Search results for: exponential functions

Authors: D. Satish Kumar, T. K. V. Iyengar

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In this paper, we study the Brinkman flow, under Stokesian assumption, past an impervious prolate spheroid and obtain the expressions for the velocity and pressure fields in terms of Legendre functions, Associated Legendre functions, prolate radial and angular spheroidal wave functions. We further obtain an expression for the drag experienced by the spheroid and numerically study its variation with respect to the flow parameters and display the results through graphs.

Keywords: prolate spheoid, porous medium, stokesian assumption, brinkman model, velocity, pressure, drag

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Authors: Marlene Rosa, Susana Lopes

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Board games have been used for different purposes in geriatric care, demonstrating good results for health in general. However, there is not a conceptual framework that can help professionals and researchers in this area to design intervention programs or to think about future studies in this area. The aim of this study was to provide a pilot collection of board games’ serious purposes in geriatric care, using a WHO framework for health and disability. Study cases were developed in seven geriatric residential institutions from the center region in Portugal that are included in AGILAB program. The AGILAB program is a serious game-based method to train and spread out the implementation of board games in geriatric care. Each institution provides 2-hours/week of experiences using TATI Hand Game for serious purposes and then fulfill questions about a study-case (player characteristics; explain changes in players health according to this game experience). Two independent researchers read the information and classified it according to the International Classification for Functioning and Disability (ICF) categories. Any discrepancy was solved in a consensus meeting. Results indicate an important variability in body functions and structures: specific mental functions (e.g., b140 Attention functions, b144 Memory functions), b156 Perceptual functions, b2 sensory functions and pain (e.g., b230 Hearing functions; b265 Touch function; b280 Sensation of pain), b7 neuromusculoskeletal and movement-related functions (e.g., b730 Muscle power functions; b760 Control of voluntary movement functions; b710 Mobility of joint functions). Less variability was found in activities and participation domains, such as purposeful sensory experiences (d110-d129) (e.g., d115 Listening), communication (d3), d710 basic interpersonal interactions, d920 recreation and leisure (d9200 Play; d9205 Socializing). Concluding, this framework designed from a brief gamed-based experience includes mental, perceptual, sensory, neuromusculoskeletal, and movement-related functions and participation in sensory, communication, and leisure domains. More studies, including different experiences and a high number of users, should be developed to provide a more comprehensive ICF framework for game-based experiences in geriatric care.

Keywords: board game, aging, framework, experience

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Authors: Manjit Singh Sidhu, Waleed Maqableh, Jee Geak Ying

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Tangible user interfaces (TUI) that employ markers in the augmented reality (AR) environment has hampered the interactivity between the user and the software application. This is because the user lacks focus on visualizing the contents due to the interaction mechanisms whereby multiple markers may need to be used to perform a particular function. In this research, we have designed a novel TUI user interface where multiple functions could be triggered similar to a natural keyboard thus allowing user to focus more on its digital contents such as 2D/3D, text input, animation and sound. Test results of the user interface with potential users and HCI experts revealed that the multiple functions user interface was new, preferred and appreciated more as opposed to marker based user interface.

Keywords: multimedia, augmented reality, engineering, user interface, visualization

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Authors: A. B. Disu, M. S. Dada

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This study was conducted to investigate two dimensional heat transfer of a free convective-radiative MHD (Magneto-hydrodynamics) flow with temperature dependent viscosity and heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The fluid viscosity is assumed to vary as an exponential function of temperature. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities were expressed in terms of complex exponential series of plane wave equation. The resultant differential equations were solved by Differential Transform Method (DTM). The numerical computations were presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number were also analyzed for various governing parameters.

Keywords: differential transform method, MHD free convection, porous medium, two dimensional radiation, two wavy walls

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Authors: Cinzia Colapinto, Davide La Torre

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Goal Programming (GP) and its variants were applied to marketing and specific marketing issues, such as media scheduling problems in the last decades. The concept of satisfaction functions has been widely utilized in the GP model to explicitly integrate the Decision-Maker’s preferences. These preferences can be guided by the available information regarding the decision-making situation. A GP model with satisfaction functions for media planning decisions is proposed and then illustrated through a case study related to a marketing/media campaign in the Italian market.

Keywords: goal programming, satisfaction functions, media planning, tourism management

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Authors: Saurabh Rawat, Anushree Sah

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K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.r

Keywords: K-maps, don’t care conditions, Boolean equations, cubes

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Marwane Ben Hcine, Ridha Bouallegue

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The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.

Keywords: LTE, OFDMA, effective SINR, log skew normal approximation

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Authors: Ethelbert Chinedu Nwokorie

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This empirical study analyzes the impact of communication and networking functions of Nigerian and Ghanaian public sector managers’ on public sector effectiveness. The focus is on which of these management functions public sector managers’ in these countries perform most, why, how and how does it affect effectiveness of public sector organizations in the two countries. This qualitative analysis was done by interviewing middle and top level managers in some selected public sector organizations in the two countries on their practical experiences. Findings reveal that ineffectiveness of public sector organizations in Ghana persists because public sector managers perform more of networking functions to promote their individual carrier success and progression in their various organizations, rather than achieving the organizations goals and objectives. In Nigeria, though majority of the interviewed public sector managers perform more communication functions than networking, they do this mostly by treating files and correspondences, instead of face-to-face communication and interaction with employees’. Hence, they hardly relate directly with their employees’ to find out how they are performing their jobs, their challenges, where they are having problems and why. The findings and recommendations of this study will help in improving effectiveness, quality and service delivery in Nigerian and Ghanaian public sector organizations and beyond.

Keywords: effectiveness, communication, employees, management, networking, organization, public sector

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Abbas Anser, Ahmad Irfan

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The main purpose of the VAV (Variable Air Volume) in Heating, Ventilation, and Air Conditioning (HVAC) system is to reduce energy consumption and make the buildings comfortable for the occupants. For better performance of the air conditioning system, different control techniques have been developed. In this paper, an Improved Sliding Mode Control (ISMC), based on Power Rate Exponential Reaching Law (PRERL), has been implemented on a VAV air conditioning system. Through the proposed technique, fast response and robustness have been achieved. To verify the efficacy of ISMC, a comparison of the suggested control technique has been made with Exponential Reaching Law (ERL) based SMC. And secondly, chattering, which is unfavorable as it deteriorates the mechanical parts of the air conditioning system by the continuous movement of the mechanical parts and consequently it increases the energy loss in the air conditioning system, has been alleviated. MATLAB/SIMULINK results show the effectiveness of the utilized scheme, which ensures the enhancement of the energy efficiency of the VAV air conditioning system.

Keywords: PID, SMC, HVAC, PRERL, feedback linearization, VAV, chattering

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Anas H. Aljemely, Jianping Xuan

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Rolling bearing fault diagnosis plays a pivotal issue in the rotating machinery of modern manufacturing. In this research, a raw vibration signal and improved deep learning method for bearing fault diagnosis are proposed. The multi-dimensional scales of raw vibration signals are selected for evaluation condition monitoring system, and the deep learning process has shown its effectiveness in fault diagnosis. In the proposed method, employing an Exponential linear unit (ELU) layer in a convolutional neural network (CNN) that conducts the identical function on positive data, an exponential nonlinearity on negative inputs, and a particular convolutional operation to extract valuable features. The identification results show the improved method has achieved the highest accuracy with a 100-dimensional scale and increase the training and testing speed.

Keywords: bearing fault prognostics, developed CNN model, multiple-scale evaluation, deep learning features

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Authors: J. R. Lee, E. V. Lau

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Ionic wind is developed when high voltage is supplied to an anode and a grounded cathode in a gaseous medium. This paper studies the ionic wind profile with different anode configurations, the relationship between electrode gap against the voltage supplied and finally a comparison of the heat transfer coefficient of ionic wind over a horizontal flat plate against a conventional fan experimentally. It is observed that increase in the distance between electrodes decreases at a rate of 1-e-0.0206x as the voltage supply is increased until a distance of 3.1536cm. It is also observed that the wind speed produced by ionic wind is stronger, 2.7ms-1 at 2W compared to conventional fan, 2.5ms-1 at 2W but the wind produced decays at a fast exponential rate and is more localized as compared to conventional fan wind that decays at a slower exponential rate and is less localized. Next, it is found out that the ionic wind profile is the same regardless of the position of the anode relative to the cathode. Lastly, it is discovered that ionic wind produced a heat transfer coefficient that is almost 1.6 times higher compared to a conventional fan with Nusselt number reaching 164 compared to 102 for conventional fan.

Keywords: conventional fan, heat transfer, ionic wind, wind profile

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Authors: Hooman Mehdizadeh Rad, Jai Singh

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Organic solar cells (OSCs) have been actively investigated in the last two decades due to their several merits such as simple fabrication process, low-cost manufacturing, and lightweight. In this paper, using the optical transfer matrix method (OTMM) and solving the drift-diffusion equations processes of recombination are studied in inverted and conventional bulk heterojunction (BHJ) OSCs. Two types of recombination processes are investigated: 1) recombination of free charge carriers using the Langevin theory and 2) of trapped charge carriers in the tail states with exponential energy distribution. These recombination processes are incorporated in simulating the current- voltage characteristics of both conventional and inverted BHJ OSCs. The results of this simulation produces a higher power conversion efficiency in the inverted structure in comparison with conventional structure, which agrees well with the experimental results.

Keywords: conventional organic solar cells, exponential tail state recombination, inverted organic solar cells, Langevin recombination

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Authors: Sarika Bahadure

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Sustainability starts with conserving resources for future generations. Since human’s existence on this earth, he has been consuming natural resources. The resource consumption pace in the past was very slow, but industrialization in 18^th century brought a change in the human lifestyle. New inventions and discoveries upgraded the human workforce to machines. The mass manufacture of goods provided easy access to products. In the last few decades, the globalization and change in technologies brought consumer oriented market. The consumption of resources has increased at a very high scale. This overconsumption pattern brought economic boom and provided multiple opportunities, but it also put stress on the natural resources. This paper tries to put forth the facts and figures of the population growth and consumption of resources with examples. This is explained with the help of the mathematical expression of doubling known as exponential growth. It compares the carrying capacity of the earth and resource consumption of humans’ i.e. ecological footprint and bio-capacity. Further, it presents the need to conserve natural resources and re-examine sustainable resource use approach for sustainability.

Keywords: consumption, exponential growth, population, resources, sustainability

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Authors: Maziyar Nouraee

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Electronic markets in recent decades contribute remarkably in business transactions. Many organizations consider traditional ways of trade non-economical and therefore they do trade only through electronic markets. There are different categorizations of electronic markets functions. In one classification, functions of electronic markets are categorized into classes as information, transactions, and value added. In the present paper, effects of the three classes on the two major elements of the supply chain management are measured. The two elements are decrease in the product unit cost and reduction in response time to the customer. The results of the current research show that among nine minor elements related to the three classes of electronic markets functions, six factors and three factors influence on reduction of the product unit cost and reduction of response time to the customer, respectively.

Keywords: electronic commerce, electronic market, B2B trade, supply chain management

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Authors: Chrysovalanto Sofia Karatosidi, Dimitra Iordanoglou

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The overlap of leadership skills with personality traits, beliefs, values, and the integration of cognitive abilities, analytical and critical thinking skills into leadership competencies raises the need to segregate further and investigate them. Hence, the domains of cognitive functions that contribute to leadership effectiveness should also be identified. Organizational cognitive neuroscience and neuroleadership can shed light on the study of these critical leadership skills. As the first part of our research, this pilot study aims to explore the relationships between higher-order cognitive functions (executive functions), trait emotional intelligence (EI), personality, and general cognitive ability in leadership. Twenty-six graduate and postgraduate students were assessed on neuropsychological tests that measure important aspects of executive functions (EF) and completed self-reported questionnaires about trait EI, personality, leadership styles, and leadership effectiveness. Specifically, we examined four core EF—fluency (phonemic and semantic), information updating and monitoring, working memory, and inhibition of prepotent responses. Leadership effectiveness was positively associated with phonemic fluency (PF), which involves mental flexibility, in turn, an increasingly important ability for future leaders in this rapidly changing world. Transformational leadership was positively associated with trait EI, extraversion, and openness to experience, a result that is following previous findings. The relationship between specific EF constructs and leadership effectiveness emphasizes the role of higher-order cognitive functions in the field of leadership as an individual difference. EF brings a new perspective into leadership literature by providing a direct, non-invasive, scientifically-valid connection between brain function and leadership behavior.

Keywords: cognitive neuroscience, emotional intelligence, executive functions, leadership

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: job-shop scheduling, classification, constraints, objective functions

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

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Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: kinematic constraints, motion planning, trigonometric function, 6-DOF robots

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

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Authors: Sultan Ayoub Meo

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Environmental pollution is a highly challenging global concern of the 21st century and is a major cause of various communicable and non-communicable diseases. We investigate the impact of air pollution on "lung function, fractional exhaled nitric oxide, and cognitive function"in a group of one hundred young students studying in a traffic-polluted school. The students wereselected based on their age, gender, height, weight, and ethnicity. After the clinical history, one hundred students were recruited from the schoolnear and away from the polluted areas. The lung and cognitive functions were recorded. The results revealed that lung and cognitive function parameters were reduced in groups of students studying in a school located in a traffic-polluted area compared to thosestudying in a schoolsituated away from the traffic-polluted area. Environmental pollution impairs students' lung and cognitive functions studying in schools located within traffic-polluted areas. The health officials and policymakers establish strategies to minimize environmental pollution and its allied health hazards. Prof. Sultan Ayoub Meo, MD, Ph.D Professor, Department of Physiology, College of Medicine, King Saud University, Saudi Arabia Email. [email protected] / [email protected]

Keywords: environmental pOllution, lung physiology, cognitive functions, air pollution

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Authors: Owolabi Kolade Matthew

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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

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Authors: Magdy Roman, Mostafa Shoeib, Mostafa Rostom

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Global vision, whether provided by overhead fixed cameras, on-board aerial vehicle cameras, or satellite images can always provide detailed information on the environment around mobile robots. In this paper, an intelligent vision-based method of path planning and obstacle avoidance for mobile robots is presented. The method integrates visual perception with a new proposed field-based path-planning method to overcome common path-planning problems such as local minima, unreachable destination and unnecessary lengthy paths around obstacles. The method proposes an exponential angle deviation field around each obstacle that affects the orientation of a close robot. As the robot directs toward, the goal point obstacles are classified into right and left groups, and a deviation angle is exponentially added or subtracted to the orientation of the robot. Exponential field parameters are chosen based on Lyapunov stability criterion to guarantee robot convergence to the destination. The proposed method uses obstacles' shape and location, extracted from global vision system, through a collision prediction mechanism to decide whether to activate or deactivate obstacles field. In addition, a search mechanism is developed in case of robot or goal point is trapped among obstacles to find suitable exit or entrance. The proposed algorithm is validated both in simulation and through experiments. The algorithm shows effectiveness in obstacles' avoidance and destination convergence, overcoming common path planning problems found in classical methods.

Keywords: path planning, collision avoidance, convergence, computer vision, mobile robots

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Authors: Sidi Mohamed Mesli, Mohamed Habchi, Arslane Boudghene Stambouli, Rafik Benallal

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The BaMnMF7 (M=Fe,V, transition metal fluoride glass, assuming isomorphous replacement) have been structurally studied through the simultaneous simulation of their neutron diffraction patterns by reverse Monte Carlo (RMC) and by the Hybrid Reverse Monte Carlo (HRMC) analysis. This last is applied to remedy the problem of the artificial satellite peaks that appear in the partial pair distribution functions (PDFs) by the RMC simulation. The HRMC simulation is an extension of the RMC algorithm, which introduces an energy penalty term (potential) in acceptance criteria. The idea of this work is to apply the Buckingham potential at the title glass by ignoring the van der Waals terms, in order to make a fit of the partial pair distribution functions and give the most possible realistic features. When displaying the partial PDFs, we suggest that the Buckingham potential is useful to describe average correlations especially in similar interactions.

Keywords: fluoride glasses, RMC simulation, hybrid RMC simulation, Buckingham potential, partial pair distribution functions

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Authors: Timea Harmath-Tánczos

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Drug-resistant epilepsy (DRE) is defined as the persistence of seizures despite at least two syndrome-adapted antiseizure drugs (ASD) used at efficacious daily doses. About a third of patients with epilepsy suffer from drug resistance. Cognitive assessment has a crucial role in the diagnosis and clinical management of epilepsy. Previous studies have addressed the clinical targets and indications for measuring neuropsychological functions; best to our knowledge, no studies have examined it in a Hungarian therapy-resistant population. To fill this gap, we investigated the Hungarian diagnostic protocol between 18 and 65 years of age. This study aimed to describe and analyze neuropsychological functions in patients with drug-resistant epilepsy and identify factors associated with neuropsychology deficits. We perform a prospective case-control study comparing neuropsychological performances in 50 adult patients and 50 healthy individuals between March 2023 and July 2023. Neuropsychological functions were examined in both patients and controls using a full set of specific tests (general performance level, motor functions, attention, executive facts., verbal and visual memory, language, and visual-spatial functions). Potential risk factors for neuropsychological deficit were assessed in the patient group using a multivariate analysis. The two groups did not differ in age, sex, dominant hand and level of education. Compared with the control group, patients with drug-resistant epilepsy showed worse performance on motor functions and visuospatial memory, sustained attention, inhibition and verbal memory. Neuropsychological deficits could therefore be systematically detected in patients with drug-resistant epilepsy in order to provide neuropsychological therapy and improve quality of life. The analysis of the classical and complex indices of the special neuropsychological tasks presented in the presentation can help in the investigation of normal and disrupted memory and executive functions in the DRE.

Keywords: drug-resistant epilepsy, Hungarian diagnostic protocol, memory, executive functions, cognitive neuropsychology

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Authors: H. Taylan Selamlar, I. Yavuz, G. Yapar

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It is difficult to make predictions especially about the future and making accurate predictions is not always easy. However, better predictions remain the foundation of all science therefore the development of accurate, robust and reliable forecasting methods is very important. Numerous number of forecasting methods have been proposed and studied in the literature. There are still two dominant major forecasting methods: Box-Jenkins ARIMA and Exponential Smoothing (ES), and still new methods are derived or inspired from them. After more than 50 years of widespread use, exponential smoothing is still one of the most practically relevant forecasting methods available due to their simplicity, robustness and accuracy as automatic forecasting procedures especially in the famous M-Competitions. Despite its success and widespread use in many areas, ES models have some shortcomings that negatively affect the accuracy of forecasts. Therefore, a new forecasting method in this study will be proposed to cope with these shortcomings and it will be called ATA method. This new method is obtained from traditional ES models by modifying the smoothing parameters therefore both methods have similar structural forms and ATA can be easily adapted to all of the individual ES models however ATA has many advantages due to its innovative new weighting scheme. In this paper, the focus is on modeling the trend component and handling seasonality patterns by utilizing classical decomposition. Therefore, ATA method is expanded to higher order ES methods for additive, multiplicative, additive damped and multiplicative damped trend components. The proposed models are called ATA trended models and their predictive performances are compared to their counter ES models on the M3 competition data set since it is still the most recent and comprehensive time-series data collection available. It is shown that the models outperform their counters on almost all settings and when a model selection is carried out amongst these trended models ATA outperforms all of the competitors in the M3- competition for both short term and long term forecasting horizons when the models’ forecasting accuracies are compared based on popular error metrics.

Keywords: accuracy, exponential smoothing, forecasting, initial value

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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