Since its seminal introduction by Molodtsov in 1999, soft set theory has evolved into a pivotal mathematical paradigm for the formal representation and management of uncertainty, offering a flexible and conceptually robust alternative to classical approaches. Its methodological versatility and abstract generality have fostered an expanding body of theoretical inquiry and practical deployment across diverse scientific domains. Central to the structural framework of soft set theory are its operations, which constitute the algebraic backbone of the theory and have consequently remained an enduring focus of research interest. Within this operational landscape, several soft product variants of the soft sets have been introduced; however, the extant literature provides only fragmentary examinations of their interrelations as regard soft subsets. The present study seeks to rectify this deficiency by delivering a comprehensive and rigorous analysis of this issue, with particular reference to the fundamental conditions which soft product, starting with intersection and union, is is soft subset of another soft product, and when these soft products are equal. That is, the study has been further expanded to provide a deeper analysis of which soft product is a subset of another and the circumstances under which they become equal. In pursuing this objective, the investigation elucidates a series of structural and distributive properties that not only reinforce the algebraic coherence of the soft product variants of the soft sets but also reveal their potential to generate rich algebraic configurations. Thus, the present theoretical exposition advances the foundational algebraic framework of soft set theory and contributes to a deeper understanding of its operational architecture. Beyond its intrinsic theoretical relevance, this deepened analysis is of substantial theoretical significance, as it elucidates the hierarchical and structural relationships among distinct soft products, thereby enhancing the algebraic understanding of the internal organization of soft set theory and facilitating the identification of operational dependencies and equivalences.
Control chart is not only used in manufacturing process for monitoring quality characteristics of the output it is extensively used in the field of reliability. It can be used to monitor the number of failures or breakdown of a machine, time between failure, life time data (censored or un censored). A number of researchers invested their time and thought in developing control chart techniques applicable in the field of reliability in the past few decades. In this paper we have summarized different methodologies available in the literature for controlling reliability data and discussed their merits and demerits.
Soft set theory has developed into a crucial mathematical paradigm for the formal representation and management of uncertaintysince Molodtsov's groundbreaking 1999 introduction. It provides a versatile and conceptually sound substitute for traditionalmethods. Its abstract generality and methodological adaptability have encouraged a growing corpus of theoretical research and realworld application in a variety of scientific fields. Soft set theory's operations are essential to its structural framework since they formthe algebraic foundation of the theory and have thus continued to be a subject of intense academic interest. Several soft productversions of the soft sets have been introduced within this operational landscape; nevertheless, the existing literature only offerspartial analyses of their relationships with respect to soft subsets. By providing a thorough and rigorous examination of this problem,the current study aims to address this shortcoming. It specifically addresses the essential circumstances under which one soft product,starting with symmetric difference and symmetric difference complement, is a soft subset of another soft product and when these softproducts are equal. In other words, the study has been extended to offer a more thorough examination of which soft product is asubset of another and the conditions that render them equal. In order to achieve this goal, the study clarifies a number of distributiveand structural characteristics that support the algebraic coherence of the soft product variations of the soft sets and demonstrate theircapacity to produce complex algebraic configurations. Therefore, the current theoretical exposition adds to a better understanding ofthe operational architecture of soft set theory and advances its fundamental algebraic framework. Beyond its inherent theoreticalvalue, this expanded analysis has significant theoretical importance because it clarifies the structural and hierarchical relationshipsbetween various soft products, improving algebraic comprehension of the internal structure of soft set theory and making it easier toidentify operational dependencies and equivalencies.
Construction industry is a catalyst for holistic development that drives economic growth, enhances social equity, pioneers’ technological advancements, and promotes environmental stewardship. The execution of construction practices requires resources, which include financial, technical and human. Despite recognition of environmental degradation and economic opportunities, there remains a notable gap in understanding how construction actors reconcile cost-efficiency with sustainability, particularly in applying financial planning tools to curb cost overruns while promoting environmentally responsible practices. This paper assesses construction practices in building development projects in Ruiru Municipality, Kenya. Data from 95 building development projects sampled through stratified sampling based on project value followed by administration of questionnaires to respondents comprising of contractors, site supervisors and project managers. The data was analyzed using frequency and percentages. The findings revealed that, while material planning and site preparation are generally wellimplemented, critical deficiencies in financial and human resource planning, particularly within residential and religious projects. The study recommends introducing targeted capacity building initiatives to enhance financial and human resourceplanning by training stakeholders in budget forecasting, cost control, and workforce scheduling, and by developing standardized frameworks to ensure consistency and accountability.
Since its introduction by Molodtsov, soft set theory has developed in prominence as an innovative method for dealing with uncertainty-related problems and modeling uncertainty. Soft set operations, the theory's main concept, have served as the foundation for theoretical and practical advances in the theory; thus, deriving the algebraic properties of soft set operations and studying the algebraic structure of soft sets associated with soft set operations has piqued researchers' interest continuously. Many soft union operations have been proposed in soft set theory, but there are some differences. Even though the definition of restricted union is widely acknowledged in the literature and applied in many studies, it is still lacking in its current form owing to the fact that a specific case where the soft sets' parameter sets may be disjoint is ignored in the definition. As a result, all the cases in the theorems are not taken into account, leading to errors or deficiencies in the studies that use this operation or investigate this operation’s properties. Regarding this, a thorough examination of the properly defined restricted union operation and extended union operation, together with their appropriate distributions and properties, as well as the appropriate algebraic structures connected to these soft set operations, is conspicuously lacking in the body of current literature. This study is primarily intended to fill this critical and significant gap by first fixing the presentational flaws of the restricted union definition and updating it. Furthermore, in many works on these operations, numerous theorems were offered without their proofs, or the proofs had some incorrect parts. In this paper, all the proofs based on function equality are supplied regularly, and the relations between the concept of soft subset and restricted and extended union operations are obtained for the first time with their extensive proofs. Furthermore, we explore numerous novel properties of these operations as analogies and counterparts of the union operation in classical set theory. We show that when restricted/extended union operations are combined with other types of soft set operations, several significant algebraic structures are formed, including monoid, bounded semi-lattice, semiring, hemiring, bounded distributive lattice, Bool algebra, De Morgan Algebra, and MV-algebra with detailed explanations. In this regard, this overall study represents the most comprehensive analysis of restricted union and extended union in the literature to date, as it covers all of the earlier important research on this topic with the corrected theorems and their proofs, thus advancing the theory by bridging a significant gap in the literature, serving as a guide for newcomers to this popular theory, and providing insight for further future research.
Since its introduction by Molodtsov in 1999, soft set theory has gained significance as an innovative approach for handling uncertainty-related issues and modeling uncertainty. It has several applications in both theoretical and real-world settings. Researchers have been interested in soft set operations, the theory's fundamental concept, since its inception. Several restricted and extended soft set operations, one of which is restricted and extended difference operation, were defined, and their characteristics were partially investigated. The present study gives a full analysis of the properties of restricted and extended difference soft set operations, particularly in comparison to the fundamental characteristics of the difference operation existing in classical set theory, as the existing studies regarding restricted and extended set operations are quite incomplete in that all the properties of the operations have been examined in depth. In this regard, this paper is a complete study of the aforesaid soft set operations. We also observe several noteworthy properties that bear analogies to the difference operation of classical set theory. Furthermore, by investigating the distributions of these operations over all other types soft set operations including the new types of soft set operations, and taking into account the algebraic properties of the operation and its distribution rules, we demonstrate that the extended difference operation, when combined with other kinds of soft set operations, forms several significant algebraic structures, such as semiring and near-semirings in the collection of soft sets over the universe, This theoretical study has considerable significance both theoretically and practically, as the fundamental concept of the soft set theory is the operations of soft sets since they serve as the foundation for numerous applications, including cryptology, as well as the decision-making processes as correctly as possible.
The effect of ethanol concentration in the feed (XFAZ) and feed thermal conditions (FTCs) on ethanol dehydration plant performance was investigated. The heterogeneous azeotropic distillation model with cyclohexane as an entrainer was built using Aspen Plus® V10 software. Non-random two liquid Redlich-Kwong (NRTL-RK) thermodynamic model was used for property analysis and performance prediction. The distillate product purity, streams compositions, flows and energy requirements were monitored. The XFAZ was varied from 81% to 86% following pre-concentration while FAZ ranged between 10 and 20 kmol/h. The distillate purity ranging between 95.5% and 99.84% mol ethanol was obtained and the plant consisted of a pre-heater, decanter and twin distillation columns operational blocks. Results show that XFAZ, FAZ and FTCs are the key operating parameters affecting plant performance. The main column operates at higher throughput resulting into higher condenser and reboiler duties compared to the recycle column leading to a higher Qc/Qr ratio for the main column. Similarly, the ratios of Qc1/F3 and Qr1/F3 were higher for the main column as compared to the ratios of Qc2/F3 and Qr2/F3 for the recycle column. Moreover, the ratio of the duty to FAZ was also higher for main column than recycle column. The study concluded that for higher energy efficiency and product purity, the plant should be operated with XFAZ= 0.81 to 0.86 mol/mol and at higher flows, FAZ= 16 to 20 kmol/h, F5>11.8 kmol/h and increased recycle stream flow rate (>1.2 kmol/h).
Cement is a key material in the construction industry, and its quality significantly influences the strength and durability of structures. This study aims to analyze the chemical composition of different brands of cement commercialized in Burundi using Wavelength Dispersive X-ray Fluorescence (WD-XRF). The results are compared with international standards (ASTM C150-12 and EAS 18-1:2001) to assess compliance and quality. The Congolese made GLC 42.5N cement appears to meet key quality parameters, including a balanced C3S/C2S ratio and acceptable AM and SM values. The results provide insights into the cement performance characteristics, particularly their early and long-term strength development. However, further mechanical testing is recommended to assess durability.
As the bee products such as honey, have inhibitory effects against bacteria and fungi, several ethnic communities have used them to manage forms of disorders. In this study, honey taken from tobacco growing area was screened for their antimicrobial activity, quality and phytochemical screening. All honey samples were also subjected for determination of moisture content, reducing sugars, pH and ash contents. By serial microdilution method, antimicrobial activity of honey samples was assessed against nine pathogenic bacterial and two fungal strains namely S. aureus, P. mirabilis, E. faecalis, E. faecium, K. pneumoniae, K. oxytoca, E. coli, P. aeruginosa, A. niger, C. albicans and C. neoformans respectively. Findings from this study revealed that sampled honey was more sensitive towards tested pathogenic microbes. Additionally, all honey parameters analyzed are within acceptable international standards as per Tanzanian Honey Quality Guideline and European Honey Commission. Additionally, the presence of bioactive constituents in honey under investigation that facilitates the utilization of honey in management of diseases in Africa brings a conclusion that honey from tobacco growing area is of quality and therefore recommended for human consumption.
This study analyzed the axial temperature, K-value, molar composition, flows and enthalpy profiles for the main and recycle column of an azeotropic distillation plant. The overall process was developed block-wise via Aspen Plus® V10 software. Nonrandom two liquid Redlich-Kwong (NRTL-RK) thermodynamic model was selected as base method for property analysis and performance prediction. Ethanol concentration in the feed, XFAZ was varied from 81% to 86% and tested for each feed flow rate, FAZ ranging from 10 to 20 kmol/h. Results show that temperature and hence enthalpy increases down the column from 56℃ in stage 1 (condenser) to 80℃ in stage 12 (reboiler). Molar composition across the column stages continuously varies due to changes in temperature and phase distribution. The K-value profiles were non-uniform with values changing between 0.4 to 1.6 mol/mol for ethanol, 0 to 1 mol/mol for water and 0 to 42 mol/mol for cyclohexane. The liquid and vapor flows were approximately 8.24 and 12.55 times greater than the liquid and vapor flows in the recycle column. Further, results show that increasing FAZ and XFAZ resulted into decrease in number of stages in water-free extractive region and enhances the dehydration plant performance in terms of product ethanol purity. The study concluded that the axial column profiles provide a powerful tool for effective design and optimization of a distillation column towards higher energy efficiency and dehydration performance
Native fruits and vegetables have medicinal and nutritional value despite that their potential are not well understood by the community. A total of 120 respondents participated in evaluating the mostly consumed species. The assessment of their antioxidant level was conducted at Kiwere ward in 2023 through a questionnaire distributed in specifically selected areas. Samples for extraction were collected using standard methods and were evaluated calorimetrically with a UV-Visible Spectrophotometer Model 6305 Jenway, UK. DPPH method was used to assess the antioxidant contents. The chi-square test and post hoc tests were employed to determine statistical differences among respondents and in antioxidant contents, respectively. Gallic acid ranged from 100.894 to 176.033 mg GAE/g, and the total flavonoid level ranged from 41.248 to 177.991 mg RUE/g. Vitex mombasae demonstrated the highest antioxidant capacity with galic acid 176.033 mg. Antiradical activities for the fruits varied from 0.477 to 0.577 taurine (TAU) for total phenolic content and 0.433 to 5.68 TAU for total flavonoid levels. The highest value was recorded for Solanum elaeagnifolium (42.70 TAU). There was a statistically significant difference among the studied species (p<0.001). Based on their antioxidant values, All studied species exhibit significant antioxidant potential. The community is encouraged to increase the consumption of the native fruits and vegetables. More studies on mineral composition are recommended for the studied species in order to add value to the nutritional values of these species.
One of the key components of computer hardware is the design of processor that comes under the domain of Electronic Engineering. To design a microprocessor, first an instruction set is chosen and a microarchitecture is defined and the entire module can be described by means of Hardware Description Language. After the processor is designed it is subjected into design verification and validation and then it is fabricated. The design of the RISC-V processor is too simple as the architecture is open source and consists of load/store architecture. The main aim of the paper is to design the synchronous RISC-V reversible gates processor using VerilogHDL and to figure out performance issues such as area, power dissipation and execution time. The synchronous processors reduce crosstalk thereby integrating multi rate circuits easily along with component reusability and less power dissipation. The processor with reversible logic gates have an advantage that the data stored cannot be erased as it has one to one mapping. In this paper, the 32 bit synchronous processor is designed with RISC-V architecture and several modules like jump adder, Program Counter Adder, Arithmetic and Logic Unit, Arithmetic and Logic Control Unit, Program Counter Mux, Control Unit, Instruction Memory, Register, Write Data Mux, ALU Decoder, Data Memory, Immediate Generation, Program Counter Assign are designed using Verilog HDL and Simulation results are obtained using testbench code collected from GitHub repository titled VLSI System Design. The analogy between Synchronous Processor and Asynchronous Processor, RISC-V and MIPS architecture, Reversible and Irreversible Logic Gates are analysed and performance metrics like execution time, power consumption and area are significantly reduced as the synchronous processor is designed with one to one mapping logic which can be used in quantum applications.
A two-parameter zero-inflated Poisson (ZIP) distribution is commonly used for modelling the defects data in the outputs of a high- quality process. Usually, online inspection system is an integral part of a high-quality process and therefore, most of the control charts for monitoring high-quality processes are developed assuming that all the outputs are inspected one by one. However, high-quality processes without online inspection system are not uncommon in reality. In such cases, a feasible strategy for monitoring a high-quality process can be to inspect offline a large number of items collected from the outputs of a shift or day. Recently, Pal et al. (2025) have proposed two one-chart schemes (Max chart and DS chart) for joint monitoring of the two parameters of a ZIP process using offline samples of large size. The in-control and out-of-control performances of these charts are found to be very satisfactory. However, no closed form equations are available for determination of the control limits of these charts. Therefore, simulation studies are needed for designing these charts, which are cumbersome for many practitioners. In this article, approximate equations are derived for determination of the control limits and β-risks of these charts. Subsequently, simulation studies are carried out for validation of the derived approximate equations. The results of simulation studies reveal that the derived equations for determination of the UCLs of these charts work quite well if the acceptable type I error, a ≥ 0.02. The derived formula for the computation of β - risk also works quite well for a Max chart if sample size, n ≥ 500.
This paper presents the effect of distillate purity on the performance of ethanol-water distillation column before azeotrope. The factors affected include the required number of stages, reflux ratio, reboiler and condenser duties, investigated using different feed thermal conditions. The model was set using Aspen Plus® V10 simulation software and used to establish the impact of operating conditions due to high distillate purity. The aim was to increase distillate purity while minimizing energy consumption. The research highlights the importance of modeling and simulation for optimizing distillation processes to reduce energy consumption. The feed flow rate was 1000 kmol/h, with composition ranging from 0.1 to 0.6 mol/mol. The number of stages varied from 8 to 20 while the reflux ratio ranged between 1 and 8. The required number of stages, reflux ratio, condenser and reboiler duties increased with increasing desired distillate purity. The reboiler and condenser duties increased with distillate purity according to 3rd order polynomial functions. It was concluded that the pre-concentration column can concentrate dilute solutions to higher purity closer to the azeotropic point. Further studies were recommended on the non-linear behavior and large energy consumption.
Due to its geographical position, Burundi benefits from several soil genesis factors and large variations in microclimates to which are added water resources, which give to Burundi a floral heritage of great diversity. This study therefore aimed to assess the physicochemical properties (density, refractive index, acid index and ester index) as well as the associated organoleptic characteristics (odor, color and appearance), of the essential oil extracted by hydrodistillation from fresh flowers of Annonaceae family tropical trees C. Odorata, a chemotype cultivated and grown in Bujumbura, Burundi. Analyses of physicochemical properties values were done and compared to reference values. It appears that for the refractive index, density and acid number, the findings of this study are within the pre-established standards. More interesting, the value of ester number was very beyond the norm by a factor of almost two, breaking the record already registered by AFNOR, therefore suggesting of an essential oil of exceptional quality. The findings presented in this study also highlight the importance of C. Odorata chemotype from the plains of Burundi as a promising potential candidate for bio-based products of public interests such as bio-based cosmetics and bio-based pharmaceuticals products, and therefore offer new insights bioeconomics in health and well-being. Finally, this plant can easily be cultivated, not only in Burundi, but also in countries of the Eastern Africa that share the same geoclimatic conditions as the Great African Rift.
Demand for ethanol has increased globally due to the need for energy and consumer chemicals, necessitating use of distillation to concentrate dilute sources. This paper presents the effect of reflux ratio, number of stages, feed thermal conditions (FTCs), feed composition (XF), and feed plate location on the performance of a normal distillation column separating ethanol-water mixtures ranging between 0.1 and 0.6 mol/mol. The model was created using Aspen Plus® Software. The FTCs studied include: feed at room temperature (FRT), partially vaporized feed (PVF), feed at its boiling point (FBP), superheated vapor (SHV) and feed at dew-point (FDP). The performance factors studied were: distillate composition (XD), reboiler and condenser duties. The axial profiles of temperature and ethanol concentration in the liquid across the column revealed stronger dependence on XF in the stripping section and on feed plate location. Increasing reflux ratio increased distillate composition, reboiler and condenser duties. Increasing feed composition increased distillate composition and lowered reboiler and condenser duties depending on the FTCs. Locating the feed plate further down the column increased the distillate composition. The QR was highest for FRT while QC values were highest for FTC and SHV. The FBP led to minimum energy demands for both QR and QC. To minimize energy, switch all FTCs to FBP was recommended, with highest savings observed for switching from FRT to FBP.
Groundwater quality variation due to consequent changes in the standard of living of a community is of great unease owing to the fact that the groundwater is regarded as one of the significant water supply sources available. For the sustainable use of water resources and water quality management, monitoring and assessment of water quality acts a catalyst for an appropriate judgment on the water quality. In this study, groundwater samples were collected from Lingayas Institute of Management and Technology (LIMAT), Vijayawada campus and Mudirajupalem, Krishna district, Andhra Pradesh, India for monitoring and assessing the water quality for alkalinity, total dissolved solids (TDS), pH, acidity and total hardness (TH) using standard methods. Very high values of pH and TDS were obtained in the groundwater collected from Mudirajupalem, which is within the vicinity of agricultural fields. Added to this, Student’s t test analysis of TDS values signposted a noteworthy P value (<0.001) for which the mean difference was substantial statistically. The groundwater collected from Mudirajupalem further affirmed that the water is unfit for drinking, which is evident from water quality index (WQI) values. This study emphasizes on implementing various locale specific rainwater garnering schemes, which is one of the solution for augmenting the groundwater recharge and maintaining the groundwater balance.
Infinity divided by infinity, zero divided by zero, one divided by zero are the most important indeterminate forms obtained when evaluating limits for single variable functions and series. Well-known method; L' Hôpital rule has been employed to simplify and resolve these indeterminate forms' limits such that 0/0, ∞/∞ , 1/0 in terms of quotients of their derivatives. In some cases, L' Hôpital rule is applied more than once to solve indeterminate limits. Besides, it is so complicated to take the derivative for some functions of a single variable and series, so L' Hôpital rule is ineffective and not practical to solve limits with indeterminate forms for those functions and series. L' Hôpital rule is also impractical for the indeterminate limits in the form: - ∞∙0By considering all these facts, new approaches including Central Finite Difference (CFD), Forward Finite Difference (FFD), Backward Finite Difference (BFD), High Accurate Central Finite Difference (HACFD), High Accurate Forward Finite Difference (HAFFD), High Accurate Backward Finite Difference (HABFD) methods are presented that provides efficient ways to solve these limits. Taking derivative is not required in all approaches. HACFD with step size: 0.0001 is the most preferred technique here to obtain exact results among all other techniques.
This study was conducted for the assessment of the nutrition, minerals and antibacterial activities of leaves, stem and flower of Mentha longifolia (wild mint). Proximate compositions were carried out using standards methods, mineral analysis were determined using Atomic Absorption Spectrophotometer and Flame Photometer, antibacterial activities were assessed using Zone of Inhibition Assay. Broth dilution method was used to determine the Minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC). The proximate composition of Mentha longifolia observed that moisture was found in the range of 2.3-2.8%, ash was 2.5-7.5%, crude fat was 0.5-2.1%, crude fiber was 8.5-22.5%, protein was 2.1-4.5%, carbohydrate was 69.6-78.7% and energy was 291.3-347.7 Kcal/100 g dw. Sodium concentration was found in the range of 1250-1590 mg/kg, Potassium was 3240-4820 mg/kg, Calcium was 12400-24000 mg/kg, Magnesium was 4800-9600 mg/kg, Zinc was 32-64 mg/kg, Iron was 140-498 mg/kg, Manganese was 32-107 mg/kg and Chromium was 3-6 mg/kg in Mentha longifolia leaves, flower and stem. The highest zone of inhibition (23±0.2) of Mentha longifolia leaves extract (tincture) was calculated against Bacillus cereus. Similarly the highest zone of inhibition of Mentha longifolia flower and stem was noted against Bacillus cereus in tincture extract were 17±01 mm and 16±01 mm respectively. The Mentha longifolia leaves MIC range was 40–120 mg/mL and MBC 60–200 mg/mL. The flower extracts MIC range 70–220 mg/mL and MBC 110–300 mg/mL. Generally the antibacterial activities of wild mint leaves extracts were higher as compared to flower and stem extracts (p<0.05). The results commonly observed Gram-negative bacteria are typically high opposed to the Mentha longifolia extracts as compared to Gram-positive bacteria. The proximate and minerals analysis concludes that this herb is used to formulate nutraceutical products and their extracts can be used against multi drug resistance bacteria accomplished of causing foodborne diseases.
Investigation on the influence of near azeotropic feed molar flow rate on properties of key streams connecting main process units of an ethanol-water azeotropic distillation pilot processis presented. The heterogeneous azeotropic distillation model with cyclohexane entrainer was configured in Aspen Plus® V10 commercial simulation software. Property analysis and prediction of plant’s performancewere achieved using Non-Random Two Liquid Redlich-Kwong thermodynamic model. Both residual curve maps and ternary diagrams were used to determineseparation possibility and presence of ethanol-water azeotrope in the formed ternary mixtureduring distillation synthesis. The process convergence was addressed using flowsheet convergence and balance node. Distillation of ethanol- water azeotropic mixture was simulated at constant recycle ratio (R = 5), numberof stages (N = 12) and pressure (P = 1 atm). Data obtained were analysed in MS Excel 2013. Results showed that simultaneous increase ofmolar flow rate of the near azeotropic feed and feed ethanol concentration improves ethanol purity but results in retrograde phenomenon which may humper plant’s performance and increase stream flow rates and therefore increase energy duties. The condenser duty of the main column wasaround 90.94% higher than the recycle column’scondenser duty. Also, reboiler duty of the main column were nearly 90.25% higher than the recycle column’s reboiler duty.It was concluded that setting 18 to 20 kmol/h feed molar flow rate enhances higher energy efficiency and improves ethanol product purity. Careful distillation synthesis and plant’s monitoring are recommended to improve ethanol-water azeotropic distillation plant’s performance and address retrograde phenomena.
