Search results for: second order linearization

Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Benjamin Goldsmith, Felix Heisel

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The building industry must reduce its emissions in order to meet 2030 neutrality targets, and modular and/or offsite construction is seen as an alternative to conventional construction methods which could help achieve this goal. Modular construction has previously been shown to be less wasteful and has a lower global warming potential (GWP). While many studies have been conducted investigating the life cycle impacts of modular and conventional construction, few studies have compared different types of modular assembly and construction in order to determine which offer the greatest environmental benefits over their whole life cycle. This study seeks to investigate three different modular construction types -infill frame, core, and podium- in order to determine environmental impacts such as GWP as well as circularity indicators. The study will focus on the emissions of the production, construction, and end-of-life phases. The circularity of the various approaches will be taken into consideration in order to acknowledge the potential benefits of the ability to reuse and/or reclaim materials, products, and assemblies. The study will conduct hypothetical case studies for the three different modular construction types, and in doing so, control the parameters of location, climate, program, and client. By looking in-depth at the GWP of the beginning and end phases of various simulated modular buildings, it will be possible to make suggestions on which type of construction has the lowest global warming potential.

Keywords: modular construction, offsite construction, life cycle analysis, global warming potential, environmental impact, circular economy

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Authors: Zhenjie Liu

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This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

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Authors: Stuart W. Campbell, Alexander M. Galloway, Norman A. McPherson, Duncan Camilleri, Daniel Micallef

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Gas tungsten arc welding requires a gas shield to be present in order to protect the arc area from contamination by atmospheric gases. As a result of each gas having its own unique thermophysical properties, the shielding gas selected can have a major influence on the arc stability, welding speed, weld appearance and geometry, mechanical properties and fume generation. Alternating shielding gases is a relatively new method of discreetly supplying two different shielding gases to the welding region in order to take advantage of the beneficial properties of each gas, as well as the inherent pulsing effects generated. As part of an ongoing process to fully evaluate the effects of this novel supply method, a computational fluid dynamics model has been generated to include the gas dependent thermodynamic and transport properties in order to evaluate the effects that an alternating gas supply has on the arc plasma. Experimental trials have also been conducted to validate the model arc profile predictions.

Keywords: Alternating shielding gases, ANSYS CFX, Gas tungsten arc welding(GTAW), magnetohydrodynamics(MHD)

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Authors: Joonas Pääkkönen

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In sports, individuals and teams are typically interested in final rankings. Final results, such as times or distances, dictate these rankings, also known as places. Places can be further associated with ordered random variables, commonly referred to as order statistics. In this work, we introduce a simple, yet accurate order statistical ordinal regression function that predicts relay race places with changeover-times. We call this function the Fenton-Wilkinson Order Statistics model. This model is built on the following educated assumption: individual leg-times follow log-normal distributions. Moreover, our key idea is to utilize Fenton-Wilkinson approximations of changeover-times alongside an estimator for the total number of teams as in the notorious German tank problem. This original place regression function is sigmoidal and thus correctly predicts the existence of a small number of elite teams that significantly outperform the rest of the teams. Our model also describes how place increases linearly with changeover-time at the inflection point of the log-normal distribution function. With real-world data from Jukola 2019, a massive orienteering relay race, the model is shown to be highly accurate even when the size of the training set is only 5% of the whole data set. Numerical results also show that our model exhibits smaller place prediction root-mean-square-errors than linear regression, mord regression and Gaussian process regression.

Keywords: Fenton-Wilkinson approximation, German tank problem, log-normal distribution, order statistics, ordinal regression, orienteering, sports analytics, sports modeling

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Authors: Ahmed A. Abdel-Khalek, Reham A. Mohamed

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The kinetics of oxidation of binary complex [CrIII(DMG)2(H2O)4 ]+ to Cr(VI) by periodate has been investigated spectrophotometrically where, [DMG= Dimethylglyoxime] at 370nm under pseudo first order reaction conditions in aqueous medium over 20- 40ºC range, PH 2-3, and I=0.07 mol dm-3. The reaction is first order with respect to both [IO4-] and Cr(III), and the reaction increased with PH increased. Thermodymanic activation parameters have been calculated. It is suggested that electron transfer proceeds through an inner sphere mechanism via coordination of IO4- to Cr (III). The reaction obeys the following rate law Rate= {k1 K5+ k2 K6 K2 } [Cr III (DMG)2(H2O)4 ]+ [H5IO6].

Keywords: chromium, dimethylglyoxime, kinetics, oxidation, periodate

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Authors: Naghmeh Moradpoor Sheykhkanloo

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Structured Query Language Injection (SQLI) attack is a code injection technique in which malicious SQL statements are inserted into a given SQL database by simply using a web browser. Losing data, disclosing confidential information or even changing the value of data are the severe damages that SQLI attack can cause on a given database. SQLI attack has also been rated as the number-one attack among top ten web application threats on Open Web Application Security Project (OWASP). OWASP is an open community dedicated to enabling organisations to consider, develop, obtain, function, and preserve applications that can be trusted. In this paper, we propose an effective pattern recognition neural network model for detection and classification of SQLI attacks. The proposed model is built from three main elements of: a Uniform Resource Locator (URL) generator in order to generate thousands of malicious and benign URLs, a URL classifier in order to: 1) classify each generated URL to either a benign URL or a malicious URL and 2) classify the malicious URLs into different SQLI attack categories, and an NN model in order to: 1) detect either a given URL is a malicious URL or a benign URL and 2) identify the type of SQLI attack for each malicious URL. The model is first trained and then evaluated by employing thousands of benign and malicious URLs. The results of the experiments are presented in order to demonstrate the effectiveness of the proposed approach.

Keywords: neural networks, pattern recognition, SQL injection attacks, SQL injection attack classification, SQL injection attack detection

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Authors: T. A. Faria, C. C. Toniolo, L. F. Ribeiro

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In order to satisfy the costumer’s needs, many sectors of industry and services has been spending major effort to make its processes more efficient. Facing a situation, when its production cannot cover the demand, the traditional way to achieve the production required involves, mostly, adding shifts, workforce, or even more machines. This paper narrates how lean manufacturing supported a dramatic increase of productivity at a rail welding plant in Brazil in order to meet the demand for the next years.

Keywords: productivity, lean manufacturing, rail welding, value stream mapping

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Gorana Jelic Mrcelic

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In order to reduce greenhouse gas emissions from ships, technical and operational measures can be used. Operational measures are easier and cheaper compared to technical measures, so are well recommended. One of the most cost-effective operational measure is fuel consumption. Fuel consumption can be reduced by various options but it sometimes needs investments in new equipment, new procedures and crew education. In order to implement operational measures in everyday procedures and routines on board, good understanding of the mechanisms by which these measures work is essential for the seamen.

Keywords: green shipping, gas emission reduction, operational measures, seamen

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Authors: Karima Bouakaz, Amel Youcefi, Abdessamad Abada

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We determine a compact analytic expression for the complete next-to-leading contribution to the retarded transverse photons self-energy in the context of hard-thermal-loop summed perturbation of massless quantum electrodynamics (QED) at high temperature to calculate the next-to-leading order dispersion relations for slow-moving transverse photons at high temperature scalar quantum electrodynamics (Scalar QED), using the real time formalism (RTF) in physical representation. We derive the analytic expressions of hard thermal loop (HTL) contributions to propagators and vertices to determine the expressions of the effective propagators and vertices in RTF that contribute to the complete next-to leading order contribution of retarded transverse photons self-energy.

Keywords: hard thermal loop, hot scalar QED, NLO computations, soft transverse photons

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Authors: Hélène Knoerr

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In an increasingly global world, more and more international students attend academic courses and programs in a second or foreign language, and local students register in language learning classes in order to improve their employability. These students need to quickly become proficient in the new language. How can we, as administrators, curriculum developers and teachers, make sure that they have the tools they need in order to develop their language skills in an academic context? This paper will describe the development and implementation of a new course, Learning to learn, as part of the Major in French/English as a Second Language at the University of Ottawa. This academic program was recently completely overhauled in order to reflect the current approaches in language learning (more specifically, the action-oriented approach as embodied in the Common European Framework of Reference for Languages, and the concept of life-long autonomous learning). The course itself is based on research on language learning strategies, with a particular focus on the characteristics of the “good language learner”. We will present the methodological and pedagogical foundations, describe the course objectives and learning outcomes, the language learning strategies, and the classroom activities. The paper will conclude with students’ feedback and suggest avenues for further exploration.

Keywords: curriculum development, language learning, learning strategies, second language

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Authors: H. Kiani, S. Moradi, B. Soltani Soulgani, S. Mousavian

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Desalting/dehydration plants (DDP) are often installed in crude oil production units in order to remove water-soluble salts from an oil stream. In order to optimize this process, desalting unit should be modeled. In this research, artificial neural network is used to model efficiency of desalting unit as a function of input parameter. The result of this research shows that the mentioned model has good agreement with experimental data.

Keywords: desalting unit, crude oil, neural networks, simulation, recovery, separation

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Rouhallah Bagheri, Morteza Mahmoudi, Hadi Moheb-Alizadeh

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This paper aims at developing a multi-objective model for supplier selection and order allocation problem in stochastic environment, where purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. In this regard, dependent chance programming is used which maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. The abovementioned stochastic multi-objective programming problem is then transformed into a stochastic single objective programming problem using minimum deviation method. In the next step, the further problem is solved applying a genetic algorithm, which performs a simulation process in order to calculate the stochastic objective function as its fitness function. Finally, the impact of stochastic parameters on the given solution is examined via a sensitivity analysis exploiting coefficient of variation. The results show that whatever stochastic parameters have greater coefficients of variation, the value of the objective function in the stochastic single objective programming problem is deteriorated.

Keywords: supplier selection, order allocation, dependent chance programming, genetic algorithm

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Authors: M. Barsa

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This paper argues that current jurisprudence under the Dormant Commerce Clause of the United States Constitution and the WTO should be altered to allow states to more freely foster clean energy production. In particular, free trade regimes typically prevent states from discriminating against 'like' products, and whether these products are considered 'like' is typically measured by how they appear to the consumer. This makes it challenging for states to discriminate in favor of clean energy, such as low-carbon fuels. However, this paper points out that certain courts in the US—and decisions of the WTO—have already begun taking into account how a product is manufactured in order to determine whether a state may discriminate against it. There are also compelling reasons for states to discriminate against energy sources with high carbon footprints in order to allow those states to protect themselves against climate change. In other words, fuel sources with high and low carbon footprints are not, in fact, 'like' products, and courts should more freely recognize this in order to foster clean energy production.

Keywords: clean energy, climate change, discrimination, free trade

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Authors: Amani Hamdan

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A post-workshop of higher-order thinking skills (HOTS), for faculty from diverse academic disciplines, was conducted and the researcher surveyed the participants’ intentions and plans to include HOTS as a goal, as learning and teaching task in their practices. Follow-up interviews with a random sample of participants were used to determine if they fulfilled their intentions three 3 months after the workshop. The degree of planned and enacted HOTS then was analyzed against the post-workshop HOT ability and knowledge. This is one topic that has not been adequately explored in faculty professional development literature where measuring the effect of learning on their ability to use what they learned. This qualitative method study explored a group of male and female faculty members (n=85) enrolled in HOTS 2 day workshop. The results showed that 89% of faculty members although were mostly enthused to apply what they learned after a 3 months period they were caught up with routine presentations and lecturing.

Keywords: higher education, faculty development, Saudi Arabia, higher order thinking skills

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Authors: Alvaro Javier Ortega

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A large number of companies face the challenge of matching highly-skilled professionals to high-end positions by human resource deployment professionals. However, when the professional list and tasks to be matched are larger than a few dozens, this process result is far from optimal and takes a long time to be made. Therefore, an automated assignment algorithm for this workforce management problem is needed. The majority of companies are divided into several sectors or departments, where trained employees with different experience levels deal with a large number of tasks daily. Also, the execution order of all tasks is of mater consequence, due to some of these tasks just can be run it if the result of another task is provided. Thus, a wrong execution order leads to large waiting times between consecutive tasks. The desired goal is, therefore, creating accurate matches and a near-optimal execution order that maximizes the number of tasks performed and minimizes the idle time of the expensive skilled employees. The problem described before can be model as a mixed-integer non-linear programming (MINLP) as it will be shown in detail through this paper. A large number of MINLP algorithms have been proposed in the literature. Here, genetic algorithm solutions are considered and a comparison between two different mutation approaches is presented. The simulated results considering different complexity levels of assignment decisions show the appropriateness of the proposed model.

Keywords: employees, genetic algorithm, industry management, workforce

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Authors: Mehrnoosh Askarizadeh

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Agile manufacturing concept was first coined by Iacocca institute in 1991 as a new manufacturing paradigm in order to provide and ensure competitiveness in the emerging global manufacturing order. Afterward, a considerable number of studies have been conducted in this area. Reviewing these studies reveals that they mostly focus on agile manufacturing drivers, definition and characteristics but few of them propose practical solutions to achieve it. Agile manufacturing is recommended as a successful paradigm after lean for the 21st manufacturing firms. This competitive concept has been developed in response to the continuously changes and uncertainties in today’s business environment. In order to become an agile competitor, a manufacturing firm should focus on enriching its agility capabilities. These agility capabilities can be categorized into seven groups: proactiveness, customer focus, responsiveness, quickness, flexibility, basic competence and partnership. A manufacturing firm which is aiming at achieving agility should first develop its own appropriate agility strategy. This strategy prioritizes required agility capabilities.

Keywords: agile manufacturing, product architecture, customer focus, responsiveness, quickness, flexibility, basic competence

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Authors: Heiko Diefenbach, Christoph H. Glock

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Order picking, i.e., the order-based retrieval of items in a warehouse, is an important time- and cost-intensive process for many logistic systems. Despite the ongoing trend of automation, most order picking systems are still manual picker-to-parts systems, where human pickers walk through the warehouse to collect ordered items. Human work in warehouses is not free from errors, and order pickers may at times pick the wrong or the incorrect number of items. Errors can cause additional costs and significant correction efforts. Moreover, age might increase a person’s likelihood to make mistakes. Hence, the negative impact of picking errors might increase for an aging workforce currently witnessed in many regions globally. A significant amount of research has focused on making order picking systems more efficient. Among other factors, storage assignment, i.e., the assignment of items to storage locations (e.g., shelves) within the warehouse, has been subject to optimization. Usually, the objective is to assign items to storage locations such that order picking times are minimized. Surprisingly, there is a lack of research concerned with picking errors and respective prevention approaches. This paper hypothesize that the storage assignment of items can affect the probability of pick errors. For example, storing similar-looking items apart from one other might reduce confusion. Moreover, storing items that are hard to count or require a lot of counting at easy-to-access and easy-to-comprehend self heights might reduce the probability to pick the wrong number of items. Based on this hypothesis, the paper discusses how to incorporate error-prevention measures into mathematical models for storage assignment optimization. Various approaches with respective benefits and shortcomings are presented and mathematically modeled. To investigate the newly developed models further, they are compared to conventional storage assignment strategies in a computational study. The study specifically investigates how the importance of error prevention increases with pickers being more prone to errors due to age, for example. The results suggest that considering error-prevention measures for storage assignment can reduce error probabilities with only minor decreases in picking efficiency. The results might be especially relevant for an aging workforce.

Keywords: an aging workforce, error prevention, order picking, storage assignment

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Authors: Sabine A. Zauchner-Studnicka

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As the term indicates, reverse-mentoring flips the classical roles of mentoring: In school, students take over the role of mentors for adults, i.e. teachers or parents. Originally reverse-mentoring stems from US enterprises, which implemented this innovative method in order to benefit from the resources of skilled younger employees for the enhancement of IT competences of senior colleagues. However, reverse-mentoring in schools worldwide is rare. Based on empirical studies and theoretical approaches, in this article an implementation model for reverse-mentoring is developed in order to bring the significant potential reverse-mentoring has for education into practice.

Keywords: reverse-mentoring, innovation in education, implementation model, school education

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Authors: Yousef Abu Nahleh, Alhasan Hakami, Arun Kumar, Fugen Daver

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This study considers the problem of calculating safety stocks in disaster situations inventory systems that face demand uncertainties. Safety stocks are essential to make the supply chain, which is controlled by forecasts of customer needs, in response to demand uncertainties and to reach predefined goal service levels. To solve the problem of uncertainties due to the disaster situations affecting the industry sector, the concept of Emergency Safety Stock (ESS) was proposed. While there exists a huge body of literature on determining safety stock levels, this literature does not address the problem arising due to the disaster and dealing with the situations. In this paper, the problem of improving the Order Quantity Model to deal with uncertainty of demand due to disasters is managed by incorporating a new idea called ESS which is based on the probability of disaster occurrence and uses probability matrix calculated from the historical data.

Keywords: Emergency Safety Stocks, safety stocks, Order Quantity Model, supply chain

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Authors: S. W. Chen, W. K. Lin, J. R. Wang, C. Shih, H. T. Lin, H. C. Chang, W. Y. Li

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Kuosheng nuclear power plant (NPP) is a BWR/6 type NPP and located on the northern coast of Taiwan. First, Kuosheng NPP TRACE model were developed in this research. In order to assess the system response of Kuosheng NPP TRACE model, startup tests data were used to evaluate Kuosheng NPP TRACE model. Second, the over pressurization transient analysis of Kuosheng NPP TRACE model was performed. Besides, in order to confirm the mechanical property and integrity of fuel rods, FRAPTRAN analysis was also performed in this study.

Keywords: TRACE, safety analysis, BWR/6, FRAPTRA

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Authors: Zelal Çınar

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This paper claims that architecture is a contingent discipline, despite the fact that its contingency has long been denied through a retreat to Vitruvian writing. It is evident that contingency is rejected not only by architecture but also by modernity as a whole. Vitruvius attempted to cover the entire field of architecture in a systematic form in order to bring the whole body of this great discipline to a complete order. The legacy of his theory hitherto lasted not only that it is the only major work on the architecture of Classical Antiquity to have survived, but also that its conformity with the project of modernity. In the scope of the paper, it will be argued that contingency should be taken into account rather than avoided as a potential threat.

Keywords: architecture, contingency, modernity, Vitruvius

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Authors: Lei Zhao, Zhe Yuan, Wenyue Kuang

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This paper studies two-warehouse inventory models for a deteriorating item considering that the demand is influenced by inventory levels. The problem mainly focuses on the optimal order policy and the optimal order cycle with inventory-level-dependent demand in two-warehouse system for retailers. It considers the different deterioration rates and the inventory holding costs in owned warehouse (OW) and rented warehouse (RW), and the conditions of transportation cost, allowed shortage and partial backlogging. Two inventory models are formulated: last-in first-out (LIFO) model and first-in-first-out (FIFO) model based on the policy choices of LIFO and FIFO, and a comparative analysis of LIFO model and FIFO model is made. The study finds that the FIFO policy is more in line with realistic operating conditions. Especially when the inventory holding cost of OW is high, and there is no difference or big difference between deterioration rates of OW and RW, the FIFO policy has better applicability. Meanwhile, this paper considers the differences between the effects of warehouse and shelf inventory levels on demand, and then builds retailers’ inventory decision model and studies the factors of the optimal order quantity, the optimal order cycle and the average inventory cost per unit time. To minimize the average total cost, the optimal dispatching policies are provided for retailers’ decisions.

Keywords: FIFO model, inventory-level-dependent, LIFO model, two-warehouse inventory

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Authors: Ti-Jun Xiao, Zhe Xu

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Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem.

Keywords: evolutional control system, controllability, boundary control, existence and uniqueness

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Authors: Pramod K. Prabhakar, Prem P. Srivastav

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Rohu (Labeo rohita) is an Indian major carp and highly relished freshwater food for its unique flavor, texture, and culinary properties. It is highly perishable and, spoilage occurs as a result of series of complicated biochemical changes brought about by enzymes which are the function of time and storage temperature also. The influence of storage temperature (5, 0, and -5 °C) on colour and texture of fish were studied during 14 days storage period in order to analyze kinetics of colour and textural changes. The rate of total colour change was most noticeable at the highest storage temperature (5°C), and these changes were well described by the first order reaction. Texture is an important variable of quality of the fish and is increasing concern to aquaculture industries. Textural parameters such as hardness, toughness and stiffness were evaluated on a texture analyzer for the different day of stored fish. The significant reduction (P ≤ 0.05) in hardness was observed after 2nd, 4th and 8th day for the fish stored at 5, 0, and -5 °C respectively. The textural changes of fish during storage followed a first order kinetic model and fitted well with this model (R2 > 0.95). However, the textural data with respect to time was also fitted to modified Maxwell model and found to be good fit with R2 value ranges from 0.96 to 0.98. Temperature dependence of colour and texture change was adequately modelled with the Arrhenius type equation. This fitted model may be used for the determination of shelf life of Rohu Rohu (Labeo rohita) Fish.

Keywords: first order kinetics, biochemical changes, Maxwell model, colour, texture, Arrhenius type equation

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: Utsav Bhardwaj, Shyama Prasad Das

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To meet the extensive requirements of thermal management of the circuit card assemblies (CCAs), satellites, PCBs, microprocessors, any other electronic circuitry, pulsating heat pipes (PHPs) have emerged in the recent past as one of the best solutions technically. But industrial application of PHPs is still unexplored up to a large extent due to their poor reliability. There are several systems as well as operational parameters which not only affect the performance of an operating PHP, but also decide whether the PHP can operate sustainably or not. Functioning may completely be halted for some particular combinations of the values of system and operational parameters. Among the system parameters, adiabatic length is one of the important ones. In the present work, a simplest single branch PHP system with an adiabatic section has been considered. It is assumed to have only one vapour bubble and one liquid plug. First, the system has been mathematically modeled using film evaporation/condensation model, followed by the steps of recognition of equilibrium zone, non-dimensionalization and linearization. Then proceeding with a periodical solution of the linearized and reduced differential equations, stability analysis has been performed. Slow and fast variables have been identified, and averaging approach has been used for the slow ones. Ultimately, temporal evolution of the PHP is predicted by numerically solving the averaged equations, to know whether the oscillations are likely to sustain/decay temporally. Stability threshold has also been determined in terms of some non-dimensional numbers formed by different groupings of system and operational parameters. A combined analytical and numerical approach has been used, and it has been found that for each combination of all other parameters, there exists a maximum length of the adiabatic section beyond which the PHP cannot function at all. This length has been called as “Critical Adiabatic Length (L_ac)”. For adiabatic lengths greater than “L_ac”, oscillations are found to be always decaying sooner or later. Dependence of “L_ac” on some other parameters has also been checked and correlated at certain evaporator & condenser section temperatures. “L_ac” has been found to be linearly increasing with increase in evaporator section length (L_e), whereas the condenser section length (L_c) has been found to have almost no effect on it upto a certain limit. But at considerably large condenser section lengths, “L_ac” is expected to decrease with increase in “L_c” due to increased wall friction. Rise in static pressure (p_r) exerted by the working fluid reservoir makes “L_ac” rise exponentially whereas it increases cubically with increase in the inner diameter (d) of PHP. Physics of all such variations has been given a good insight too. Thus, a methodology for quantification of the critical adiabatic length for any possible set of all other parameters of PHP has been established.

Keywords: critical adiabatic length, evaporation/condensation, pulsating heat pipe (PHP), thermal management

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