Search results for: mathematical sciences

Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

Abstract:

This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are, therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: performance modeling, markov process, steady state availability, availability analysis

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Authors: Mikhail Zarechnev, Bora I. Kumova

Abstract:

A syllogism is a deductive inference scheme used to derive a conclusion from a set of premises. In a categorical syllogisms, there are only two premises and every premise and conclusion is given in form of a quantified relationship between two objects. The different order of objects in premises give classification known as figures. We have shown that the ordered combinations of 3 generalized quantifiers with certain figure provide in total of 108 syllogistic moods which can be considered as different inference rules. The classical syllogistic system allows to model human thought and reasoning with syllogistic structures always attracted the attention of cognitive scientists. Since automated reasoning is considered as part of learning subsystem of AI agents, syllogistic system can be applied for this approach. Another application of syllogistic system is related to inference mechanisms on the Semantic Web applications. In this paper we proposed the mathematical model and algorithm for syllogistic reasoning. Also the model of iterative syllogistic reasoning in case of continuous flows of incoming data based on case–based reasoning and possible applications of proposed system were discussed.

Keywords: categorical syllogism, case-based reasoning, cognitive architecture, inference on the semantic web, syllogistic reasoning

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Authors: Mohieddine Benghersallah, Mohamed Zakaria Zahaf, Ali Medjber, Idriss Tibakh

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The objective of this study is to analyse the effects of cutting parameters on surface roughness in dry face milling using statistical techniques. We studied the effect of the microstructure of AISI 52100 steel on machinability before and after hardening. The machining tests were carried out on a high rigidity vertical milling machine with a 25 mm diameter face milling cutter equipped with micro-grain bicarbide inserts with PVD (Ti, AlN) coating in GC1030 grade. A Taguchi L9 experiment plan is adopted. Analysis of variance (ANOVA) was used to determine the effects of cutting parameters (Vc, fz, ap) on the roughness (Ra) of the machined surface. Regression analysis to assess the machinability of steel presented mathematical models of roughness and the combination of parameters to minimize it. The recorded results show that feed per tooth has the most significant effect on the surface condition for both steel treatment conditions. The best roughnesses were obtained for the hardened AISI 52100 steel.

Keywords: machinability, heat treatment, microstructure, surface roughness, Taguchi method

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Authors: Li Ma, Meishuang Ma, Mengying Huang

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The quality of construction projects reflects the credit and responsibilities of construction contractors for the owners and the whole society. Because the construction contractors master more relevant information about the entrusted engineering project under construction while the owners are in unfavorable position of gaining information, asymmetric information may lead the contractors act against the owners in order to pursue their own interests. Building a powerful motivation mechanism is the key to guarantee investor economic interests and the life and property of users in construction projects. Based on principal-agent theory and game theory, the authors develop relevant mathematical models to analyze and compare the contractor’s utility functions under different combinations of contracts’ explicit incentive mechanism and reputation’s implicit incentive mechanism aiming at finding out the conditions for incentive validity. The research concludes that the most rational motivation way is to combine the explicit and implicit incentive effects of both contracts and reputation mechanism, and puts forth some measures for problems on account of China’s current situation.

Keywords: construction contractors, contract, reputation, incentive mechanism

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Authors: Lucas Wilman Crispim, Patrícia Hallack, Maikel Ballester

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This work aims at modeling electric discharges in gas mixtures. The mathematical model mimics the ignition process in a commercial spark-plug when a high voltage is applied to the plug terminals. A longitudinal unidimensional Cartesian domain is chosen for the simulation region. Energy and mass transfer are considered for a macroscopic fluid representation, while energy transfer in molecular collisions and chemical reactions are contemplated at microscopic level. The macroscopic model is represented by a set of uncoupled partial differential equations. Microscopic effects are studied within a discrete model for electronic and molecular collisions in the frame of ZDPlasKin, a plasma modeling numerical tool. The BOLSIG+ solver is employed in solving the electronic Boltzmann equation. An operator splitting technique is used to separate microscopic and macroscopic models. The simulation gas is a mixture of atomic Argon neutral, excited and ionized. Spatial and temporal evolution of such species and temperature are presented and discussed.

Keywords: CFD, electronic discharge, ignition, spark plug

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Authors: A. Chateauneuf, M. Mostoufi, D. Vyncke

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Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo, comonotonicity, option pricing, scientific computing

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Authors: Jaime Muñoz, José Arcos, Oscar Bautista Federico Méndez

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The influence of a pulsatile electroosmotic flow (PEOF) at the rate of spread, or dispersivity, for a non-reactive solute released in a microcapillary with slippage at the boundary wall (modeled by the Navier-slip condition) is theoretically analyzed. Based on the flow velocity field developed under such conditions, the present study implements an analytical scheme of scaling known as the Theory of Homogenization, in order to obtain a mathematical expression for the dispersivity, valid at a large time scale where the initial transients have vanished and the solute spreads under the Taylor dispersion influence. Our results show the dispersivity is a function of a slip coefficient, the amplitude of the imposed electric field, the Debye length and the angular Reynolds number, highlighting the importance of the latter as an enhancement/detrimental factor on the dispersivity, which allows to promote the PEOF as a strong candidate for chemical species separation at lab-on-a-chip devices.

Keywords: dispersivity, microcapillary, Navier-slip condition, pulsatile electroosmotic flow, Taylor dispersion, Theory of Homogenization

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Authors: Benjamin Aina Peter, Amos Wale Ogunsola

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In this paper, a mathematical model of malaria transmission was presented with the effect of seasonal shift, due to global fluctuation in temperature, on the increase of conveyor of the infectious disease, which probably alters the region transmission potential of malaria. A deterministic compartmental model was proposed and analyzed qualitatively. Both qualitative and quantitative approaches of the model were considered. The next-generation matrix is employed to determine the basic reproduction number of the model. Equilibrium points of the model were determined and analyzed. The numerical simulation is carried out using Excel Micro Software to validate and support the qualitative results. From the analysis of the result, the optimal temperature for the transmission of malaria is between and . The result also shows that an increase in temperature due to seasonal shift gives rise to the development of parasites which consequently leads to an increase in the widespread of malaria transmission in Kampala. It is also seen from the results that an increase in temperature leads to an increase in the number of infectious human hosts and mosquitoes.

Keywords: seasonal variation, indoor residual spray, efficacy of spray, temperature-dependent model

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Authors: A. A. Abdullah, K. A. Lindsay

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The management of a salt-gradient is investigated with respect to the interaction between the solar pond and its associated evaporation pond. Issues considered are the impact of precipitation and the operation of the flushing system with particular reference to the case in which the flushing fluid is pure water. Results suggest that a management strategy based on a flushing system that simply replaces evaporation losses of water from the solar pond and evaporation pond will be optimally efficient. Such a management strategy will maintain the operational viability of a salt-gradient solar pond as a reservoir of cheap heat while simultaneously ensuring that the associated evaporation pond can feed the storage zone of the solar pond with sufficient saturated brine to balance the effect of salt diffusion. Other findings are, first, that once near saturation is achieved in the evaporation pond, the efficacy of the proposed management strategy is relatively insensitive to both the size of the evaporation pond or its depth, and second, small changes in the extraction of heat from the storage zone of a salt-gradient solar pond have an amplified effect on the temperature of that zone. The possibility of boiling of the storage zone cannot be ignored in a well-configured salt-gradient solar pond.

Keywords: aqueous sodium chloride, constitutive expression, solar pond, salt-gradient

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Authors: Roselyn Zaman, Mobarak Hossain

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A new mathematical model is developed to study crack breathing behavior considering effect of angular position of unbalanced force at different crack locations. Crack breathing behavior has been determined using effectual bending angle by studying the transient change of the crack area. Different crack breathing behavior of the unbalanced shaft has been observed for different combination of angular position of unbalanced force with crack location except crack locations 0.3L and 0.8335L, where L is the total length of the shaft, where unbalanced shaft behave completely like the balanced shaft. Based on different combination of angular position of unbalanced force with crack location, the stiffness of unbalanced shaft can be divided into three regions. An unbalanced shaft is overall stiffer than a balanced shaft when angular position of unbalance force is between 90° to 270° and crack located between 0.3L and 0.8335L, and it is overall flexible when the crack located in outside this crack region. On the other hand, it is overall flexible when angular position of unbalanced force is between 0° to 90° or 270° to 360° and crack located in middle region and it is overall stiffer for outside this crack region.

Keywords: cracked shaft, crack location, shaft stiffness, unbalanced force, and unbalanced force orientation

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Authors: Vaclav Mentl, Josef Volak

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In many industrial applications, materials are subjected to degradation of mechanical properties as a result of real service conditions, temperature, cyclic loading, humidity or other corrosive media, irradiation, their combination etc. The assessment of the remaining lifetime of components and structures is commonly based on correlated procedures including numerous destructive, non-destructive and mathematical techniques that should guarantee reasonably precise assessment of the current damage extent of materials in question and the remaining lifetime evaluation of the component under consideration. The answers to demands of customers to extend the lifetime of existing components beyond their original design life must be based on detailed assessment of the current degradation extent, what can be rarely realised by means of traditional mechanical (standardised) tests that need relatively large volumes of representative material for the test specimen manufacturing. This fact accelerated the research of miniaturised test specimen that can be sampled non-invasively from the component.

Keywords: small punch test, correlation, creep, mechanical properties

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Authors: Vinay Kumar K. S., Shravani V., Spoorthi G., Udith K. S., Divya T. M., Venkatesha M.

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In this work, the mathematical modeling, design and analysis of a 2×2 microstrip patch antenna array (MSPA) antenna configuration is presented. Array utilizes a tiny strip antenna module with two vertical slots for 5G applications at an operating frequency of 5.3 GHz. The proposed array of antennas where the phased array antenna systems (PAAS) are used ubiquitously everywhere, from defense radar applications to commercial applications like 5G/6G. Microstrip patch antennae with slot arrays for linear polarisation parallel and perpendicular to the axis, respectively, are fed through transverse slots in the side wall of the circular waveguide and fed through longitudinal slots in the small wall of the rectangular waveguide. The microstrip patch antenna is developed using Ansys HFSS (High-Frequency Structure Simulator), this simulation tool. The maximum gain of 6.14 dB is achieved at 5.3 GHz for a single MSPA. For 2×2 array structure, a gain of 7.713 dB at 5.3 GHz is observed. Such antennas find many applications in 5G devices and technology.

Keywords: Ansys HFSS, gain, return loss, slot array, microstrip patch antenna, 5G antenna

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Authors: S. Ebisintei, M. A. Olutoye, A. S. Kovo, U. G. Akpan

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The effect of soil degradation due to ion leachate migration using dumpsite located at Idu industrial area of Abuja was investigated. It was done to assess the health and environmental pollution consequences caused by heavy metals’ concentration in the soil on inhabitants around the settlement. Soil samples collected from four cardinal points and at the center during the dry and wet season were pretreated, digested and heavy metal concentrations present were analyzed using Atomic Absorption Spectrophotometer. The concentrations of Pb, Cu, Mn, Ni, and Cr, were determined and also for control sample obtained 300 m away from the dumpsite. Water samples were collected from three wells to test for physiochemical properties of pH, COD, BOD, DO, hardness, conductivity, and alkalinity. The result showed a significant difference in concentration of toxic heavy metals in the dumpsite as compared to the control sample. A mathematical model was developed to predict the heavy metal concentrations beyond the sampling point. The results indicate that metal concentrations in both dry and wet season were above the WHO, and SON set standards. The trend, if unrestrained, portends danger to human life, reduces agricultural productivity and sustainability.

Keywords: soil degradation, ion leachate, productivity, environment, sustainability

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Authors: Yousfi Abdelkader, Chaker Abdelkader, Bot Youcef

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This article proposes a five-level shunt active power filter for power quality improvement using a interval type-2 fuzzy logic controller (IT2 FLC). The reference compensating current is extracted using the P-Q theory. The majority of works previously reported are based on two-level inverters with a conventional Proportional integral (PI) controller, which requires rigorous mathematical modeling of the system. In this paper, a IT2 FLC controlled five-level active power filter is proposed to overcome the problem associated with PI controller. The IT2 FLC algorithm is applied for controlling the DC-side capacitor voltage as well as the harmonic currents of the five-level active power filter. The active power filter with a IT2 FLC is simulated in MATLAB Simulink environment. The simulated response shows that the proposed shunt active power filter controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the source voltage.

Keywords: power quality, shunt active power filter, interval type-2 fuzzy logic controller (T2FL), multilevel inverter

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Authors: Essa Abrahim Abdulgader Saleem, Thien-My Dao

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The main objective of this paper is to optimize series-parallel system reliability using Genetic Algorithm (GA) and statistical analysis; considering system reliability constraints which involve the redundant numbers of selected components, total cost, and total weight. To perform this work, firstly the mathematical model which maximizes system reliability subject to maximum system cost and maximum system weight constraints is presented; secondly, a statistical analysis is used to optimize GA parameters, and thirdly GA is used to optimize series-parallel systems reliability. The objective is to determine the strategy choosing the redundancy level for each subsystem to maximize the overall system reliability subject to total cost and total weight constraints. Finally, the series-parallel system case study reliability optimization results are showed, and comparisons with the other previous results are presented to demonstrate the performance of our GA.

Keywords: reliability, optimization, meta-heuristic, genetic algorithm, redundancy

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Authors: D. Maneetham, L. Sivhour

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Robotic arm manipulators are widely used to accomplish many kinds of tasks. SCORBOT-ER 4u is a 5-degree of freedom (DOF) vertical articulated educational robotic arm, and all joints are revolute. It is specifically designed to perform pick and place task with its gripper. The pick and place task consists of consideration of the end effector coordinate of the robotic arm and the desired position coordinate in its workspace. This paper describes about forward kinematics modeling and analysis of the robotic end effector motion through joint space. The kinematics problems are defined by the transformation from the Cartesian space to the joint space. Denavit-Hartenberg (D-H) model is used in order to model the robotic links and joints with 4x4 homogeneous matrix. The forward kinematics model is also developed and simulated in MATLAB. The mathematical model is validated by using robotic toolbox in MATLAB. By using this method, it may be applicable to get the end effector coordinate of this robotic arm and other similar types to this arm. The software development of SCORBOT-ER 4u is also described here. PC-and EtherCAT based control technology from BECKHOFF is used to control the arm to express the pick and place task.

Keywords: forward kinematics, D-H model, robotic toolbox, PC- and EtherCAT-based control

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Authors: Tao Ding, Danjia Yan, Jinye Li, Chao Ren, Xinhua Hu

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The paper based on the research background of the current situation of water shortage in China and intelligent management of water resources in the information era. And the paper adopts WebGIS technology, combining the mathematical model of water resources management to develop a WebGIS-based water environment capacity inquiry and polluted water emission planning. The research significance of the paper is that it can inquiry the water environment capacity of Jinhua City in real time and plan how to drain polluted water into the river, so as to realize the effective management of water resources. This system makes sewage planning more convenient and faster. For the planning of the discharge enterprise, the decision on the optimal location of the sewage outlet can be achieved through calculation of the Sewage discharge planning model in the river, without the need for site visits. The system can achieve effective management of water resources and has great application value.

Keywords: sewerage planning, water environment capacity, water resources management, WebGIS

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Authors: M. Rodionov, N. Sharapova, Z. Dedovets

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The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

Keywords: education, methodological approaches, teacher, secondary school

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Authors: Fayssal Amrane, Azeddine Chaiba

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In this paper, type-2 fuzzy logic control (T2FLC) and neuro-fuzzy control (NFC) for a doubly fed induction generator (DFIG) based on direct power control (DPC) with a fixed switching frequency is proposed for wind generation application. First, a mathematical model of the doubly-fed induction generator implemented in d-q reference frame is achieved. Then, a DPC algorithm approach for controlling active and reactive power of DFIG via fixed switching frequency is incorporated using PID. The performance of T2FLC and NFC, which is based on the DPC algorithm, are investigated and compared to those obtained from the PID controller. Finally, simulation results demonstrate that the NFC is more robust, superior dynamic performance for wind power generation system applications.

Keywords: doubly fed induction generator (DFIG), direct power control (DPC), neuro-fuzzy control (NFC), maximum power point tracking (MPPT), space vector modulation (SVM), type 2 fuzzy logic control (T2FLC)

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Authors: Adi A. Maaita, Hamza A. A. Al Sewadi

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One of the crucial parameters of digital cryptographic systems is the selection of the keys used and their distribution. The randomness of the keys has a strong impact on the system’s security strength being difficult to be predicted, guessed, reproduced or discovered by a cryptanalyst. Therefore, adequate key randomness generation is still sought for the benefit of stronger cryptosystems. This paper suggests an algorithm designed to generate and test pseudo random number sequences intended for cryptographic applications. This algorithm is based on mathematically manipulating a publically agreed upon information between sender and receiver over a public channel. This information is used as a seed for performing some mathematical functions in order to generate a sequence of pseudorandom numbers that will be used for encryption/decryption purposes. This manipulation involves permutations and substitutions that fulfills Shannon’s principle of “confusion and diffusion”. ASCII code characters wereutilized in the generation process instead of using bit strings initially, which adds more flexibility in testing different seed values. Finally, the obtained results would indicate sound difficulty of guessing keys by attackers.

Keywords: cryptosystems, information security agreement, key distribution, random numbers

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Authors: Fernando L. P. Santos, Luiz G. Lyra, Helenice O. Florentino, Daniela R. Cantane

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Dengue is a febrile infectious disease caused by a virus of the family Flaviridae. It is transmitted by the bite of mosquitoes, usually of the genus Aedes aegypti. It occurs in tropical and subtropical areas of the world. This disease has been a major public health problem worldwide, especially in tropical countries such as Brazil, and its incidence has increased in recent years. Dengue is a subject of intense research. Efficient forms of mosquito control must be considered. In this work, the mono-objective optimal control problem was solved for analysing the dengue disease problem. Chemical and biological controls were considered in the mathematical aspect. This model describes the dynamics of mosquitoes in water and winged phases. We applied the genetic algorithms (GA) to obtain optimal strategies for the control of dengue. Numerical simulations have been performed to verify the versatility and the applicability of this algorithm. On the basis of the present results we may recommend the GA to solve optimal control problem with a large region of feasibility.

Keywords: genetic algorithm, dengue, Aedes aegypti, biological control, chemical control

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Authors: Farooq A. Al-Sheikh, Ali Elkamel, William A. Anderson

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A fluidized catalytic cracking unit (FCCU) is one of the effective units in many refineries. Modeling and optimization of FCCU were done by many researchers in past decades, but in this research, comparison between post- and oxy-combustion was studied in the regenerator-FCCU. Therefore, a simplified mathematical model was derived by doing mass/heat balances around both reactor and regenerator. A state space analysis was employed to show effects of the flow rates variables such as air, feed, spent catalyst, regenerated catalyst and flue gas on the output variables. The main aim of studying dynamic responses is to figure out the most influencing variables that affect both reactor/regenerator temperatures; also, finding the upper/lower limits of the influencing variables to ensure that temperatures of the reactors and regenerator work within normal operating conditions. Therefore, those values will be used as side constraints in the optimization technique to find appropriate operating regimes. The objective functions were modeled to be maximizing the energy in the reactor while minimizing the energy consumption in the regenerator. In conclusion, an oxy-combustion process can be used instead of a post-combustion one.

Keywords: FCCU modeling, optimization, oxy-combustion, post-combustion

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Authors: Hany Mohamed Abdu, Mohamed Hassan Gadallah, El-Giushi Mokhtar, Yehia Mahmoud Ismail

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Laser beam cutting is one nontraditional machining process. This paper optimizes the parameters of Laser beam cutting machining parameters of Stainless steel (316L) by considering the effect of input parameters viz. power, oxygen pressure, frequency and cutting speed. Statistical design of experiments are carried in three different levels and process responses such as 'Average kerf taper (Ta)' and 'Surface Roughness (Ra)' are measured accordingly. A quadratic mathematical model (RSM) for each of the responses is developed as a function of the process parameters. Responses predicted by the models (as per Taguchi’s L27 OA) are employed to search for an optimal parametric combination to achieve desired yield of the process. RSM models are developed for mean responses, S/N ratio, and standard deviation of responses. Optimization models are formulated as single objective problem subject to process constraints. Models are formulated based on Analysis of Variance (ANOVA) using MATLAB environment. Optimum solutions are compared with Taguchi Methodology results.

Keywords: optimization, laser cutting, robust design, kerf width, Taguchi method, RSM and DOE

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Authors: Nikolaos Mamalis

Abstract:

The work of the eminent architect and composer has undoubtedly been influenced both by his architecture and collaboration with Le Corbusier and by the conquests of the musical avant-garde of the 20th century (Schoenberg, Messian, Bartock, electroacoustic music). It is known that the golden mean and the Fibonacci sequence played a momentous role in the Architectural Avant-garde (Modulor) and expanded on musical pursuits. Especially in the 50s (serialism), it was a structural tool for composition. Xenakis' architectural and musical work (Sacrifice, Metastasis, Rebonds, etc.) received the influence of the Golden Section, as has been repeatedly demonstrated. However, the idea of this retrospective sequence and the reflection raised by the search for new proportions, both in the architectural and the musical work of Xenakis, was not limited to constituting a step, a workable formula that acted unifyingly with regard to the other parameters of the musical work, or as an aesthetic model that makes sense - philosophically and poetically - an anthropocentric dimension as in other composers (see Luigi Nono) ̇ triggered a qualitative leap, an opening of the composer to the assimilation of mathematical concepts and scientific types in music and the consolidation of new sound horizons of stochastic music.

Keywords: golden ratio, music, space, stochastic music

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Authors: Odunayo E. Popoola, Charles A. Aladesaye, Sunday O. Gbenro

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The study investigated the impact of technological advancement on the academic performance of Mathematics students in tertiary institutions in Ekiti State, Nigeria. The quasi-experimental research design was adopted for the study. The population for the study consisted of all the 100 level undergraduates and all Mathematics lecturers in the Department of Mathematics in all the five tertiary institutions in the State. The sample of this study was made of one hundred (100) students and fifty (50) lecturers randomly selected using stratified sampling technique. Hypotheses were postulated to find out whether (i) advancement in technology influences the academic performance of students in Mathematics (ii) teaching method and gender disparity influences the academic performance of students in Mathematics. The study revealed that teaching method, gender, and technology influence academic performance of students in Mathematics. Based on the findings, it is recommended that curriculum and assessment in school Mathematics should explicitly require that all undergraduate become proficient in using digital technologies for mathematical purposes so as to enhance the better performance of students in Mathematics.

Keywords: mathematics, performance, tertiary institutions, technology

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Authors: Tadesse Desta Gidey, Gebregziabher Kahsay, Pooran Singh

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This work focuses on the theoretical investigation of the coexistence of superconductivity and Spin Density Wave (SDW)in Ferropnictide Ba₁₋ₓKₓFe₂As₂. By developing a model Hamiltonian for the system and by using quantum field theory Green’s function formalism, we have obtained mathematical expressions for superconducting transition temperature TC), spin density wave transition temperature (Tsdw), superconductivity order parameter (Sc), and spin density wave order parameter (sdw). By employing the experimental and theoretical values of the parameters in the obtained expressions, phase diagrams of superconducting transition temperature (TC) versus superconducting order parameter (Sc) and spin density wave transition temperature (Tsdw), versus spin density wave order parameter (sdw) have been plotted. By combining the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and spin density wave (SDW) in ferropnictide Ba1−xKxFe2As2.

Keywords: Superconductivity, Spin density wave, Coexistence, Green function, Pnictides, Ba₁₋ₓKₓFe₂As₂

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani, S. Zolghadri

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Dosimetry is an indispensable and precious factor in patient treatment planning to minimize the absorbed dose in vital tissues. In this study, compartmental model was used in order to estimate the human absorbed dose of ¹⁷⁷Lu-DOTATOC from the biodistribution data in wild type rats. For this purpose, ¹⁷⁷Lu-DOTATOC was prepared under optimized conditions and its biodistribution was studied in male Syrian rats up to 168 h. Compartmental model was applied to mathematical description of the drug behaviour in tissue at different times. Dosimetric estimation of the complex was performed using radiation absorbed dose assessment resource (RADAR). The biodistribution data showed high accumulation in the adrenal and pancreas as the major expression sites for somatostatin receptor (SSTR). While kidneys as the major route of excretion receive 0.037 mSv/MBq, pancreas and adrenal also obtain 0.039 and 0.028 mSv/MBq. Due to the usage of this method, the points of accumulated activity data were enhanced, and further information of tissues uptake was collected that it will be followed by high (or improved) precision in dosimetric calculations.

Keywords: compartmental modeling, human absorbed dose, ¹⁷⁷Lu-DOTATOC, Syrian rats

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Authors: Azad Hussain, Shoaib Ali, M. Y. Malik, Saba Nazir, Sarmad Jamal

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This article reports a fundamental numerical investigation to analyze the impact of thermal radiations on MHD flow of differential type nanofluid past a porous plate. Here, viscosity is taken as function of temperature. Energy equation is deliberated in the existence of viscous dissipation. The mathematical terminologies of nano concentration, velocity and temperature are first cast into dimensionless expressions via suitable conversions and then solved by using Shooting technique to obtain the numerical solutions. Graphs has been plotted to check the convergence of constructed solutions. At the end, the influence of effective parameters on nanoparticle concentration, velocity and temperature fields are also deliberated in a comprehensive way. Moreover, the physical measures of engineering importance such as the Sherwood number, Skin friction and Nusselt number are also calculated. It is perceived that the thermal radiation enhances the temperature for both Vogel's and Reynolds' models but the normal stress parameter causes a reduction in temperature profile.

Keywords: MHD flow, differential type nanofluid, Porous medium, variable viscosity, thermal radiation

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Authors: Jun Yuan

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Shipping is a major transportation mode all over the world, and it has a significant contribution to global carbon emissions. Electrification of ships is one of the main strategies to reduce shipping carbon emissions. The number of electric ships has continued to grow in recent years. However, charging infrastructure is still scarce, which severely restricts the development of electric ships. Therefore, it is very important to design ship charging stations reasonably by comprehensively considering charging demand and investment costs. This study aims to minimize the full life cycle cost of charging stations, considering the uncertainty of charging demand. A mixed integer programming model is developed for this optimization problem. Based on the characteristics of the mathematical model, a simulation based optimization method is proposed to find the optimal number and rated power of chargers. In addition, the impact of renewable energy and storage systems is analyzed. The results can provide decision support and a reference basis for the design of ship charging stations.

Keywords: shipping emission, electricity ship, charging station, optimal design

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