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.
One-chart scheme for joint monitoring of two parameters allows the practitioners to focus on a single chart and thus, it offers significant operational advantages. Recently, four one-chart schemes are reported in literature for joint monitoring of the two parameters (Φ, λ) of a zero-inflated Poisson (ZIP) process. One of these schemes, namely - Gamma chart, is developed assuming samples of large size will be inspected and other three charts, namely DS-chart, Max-chart and LR chart, are developed assuming samples of small size will be inspected after every certain interval. The plotting statistics of these three charts are computed using the estimated ZIP parameters. However, unless the sample size (n) is sufficiently large, the excessive number of zeros in the ZIP process may offer a sample of zeros only. Therefore, these three schemes require estimation of ZIP parameters and subsequent computation of the plotting statistic based on the accumulated samples till the sampling stage. Because of the accumulation of samples, these schemes suffer from several limitations. In this paper, these one-chart schemes are modified for large sample size to make them free from their limitations. Subsequently, the performances of the four one-chart schemes are evaluated extensively using simulation studies. The results reveal that among the three modified charts likelihood ratio (LR) chart is the most preferable with respect to in-control and out-of-control average run length (ARL) performances. However, all these three modified charts give false alarms when the process parameter(s) shift towards desirable direction(s) implying process improvement. On the other hand, the Gamma chart is slightly inferior with respect to out-of-control ARL performances. But it does not give false alarm when there is a process improvement. Further, since Gamma chart directly monitors the average number of defects, it offers significant advantages in terms of implementation and interpretations.
Image Denoising, Deblurring, and Enhancement techniques are most commonly used on the images to reduce or completely remove the noise. The noisy images are not capable of perfectly using the solution of the desired problems such as object edge detection, object segmentation, and object classification. Because the edges of these objects have much bluer or more noise pixels for clearly stable detection. The main motivation of this study is to solve the problem of detection and elimination of the undesired noisy pixels on the encountered images. These noisy pixels are needed to be removed from the obtained images which are the results of throughout determined image processing steps. The main reason for this study motivation come out that to find the actual inscription fault has some noisy (undesired) pixels when extracting the true difference between the two images has been subtracted from each other. The subtracted image results are used in the inscription inspection process that controls the accuracy of the inscription quality. In the inscription inspection process, subtracted image results are used to determine the accuracy of the inscription quality. These subtracted images are formed by subtraction from each other of reference images and sample images. In these subtracted images if truly exist inscriptions faults or sometimes that could be occurred undesired noisy pixels at the same time in the subtraction process. This study focused on detecting and eliminating the undesired noisy pixels in order to reach actual inscription faults in the images. Thus, the remove pixels as width algorithm (RPW) has been developed and applied to these specified images.
In the typical, academic career path, individuals enter faculty roles immediately after graduate school, commencing their academic careers with research skills and a fledgling research agenda. Many faculty, however, take an indirect route to research. They may work in the commercial or nonprofit sector for years before joining the academy, allowing their research skills to fade. Some individuals who never completed research training are recruited as faculty due to their years of professional experience; this is especially true in business, engineering, and health care. When institutional expectations and personal goals change, however, these individuals may suddenly face the need to conduct research. They have the motivation but lack the necessary skills and confidence. This is especially true when institutions decide to seek accreditation that requires research activity among faculty. To help Bolivian faculty achieve research success, we developed a condensed workshop on qualitative, applied research and conducted it four times, in-person and online, following the action research model. The condensed workshop proved effective in helping faculty boost their research productivity, though participants expressed a desire for more extended coaching and support. Future workshops will include increased opportunity for collaboration. The workshop can be adapted to other regions.
The city of dhaka has been seeing a significant number of fire incidents. The exacerbation of the crisis is mostly attributed to a combination of institutional incompetence, insufficient equipment support, poor preventative measures, and a lack of awareness among people. The occurrence of fires in various shopping malls has become more prevalent in contemporary times. In the event of fire incidents inside shopping malls, there is a potential for both human casualties and property damage to occur. Contemporary shopping practices include the use of ornamental materials that possess a heightened susceptibility to combustion, hence amplifying the risk of fire incidents. The objective of this research is to assess the state of fire safety management in retail complexes. This research focuses on conducting a survey to assess fire safety in four high rise retail complexes located in the Mirpur region of Dhaka city. This study aimed to design a checklist methodology for assessing the fire safety standards of retail complexes. The assessment of fire safety levels in shopping malls by the Bangladesh Fire Service and Civil Defense directorate involves assigning varying weights to several parameters related to fire safety management. A study has shown that the majority of shopping malls exhibit characteristics of being high rise and mixed use, hence exacerbating their susceptibility to fires and subsequently increasing the associated fire risk. The majority of the shopping centers that were assessed are situated next to important roads, which are often broad enough to accommodate fire engines. However, a recurring issue arises as these roadways often experience congestion or occupation. Out of the shopping centers surveyed, only Mirpur Shopping Center possesses an emergency exit and some essential fire signs and symbols. Conversely, the remaining three shopping centers, namely Shah Ali Plaza, Muktobangla Shopping Complex, and Shah Ali Shopping Complex, do not have designated emergency exits, signs, and symbols altogether. This deficiency causes these shopping centers to be more vulnerable to fire hazards and reduces their overall level of safety. These shopping malls are extensively encompassed by various electric poles and transformers. The fire safety score of Mirpur Shopping Center is 56.57 (excellent), Shah Ali Plaza is 33.55 (average) and Shah Ali Complex and Muktobangla is 25.44 and 26.75 (poor) respectively. The Fire hazard vulnerability score of Mirpur Shopping Center is 11 (less vulnerable), Shah Ali Plaza is 26 (moderate vulnerable), Muktobangla Shopping Complex is 31 (highly vulnerable) and Shah Ali Shopping Complex is 35 (highly vulnerable). A lot of people are talking about how the fire brigade in our country doesn't have the right tools or the most up-to-date training, and they aren't keeping an eye on safety measures closely enough.
For assessing capability of a normal process with upper specification limit (USL) conventionally Cpu index is estimated to facilitate better decision making in product and process management. But, in practice, many quality characteristics having USL only, e.g. count data, proportion defective etc. are discrete and follow Poisson or binomial distributions. Some unconventional indices (e.g. Cu , Cfu ¸ Cpcu and Cpyu) are proposed in literature for assessing capability of Poisson or binomial processes. Due to legacy of usages of Cpu index and its interpretations, a user of an unconventional index often tends to interpret its values with reference to the values of Cpu for the bad, good or highly capable normal processes, and get a false impression about the capability of the concerned Poisson or binomial process. In this paper, the key features of those unconventional indices are highlighted and then some numerical analysis is carried out for assessing the interpretation issues associated with these unconventional indices. The results of these analyses reveal that although there is no interpretation issue for the unconventional index Cu , there are serious interpretation issues with all other unconventional indices. The mathematical relationships of estimates of other unconventional indices with the estimate of Cu index are established. It is recommended to convert the estimates of other unconventional indices into estimated Cu value using those relationships before any decision making. Otherwise, users of the other unconventional indices may inadvertently be led to erroneous decision making.
