Search results for: exact controllability

Authors: Rabia Saleem

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This research has a recently proposed strategy to find the exact inflationary solution of the Friedman equations in the context of the Rastall theory of gravity (RTG), known as constant-roll warm inflation, including dissipation effects. We establish the model to evaluate the effective potential of inflation and entropy. We develop the inflationary observable like scalar-tensor power spectra, scalar-tensor spectral indices, tensor-to-scalar ratio, and running of spectral-index. The theory parameter $\lambda$ is constrained to observe the compatibility of our model with Planck 2013, Planck TT, TE, EE+lowP (2015), and Planck 2018 bounds. The results are feasible and interesting up to the 2$\sigma$ confidence level.

Keywords: modified gravity, warm inflation, constant-roll limit, dissipation

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Authors: Feras Hanandeh, Izzat Alsmadi, Muhammad M. Kwafha

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Prefix trees or tries are data structures that are used to store data or index of data. The goal is to be able to store and retrieve data by executing queries in quick and reliable manners. In principle, the structure of the trie depends on having letters in nodes at the different levels to point to the actual words in the leafs. However, the exact structure of the trie may vary based on several aspects. In this paper, we evaluated different structures for building tries. Using datasets of words of different sizes, we evaluated the different forms of trie structures. Results showed that some characteristics may impact significantly, positively or negatively, the size and the performance of the trie. We investigated different forms and structures for the trie. Results showed that using an array of pointers in each level to represent the different alphabet letters is the best choice.

Keywords: data structures, indexing, tree structure, trie, information retrieval

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Authors: Y. T. Chui, W. M. Au, L. Li

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Recently, wearable electronic textiles have been emerging in today’s market and were developed rapidly since, beside the needs for the clothing uses for leisure, fashion wear and personal protection, there also exist a high demand for the clothing to be capable for function in this electronic age, such as interactive interfaces, sensual being and tangible touch, social fabric, material witness and so on. With the requirements of wearable electronic textiles to be more comfortable, adorable, and easy caring, conductive yarn becomes one of the most important fundamental elements within the wearable electronic textile for interconnection between different functional units or creating a functional unit. The properties of conductive yarns from different companies can vary to a large extent. There are vitally important criteria for selecting the conductive yarns, which may directly affect its optimization, prospect, applicability and performance of the final garment. However, according to the literature review, few researches on conductive yarns on shelf focus on the assessment methods of conductive yarns for the scientific selection of material by a systematic way under different conditions. Therefore, in this study, direction of selecting high-quality conductive yarns is given. It is to test the stability and reliability of the conductive yarns according the problems industrialists would experience with the yarns during the every manufacturing process, in which, this assessment system can be classified into four stage. That is 1) Yarn stage, 2) Fabric stage, 3) Apparel stage and 4) End user stage. Several tests with clear experiment procedures and parameters are suggested to be carried out in each stage. This assessment method suggested that the optimal conducting yarns should be stable in property and resistant to various corrosions at every production stage or during using them. It is expected that this demonstration of assessment method can serve as a pilot study that assesses the stability of Ag/nylon yarns systematically at various conditions, i.e. during mass production with textile industry procedures, and from the consumer perspective. It aims to assist industrialists to understand the qualities and properties of conductive yarns and suggesting a few important parameters that they should be reminded of for the case of higher level of suitability, precision and controllability.

Keywords: applicability, assessment method, conductive yarn, wearable electronics

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Authors: Henda Gnakate Biba, Ndassa Mouafon Issa

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Dictionaries modeled on the Western model [tonic accent languages] are not suitable and do not account for tonal languages phonologically, which is why the [prosodic and phonological] ethnographic dictionary was designed. It is a glossary that expresses the tones and the rhythm of words. It recreates exactly the speaking or singing of a tonal language, and allows the non-speaker of this language to pronounce the words as if they were a native. It is a dictionary adapted to tonal languages. It was built from ethnomusicological theorems and phonological processes, according to Jean. J. Rousseau 1776 hypothesis /To say and to sing were once the same thing/. Each word in the French dictionary finds its corresponding language, ekaη. And each word ekaη is written on a musical staff. This ethnographic dictionary is also an inventive, original and innovative research thesis, but it is also an inventive, original and innovative research thesis. A contribution to the theoretical, musicological, ethno musicological and linguistic conceptualization of languages, giving rise to the practice of interlocution between the social and cognitive sciences, the activities of artistic creation and the question of modeling in the human sciences: mathematics, computer science, translation automation and artificial intelligence. When you apply this theory to any text of a folksong of a world-tone language, you do not only piece together the exact melody, rhythm, and harmonies of that song as if you knew it in advance but also the exact speaking of this language. The author believes that the issue of the disappearance of tonal languages and their preservation has been structurally resolved, as well as one of the greatest cultural equations related to the composition and creation of tonal, polytonal and random music. The experimentation confirming the theorization designed a semi-digital, semi-analog application which translates the tonal languages of Africa (about 2,100 languages) into blues, jazz, world music, polyphonic music, tonal and anatonal music and deterministic and random music). To test this application, I use a music reading and writing software that allows me to collect the data extracted from my mother tongue, which is already modeled in the musical staves saved in the ethnographic (semiotic) dictionary for automatic translation ( volume 2 of the book). Translation is done (from writing to writing, from writing to speech and from writing to music). Mode of operation: you type a text on your computer, a structured song (chorus-verse), and you command the machine a melody of blues, jazz and, world music or, variety etc. The software runs, giving you the option to choose harmonies, and then you select your melody.

Keywords: music, language, entenglement, science, research

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Authors: M. Salmanzadeh

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In paper, we will deal with incompressible Couette flow, which represents an exact analytical solution of the Navier-Stokes equations. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. The numerical technique that we will employ for the solution of the Couette flow is the Crank-Nicolson implicit method. Parabolic partial differential equations lend themselves to a marching solution; in addition, the use of an implicit technique allows a much larger marching step size than would be the case for an explicit solution. Hence, in the present paper we will have the opportunity to explore some aspects of CFD different from those discussed in the other papers.

Keywords: incompressible couette flow, numerical method, partial differential equation, Crank-Nicolson implicit

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Authors: A. Amiri Delouei

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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: functionally graded materials, unsteady heat conduction, cylinder, temperature distribution

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Authors: Saowanit Sukparungsee

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Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: number of defects, exponentially weighted moving average, average run length, square root transformations

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Authors: Shota Gulbani

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At the present stage, for the countries with developing economies, studying, and researching financial markets, gains special importance, because the situation of financial markets shapes an exact views about the carried out economic policy of the country. Besides, it’s unimaginable any country with developed economy, without healthy and functioning financial markets, whereas, for any kind of business it has got a great importance in terms of finding diversified and alternative capital. In this regard; it should be noted that the segments of Georgian financial markets are developed quite unequally, as evidenced by the fact that the Georgian financial sector is represented by 93% of commercial banks, what does not create an conformable environment for non-bank financial institutions development. In spite of the fact that Georgia has got one of the best banking system of region, it is important to properly analyze that this system should not hinder the development of other participants of Georgian financial sector.

Keywords: financial markets, macroeconomics, investments, stock exchange

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Authors: M. O. Durojaye, J. T. Agee

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This paper is on the one-dimensional, positive temperature coefficient (PTC) thermistor model with a hyperbolic tangent function approximation for the electrical conductivity. The method of asymptotic expansion was adopted to obtain the steady state solution and the unsteady-state response was obtained using the method of lines (MOL) which is a well-established numerical technique. The approach is to reduce the partial differential equation to a vector system of ordinary differential equations and solve numerically. Our analysis shows that the hyperbolic tangent approximation introduced is well suitable for the electrical conductivity. Numerical solutions obtained also exhibit correct physical characteristics of the thermistor and are in good agreement with the exact steady state solutions.

Keywords: electrical conductivity, hyperbolic tangent function, PTC thermistor, method of lines

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Yossiri Ariyakul, Piyakiat Insom, Poonyawat Sangiamkulthavorn, Takamichi Nakamoto

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In this paper, the method of optimization algorithm for sensor network comprised of movable sensor nodes which can be used for odor source localization was proposed. A sensor node is composed of an odor sensor, an anemometer, and a wireless communication module. The odor intensity measured from the sensor nodes are sent to the processor to perform the localization based on optimization algorithm by which the odor source localization map is obtained as a result. The map can represent the exact position of the odor source or show the direction toward it remotely. The proposed method was experimentally validated by creating the odor source localization map using three, four, and five sensor nodes in which the accuracy to predict the position of the odor source can be observed.

Keywords: odor sensor, odor source localization, optimization, sensor network

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Sachil Kumar, Anoop K.Verma, Uma Shankar Singh

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It’s extremely important to study postmortem interval in different causes of death since it assists in a great way in making an opinion on the exact cause of death following such incident often times. With diligent knowledge of the interval one could really say as an expert that the cause of death is not feigned hence there is a great need in evaluating such death to have been at the CRIME SCENE before performing an autopsy on such body. The approach described here is based on analyzing the degradation or proteolysis of a cardiac protein in cases of deaths due to burn as a marker of time since death. Cardiac tissue samples were collected from (n=6) medico-legal autopsies, (Department of Forensic Medicine and Toxicology), King George’s Medical University, Lucknow India, after informed consent from the relatives and studied post-mortem degradation by incubation of the cardiac tissue at room temperature (20±2 OC) for different time periods (~7.30, 18.20, 30.30, 41.20, 41.40, 54.30, 65.20, and 88.40 Hours). The cases included were the subjects of burn without any prior history of disease who died in the hospital and their exact time of death was known. The analysis involved extraction of the protein, separation by denaturing gel electrophoresis (SDS-PAGE) and visualization by Western blot using cTnT specific monoclonal antibodies. The area of the bands within a lane was quantified by scanning and digitizing the image using Gel Doc. As time postmortem progresses the intact cTnT band degrades to fragments that are easily detected by the monoclonal antibodies. A decreasing trend in the level of cTnT (% of intact) was found as the PM hours increased. A significant difference was observed between <15 h and other PM hours (p<0.01). Significant difference in cTnT level (% of intact) was also observed between 16-25 h and 56-65 h & >75 h (p<0.01). Western blot data clearly showed the intact protein at 42 kDa, three major (28 kDa, 30kDa, 10kDa) fragments, three additional minor fragments (12 kDa, 14kDa, and 15 kDa) and formation of low molecular weight fragments. Overall, both PMI and cardiac tissue of burned corpse had a statistically significant effect where the greatest amount of protein breakdown was observed within the first 41.40 Hrs and after it intact protein slowly disappears. If the percent intact cTnT is calculated from the total area integrated within a Western blot lane, then the percent intact cTnT shows a pseudo-first order relationship when plotted against the time postmortem. A strong significant positive correlation was found between cTnT and PM hours (r=0.87, p=0.0001). The regression analysis showed a good variability explained (R2=0.768) The post-mortem Troponin-T fragmentation observed in this study reveals a sequential, time-dependent process with the potential for use as a predictor of PMI in cases of burning.

Keywords: burn, degradation, postmortem interval, troponin-T

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Safa Ougoujil, Sidi Mohamed Rigar

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Economics is not an exact science. It cannot be from the moment it is a social science that concerns society organization, a human science that depends on the behavior of the men and women who make a part of this society. Therefore, it cannot ignore morality, the instinctive sense of good and evil, the natural order which place us between certain values, and which religion often sheds light on. In terms of finance, the reference to ethics is becoming more popular than ever. This is naturally due to the growing financial crises. Finance is less and less ethical, but some financial practices have continued to do so. This is the case of ethical finance and Islamic finance. After attempting to define the concepts of ethical finance and Islamic finance, in a period when financial innovation seeks to encourage differentiation in order to create more profit margins, this article attempts to expose the particularities, the convergences and the potentialities of development of these two sensibilities.

Keywords: convergences, ethical finance, Islamic finance, potential development

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Authors: K. Khadidja

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Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

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Authors: Özgür Cavbozar, Rasih Hakan Demirkol

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In many industries, it is occasionally essential to mount heavy modules to stationary racks or constructions in correct position in minimum time. With the rapid advancement in technology, consumption has increased. Therefore, to meet the higher demands, manufacturers should develope innovative methods to produce and store rapidly manufactured products faster. It is usually very tough to fix the heavy modules in two axes in correct position with fasteners like bolts. This paper represents a design solution for fixing the heavy modules to their racks of stationary shelves exactly with minimum effort. The design solution for a particular study has been proposed. Regarding quick mounting and easily adjustable operations for heavy modules, design and production suggestions have been carried out.

Keywords: exact mounting, mounting of heavy modules, quick mounting, two axial fixturing

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Authors: Prasad Pokkunuri

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Visco-elastic materials combine the stress response properties of both solids and fluids and have found use in a variety of damping applications – both vibrational and acoustic. Defense and automotive applications, in particular, are subject to high impact and shock loading – for example: aircraft landing gear, firearms, and shock absorbers. Field responsive fluids – a class of smart materials – are the preferred choice of energy absorbents because of their controllability. These fluids’ stress response can be controlled by the application of a magnetic or electric field, in a closed loop. Their rheological properties – elasticity, plasticity, and viscosity – can be varied all the way from that of a liquid such as water to a hard solid. This work presents a simplified model to study the impulse response behavior of such fluids for use in recoil damping systems. The well-known Burger’s equation, in conjunction with various visco-elastic constitutive models, is used to represent fluid behavior. The Kelvin-Voigt, Upper Convected Maxwell (UCM), and Oldroyd-B constitutive models are implemented in this study. Using these models in a one-dimensional framework eliminates additional complexities due to geometry, pressure, body forces, and other source terms. Using a finite difference formulation to numerically solve the governing equation(s), the response to an initial impulse is studied. The disturbance is confined within the problem domain with no-inflow, no-outflow boundary conditions, and its decay characteristics studied. Visco-elastic fluids typically involve a time-dependent stress relaxation which gives rise to interesting behavior when subjected to an impulsive load. For particular values of viscous damping and elastic modulus, the fluid settles into a stable oscillatory state, absorbing and releasing energy without much decay. The simplified formulation enables a comprehensive study of different modes of system response, by varying relevant parameters. Using the insights gained from this study, extension to a more detailed multi-dimensional model is considered.

Keywords: Burgers Equation, Impulse Response, Recoil Damping Systems, Visco-elastic Fluids

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Authors: Hasan Jumaah Mrayeh, Fue-Sang Lien

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ANSYS Fluent will be used to simulate Computational Fluid Dynamics (CFD) for an efficient lens and nozzle design which will be explained in this paper. We have designed and characterized an aerodynamic lens and a divergent nozzle for focusing flow that transmits sub 25 nm particles through the aerodynamic lens. The design of the lens and nozzle has been improved using CFD for particle trajectories. We obtained a case for calculating nanoparticles (25 nm) flowing through the aerodynamic lens and divergent nozzle. Nanoparticles are transported by air, which is pumped into the aerodynamic lens through the nozzle at 1 atmospheric pressure. We have also developed a computational methodology that can determine the exact focus characteristics of aerodynamic lens systems. Particle trajectories were traced using the Lagrange approach. The simulation shows the ability of the aerodynamic lens to focus on 25 nm particles after using a divergent nozzle.

Keywords: aerodynamic lens, divergent nozzle, ANSYS Fluent, Lagrange approach

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Authors: Remy Mpulumba Badiambile, Paul Musa Obadia, Malick Useni Mutayo, Jeef Numbi Mukanya, Patient Nkulu Banza, Tony Kayembe Kitenge, Erik Smolders, Jean-François Picron, Vincent Haufroid, Célestin Banza Lubaba Nkulu, Benoit Nemery

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Background: In July 2021, the Tshikapa river became heavily polluted by mining wastes from a diamond mine in neighboring Angola, leading to massive killing of fish, as well as disease and even deaths among residents living along the Tshikapa and Kasai rivers, a major contributory of the Congo river. The exact nature of the pollutants was unknown. Methods: In a cross-sectional study conducted in the city of Tshikapa in August 2021, we enrolled by opportunistic sampling 65 residents (11 children < 16y) living alongside the polluted rivers and 65 control residents (5 children) living alongside a non-affected portion of the Kasai river (upstream from the Tshikapa-Kasai confluence). We administered a questionnaire and obtained spot urine samples for measurements of thiocyanate (a metabolite of cyanide) and 26 trace metals (by ICP-MS). Metals (and pH) were also measured in samples of river water. Results: Participants from both groups consumed river water. In the area affected by the pollution, most participants had eaten dead fish. Prevalences of reported health symptoms were higher in the exposed group than among controls: skin rashes (52% vs 0%), diarrhea (40% vs 8%), abdominal pain (8% vs 3%), nausea (3% vs 0%). In polluted water, concentrations [median (range)] were only higher for nickel [(2.2(1.4–3.5)µg/L] and uranium [78(71–91)ng/L] than in non-polluted water [0.8(0.6–1.9)µg/L; 9(7–19)ng/L]. In urine, concentrations [µg/g creatinine, median(IQR)] were significantly higher in the exposed group than in controls for lithium [19.5(12.4–27.3) vs 6.9(5.9–12.1)], thallium [0.41(0.31–0.57) vs 0.19(0.16–0.39)], and uranium [0.026(0.013–0.037)] vs 0.012(0.006–0.024)]. Other elements did not differ between the groups, but levels were higher than reference values for several metals (including manganese, cobalt, nickel, and lead). Urinary thiocyanate concentrations did not differ. Conclusion: This study, after an ecological disaster in the DRC, has documented contamination of river water by nickel and uranium and high urinary levels of some trace metals among affected riverine populations. However, the exact cause of the massive fish kill and disease among residents remains elusive. The capacity to rapidly investigate toxic pollution events must be increased in the area.

Keywords: metal contaminants, river water and human urine, pollution by mining wastes, DR Congo

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Authors: P. R. Maiti, S. K. Bhattacharyya

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Sloshing is a physical phenomenon characterized by the oscillation of unrestrained free surface of liquid in a partially liquid filled container subjected to external excitation. Determination of sloshing frequency in container is important to avoid resonance condition of the system. The complex behavior of the free surface movement and its combined mode of vibration make difficulty for exact analysis of sloshing. In the present study, numerical analysis is carried out for a partially liquid filled tank under external forces. Boundary element approach is used to formulate the sloshing problem in two -dimensional prismatic container with potential flow. Effort has been made to find slosh response for two dimensional problems in partially liquid filled prismatic container.

Keywords: sloshing, boundary element method, prismatic container, oscillation

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Anjushi Verma, Tirthankar Gayen

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Although, reliability is an important attribute of quality, especially for mission critical systems, yet, there does not exist any versatile model even today for the reliability assessment of component-based software. The existing Black Box models are found to make various assumptions which may not always be realistic and may be quite contrary to the actual behaviour of software. They focus on observing the manner in which the system behaves without considering the structure of the system, the components composing the system, their interconnections, dependencies, usage frequencies, etc.As a result, the entropy (uncertainty) in assessment using these models is much high.Though, there are some models based on operation profile yet sometimes it becomes extremely difficult to obtain the exact operation profile concerned with a given operation. This paper discusses the drawbacks, deficiencies and limitations of Black Box approaches from the perspective of various authors and finally proposes a conceptual model for the reliability assessment of software.

Keywords: black box, faults, failure, software reliability

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

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We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: indentation, contact problem, stress distribution, coating materials, layer-substrate body

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

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In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index (PCI), average sample number (ASN), Bayesian approach

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Daijun Chen

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Affordable housing is subsidized by the government to meet the housing demand of low and middle-income urban residents in the process of urbanization and to alleviate the housing inequality caused by market-based housing reforms. It is a recognized fact that the living conditions of the insured have been improved while constructing the subsidized housing. However, the choice of affordable housing is mostly in the suburbs, where the surrounding urban functions and infrastructure are incomplete, resulting in the spatial mismatch of "jobs-housing" in affordable housing. The main reason for this problem is that the residents of affordable housing are more sensitive to the spatial location of their residence, but their selectivity and controllability to the housing location are relatively weak, which leads to higher commuting costs. Their real cost of living has not been effectively reduced. In this regard, 92 subsidized housing communities in Nanjing, China, are selected as the research sample in this paper. The residents of the affordable housing and their commuting Spatio-temporal behavior characteristics are identified based on the LBS (location-based service) data. Based on the spatial mismatch theory, spatial mismatch indicators such as commuting distance and commuting time are established to measure the spatial mismatch degree of subsidized housing in different districts of Nanjing. Furthermore, the geographically weighted regression model is used to analyze the influencing factors of the spatial mismatch of affordable housing in terms of the provision of employment opportunities, traffic accessibility and supporting service facilities by using spatial, functional and other multi-source Spatio-temporal big data. The results show that the spatial mismatch of affordable housing in Nanjing generally presents a "concentric circle" pattern of decreasing from the central urban area to the periphery. The factors affecting the spatial mismatch of affordable housing in different spatial zones are different. The main reasons are the number of enterprises within 1 km of the affordable housing district and the shortest distance to the subway station. And the low spatial mismatch is due to the diversity of services and facilities. Based on this, a spatial optimization strategy for different levels of spatial mismatch in subsidized housing is proposed. And feasible suggestions for the later site selection of subsidized housing are also provided. It hopes to avoid or mitigate the impact of "spatial mismatch," promote the "spatial adaptation" of "jobs-housing," and truly improve the overall welfare level of affordable housing residents.

Keywords: affordable housing, spatial mismatch, commuting characteristics, spatial adaptation, welfare benefits

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Authors: Pius W. Molo Chin

Abstract:

Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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