Search results for: accelerating numerical solutions

Authors: Wafa’ Alsharafat, Khalid Batiha, Alaa Kassab

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Wireless sensor network (WSN) is comprised of a huge number of small and cheap devices known as sensor nodes. Usually, these sensor nodes are massively and deployed randomly as in Ad-hoc over hostile and harsh environment to sense, collect and transmit data to the needed locations (i.e., base station). One of the main advantages of WSN is that the ability to work in unattended and scattered environments regardless the presence of humans such as remote active volcanoes environments or earthquakes. In WSN expanding network, lifetime is a major concern. Clustering technique is more important to maximize network lifetime. Nature-inspired algorithms are developed and optimized to find optimized solutions for various optimization problems. We proposed Energy Efficient Firefly Algorithm to improve network lifetime as long as possible.

Keywords: wireless network, SN, Firefly, energy efficiency

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Authors: Muhammad Azmain Abdullah, Ar Rashedul, Mohammad Ali

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This paper scrutinizes the influences of turbulence on heat transport rate, Nusselt number. The subject matter of this investigation also deals with the improvement of heat transfer efficiency of the swirl flow obtained by rotating a twisted tape in a circular pipe. The conditions to be fulfilled to observe the impact of Reynolds number and rotational speed of twisted tape are: a uniform temperature on the outer surface of the pipe, the magnitude of velocity of water varying from 0.1 m/s to 0.7 m/s in order to alter Reynolds number and a rotational speed of 200 rpm to 600 rpm. The gyration of twisted tape increase by 17%. It is also observed that heat transfer is exactly proportional to inlet gauge pressure and reciprocally proportional to increase of twist ratio.

Keywords: swirl flow, twisted tape, twist ratio, heat transfer

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Authors: Hatam H. Ali, Mohd Shahrizal Sunar, Hoshang Kolivand, Mohd Azhar Bin M. Arsad

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Rendering light shafts is one of the important topics in computer gaming and interactive applications. The methods and models that are used to generate light shafts play crucial role to make a scene more realistic in computer graphics. This article discusses the image-based shadows and geometric-based shadows that contribute in generating volumetric shadows and light shafts, depending on ray tracing, radiosity, and ray marching technique. The main aim of this study is to provide researchers with background on a progress of light scattering methods so as to make it available for them to determine the technique best suited to their goals. It is also hoped that our classification helps researchers find solutions to the shortcomings of each method.

Keywords: shaft of lights, realistic images, image-based, and geometric-based

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Authors: M. Kowalski, M. Kastek, M. Szustakowski

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Multispectral screening systems are becoming more popular because of their very interesting properties and applications. One of the most significant applications of multispectral screening systems is prevention of terrorist attacks. There are many kinds of threats and many methods of detection. Visual detection of objects hidden under clothing of a person is one of the most challenging problems of threats detection. There are various solutions of the problem; however, the most effective utilize multispectral surveillance imagers. The development of imaging devices and exploration of new spectral bands is a chance to introduce new equipment for assuring public safety. We investigate the possibility of long lasting detection of potentially dangerous objects covered with various types of clothing. In the article we present the results of comparative studies of passive imaging in three spectrums – visible, infrared and terahertz

Keywords: terahertz, infrared, object detection, screening camera, image processing

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Authors: Thuy Bui Anh, Ngan Nguyen Thi Thanh

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Currently, social work in Vietnam is entering the first step in the development process to become a true profession with a strong position in society. However, Spirit of helping and sharing of social work has already existed in the daily life of Vietnamese people for a very long time, becoming a precious heritage passed down from ancestors to the next generations while expanding the territory, building and defending for the country. Following the stream of history, charity work in Vietnam has gradually transformed itself towards a more professional work, especially in the last 2 decades. Accordingly, more than 50 universities and educational institutions in Vietnam have been licensed to train social work, ensuring a stronger foundation on human resources working in this field. Despite the strong growth, social work profession, social work education and the recognition of the role of the social workers still need to be fueled to develop, responded to the increasing demand of Vietnam society.

Keywords: education, history, recognition, social work, Vietnam

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Authors: Madhu Jain, Rakesh Kumar Meena

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This paper investigates a finite M/G/1 fault tolerant multi-component machining system. The system incorporates the features such as standby support, threshold recovery and imperfect coverage make the study closer to real time systems. The performance prediction of M/G/1 fault tolerant system is carried out using recursive approach by treating remaining service time as a supplementary variable. The numerical results are presented to illustrate the computational tractability of analytical results by taking three different service time distributions viz. exponential, 3-stage Erlang and deterministic. Moreover, the cost function is constructed to determine the optimal choice of system descriptors to upgrading the system.

Keywords: fault tolerant, machine repair, threshold recovery policy, imperfect coverage, supplementary variable technique

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: basins of attraction, nonlinear equations, simple roots, super-Halley

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Authors: Jonathan Munyoro, Takawira Machimbidza, Stephen Mutula

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The study investigates the current status of Intellectual Property (IP) information services in Zimbabwe's university libraries. Specifically, the study assesses the current IP information services offered in Zimbabwe’s university libraries, identifies challenges to the development of comprehensive IP information services in Zimbabwe’s university libraries, and suggests solutions for the development of IP information services in Zimbabwe’s university libraries. The study is born out of a realisation that research on IP information services in university libraries has received little attention, especially in developing country contexts, despite the fact that there are calls for heightened participation of university libraries in IP information services. In Zimbabwe, the launch of the National Intellectual Property Policy and Implementation Strategy 2018-2022 and the introduction of the Education 5.0 concept are set to significantly change the IP landscape in the country. Education 5.0 places more emphasis on innovation and industrialisation (in addition to teaching, community service, and research), and has the potential to shift the focus and level of IP output produced in higher and tertiary education institutions beyond copyrights and more towards commercially exploited patents, utility models, and industrial designs. The growing importance of IP commercialisation in universities creates a need for appropriate IP information services to assist students, academics, researchers, administrators, start-ups, entrepreneurs, and inventors. The critical challenge for university libraries is to reposition themselves and remain relevant in the new trajectory. Designing specialised information services to support increased IP generation and commercialisation appears to be an opportunity for university libraries to stay relevant in the knowledge economy. However, IP information services in Zimbabwe’s universities appear to be incomplete and focused mostly on assisting with research publications and copyright-related activities. Research on the existing status of IP services in university libraries in Zimbabwe is therefore necessary to help identify gaps and provide solutions in order to stimulate the growth of new forms of such services. The study employed a quantitative approach. An online questionnaire was administered to 57 academic librarians from 15 university libraries. Findings show that the current focus of the surveyed institutions is on providing scientific research support services (15); disseminating/sharing university research output (14); and copyright activities (12). More specialised IP information services such as IP education and training, patent information services, IP consulting services, IP online service platforms, and web-based IP information services are largely unavailable in Zimbabwean university libraries. Results reveal that the underlying challenge in the development of IP information services in Zimbabwe's university libraries is insufficient IP knowledge among academic librarians, which is exacerbated by inadequate IP management frameworks in university institutions. The study proposes a framework for the entrenchment of IP information services in Zimbabwe's university libraries.

Keywords: academic libraries, information services, intellectual property, IP knowledge, university libraries, Zimbabwe

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Authors: Gaokai Liu

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Automatic defect detection for nanomaterial images is widely required in industrial scenarios. Deep learning approaches are considered as the most effective solutions for the great majority of image-based tasks. In this paper, an edge guidance network for defect segmentation is proposed. First, the encoder path with multiple convolution and downsampling operations is applied to the acquisition of shared features. Then two decoder paths both are connected to the last convolution layer of the encoder and supervised by the edge and segmentation labels, respectively, to guide the whole training process. Meanwhile, the edge and encoder outputs from the same stage are concatenated to the segmentation corresponding part to further tune the segmentation result. Finally, the effectiveness of the proposed method is verified via the experiments on open nanofibrous datasets.

Keywords: deep learning, defect detection, image segmentation, nanomaterials

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Authors: M. Goerke, J. Gehrmann

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Caused by shorter product life cycles and higher product variety the importance of production ramp ups is increasing. Even though companies are aware of that fact, up to 40% of the ramp up projects still miss technical and economical requirements. The success of a ramp up depends on the planning of human factors, organizational aspects and technological solutions. Since only partly considered in scientific literature, this paper lays its focus on the human factor during production ramp up. There are only incoherent methods which address the problems in this area. A systematic and holistic method to improve the capabilities of the employees during ramp up is missing. The Harada Method is a relatively young approach for developing highly-skilled workers. It consists of different worksheets which help employees to set guidelines and reach overall objectives. This approach is going to be transferred into a tool for ramp up management.

Keywords: employee development, Harada, production ramp up, organizational aspects

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Authors: O. Hassoon, M. Tarfoui, A. El Malk

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Fiber Bragg optic sensor embedded in composite material to detect and monitor the damage which is occur in composite structure. In this paper we deal with the mode-Ι delamination to determine the resistance of material to crack propagation, and use the coupling mode theory and T-matrix method to simulating the FBGs spectrum for both uniform and non-uniform strain distribution. The double cantilever beam test which is modeling in FEM to determine the Longitudinal strain, there are two models which are used, the first is the global half model, and the second the sub-model to represent the FBGs with refine mesh. This method can simulate the damage in the composite structure and converting the strain to wavelength shifting of the FBG spectrum.

Keywords: fiber bragg grating, delamination detection, DCB, FBG spectrum, structure health monitoring

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Authors: C. E. Madubueze, S. C. Madubueze, S. Ajama

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Cholera is a disease that is predominately common in developing countries due to poor sanitation and overcrowding population. In this paper, a deterministic model for the dynamics of cholera is developed and control measures such as health educational message, therapeutic treatment, and vaccination are incorporated in the model. The effective reproduction number is computed in terms of the model parameters. The existence and stability of the equilibrium states, disease free and endemic equilibrium states are established and showed to be locally and globally asymptotically stable when R0 < 1 and R0 > 1 respectively. The existence of backward bifurcation of the model is investigated. Furthermore, numerical simulation of the model developed is carried out to show the impact of the control measures and the result indicates that combined control measures will help to reduce the spread of cholera in the population

Keywords: backward bifurcation, cholera, equilibrium, dynamics, stability

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Authors: H. Nouri, A. Tabbel, N. Douib, H. Aitsaid, Y. Zebboudj

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This study and the field test comparisons were carried out on the Algerian Derguna-Setif transmission systems. The transmission line of normal voltage 225 kV is 65 km long, transported and uses twin bundle conductors protected with two shield wires of transposed galvanized steel. An iterative finite-element method is used to solve Poisons equation. Two algorithms are proposed for satisfying the current continuity condition and updating the space-charge density. A new approach to the problem of corona discharge in transmission system has been described in this paper. The effect of varying the configurations and wires number is also investigated. The analysis of this steady is important in the design of HVDC transmission lines. The potential and electric field have been calculating in locations singular points of the system.

Keywords: corona discharge, finite element method, electric field, HVDC

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Authors: Ahmed M. Eltohamy

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In this paper, an experimental and numerical study was adopted to investigate the effect geogrid soil reinforcement pre-stressing on the pressure settlement relation of sand bed supporting a strip foundation. The studied parameters include foundation depth and pre-stress ratio for the cases of one and two pre-stressed reinforcement layers. The study reflected that pre-stressing of soil reinforcement resulted in a marked enhancement in reinforced bed soil stiffness compared to the reinforced soil without pre-stress. The best benefit of pre-stressing reinforcement was obtained as the overburden pressure and pre-straining ratio increase. Pre-stressing of double reinforcement topmost layers results in further enhancement of stress strain relation of bed soil.

Keywords: geogrid reinforcement, prestress, strip footing, bearing capacity

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Authors: Woo-Young Jung, Minho Kwon

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Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both the strength and ductility is needed to analyze reinforced concrete (RC) structures under such event. A three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC members. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC members are performed to validate the proposed model. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results.

Keywords: torsion, non-linear analysis, three-dimensional lattice, high-strength concrete

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Authors: Karima Megdouli, Bourhan Taschtouch

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Supersonic ejectors have many applications in refrigeration systems. And improving ejector performance is the key to improve the efficiency of these systems. One of the main advantages of the ejector is its geometric simplicity and the absence of moving parts. This paper presents a theoretical model for evaluating the performance of a new supersonic ejector configuration for refrigeration system applications. The relationship between the flow field and the key parameters of the new configuration has been illustrated by analyzing the Mach number and flow velocity contours. The method of characteristics (MOC) is used to design the supersonic nozzle of the ejector. The results obtained are compared with those obtained by CFD. The ejector is optimized by minimizing exergy destruction due to irreversibility and shock waves. The optimization converges to an efficient optimum solution, ensuring improved and stable performance over the whole considered range of uncertain operating conditions.

Keywords: supersonic ejector, theoretical model, CFD, optimization, performance

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Authors: Fatima El Kandoussi, Lamiae El Hdiddioui, Mustapha Bouragba

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The woodwork of thuja in Essaouira is one of the main crafts in Morocco. Certainly, marquetry reflects both cultural and artistic identity of the city, considering the talent and ancestral knowledge of craftsman working in marquetry. Yet, the production units encounter a considerable number of difficulties among which insufficiencies within marketing practices. Consequently, it is obvious that major improvements are needed, and supportive solutions must be provided in order to improve the Essaouira’s marquetry, as a symbol of the entire province. Thus, the establishment of Thuja Label is a necessary measure that would be the key to ensuring sustainability of this vital craft. The main purpose of this paper is to study marketing practices’ current state of the production units in the marquetry of Essaouira, therefore to recommend remedial actions likely to raise them up to the required functional level.

Keywords: craft, marketing practices, marquetry, thuja label

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Authors: J. P. Gorninski, J. M. L. Reis

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This present work was aimed to develop polymeric mortars having as binder two polyester resins namely isophtalic and orthophtalic polyester. The inorganic phase was composed by medium-size river sand and fly ash fíller, a by-product of the burning of coal in power plants. The compositions in this study are high performance mortars and were assessed by mechanical properties, through compressive strength and flexural strength, by durability strength when exposed to the cyclical variation of temperature from -400C to +300C and by the chemical aggression test. The composites displayed good performance when exposed to cyclical temperature variations and chemical solutions. The mechanical strength values reached the 100 MPa, the flexural strength yielded values of about twenty percent of mechanical strength.

Keywords: polymer mortar, mechanical strength, cyclical temperatures, chemical strength, sustainability

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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: Vahid Zeighami, Mohsen Ghsemi, Reza Akbari

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In this work, a Multi-Level Artificial Bee Colony (called MLABC) is presented. In MLABC two species are used. The first species employs n colonies in which each of the them optimizes the complete solution vector. The cooperation between these colonies is carried out by exchanging information through a leader colony, which contains a set of elite bees. The second species uses a cooperative approach in which the complete solution vector is divided to k sub-vectors, and each of these sub-vectors is optimized by a a colony. The cooperation between these colonies is carried out by compiling sub-vectors into the complete solution vector. Finally, the cooperation between two species is obtained by exchanging information between them. The proposed algorithm is tested on a set of well known test functions. The results show that MLABC algorithms provide efficiency and robustness to solve numerical functions.

Keywords: artificial bee colony, cooperative, multilevel cooperation, vector

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Authors: E. H. N. Gashti, J. Razzaghi, K. Kujala

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In general, codes and regulations consider seismic loads only for completed structures of the bridges while, evaluation of incomplete structure of bridges, especially those constructed by free cantilever method, under these loads is also of great importance. Hence, this research tried to study the behavior of incomplete structure of common bridge type (box girder bridge), in construction phase under vertical seismic loads. Subsequently, the paper provided suitable guidelines and solutions to withstand this destructive phenomena. Research results proved that use of preventive methods can significantly reduce the stresses resulted from vertical seismic loads in box cross sections to an acceptable range recommended by design codes.

Keywords: box girder bridges, prestress loads, free cantilever method, seismic loads, construction phase

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

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Authors: Rishabh Garg

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Traditionally, business parties build trust with a centralized operating mechanism, such as payment by letter of credit. However, the increase in cyber-attacks and malicious hacking has jeopardized business operations and finance practices. Emerging markets, owing to their higher banking risks and bigger presence of digital financing, are looking forward to technology-driven solutions, financial inclusion and innovative working paradigms. Blockchain has the potential to enhance transaction transparency and supply chain traceability. It has captured a vast landscape with 200 million crypto users worldwide. Fintech and blockchain products are popping up across brokerage, digital wallets, exchanges, post-trade clearance, settlement, middleware, infrastructure, and base protocols.

Keywords: blockchain, distributed ledger technology, decentralized applications, ethereum, smart contracts, trade finance

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Authors: Shankaran Sitarama

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New Product Development involves team members coming together and working in teams to come up with innovative solutions to problems, resulting in new products. Thus, a core attribute of a successful NPD team is their creativity and innovation. They need to be creative as a group, generating a breadth of ideas and innovative solutions that solve or address the problem they are targeting and meet the user’s needs. They also need to be very efficient in their teamwork as they work through the various stages of the development of these ideas, resulting in a POC (proof-of-concept) implementation or a prototype of the product. There are two distinctive traits that the teams need to have, one is ideational creativity, and the other is effective and efficient teamworking. There are multiple types of tensions that each of these traits cause in the teams, and these tensions reflect in the team dynamics. Ideational conflicts arising out of debates and deliberations increase the collective knowledge and affect the team creativity positively. However, the same trait of challenging each other’s viewpoints might lead the team members to be disruptive, resulting in interpersonal tensions, which in turn lead to less than efficient teamwork. Teams that foster and effectively manage these creative tensions are successful, and teams that are not able to manage these tensions show poor team performance. In this paper, it explore these tensions as they result in the team communication social network and propose a Creative Tension Balance index along the lines of Degree of Balance in social networks that has the potential to highlight the successful (and unsuccessful) NPD teams. Team communication reflects the team dynamics among team members and is the data set for analysis. The emails between the members of the NPD teams are processed through a semantic analysis algorithm (LSA) to analyze the content of communication and a semantic similarity analysis to arrive at a social network graph that depicts the communication amongst team members based on the content of communication. This social network is subjected to traditional social network analysis methods to arrive at some established metrics and structural balance analysis metrics. Traditional structural balance is extended to include team interaction pattern metrics to arrive at a creative tension balance metric that effectively captures the creative tensions and tension balance in teams. This CTB (Creative Tension Balance) metric truly captures the signatures of successful and unsuccessful (dissonant) NPD teams. The dataset for this research study includes 23 NPD teams spread out over multiple semesters and computes this CTB metric and uses it to identify the most successful and unsuccessful teams by classifying these teams into low, high and medium performing teams. The results are correlated to the team reflections (for team dynamics and interaction patterns), the team self-evaluation feedback surveys (for teamwork metrics) and team performance through a comprehensive team grade (for high and low performing team signatures).

Keywords: team dynamics, social network analysis, new product development teamwork, structural balance, NPD teams

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

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The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method, wire coating die

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Authors: Mohammad Mahdi Mohammadi Dehnavi, Alessandra De Angelis, Maria Rosaria Pecce

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This paper deals with the role of studs in the structural response of steel-concrete composite beams. A tri-linear slip-shear strength law is assumed according to literature and codes provisions for developing a finite element (FE) model of a case study of a composite deck. The variation of the strength and ductility of the connection is implemented in the numerical model carrying out nonlinear analyses. The results confirm the utility of the model to evaluate the importance of the studs capacity, ductility and strength on the global response (ductility and strength) of the structures but also to analyze the trend of slip and shear at interface along the beams.

Keywords: stud connectors, finite element method, slip, shear load, steel-concrete composite bridge

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Authors: Ramazan I. Kadiev, Arcady Ponosov

Abstract:

Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Amir Bahrami

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In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index or a descriptor index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper some descriptor index (descriptor index) of single-walled carbon nanotubes, is determined.

Keywords: chemical graph theory, molecular topology, molecular descriptor, single-walled carbon nanotubes

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Authors: Parham Bakhtiari

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George Crumb's Makrokosmos Volumes are considered significant pieces in twentieth-century piano music and showcase the extensive use of different tones and extended techniques on the piano. Crumb's works are known for making references, particularly to music from previous eras which the visual, aural, and numerical characteristics are symbolic in nature. Crumb created a list of symbols and shortened letters to clarify his unique directions to those who performed his compositions. The pianists who prepare to play Makrokosmos must dedicate time to study and analyze Crumb's markings diligently to accurately capture the composer's wishes. The aim of this paper is to provide a collection for pianists looking to perform George Crumb's compositions known as Makrokosmos Volumes. The research traits of unconventional playing techniques and discussions on the music explored by the composer are being described.

Keywords: music, piano, Crumb, Makrokosmos, performance

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