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This paper provides a mathematical basis for the well-known cat’s-eye effect appearing on chatoyant gemstones. After reminding the reader of the physical origin of this effect and the conditions for observing it, we introduce all required parameters and some reasonable assumptions in order to simplify the calculations. In fact, we describe the motion of a point located at the apex of the cat’s-eye line in the “main” plane, defined by the directions of the source and the observer and perpendicular to the set of acicular inclusions responsible for the optical phenomenon. These calculations confirm the qualitative cat’s-eye behavior commonly observed in various situations, when the source or the observer moves around the cabochon or when the stone rotates under them.

Soil particle-size distribution or soil texture presents one of the most important physical properties. There are various systems of the classification systems for soil particle-size fractions with different boundaries. Our effort was concentrated on the mathematical approach to evaluate the existing data and convert it to the form of a reconstructed cumulative particle-size curve which will allow reading concentration of any desired particle size. Non-Uniform Rational B-Splines (NURBS) curves therefore represent a generalization of B-splines and Bézier curves by extending the definition by an element of rationality, which is represented by the weights of the control points, and a nodal vector of parametrization, which represents the element of uniformity. The NURBS curve was used for smooth (depending on the degree of the curve used) and as tight as possible approximation of the arranged control points, the connecting lines of which forms a convex envelope for its individual parts. The NURBS approximation curve is therefore determined by the ordered control points and their connecting lines, the weights of these points, the degree of the curve and the nodal vector of parametrization. However, the construction of the approximation curve is primarily dependent on a limited number of points of the experimentally determined particle-size distribution curves, and for curves with significant breaks in the course, one must consider either a lower accuracy of the approximation or the necessity of "improving" the approximation using the weights of individual points, inserting additional points or working with a nodal vector of parametrization. For basic approximation, the PUGIS system (Czech soil information system) offers automatic approximation using all variants mentioned in the article as well as the possibility of individual changes in the weights of control points, in their number and position, and in the nodal vector of parametrization.

Emptying processes are operations frequently required in hydraulic installations by water utilities. These processes can result in drops to sub-atmospheric pressure pulses, which may lead to pipeline collapse depending on soil characteristics and the stiffness of a pipe class. One-dimensional mathematical models and 3D computational fluid dynamics (CFD) simulations have been employed to analyse the behaviour of the air–water interface during these events. The numerical resolution of these models is challenging, as 1D models necessitate solving a system of algebraic differential equations. At the same time, 3D CFD simulations can take months to complete depending on the characteristics of the pipeline. This presents a mathematical approach for directly solving air–water interactions in emptying processes involving entrapped air, providing a predictive tool for water utilities. The proposed mathematical approach enables water utilities to predict emptying operations in water pipelines without needing 2D/3D CFD simulations or the resolution of a differential algebraic equations system (1D model). A practical application is demonstrated in a case study of a 350 m long pipe with an internal diameter of 350 mm, investigating the influence of air pocket size, friction factor, polytropic coefficient, pipe diameter, resistance coefficient, and pipe slope. The mathematical approach is validated using an experimental facility that is 7.36 m long, comparing it with 1D mathematical models and 3D CFD simulations. The results confirm that the derived mathematical expression effectively predicts emptying operations in single water installations. [ABSTRACT FROM AUTHOR]

Quantitative structure permeation relationship (QSPR) models have gained prominence in recent years owing to their capacity to elucidate the influence of physicochemical properties on the dermal absorption of chemicals. These models facilitate the prediction of permeation coefficient (Kp) values, indicating the skin permeability of a chemical under infinite dose conditions. Conversely, obtaining dermal absorption rates (DAs) under finite dose conditions, which are crucial for skin product safety evaluation, remains a challenge when relying solely on Kp predictions from QSPR models. One proposed resolution involves using Kroes' methodology, categorizing DAs based on Kp values; however, refinement becomes necessary owing to discreteness in the obtained values. We previously developed a mathematical model using Kp values obtained from in vitro dermal absorption tests to predict DAs. The present study introduces a new methodology, Integrating Mathematical Approaches (IMAS), which combines QSPR models and our mathematical model to predict DAs for risk assessments without conducting in vitro dermal absorption tests. Regarding 40 chemicals (76.1 ≤ MW ≤ 220; -1.4 ≤ Log Ko/w o/w 3.1), IMAS showed that 65.0% (26/40) predictions of DA values were accurate to within twofold of the observed values in finite dose experiments. Compared to Kroes' methodology, IMAS notably mitigated overestimation, particularly for hydrophilic chemicals with water solubility exceeding 57.0 mg/cm3. These findings highlight the value of IMAS as a tool for skin product risk assessments, particularly for hydrophilic compounds. [ABSTRACT FROM AUTHOR]

Hydrothermal scheduling is a significant concern in the field of power system economics that seeks to reduce the overall cost of generation by optimizing the hourly output of generators. However, this scheduling process suffers from a non-linear and complex problem due to set of uncertainty constraints from hydro and thermal units. Hence $\vartheta $ -constraint method has been proposed in which ramp constraints are considered that supply a feasible power region of the thermal units and minimize the uncertainty constraints. In addition, the existing solution techniques of hydro and thermal unit, commitment problems have not considered thermal constraints and their losses. This results in the frequent swapping of hydro units which decreases the energy conversion efficiency by a percentage at each repetition and increases the cost of the system. Therefore, a novel Chaotic geometric programming and chaotic approximation approach has been proposed that balance water discharge level without frequency swapping based on Armijo’s rule and Hazen Williams’s rule. Further, dynamic indexing is performed to increase the energy conversion efficiency. These balanced values are given to multiple-wave neural networks, to solve the hydro and thermal unit commitment problems. Furthermore, the cost of the system is minimized using Enhanced Ebola Optimization Search (EEOS) Algorithm in which the Srate parameter has been modified, thereby normalizing the hydrothermal scheduling problem for matured convergence. The proposed mathematical model has been implemented in the MATLAB R2022b on a 2.10 GHz, AMD Ryzen 5 3500U with Raden Vega Mobile Gfx processor, 8 GB RAM, 64 bit personal computer, and the results obtained show better performance than the previous approaches in terms of mean, median and standard deviation.

Background: To investigate whether ultrasound-based optic nerve sheath diameter (US-ONSD) is a reliable measure to follow up children with idiopathic intracranial hypertension (IIH). In addition, to analyze the inter- and intra-individual relationships between US-ONSD and intracranial pressure (ICP), and to investigate whether an individualized mathematical regression equation obtained from two paired US-ONSD/ICP values can be used to approximate ICP from US-ONSD values. Methods: 159 US examinations and 53 invasive ICP measures via lumbar puncture (LP) were performed in 28 children with IIH. US-ONSD was measured using a 12 Mhz linear transducer and compared to ICP values. In 15 children, a minimum of 2 paired US-ONSD/ICP determinations were performed, and repeated-measures correlation (rmcorr) and intra-individual correlations were analyzed. Results: The cohort correlation between US-ONSD and ICP was moderate (r = 0.504, p < 0.01). Rmcorr (r = 0.91, p < 0.01) and intra-individual correlations (r = 0.956–1) of US-ONSD and ICP were excellent. A mathematical regression equation can be calculated from two paired US-ONSD/ICP values and applied to the individual patient to approximate ICP from US-ONSD. Conclusions: Related to excellent intra-individual correlations between US-ONSD and ICP, an individualized regression formula, created from two pairs of US-ONSD/ICP values, may be used to directly approximate ICP based on US-ONSD values. Hence, US-ONSD may become a non-invasive and reliable measure to control treatment efficacy in pediatric IIH. [ABSTRACT FROM AUTHOR]

Water is the meaning of life for humans, agricultural and industrial processes; controlling the distribution of water and wastewater between industrial processes is very vital for rationalizing water and preserving the environment. This paper addresses a mathematical approach to optimizing water inter-plant networks. The water network problem is formulated as a nonlinear program (NLP) that is solved by LINGO Software, version 14.0. A generalized two-step mathematical model is designed to be valid for solving networks containing large numbers of sources and sinks. The introduced model is proposed to be used for both single and multiple contaminant problems with up to six contaminants. Two mathematical models are presented to design water inter-plant networks efficiently. Firstly, the introduced model is solved by LINGO, in which the data given are applied; the obtained results are simultaneously sent to a second model (based on Excel Software 2019, v. 16.0), by which the obtained water networks are automatically drawn. The proposed approach has been applied in three case studies; the first case study contains five plants of single contaminants, the second case study contains three plants of single contaminants, and the third case study contains three plants of multiple contaminants. The results showed a noticeable reduction in the percentages of freshwater consumption in the investigated three case studies, which were 38.6, 4.74 and 8.64%, respectively, and the wastewater discharge of the three case studies were decreased by 38.1, 4.61 and 8.65%, respectively. [ABSTRACT FROM AUTHOR]

The field of managing the logistics of agricultural products under significant dynamic changes in today's conditions requires the formation of new approaches using the possibilities of modern information tools. The article presents a systematic mathematical approach to logistics management in agriculture for conditions with an insignificant level of risk and under conditions of significant threats to the logistics processes of the agricultural industry. The presented study also examines the issue of analyzing the effectiveness of management actions in the logistics process, both operationally and strategically. The developed mathematical approach takes into account a wide range of conditions for carrying out logistics activities - both at a low level of risk in the implementation of the logistics process, and in circumstances of significant threats that lead to the minimization of the reliability of logistics in the agricultural sector. This is especially important today, given the significant level of negative impacts on logistics processes due to military threats. The growth of these influences even leads to the destabilization of the world food market, and the threat of famine in some regions of the world. The proposed mathematical approach takes into account both the emergence of new risks, the significantly increased dynamic nature of the effects on logistics activities in the agricultural sector of the economy, and the traditional specificity of the conditions for the implementation of logistics processes in the agricultural sector. The specificity of logistics management in the agricultural sector is due to the peculiarities of the agricultural production process; properties inherent in agricultural products, conditions of distribution of these products. This determines a wide range of tasks that must be performed by the logistics of the agricultural sector. This, in turn, creates a need for a highly adaptive dynamic approach when forming a set and combination of logistics tasks and goals. Algorithms, tools and methods were specially developed to implement this approach. In particular: the unification of target functions; the approach of flexible adaptive changes in the ranks of target functions to ensure the appropriate level of rationality of logistics process management; a compromise approach in the case of the need to simultaneously achieve a group of set goals or a group of goals; the approach of assessing the strategic impact of a management decision for operating not with static values of parameters, but with their trends over time. In general, this makes it possible to achieve the appropriate level of economic efficiency of agricultural logistics management even with dynamic changes in the conditions of its implementation and to ensure a high level of reliability of the logistics process even with an increase in the level of threats. [ABSTRACT FROM AUTHOR]

The field of managing the logistics of agricultural products under significant dynamic changes in today's conditions requires the formation of new approaches using the possibilities of modern information tools. The article presents a systematic mathematical approach to logistics management in agriculture for conditions with an insignificant level of risk and under conditions of significant threats to the logistics processes of the agricultural industry. The presented study also examines the issue of analyzing the effectiveness of management actions in the logistics process, both operationally and strategically. The developed mathematical approach takes into account a wide range of conditions for carrying out logistics activities - both at a low level of risk in the implementation of the logistics process, and in circumstances of significant threats that lead to the minimization of the reliability of logistics in the agricultural sector. This is especially important today, given the significant level of negative impacts on logistics processes due to military threats. The growth of these influences even leads to the destabilization of the world food market, and the threat of famine in some regions of the world. The proposed mathematical approach takes into account both the emergence of new risks, the significantly increased dynamic nature of the effects on logistics activities in the agricultural sector of the economy, and the traditional specificity of the conditions for the implementation of logistics processes in the agricultural sector. The specificity of logistics management in the agricultural sector is due to the peculiarities of the agricultural production process; properties inherent in agricultural products, conditions of distribution of these products. This determines a wide range of tasks that must be performed by the logistics of the agricultural sector. This, in turn, creates a need for a highly adaptive dynamic approach when forming a set and combination of logistics tasks and goals. Algorithms, tools and methods were specially developed to implement this approach. In particular: the unification of target functions; the approach of flexible adaptive changes in the ranks of target functions to ensure the appropriate level of rationality of logistics process management; a compromise approach in the case of the need to simultaneously achieve a group of set goals or a group of goals; the approach of assessing the strategic impact of a management decision for operating not with static values of parameters, but with their trends over time. In general, this makes it possible to achieve the appropriate level of economic efficiency of agricultural logistics management even with dynamic changes in the conditions of its implementation and to ensure a high level of reliability of the logistics process even with an increase in the level of threats.

The rheological and filtration properties of the biopolymer solutions based on natural polymers, gum and starch, that affect the removal of drilled cuttings to the day surface, the creation of hydrodynamic pressure, and the borehole cleaning, were considered. Hydrodynamic pressure, in turn, predetermines possible arising of complications during well construction such as absorption of the drilling fluid or influx of formation fluids, hydraulic fracturing of the rocks, and contamination of the productive formations which are opened mainly via horizontal wellbore drilling. The peculiar features of the use of a combination of gums and starch in biopolymer drilling fluids, manifested in changes in the values of the process parameters of the drilling fluids, as well as in the physicomechanical processes of solution circulation in the well, were studied. By means of mathematical modeling, the change in the annular velocity profile for the biopolymer solutions containing the studied reagents (gum and starch) separately and jointly was demonstrated. In this regard, the basic equation describing the motion of a pseudoplastic liquid (the Ostwald–de Waele model) was used for finding the velocity profiles in an annular gap of 10 mm for the biopolymer solutions, and the optimal velocity profiles were graphically determined for the aqueous solutions of the biopolymer reagents. Basing on analysis of the obtained velocity solutions and the experimental data on the filtration and transport properties of the biopolymer compositions, the optimal concentrations of the reagents were determined. [ABSTRACT FROM AUTHOR]

This paper presents a Model-Based Design (MBD) approach for the design and control of a customized manipulator intended for drilling and positioning of dental implants accurately with minimal human intervention. While performing an intra-oral surgery for a prolonged duration within a limited oral cavity, the tremor of dentist's hand is inevitable. As a result, wielding the drilling tool and inserting the dental implants safely in accurate position and orientation is highly challenging even for experienced dentists. Therefore, we introduce a customized manipulator that is designed ergonomically by taking in to account the dental chair specifications and anthropomorphic data such that it can be readily mounted onto the existing dental chair. The manipulator can be used to drill holes for dental inserts and position them with improved accuracy and safety. Furthermore, a thorough multi-body motion analysis of the manipulator was carried out by creating a virtual prototype of the manipulator and simulating its controlled movements in various scenarios. The overall design was prepared and validated in simulation using Solid works, MATLAB and Simulink through Model Based Design (MBD) approach. The motion simulation results indicate that the manipulator could be built as a prototype readily. [ABSTRACT FROM AUTHOR]

The present paper proposes the theoretical study and mathematical approach of laser induced cavitation microbubble during lithotripsy process in soft tissue. The mathematical model is constructed via the potential function and Lagrangian equation of radial and translational dynamics of microbubble. The given model of laser-induced cavitation microbubble (as like Rayleigh–Plesset equation) is analytically solved and investigated via Plesset–Zwick method to investigate the behaviour of laser-induced cavitation microbubble and energy produced by laser-induced cavitation microbubble during lithotripsy in soft tissue. From our results, we get the energy produced by laser-induced cavitation bubble increases with increasing of the time and decreasing of the parameter which is calculated experimentally. The present mathematical approach and its analytical results are satisfied by comparing with the published experimentally results. [ABSTRACT FROM AUTHOR]

The high-yield optical wireless network (OWN) is a promising framework to strengthen 5G and 6G mobility. In addition, high direction and narrow bandwidth-based laser beams are enormously noteworthy for high data transmission over standard optical fibers. Therefore, in this paper, the performance of a vertical cavity surface emitting laser (VCSEL) is evaluated using the machine learning (ML) technique, aiming to purify the optical beam and enable OWN to support high-speed, multi-user data transmission. The ML technique is applied on a designed VCSEL array to optimize paths for DC injection, AC signal modulation, and multiple-user transmission. The mathematical model of VCSEL narrow beam, OWN, and energy loss through nonlinear interference in an optical wireless network is studied. In addition, the mathematical model is then affirmed with a simulation model following the bit error rate (BER), the laser power, the current, and the fiber-length performance matrices. The results estimations declare that the presented methodology offers a narrow beam of VCSEL, mitigating nonlinear interference in OWN and increasing energy efficiency. [ABSTRACT FROM AUTHOR]

In this paper, different mathematical expressions are derived to compute the residual magnitude of voltage caused by faults along the line and on the bus. Symmetrical and unsymmetrical faults are taken into consideration, and the consequences of the various fault distributions are considered. A new way of assessing a sag is proposed that incorporates the method of fault position and mathematical expression based on sequence currents and voltages. The fault impedance is introduced to obtain a better result. A fast and efficient load flow analysis technique produces quick computational results. In addition, the sag analysis is performed using the bivariate joint discrete probability distribution method that gives a clear idea about the probability of occurrence of sag in a meshed network. The suggested approach is applied in the IEEE 39-bus system and with an existing real-time electrical power distribution system in India. [ABSTRACT FROM AUTHOR]

At the end of 2019, the COVID-19 disease emerged in the city of Wuhan, China, and caused an outbreak of unusual viral pneumonia. Being highly transmissible, this novel coronavirus disease has spread fast all over the world. COVID-19 continues to challenge most developed countries in the search for an effective strategy to either prevent infection or to avoid the spreading of the disease. While several developed countries have managed to contain COVID-19, several countries in Latin America continue to report an increase in the daily number of infected people. Ecuador, particularly, became the epicenter of the COVID-19 outbreak in the region during March and April 2020. In this context, the present study shows a simple mathematical approach to understand the effect of the COVID-19 outbreak in Ecuador (and some Latin American countries such as Brazil, Peru, and Colombia). The proposed method is based on the exponential model, discrete logistic equation, and differential logistic model using one-year data from March 1, 2020, to February 28, 2021. This study presents the estimated growth rate coefficient (λ), the total number of cases (N), and the midpoint of maximum infection (t_0) as well as the variability of the λ coefficient as a function of total cases and time. The exponential model shows a high value of λ=0.185 which decreases to λ=0.014 and λ=0.056 according to the discrete and differential logistic models, respectively. An accurate value of the total number of cases of infected people was found by analyzing the number of daily cases as a function of the total of cases whose value (N~409 K) agrees with the data reported at the end of May 2021, validating the proposed approach. How to use the current mathematical approach for long-term prediction is also discussed here. Most importantly, the proposed method has two important characteristics: (i) the mathematical model is as simple as possible compared to other time-consuming approaches, and (ii) it can be used to study the effect of COVID-19 and predicts its consequences in other countries, allowing revenue new decisions against the COVID-19 disease. Doi: 10.28991/esj-2021-SPER-09 Full Text: PDF

Rectangular barrettes are used in place of circular piles for their improved geotechnical performance. In this paper, a new mathematical approach is proposed for predicting the natural frequency and mode shape of vertically loaded barrettes. Unlike previous studies of the problem, the approach allows the investigation of nonhomogeneity for side friction resistance as well as rectangular cross-section of piles. The differential governing equation and boundary conditions are derived for the lateral free vibration of the barrettes, and solutions are numerically obtained by means of the Runge–Kutta scheme in conjunction with the determinant search algorithm. The calculated natural frequencies are in good agreement with those reported in the literature. The free vibration response and the results of a parametric study of barrettes are presented in non-dimensional form. The proposed approach is considered to provide a viable tool for studying the free vibration of rectangular barrettes for practical applications. [ABSTRACT FROM AUTHOR]

With the extensive use of information technology and the development of education informatization infrastructure, the educational sector is placing increasingly high demands on the quality of instructors' informatization. The progress of education implementation is largely determined by level of informationization of instructors. Teachers are the most important entity of learning and determining factor. The modern and scientific assessment of the development of information learning is an essential element of education. This paper uses regression method to assess the teacher development information platform and numerical facts to confirm and determine a linear regression concept for the community. The multiple linear regression assessment techniques are used to develop the linear regression computational formula of the educational development of information stage, and the influence of different factors is analysed to develop a science-based assessment method to assess the education of instructors' information on the basis of the statistical analysis of the assessment indexes of the schooling implementation of the information stage. [ABSTRACT FROM AUTHOR]

When conducting experimental psychology, psychological phenomena are often described in mathematical terms and logic. How practical is the mathematical approach in experimental psychology? This paper aims to explain plain linguistic and mathematical expressions, how psychological phenomena are expressed mathematically in experimental psychology and how mathematical models are constructed, using examples of psychological phenomena related to sensation, perception, and cognition. First, it outlined the perspective, thinking, and utilization of mathematical models in experimental psychology, using some psychological phenomena. Second, it was introduced that several previous studies dealt with spatial properties of perceptual and cognitive phenomena, including the author's studies. It is hoped that this paper will increase familiarity with and opportunities to utilize mathematical models in experimental psychology. [ABSTRACT FROM AUTHOR]

Background: To maintain control of the coronavirus disease 2019 (COVID-19) epidemic as lockdowns are lifted, it will be crucial to enhance alternative public health measures. For surveillance, it will be necessary to detect a high proportion of any new cases quickly so that they can be isolated, and people who have been exposed to them traced and quarantined. Here we introduce a mathematical approach that can be used to determine how many samples need to be collected per unit area and unit time to detect new clusters of COVID-19 cases at a stage early enough to control an outbreak. Methods: We present a sample size determination method that uses a relative weighted approach. Given the contribution of COVID-19 test results from sub-populations to detect the disease at a threshold prevalence level to control the outbreak to 1) determine if the expected number of weekly samples provided from current healthcare-based surveillance for respiratory virus infections may provide a sample size that is already adequate to detect new clusters of COVID-19 and, if not, 2) to determine how many additional weekly samples were needed from volunteer sampling. Results: In a demonstration of our method at the weekly and Canadian provincial and territorial (P/T) levels, we found that only the more populous P/T have sufficient testing numbers from healthcare visits for respiratory illness to detect COVID-19 at our target prevalence level—assumed to be high enough to identify and control new clusters. Furthermore, detection of COVID-19 is most efficient (fewer samples required) when surveillance focuses on healthcare symptomatic testing demand. In the volunteer populations: the higher the contact rates; the higher the expected prevalence level; and the fewer the samples were needed to detect COVID-19 at a predetermined threshold level. Conclusion: This study introduces a targeted surveillance strategy, combining both passive and active surveillance samples, to determine how many samples to collect per unit area and unit time to detect new clusters of COVID-19 cases. The goal of this strategy is to allow for early enough detection to control an outbreak.

Logistics pooling presents a very important solution for companies to improve the different aspects of sustainability. The objective of this study is to propose a mathematical approach to the pooling of sustainable freight transport. In this work, the pooling performance is evaluated at different levels of sustainability. The proposed MILP (Mixed Integer Linear Programming) consists of designing a shared logistics chain, taking into account economic and environmental objectives, namely the different logistics cost and the different CO2 emissions. The social/societal level, namely the accident rates and the noise level are assessed after model resolving. Also, the transportation fill rate is calculated. Finally, we demonstrated the pooling performance with an illustrative example of freight transport, which is made up of four suppliers who collaborate to deliver six common distribution centers. Firstly, we solve the mathematical model by the mono-objective functions (economic or environmental). Secondly, we solved the model with a multi-objective function, which combines the two objectives (economic and environmental) with the Ɛ-Constraint method. [ABSTRACT FROM AUTHOR]

The high-yield optical wireless network (OWN) is a promising framework to strengthen 5G and 6G mobility. In addition, high direction and narrow bandwidth-based laser beams are enormously noteworthy for high data transmission over standard optical fibers. Therefore, in this paper, the performance of a vertical cavity surface emitting laser (VCSEL) is evaluated using the machine learning (ML) technique, aiming to purify the optical beam and enable OWN to support high-speed, multi-user data transmission. The ML technique is applied on a designed VCSEL array to optimize paths for DC injection, AC signal modulation, and multiple-user transmission. The mathematical model of VCSEL narrow beam, OWN, and energy loss through nonlinear interference in an optical wireless network is studied. In addition, the mathematical model is then affirmed with a simulation model following the bit error rate (BER), the laser power, the current, and the fiber-length performance matrices. The results estimations declare that the presented methodology offers a narrow beam of VCSEL, mitigating nonlinear interference in OWN and increasing energy efficiency.

The Ergene River Basin, which endows from the Istrranca mountains, is one of the centers of industry in the Marmara region. The industrial busy area provides substantial clues about the anthropogenic effect of contamination. Nearly all industrial, domestic and agricultural wastewater is discharged directly or indirectly to the Ergene River. With this paper, nine students (9th and 10th class) from Krrklareli Science High School intervene in the discussion of heavy metals by taking samples from 13 different locations along the Ergene River with the leadership of the teacher. The points where the samples are taken are determined by the Ministry of Environment and Urbanization. All the steps in the study are supervised by a scholar from Yildiz Technical University. The discussion commences with descriptive analysis, binary correlations and hierarchical cluster analysis of eight heavy metals. The discourse percentages of pollution of the three eigenvalues and the rotation matrix continue with linear modeling by clustering the variables. To more closely recognize the anthropogenic effect, the reader is presented with Contamination Factor (CF), Enrichment Factor (EF) and Pollution Load Index (PLI) values. [ABSTRACT FROM AUTHOR]

Background: To maintain control of the coronavirus disease 2019 (COVID-19) epidemic as lockdowns are lifted, it will be crucial to enhance alternative public health measures. For surveillance, it will be necessary to detect a high proportion of any new cases quickly so that they can be isolated, and people who have been exposed to them traced and quarantined. Here we introduce a mathematical approach that can be used to determine how many samples need to be collected per unit area and unit time to detect new clusters of COVID-19 cases at a stage early enough to control an outbreak.Methods: We present a sample size determination method that uses a relative weighted approach. Given the contribution of COVID-19 test results from sub-populations to detect the disease at a threshold prevalence level to control the outbreak to 1) determine if the expected number of weekly samples provided from current healthcare-based surveillance for respiratory virus infections may provide a sample size that is already adequate to detect new clusters of COVID-19 and, if not, 2) to determine how many additional weekly samples were needed from volunteer sampling.Results: In a demonstration of our method at the weekly and Canadian provincial and territorial (P/T) levels, we found that only the more populous P/T have sufficient testing numbers from healthcare visits for respiratory illness to detect COVID-19 at our target prevalence level-assumed to be high enough to identify and control new clusters. Furthermore, detection of COVID-19 is most efficient (fewer samples required) when surveillance focuses on healthcare symptomatic testing demand. In the volunteer populations: the higher the contact rates; the higher the expected prevalence level; and the fewer the samples were needed to detect COVID-19 at a predetermined threshold level.Conclusion: This study introduces a targeted surveillance strategy, combining both passive and active surveillance samples, to determine how many samples to collect per unit area and unit time to detect new clusters of COVID-19 cases. The goal of this strategy is to allow for early enough detection to control an outbreak. [ABSTRACT FROM AUTHOR]

The problem of setting the values and interconnections between elements of the models in the safety, protection and security field, appears as the biggest obstacle in taking crisis management decisions. The article attempts to represent a mathematical approach to modify the expected values and interconnections that can occur in the models describing the protected system in order to minimize errors caused by subjectivity. Here presented procedures are described in the examples of their potential use. The main idea is to focus on improving estimates for better response to reality, then to find new estimates, since those would still be weighed down by the subjectivity caused errors. Based on this premise this article attempts to characterize application of mathematical methods on minimizing the subjectivity caused errors in the models in risk assessment.

Spectrum sensing is the quintessence of cognitive radio network and is influenced by uncertain noise at low SNR. In such a scenario sensing duration imposes a constraint on the sensing performance. This paper presents a novel mathematical approach to obtain optimal sensing duration (number of samples) in presence of noise uncertainty for energy detection method. The effect of noise uncertainty on number of sensed samples has been analyzed and a novel approach has been presented to correlate the sensing duration with SNR to attain desired performance in terms of PFA (Probability of False Alarm) and PD (Probability of Detection). [ABSTRACT FROM AUTHOR]

This paper drives the mathematical discussion of heavy metals level of As, Pb, Cd, Ni, Cu, Co and Cr in the samples collected from the Gediz Delta. In 2006, several scientists from Ege University Faculty of Fisheries declared the data of eight different stations belonging to the basin to observe the natural and anthropogenic effect in the sediment of the delta. Based on these data, we try to look at the results with a more comprehensive mathematical perspective and attract the attention to the Gediz Basin with holistic discussions. Land use in the watershed and a data set comprised of observations of 7 heavy metals from 8 locations are described. In order to interpret the anthropogenic effect of contamination of the river, statistical analyses are performed. In the study, by investigation a covariance matrix indicates the strength of bivariate relationships, a dendrogram shows hierarchical clustering into different groups, and factor analysis indicates three distinct eigenvectors. In addition, one can find three indices Contamination Factor (CF), Enrichment Factor (BF), and Pollution Load Index (PLI) developed by Canadian sedimentologists. The fact that the findings in the discussion belong to 2006 permits the authors to understand the recent condition more clearly. The level of pollution from the past is comparable. [ABSTRACT FROM AUTHOR]

Power transformers are one of the key components of power systems. Therefore, they must be operated efficiently to obtain satisfactory system performance, since any distortion or failure in power transformer structures may cause drastic damages. In order to detect deficiencies in power transformers, various methods are utilised. Frequency response analysis (FRA) is one of the most well‐known methods used for fault detection in power transformers. However, the interpretation of FRA results is subjective, and depends primarily on the opinion of a human expert. In other words, there is no comprehensive, accepted and standardised method to interpret FRA results. Subsequently, fault detection based on FRA is prone to error. In this study, a new mathematical approach is used to interpret the frequency response of power transformers based on evidence theory method. This method is more accurate and less computationally burdensome compared to conventional methods. Simulations are implemented on an operating 125 MVA, 230/132/20 kV autotransformer using finite‐element method and the results are compared to the corresponding FRA results of the same autotransformer in order to evaluate the proposed method. The obtained results indicate the efficiency of the proposed method in detecting probable faults of transformer windings through analysing the FRA results. [ABSTRACT FROM AUTHOR]

Natural resources should not be exhausted as if they will not run out. It is a humankind duty to take care while consuming and to devise a livable world. This discussion is dedicated to the Ergene River, one of the beauties of the Yıldız mountains. Turkey has the industry's busiest area in the Ergene Basin. Industrial zones, which are the main reason of anthropogenic influence, cause excessive pollution of the Ergene River. All industrial, domestic and agricultural wastewater are discharged directly or indirectly to the Ergene River. In order to interpret the anthropogenic effect in the sediment of the river, mathematical analyses are performed and Contamination Factor (CF), Enrichment Factor (EF), and Pollution Load Index (PLI) values are presented to the reader. The Ergene Basin 2013 (2012-2013) Final Report of the Ministry of Environment and Urbanization is utilized for these results. [ABSTRACT FROM AUTHOR]

The possibility of using the method of state variables for mathematical description of the dynamics of an autonomous power supply system is considered. The main advantages of using this approach are noted. The specifics of object construction presented in the form of discrete circuits and elements is taken into account. A system of state equations for the studied element of the system is presented having the form of a linear combination of state variables, input variables, and parameters of the element. The issue of controllability and observability of calculations is taken into account. An iterative calculation algorithm of transient voltage deviations is developed. [ABSTRACT FROM AUTHOR]

Highlights • A new mathematical approach for estimation of well output rate based on CRM equations. • Using optimization for estimation of acid reaction rate in the near wellbore region. • Investigation of acid reaction rate as a main parameter of acidizing operation. • A new skin variation estimation procedure during field acidizing operations. Abstract The efficiency of an acidizing operation is usually assessed through ordinary well testing methods. These methods are performed only after the acidizing operation, and it is difficult to monitor and evaluate real-time efficiency of acidizing operation. Understanding the performance of the acidizing during the service, by analysis of the acidizing data is a viable approach to this costly and challenging process. The estimation of the skin changes needs an appropriate mathematical method that can handle the main aspects of an acidizing operation. It is tedious to model a real acidizing operation due to the heterogeneity of the reservoir, an unknown reaction rate of acid in reservoir condition, unwanted fluid loss, opening and closing of the wing valve, etc. In this paper, we have presented a new well testing method for calculating the skin variations of open hole vertically drilled carbonate reservoir during an acidizing operation, by using history matching of the surface pressure data. The proposed method is based on continuity equations of acid in the reservoir coupled with analytical equations of ORPM (Output Rate Prediction Method) in the wellbore. The novelty of the proposed method is using a new mass transfer coefficient in continuity equations of acid, and a mathematical approach (ORPM) for the appropriate estimation of bottomhole acid injection rate and fluid loss, that lead to a proper evaluation of the skin variation during a field acidizing operation. [ABSTRACT FROM AUTHOR]

Engineering plastics have wide applications in different fields of industry due to their light weight and easy shaping. In manufacturing multi-component products, assembly is an inevitable stage and drilling is one of the necessary processes before joining of the components of these products. In this study, two of the most common types of engineering plastics, polyacetal (POM) and cast polyamide (castamide), were drilled with twist drills of 0.5 mm and 1 mm diameters, under different cutting speeds and feeds. In determining the accuracy of the drilled small holes, a mathematical approach was used in which least square circle method was applied and radial error of the each drilled hole was obtained. Thus, the hole accuracy could be determined without measuring equipment such as coordinate measurement machine. It has been seen that POM gave better hole accuracy than cast polyamide due its thermal and tribological properties. The effects of feed and cutting speed on the radial error were also investigated. POM did not show apparent difference in radial error according to the cutting parameters while cast polyamide showed lower radial error in higher feeds with 0.5 mm of drill tool and lower radial error with 1 mm of drill tool. Additionally, the radial error could be reduced with decrease of spindle speed at higher feed. [ABSTRACT FROM AUTHOR]

In a modern interconnected power system, it is challenging to estimate the amount of power delivered to loads through the transmission lines due to the individual associated generator. This study presents a mathematical approach which helps in the development of an important tool viz. power contribution coefficient, via which the share of power generated from an individual generator and delivered to the rest of the power system network has been traced efficiently. The proposed method presents a modest and spontaneous way of resolving real and reactive power flows through the transmission network due to all associated generators separately. It also gives the contribution of the individual generator to overall system losses and individual load distribution. To clarify the approach, the resolution of a sample case is provided using the proposed method. The performance of the developed technique has been investigated on IEEE 14‐bus test system. To validate the method, the outcomes of the projected algorithm of the test system are compared with those obtained by using other conventional power tracing methods. Also, the execution time for different bus systems using the proposed methodology is observed to be comparatively less than other existing approaches, which justifies the fastness and robustness of the presented one. [ABSTRACT FROM AUTHOR]

The problem of setting the values and interconnections between elements of the models in the safety, protection and security field, appears as the biggest obstacle in taking crisis management decisions. The article attempts to represent a mathematical approach to modify the expected values and interconnections that can occur in the models describing the protected system in order to minimize errors caused by subjectivity. Here presented procedures are described in the examples of their potential use. The main idea is to focus on improving estimates for better response to reality, then to find new estimates, since those would still be weighed down by the subjectivity caused errors. Based on this premise this article attempts to characterize application of mathematical methods on minimizing the subjectivity caused errors in the models in risk assessment. [ABSTRACT FROM AUTHOR]