioxidant effects. Recent studies also indicate that certain essential oils demonstrate anti-amyloidogenic activity against β-amyloid, the protein implicated in Alzheimer's disease. To investigate whether the anti-aggregating properties of essential oils extend to α-synuclein, the protein involved in Parkinson's disease, we constructed and employed a whole-cell biosensor based on the split-luciferase complementation assay. We validated our biosensor by using baicalein, a known inhibitor of α-synuclein aggregation, and subsequently we tested eight essential oils commonly used in food and the hygienic industry. Two of them, citron and sage, along with their primary components, pure linalool (the main constituent in citron essential oil) and pure eucalyptol (1,8-cineole, the main constituent in sage essential oil), were able to reduce α-syn aggregation. These findings suggest that both essential oils and their main constituents could be regarded as potential components in functional foods or incorporated into complementary Parkinson's disease therapies.

Optimization of cultural and nutritional conditions to enhance mycelial biomass of Cordyceps militaris using statistical approach.

Cordyceps militaris is a fungus with numerous therapeutic properties that has gained worldwide popularity due to its potential health benefits. The fruiting body of this mushroom is highly expensive and takes a longer time to produce, making mycelial a sustainable and cost-effective alternative. The study investigates and optimizes cultural and nutritional conditions to maximize mycelial biomass. The initial optimization was done by the conventional single-factor approach, followed by Plackett-Burman design to screen the most significant variables, with yeast extract, temperature, and glucose being the most significant, contributing 11.58%, 49.74%, and 27.98%, respectively, in mycelial biomass production. These variables were then optimized using response surface methodology (RSM) based on central composite design (CCD). The study observed that temperature and glucose had the highest impact on mycelial biomass, with p-values of 0.0128 and 0.0191, respectively. Under the optimized conditions, temperature 20°C, glucose 2.5% (w/v), and yeast extract 0.8% (w/v), the maximal yield of mycelial biomass reached 547 ± 2.09mg/100mL, which was 1.95-fold higher than the yield in the basal medium. These findings suggest that optimizing the cultural and nutritional conditions can enhance mycelial biomass production of Cordyceps militaris, offering a sustainable and cost-effective source of this valuable fungus.

EEGProgress: A fast and lightweight progressive convolution architecture for EEG classification

Because of the intricate topological structure and connection of the human brain, extracting deep spatial features from electroencephalograph (EEG) signals is a challenging and time-consuming task. The extraction of topological spatial information plays a crucial role in EEG classification, and the architecture of the spatial convolution greatly affects the performance and complexity of convolutional neural network (CNN) based EEG classification models. In this study, a progressive convolution CNN architecture named EEGProgress is proposed, aiming to efficiently extract the topological spatial information of EEG signals from multi-scale levels (electrode, brain region, hemisphere, global) with superior speed. To achieve this, the raw EEG data is permuted using the empirical topological permutation rule, integrating the EEG data with numerous topological properties. Subsequently, the spatial features are extracted by a progressive feature extractor including prior, electrode, region, and hemisphere convolution blocks, progressively extracting the deep spatial features with reduced parameters and speed. Finally, the comparison and ablation experiments under both cross-subject and within-subject scenarios are conducted on a public dataset to verify the performance of the proposed EEGProgress and the effectiveness of the topological permutation. The results demonstrate the superior feature extraction ability of the proposed EEGProgress, with an average increase of 4.02% compared to other CNN-based EEG classification models under both cross-subject and within-subject scenarios. Furthermore, with the obtained average testing time, FLOPs, and parameters, the proposed EEGProgress outperforms other comparison models in terms of model complexity.

Application of Methods of Recommendations in the Analysis of Computer Components

Today, the improvement of information and technical assistance to users through information technology is relevant. To improve the design of computers, we analyze its components and study the architecture, as well as the process of improving the functionality of a computer. We conducted an analytical review of existing software solutions for analyzing computer components. We consider models for forming a set of recommendations taking into account the wishes of the user. Given the specifics of the analysis of the problem situation, it is proposed to unite users into groups. Mixed categorical-numerical clustering was used to search for user groups. This took into account the numerical (Item ratings) and demographic properties of users, as well as the sparsity coefficient of the User-Item Matrix. His algorithm of operation of the hybrid recommendation system is described, which proposes to take into account the user's requirements when analyzing and generating component variability for a computer, a hybrid model of providing recommendations with a weighted weight factor is used. UML provides a conceptual model of the system. The recommendation system allows the user to use computer analysis of components, which will offer the best components and, most importantly, the most suitable details. If the user wants a completely new computer, he can use the assembly designer. Components will be selected for the user request, or a part of the computer will be offered. The target audience of the program is PC users of any age.