Search results for: differential test functioning

Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Erin Curtis, Avraham Schwiger

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Neuropsychological testing and evaluation is a crucial step in providing patients with effective diagnoses and treatment while in clinical care. The variety of batteries used in these evaluations can help clinicians better understand the nuanced declivities in a patient’s cognitive, behavioral, or emotional functioning, consequently equipping clinicians with the insights to make intentional choices about a patient’s care. Despite the knowledge these batteries can yield, some aspects of neuropsychological testing remain largely inaccessible to certain patient groups as a result of fundamental cultural, educational, or social differences. One such battery includes the Dot Counting Test (DCT), during which patients are required to count a series of dots on a page as rapidly and accurately as possible. As the battery progresses, the dots appear in clusters that are designed to be easily multiplied. This task evaluates a patient’s cognitive functioning, attention, and level of effort exerted on the evaluation as a whole. However, there is evidence to suggest that certain social groups, particularly Latinx groups, may perform worse on this task as a result of cultural or educational differences, not reduced cognitive functioning or effort. As such, this battery fails to account for baseline differences among patient groups, thus creating questions surrounding the accuracy, generalizability, and value of its results. Accessibility and cultural sensitivity are critical considerations in the testing and treatment of marginalized groups, yet have been largely ignored in the literature and in clinical settings to date. Implications and improvements to applications are discussed.

Keywords: culture, latino, neuropsychological assessment, neuropsychology, accessibility

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

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

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Authors: Loke Mun Sei

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Software testing has become a mandatory process in assuring the software product quality. Hence, test management is needed in order to manage the test activities conducted in the software test life cycle. This paper discusses on the challenges faced in the software test life cycle, and how the test processes and test activities, mainly on test cases creation, test execution, and test reporting is being managed and automated using several test automation tools, i.e. Jira, Robot Framework, and Jenkins.

Keywords: test automation tools, test case, test execution, test reporting

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

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The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: smart material, on-line differential artificial neural network, active control, finite element method

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Yuri V. Kim

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This article presents a new approach to the Functional Testing of Space Systems (SS). It can be considered as a generic test and used for a wide class of SS that from the point of view of System Dynamics and Control may be described by the ordinary differential equations. Suggested methodology is based on using semi-natural experiment- laboratory stand that doesn’t require complicated, precise and expensive technological control-verification equipment. However, it allows for testing system as a whole totally assembled unit during Assembling, Integration and Testing (AIT) activities, involving system hardware (HW) and software (SW). The test physically activates system input (sensors) and output (actuators) and requires recording their outputs in real time. The data is then inserted in laboratory PC where it is post-experiment processed by Matlab/Simulink Identification Toolbox. It allows for estimating system dynamics in form of estimation of system differential equations by the experimental way and comparing them with expected mathematical model prematurely verified by mathematical simulation during the design process.

Keywords: system dynamics, space system ground tests and space qualification, system dynamics identification, satellite attitude control, assembling, integration and testing

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Soretha Beets, Izanette Van Schalkwyk, Doret K. Kirsten

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Children in middle childhood are exposed to various risks, for example, risks associated with poverty and/or dysfunctional families, that may threaten their social functioning. The aim of this study was to develop and design a programme that can be presented to children in middle childhood in order to enhance their social functioning towards better wellbeing. The skills and competencies needed to be included in the programme were identified by means of a literature review and 4 focus groups with educators from 4 sub-areas in a certain district in the North-West Province of South Africa. The programme consists of 8 sessions, presented in a certain order. The sessions cover the following aspects: self-esteem and gratitude, self-regulation and goal-setting, values and relationships, communication and listening, conflict management, emotional competence, and resilient coping. These aspects may benefit children in the middle child’s wellbeing and live on the short-term and may also hold long-term benefits.

Keywords: middle childhood, programme development, social functioning, wellbeing

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: K. Y. Tseng, C. Y. Wu

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This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

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Authors: Oustani Mabrouka, Halilat Md Tahar, Hannachi Slimane

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This study was conducted on representative and contrasting soils of arid regions. It focuses on the compared influence of two organic fertilizers: poultry manure (PM) and bovine manure (BM) on improving the microbial functioning of non-saline (SS) and saline (SSS) soils, in particularly, the process of mineralization of nitrogen and carbon. The microbiological activity was estimated by respirometric test (CO2–C emissions) and the extraction of two forms of mineral nitrogen (NH4+-N and NO3--N). Thus, after 56 days of incubation under controlled conditions (28 degrees and 80 per cent of the field capacity), the two types of manures showed that the mineralization activity varies according to type of soil and the organic substrate itself. However, the highest cumulative quantities of CO2–C, NH4+–N and NO3-–N obtained at the end of incubation were recorded in non-saline (SS) soil treated with poultry manure with 1173.4, 4.26 and 8.40 mg/100 g of dry soil, respectively. The reductions in rates of release of CO2–C and of nitrification under saline conditions were 21 and 36, 78 %, respectively. The influence of organic substratum on the microbial density shows a stimulating effect on all microbial groups studied. The whole results show the usefulness of two types of manures for the improvement of the microbiological functioning of arid soils.

Keywords: Salinity, Organic matter, Microorganisms, Mineralization, Nitrogen, Carbon, Arid regions

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

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

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Authors: Rachel M. Edelstein, John D. Van Horn, Karen M. Schmidt, Sydney N. Cushing

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As a consequence of sports-related concussions, female athletes have been documented as reporting more symptoms than their male counterparts, in addition to incurring longer periods of recovery. However, the role of sex and its potential influence on symptom reporting and recovery outcomes in concussion management has not been completely explored. The present aims to investigate the relationship between female concussion symptom severity and the presence of assessment bias. The Sport Concussion Assessment Tool 3 (SCAT3), collected by the NCAA and DoD CARE Consortium, was quantified at five different time points post-concussion. N= 1,258 NCAA athletes, n= 473 female (soccer, rugby, lacrosse, ice hockey) and n=785 male athletes (football, rugby, lacrosse, ice hockey). A polytomous Item Response Theory (IRT) Graded Response Model (GRM) was used to assess the relationship between sex and symptom reporting. Differential Item Functioning (DIF) and Differential Group Functioning (DGF) were used to examine potential group-level bias. Interactions for DIF were utilized to explore the impact of sex on symptom reporting among NCAA male and female athletes throughout and after their concussion recovery. DIF was significantly detected after B-H corrections displayed in limited items; however, one symptom, “Pressure in Head” (-0.29, p=0.04 vs -0.20, p =0.04), was statistically significant at both < 6 hours and 24-48 hours. Thus, implies that at < 6 hours, males were 29% less likely to indicate “Pressure in the Head” compared to female athletes and 20% less likely at 24-48 hours. Overall, the DGF suggested significant group differences, suggesting that male athletes might be at a higher risk for returning to play prematurely (logits = -0.38, p < 0.001). However, after analyzing the SCAT 3, a clinically relevant trend was discovered. Twelve out of the twenty-two symptoms suggest higher difficulty in female athletes within three or more of the five-time points. These symptoms include Balance Problems, Blurry Vision, Confusion, Dizziness, Don’t Feel Right, Feel in Fog, Feel Slow Down, Low Energy, Neck Pain, Sensitivity to Light, Sensitivity to Noise, Trouble Falling Asleep. Despite a lack of statistical significance, this tendency is contrary to current literature stating that males may be unclear on symptoms, but females may be more honest in reporting symptoms. Further research, which includes possible modifying socioecological factors, is needed to determine whether females may consistently experience more symptoms and require longer recovery times or if, parsimoniously, males tend to present their symptoms and readiness for play differently than females. Such research will help to improve the validity of current assumptions concerning male as compared to female head injuries and optimize individualized treatments for sports-related head injuries.

Keywords: female athlete, sports-related concussion, item response theory, concussion assessment

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Authors: Ekhlas Al Gamal, Tony Long

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The impact on the parents of caring for a child with cancer was intense and wide-ranging. A high level of distress and low level or resilience remains during treatment. Even completion of treatment can be a time of increased anxiety and stress for parents particularly with worries about recurrence or relapse. The purpose of this study to examine the associations between parental satisfactions with healthcare provided for their child and the impact of being a caregiver for a child with cancer. Methodology: A descriptive, correlational and cross-sectional design was employed using data from Arabic versions of self-report questionnaires which were administered to 113 parents with children with cancer in Jordan during 2015. Findings: the result indicated that Family relationship functioning was ranked as the highest (better functioning) domain while daily activities were ranked as the lowest (poorer functioning) domain. Parents were generally satisfied with the health care provided, but their emotional needs were not met adequately. Parents with better social functioning were more satisfied in all areas of healthcare satisfaction other than emotional needs and communication. Parents who had a child with more emotional and behavioural problems were more likely to experience a negative impact on the family and a poor level of family functioning. Conclusion and Significance: Nurses and other health care providers should emphasis on family centred approach rather than child centred approach.

Keywords: parents, children, cancer, Jordan

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: J. Liu, Z. P. Yu, L. Xiong, Y. Feng, J. He

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According to the independence, accuracy and controllability of the driving/braking torque of the distributed drive electric vehicle, a control strategy of differential drive assisted steering was designed. Firstly, the assisted curve under different speed and steering wheel torque was developed and the differential torques were distributed to the right and left front wheels. Then the steering return ability assisted control algorithm was designed. At last, the joint simulation was conducted by CarSim/Simulink. The result indicated: the differential drive assisted steering algorithm could provide enough steering drive-assisted under low speed and improve the steering portability. Along with the increase of the speed, the provided steering drive-assisted decreased. With the control algorithm, the steering stiffness of the steering system increased along with the increase of the speed, which ensures the driver’s road feeling. The control algorithm of differential drive assisted steering could avoid the understeer under low speed effectively.

Keywords: differential assisted steering, control strategy, distributed drive electric vehicle, driving/braking torque

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Arin Ghazarian, Cyril Rakovski

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Differential privacy has become the leading technique to protect the privacy of individuals in a database while allowing useful analysis to be done and the results to be shared. It puts a guarantee on the amount of privacy loss in the worst-case scenario. Differential privacy is not a toggle between full privacy and zero privacy. It controls the tradeoff between the accuracy of the results and the privacy loss using a single key parameter called

Keywords: arrhythmia, cardiology, differential privacy, ECG, epsilon, medi-cal data, privacy preserving analytics, statistical databases

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Mohsen Amiri

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This study aimed at investigating the relationship between familial functioning, child characteristics, demographic variables and parenting stress and mental health among parents of children with mental disabilities. 200 parents (130 mothers and 70 fathers) were studied and they completed the Parenting Stress Index, General Health Questionnaire, Family Assessment Device and demographic questionnaires for parents and children. Data were analyzed using correlation and regression analysis. Regression analysis showed that child characteristics, familial functioning and parents demographic factors could predict 8, 4 and 17 percent of variance in parental stress and 3.6, 16 and 10 percent of variance in mental health, respectively. Familial functioning, child characteristics and parental demographic variables correlated with mental health and parental stress and could predict them.

Keywords: parenting stress, mental health, mentally disabled children, familial functioning, demographic variables

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Authors: Hansoo Kim, Seunghak Shin

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The differential column shortening in tall buildings can be reduced by improving material and structural characteristics of the structural systems. This paper proposes structural methods to reduce differential column shortening in reinforced concrete tall buildings; connecting columns with rigidly jointed horizontal members, using outriggers, and placing additional reinforcement at the columns. The rigidly connected horizontal members including outriggers reduce the differential shortening between adjacent vertical members. The axial stiffness of columns with greater shortening can be effectively increased by placing additional reinforcement at the columns, thus the differential column shortening can be reduced in the design stage. The optimum distribution of additional reinforcement can be determined by applying a gradient based optimization technique.

Keywords: column shortening, long-term behavior, optimization, tall building

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