Search results for: hand written equation solver

Authors: Abdelmadjid Mammeri, Fatima Zohra Mahi, Luca Varani, H. Marinchoi

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We propose an analytical model for the admittance and the noise calculations of the InGaAs transistor and diode. The development of the small-signal admittance takes into account the longitudinal and transverse electric fields through a pseudo two-dimensional approximation of the Poisson equation. The frequency-dependent of the small-signal admittance response is determined by the total currents and the potentials matrix relation between the gate and the drain terminals. The noise is evaluated by using the real part of the transistor/diode admittance under a small-signal perturbation. The analytical results show that the admittance spectrum exhibits a series of resonant peaks corresponding to the excitation of plasma waves. The appearance of the resonance is discussed and analyzed as functions of the channel length and the temperature. The model can be used, on one hand; to control the appearance of the plasma resonances, and on other hand; can give significant information about the noise frequency dependence in the InGaAs transistor and diode.

Keywords: InGaAs transistors, InGaAs diode, admittance, resonant peaks, plasma waves, analytical model

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Authors: Okewu E. Jonathan

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There are several techniques of production in the field of ceramics. These different techniques overtime have been categorised under three methods of production which includes; casting, throwing and hand building. Hand building method of production is further broken down into other techniques and they include coiling, slabbing and pinching. Ceramic artists find the different hand building techniques to be very interesting, practicable and rewarding. This has encouraged ceramic artist in their various studios at different levels to experiment for further hand building techniques that could be unique and unusual. The art of “Clay Palm Press” is a development from studio experiment in a quest for uniqueness in conceptual ceramic practise. Clay palm press is a technique that requires no formal tutelage but at the same time, it is not easily comprehensible when viewed. It is a practice of putting semi-solid clay in the palm and inserting a closed fist pressure so as to take the imprint of the human palm. This clay production from the palm when dried, fired and explored into an art, work reveals an absolute awesomeness of what the palm imprint could result in.

Keywords: ceramics, clay palm press, conceptual forms, hand building, technique

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

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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: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: Cheng Shuk Ling

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This paper examines the English syntactic errors and their patterns in the written assignments of a General Education course at City University of Hong Kong. Subjects are 60 local and non-local (exchange) undergraduate students who are all EFL learners and L2 users with diversified education and disciplinary background (i.e. their major of study), which are unrelated to English language studies. The objective of this paper brings to the foreground a broad discussion of EFL/L2 undergraduate learners’ average syntactic ability in terms of written assessment. This paper is an attempt in classifying the patterns and categories of syntactic errors committed by students who were brought up and educated in non-native English-speaking countries. Thus, pedagogical recommendations are offered for both EFL/L2 learners and educators in tertiary education settings in such ways as to calibrate how and in what manner English language as the medium of instruction can lead to more enduring effects in learners within non-native English-speaking countries.

Keywords: syntactic errors, english as a foreign language, second language users, pedagogy

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Abdulmajid Mukhtar Afat

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This paper aims at introducing finite automata theory, the different ways to describe regular languages and create a program to implement the subset construction algorithms to convert nondeterministic finite automata (NFA) to deterministic finite automata (DFA). This program is written in c++ programming language. The program reads FA 5tuples from text file and then classifies it into either DFA or NFA. For DFA, the program will read the string w and decide whether it is acceptable or not. If accepted, the program will save the tracking path and point it out. On the other hand, when the automation is NFA, the program will change the Automation to DFA so that it is easy to track and it can decide whether the w exists in the regular language or not.

Keywords: finite automata, subset construction, DFA, NFA

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Authors: Samy Madbouly

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The relaxation behavior of biorenewable castor oil-based polyurethane-lignin thin films synthesized in homogenous waterborne dispersions was investigated as a function of concentration at different temperatures and frequencies using broadband dielectric relaxation spectroscopy (BDRS). The molecular dynamics of the glass relaxation process and the local relaxation process of the PU-LS thin films were studied over a wide range of temperatures (-70 to 30 ℃) and frequencies (5 × 10−2 to 0.5 × 107 Hz) for different lignin concentration. Four relaxation processes have been observed namely; ?-, β-, γ-relaxations and ionic conductivity for pure castor oil-based PU and castor oil-lignin-based PU thin films at different temperatures and frequencies ranges. The Vogel-Fulcher-Tammann equation was found to be well described the temperature dependence of the characteristic relaxation times of the ?-relaxation process. However, on the other hand, the molecular dynamics of both β- and γ-relaxation processes were given by the Arrhenius equation. The incorporation of lignin into the castor oil-based PU significantly increased the glass transition temperature and primitivity of the thin films. In addition, the broadness, intensity, and molecular dynamics of the only observed ?-relaxation process were found to be strongly dependent on lignin concentration.

Keywords: castor oil, lignin, polyurethane, dielectric, dispersions

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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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: Saad M. Darwish, Magda M. Madbouly, Murad B. Khorsheed

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Sign Languages (SL) are the most accomplished forms of gestural communication. Therefore, their automatic analysis is a real challenge, which is interestingly implied to their lexical and syntactic organization levels. Hidden Markov models (HMM’s) have been used prominently and successfully in speech recognition and, more recently, in handwriting recognition. Consequently, they seem ideal for visual recognition of complex, structured hand gestures such as are found in sign language. In this paper, several results concerning static hand gesture recognition using an algorithm based on Type-2 Fuzzy HMM (T2FHMM) are presented. The features used as observables in the training as well as in the recognition phases are based on Singular Value Decomposition (SVD). SVD is an extension of Eigen decomposition to suit non-square matrices to reduce multi attribute hand gesture data to feature vectors. SVD optimally exposes the geometric structure of a matrix. In our approach, we replace the basic HMM arithmetic operators by some adequate Type-2 fuzzy operators that permits us to relax the additive constraint of probability measures. Therefore, T2FHMMs are able to handle both random and fuzzy uncertainties existing universally in the sequential data. Experimental results show that T2FHMMs can effectively handle noise and dialect uncertainties in hand signals besides a better classification performance than the classical HMMs. The recognition rate of the proposed system is 100% for uniform hand images and 86.21% for cluttered hand images.

Keywords: hand gesture recognition, hand detection, type-2 fuzzy logic, hidden Markov Model

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: K. A. Schuck, J. K. Perret, A. Mehn, K. Rommel

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Consumers increasingly consider sustainability aspects in their consumption behavior. Although, few fashion brands are already active in the second-hand luxury market with their own online platforms. Separating between base and high-end luxury brands, two online discrete choice experiments determine the drivers behind consumers’ willingness-to-pay for platform characteristics like the type of ownership, giving brands the opportunity to elicit a financial scope they can operate within.

Keywords: choice experiment, luxury, preferences, second-hand, platform, online

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Authors: Marcio Leal, Marta Villamil

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Computacional recognition of sign languages aims to allow a greater social and digital inclusion of deaf people through interpretation of their language by computer. This article presents a model of recognition of two of global parameters from sign languages; hand configurations and hand movements. Hand motion is captured through an infrared technology and its joints are built into a virtual three-dimensional space. A Multilayer Perceptron Neural Network (MLP) was used to classify hand configurations and Dynamic Time Warping (DWT) recognizes hand motion. Beyond of the method of sign recognition, we provide a dataset of hand configurations and motion capture built with help of fluent professionals in sign languages. Despite this technology can be used to translate any sign from any signs dictionary, Brazilian Sign Language (Libras) was used as case study. Finally, the model presented in this paper achieved a recognition rate of 80.4%.

Keywords: artificial neural network, computer vision, dynamic time warping, infrared, sign language recognition

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Orit Zeevy-Solovey

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Grammar has traditionally been taught for its own sake, emphasizing rules and drills. However, in recent years, more emphasis is given to communicative competence. Current research suggests that form-focused instruction is notably efficient when incorporated in a meaningful communicative context. It is maintained that writing tasks related to the students’ academic fields will encourage them to express themselves openly in topics that are close to their hearts, without feeling too uneasy about grammatical forms. The teacher can further reduce students’ apprehension of grammar by announcing that credit will be given for merely doing the task and that grammar mistakes will not affect the grade. Students’ linguistic errors can then be corrected by giving metalinguistic feedback which involves providing learners with some kind of explicit remark about the nature of the errors they have made. Research has also shown that learners’ developmental readiness is an important factor influencing the effectiveness of written corrective feedback. Larger effect sizes appear as the proficiency level is higher. The purposes of this paper are to demonstrate how grammar can be taught indirectly through writing tasks, and more specifically, how the use of metalinguistic written corrective feedback given to advanced English as a Foreign Language (EFL) students can raise their linguistic awareness. Since errors are not directly corrected, the students have to work out the corrections needed through exploring grammar books and websites. Longitudinal studies of metalinguistic written corrective feedback comparing the number of errors in students’ first and fourth compositions have shown a decrease in errors.

Keywords: EFL, linguistic awareness, metalinguistic corrective feedback, teaching grammar through writing

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Authors: Razieh Khalafi

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The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli.

Keywords: brain, stimuli, partial differential equation, response, EEG signal

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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Authors: Faik Derya Ince, Ugur Topgul, Alp Gunay, Can Bayoglu, Dante J. Dorantes-Gonzalez

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Explosive attacks are arguably the most lethal threat that may occur in terrorist attacks. In order to counteract this issue, explosive ordnance disposal operators put their lives on the line to dispose of a possible improvised explosive device. Robots can make the disposal process more accurately and saving human lives. For this purpose, there is a demand for more accurate and dexterous manipulating robotic hands that can be teleoperated from a distance. The aim of this project is to design a robotic hand that contains two active and two passive DOF for each finger, as well as a minimum set of tools for mechanical cutting and screw driving within the same robotic hand. Both hand and toolset, are teleoperated from a distance from a haptic robotic glove in order to manipulate dangerous objects such as improvised explosive devices. SolidWorks® Computer-Aided Design, computerized dynamic simulation, and MATLAB® kinematic and static analysis were used for the robotic hand and toolset design. Novel, dexterous and robust solutions for the fingers were obtained, and six servo motors are used in total to remotely control the multi-tooled robotic hand. This project is still undergoing and presents currents results. Future research steps are also presented.

Keywords: Explosive Manipulation, Robotic Hand, Tele-Operation, Tool Integration

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Authors: Sriraman Kothuri, Komal Teja Mattupalli

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In this paper we proposed a novel algorithm for recognizing hulls in a hand written digits. This is an extension to the work on “Digit Recognition Using Freeman Chain code”. In order to find out the hulls in a user given digit it is necessary to follow three steps. Those are pre-processing, Boundary Extraction and at last apply the Hull Detection system in a way to attain the better results. The detection of Hull Regions is mainly intended to increase the machine learning capability in detection of characters or digits. This can also extend this in order to get the hull regions and their intensities in Black Holes in Space Exploration.

Keywords: chain code, machine learning, hull regions, hull recognition system, SASK algorithm

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Authors: Gunilla Dahlgren, Per Liv, Fredrik Öhberg, Lisbeth Slunga Järvholm, Mikael Forsman, Börje Rehn

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Background: Accuracy of risk assessment tools in hand-repetitive work is important. This can support precision in the risk management process and for a sustainable working life for women and men equally. Musculoskeletal disorders, MSDs, from the hand, wrist, and forearm, are common in the working population. Women report a higher prevalence of MSDs in these regions. Objective: The objective of this study was to compare if women and men who performed the identical hand-intensive work task were rated equally using the Hand Activity Threshold Limit Value® (HA-TLV) when self-rated and observer-rated. Method: Fifty-six workers from eight companies participated, with various intensities in hand-repetitive work tasks. In total, 18 unique identical hand-intensive work tasks were executed in 28 pairs of a woman and a man. Hand activity and force levels were assessed. Each worker executed the work task for 15 minutes, which was also video recorded. Data was collected on workers who self-rated directly after the execution of the work task. Also, experienced observers performed ratings from videos of the same work tasks. For comparing means between women and men, paired samples t-tests were used. Results: The main results showed that there was no difference in self-ratings of hand activity level and force by women and men who executed the same work task. Further, there was no difference between observer ratings of hand activity level. However, the observer force ratings of women and men differed significantly (p=0.01). Conclusion: Hand activity and force levels are rated equally in women and men when self-rated, also by observers for hand activity. However, it is an observandum that observer force rating is rated higher for women and lower for men. This indicates the need of comparing force ratings with technical measures.

Keywords: gender, equity, sex differences, repetitive strain injury, cumulative trauma disorders, upper extremity, exposure assessment, workload, health risk assessment, observation, psychophysics

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Authors: Samuel I. Becher, Tal Z. Zarsky

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The digital world becomes part of our DNA now. The way e-commerce, human behavior, and law interact and affect one another is rapidly and significantly changing. Among others things, the internet equips consumers with a variety of platforms to share information in a volume we could not imagine before. As part of this development, online information flows allow consumers to learn about businesses and their contracts in an efficient and quick manner. Consumers can become informed by the impressions that other, experienced consumers share and spread. In other words, consumers may familiarize themselves with the contents of contracts through the experiences that other consumers had. Online and offline, the relationship between consumers and businesses are most frequently governed by consumer standard form contracts. For decades, such contracts are assumed to be one-sided and biased against consumers. Consumer Law seeks to alleviate this bias and empower consumers. Legislatures, consumer organizations, scholars, and judges are constantly looking for clever ways to protect consumers from unscrupulous firms and unfair behaviors. While consumers-businesses relationships are theoretically administered by standardized contracts, firms do not always follow these contracts in practice. At times, there is a significant disparity between what the written contract stipulates and what consumers experience de facto. That is, there is a crucial gap (“the Gap”) between how firms draft their contracts on the one hand, and how firms actually treat consumers on the other. Interestingly, the Gap is frequently manifested by deviation from the written contract in favor of consumers. In other words, firms often exercise lenient approach in spite of the stringent written contracts they draft. This essay examines whether, counter-intuitively, policy makers should add firms’ leniency to the growing list of firms suspicious behaviors. At first glance, firms should be allowed, if not encouraged, to exercise leniency. Many legal regimes are looking for ways to cope with unfair contract terms in consumer contracts. Naturally, therefore, consumer law should enable, if not encourage, firms’ lenient practices. Firms’ willingness to deviate from their strict contracts in order to benefit consumers seems like a sensible approach. Apparently, such behavior should not be second guessed. However, at times online tools, firm’s behaviors and human psychology result in a toxic mix. Beneficial and helpful online information should be treated with due respect as it may occasionally have surprising and harmful qualities. In this essay, we illustrate that technological changes turn the Gap into a key component in consumers' understanding, or misunderstanding, of consumer contracts. In short, a Gap may distort consumers’ perception and undermine rational decision-making. Consequently, this essay explores whether, counter-intuitively, consumer law should sanction firms that create a Gap and use it. It examines when firms’ leniency should be considered as manipulative or exercised in bad faith. It then investigates whether firms should be allowed to enforce the written contract even if the firms deliberately and consistently deviated from it.

Keywords: consumer contracts, consumer protection, information flow, law and economics, law and technology, paper deal v firms' behavior

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Authors: Ya-Fen Lee, Yun-Yao Chi

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The study aims to explore the relationship between risk perceptions of rockfall and revisit intention using a Structural Equation Modelling (SEM) analysis. A total of 573 valid questionnaires are collected from travelers to Taroko National Park, Taiwan. The findings show the majority of travellers have the medium perception of rockfall risk, and are willing to revisit the Taroko National Park. The revisit intention to Taroko National Park is influenced by hazardous preferences, willingness-to-pay, obstruction and attraction. The risk perception has an indirect effect on revisit intention through influencing willingness-to-pay. The study results can be a reference for mitigation the rockfall disaster.

Keywords: risk perception, rockfall, revisit intention, structural equation modelling

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Authors: Syed M. Jawwad Riaz

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There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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