Search results for: form function

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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Authors: Herbert W. Corley

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A scalar equilibrium (SE) is an alternative type of equilibrium in pure strategies for an n-person normal-form game G. It is defined using optimization techniques to obtain a pure strategy for each player of G by maximizing an appropriate utility function over the acceptable joint actions. The players’ actions are determined by the choice of the utility function. Such a utility function could be agreed upon by the players or chosen by an arbitrator. An SE is an equilibrium since no players of G can increase the value of this utility function by changing their strategies. SEs are formally defined, and examples are given. In a greedy SE, the goal is to assign actions to the players giving them the largest individual payoffs jointly possible. In a weighted SE, each player is assigned weights modeling the degree to which he helps every player, including himself, achieve as large a payoff as jointly possible. In a compromise SE, each player wants a fair payoff for a reasonable interpretation of fairness. In a parity SE, the players want their payoffs to be as nearly equal as jointly possible. Finally, a satisficing SE achieves a personal target payoff value for each player. The vector payoffs associated with each of these SEs are shown to be Pareto optimal among all such acceptable vectors, as well as computationally tractable.

Keywords: compromise equilibrium, greedy equilibrium, normal-form game, parity equilibrium, pure strategies, satisficing equilibrium, scalar equilibria, utility function, weighted equilibrium

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mahdad M’hamed, Belaidi Idir

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This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

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Authors: Lanyan Peng, Ling Chen

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Leishan Miao New-Year is one of the grandest festivals in the southeastern of Guizhou Province in China. It was officially listed in the National Intangible Cultural Heritage List in 2008, as a traditional folk cultural activity organized by the local Miao people. With the rise of cultural tourism, after 19 years of exploration, the local government has successfully built Miao New-Year into a cultural card that is well-known at home and abroad. During the Miao New-Year period, it has attracted 3.8 million tourists and achieves a win-win situation in the economy and culture. However, tourism development has changed the living environment and living state of the local people. And it is accompanied by changes in the form of the festival, the content of the festival, and the local people’s needs and attitudes to the festival. This paper uses the field investigation method to achieve 410 questionnaires and 35 interviews, exploring the process and the reasons for changes of Leishan Miao New-Year’s cultural function. Among all the functions, the economic function, identity function, and entertainment function have been enhanced, and the marriage and love function has been extended. In the meanwhile, sacrificial function has been weakened. There are some trends in functions. The function of commemorating ancestor and self-entertainment has been changed to entertaining people and economic pursuit.

Keywords: Miao New-Year, Miao nationality, festival function, changes

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Diljan C. K.

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Every location on the planet has a history and culture that give it its own identity and character, making it distinct from others. urbanised world, it is fashionable to remould its original character and impression in a contemporary style. The new character and impression of places show a complete detachment from their roots. The heritage and cultural values of the place are replaced by new impressions, and as a result, they eventually lose their identity and character and never have sustenance. In this situation, form-based coding acts as a tool in the urban design process, helping to come up with solutions that strongly bind individuals to their neighbourhood and are closely related to culture through the physical spaces they are associated with. Form-based code was made by pioneers of new urbanism in 1987 in the United States of America. Since then, it has been used in various projects inside and outside the USA with varied scales, from the design of a single building to the design of a whole community. This research makes an effort to interpret the form-based code in historic corridors to establish the association of physical form and space with the public realm to uphold the context and culture. Many of the historic corridors are undergoing a tremendous transformation in their physical form, avoiding their culture and context. This will lead to it losing its identity in form and function. If the case of Valiyashala in Trivandrum is taken as the case, which is transforming its form and will lead to the loss of its identity, the form-based code will be a suitable tool to strengthen its historical value. The study concludes by analysing the existing code (KMBR) of Valiyashala and form-based code to find the requirements in form-based code for Valiyashala.

Keywords: form based code, urban conservation, heritage, historic corridor

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Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

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Authors: Ishapathik Das

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The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs

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Authors: Khandoker Akib Mohammad

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While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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Authors: Debasis Sengupta, Sudipta Das

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The class of life distributions with decreasing mean residual life (DMRL) is well known in the field of reliability modeling. It contains the IFR class of distributions and is contained in the NBUE class of distributions. While upper and lower bounds of the reliability distribution function of aging classes such as IFR, IFRA, NBU, NBUE, and HNBUE have discussed in the literature for a long time, there is no analogous result available for the DMRL class. We obtain the upper and lower bounds for the reliability function of the DMRL class in terms of first order finite moment. The lower bound is obtained by showing that for any fixed time, the minimization of the reliability function over the class of all DMRL distributions with a fixed mean is equivalent to its minimization over a smaller class of distribution with a special form. Optimization over this restricted set can be made algebraically. Likewise, the maximization of the reliability function over the class of all DMRL distributions with a fixed mean turns out to be a parametric optimization problem over the class of DMRL distributions of a special form. The constructive proofs also establish that both the upper and lower bounds are sharp. Further, the DMRL upper bound coincides with the HNBUE upper bound and the lower bound coincides with the IFR lower bound. We also prove that a pair of sharp upper and lower bounds for the reliability function when the distribution is increasing mean residual life (IMRL) with a fixed mean. This result is proved in a similar way. These inequalities fill a long-standing void in the literature of the life distribution modeling.

Keywords: DMRL, IMRL, reliability bounds, hazard functions

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Authors: Diriba Dereje

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Background: Cardiac and renal disease are the most prevalent chronic non-communicable diseases (CNCD) affecting the community in a significant manner. The best and recommended method in halting CNCD is by working on prevention as early as possible. This is only possible if early surrogate markers are identified. As part of the stated solution, this study will identify an association between microalbuminuria (an early surrogate marker of renal and cardiac disease) and lung function test among adult in the community. Objective: The main aim of this study was to assess an association between microalbuminuria (an early surrogate marker of renal and cardiac disease) and lung function test among adult in the community. Methodology: Community based cross sectional study was conducted among 384 adult in Jimma town. A systematic sampling technique was used in selecting participants to the study. In searching for the possible association, binary and multivariate logistic regression and t-test was conducted. Finally, the association between microalbuminuria and lung function test was well stated in the form of figures and written description. Result and Conclusion: A significant association was found between microalbuminuria and different lung function test parameters.

Keywords: microalbuminuria, lung function, association, test

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Authors: Bohuslava Juhasova, Martin Juhas, Renata Masarova, Zuzana Sutova

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The article deals with the tool in Matlab GUI form that is designed to analyse a mechatronic system sensitivity and tolerance. In the analysed mechatronic system, a torque is transferred from the drive to the load through a coupling containing flexible elements. Different methods of control system design are used. The classic form of the feedback control is proposed using Naslin method, modulus optimum criterion and inverse dynamics method. The cascade form of the control is proposed based on combination of modulus optimum criterion and symmetric optimum criterion. The sensitivity is analysed on the basis of absolute and relative sensitivity of system function to the change of chosen parameter value of the mechatronic system, as well as the control subsystem. The tolerance is analysed in the form of determining the range of allowed relative changes of selected system parameters in the field of system stability. The tool allows to analyse an influence of torsion stiffness, torsion damping, inertia moments of the motor and the load and controller(s) parameters. The sensitivity and tolerance are monitored in terms of the impact of parameter change on the response in the form of system step response and system frequency-response logarithmic characteristics. The Symbolic Math Toolbox for expression of the final shape of analysed system functions was used. The sensitivity and tolerance are graphically represented as 2D graph of sensitivity or tolerance of the system function and 3D/2D static/interactive graph of step/frequency response.

Keywords: mechatronic systems, Matlab GUI, sensitivity, tolerance

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Authors: Osama Al-Sehail

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This paper argues for sustainability as a necessity in the evolution of tall architecture. It provides a different mode for dealing with sustainability in tall architecture, taking into consideration the speciality of its typology. To this end, the article develops a Biomimetic Structural Form as a paradigm to attain Vital Sustainability. A Biomimetic Structural Form, which is derived from the amalgamation of biomimicry as an approach for sustainability defining nature as source of knowledge and inspiration in solving humans’ problems and a Structural Form as a catalyst for evolving tall architecture, is a dynamic paradigm emerging from a conceptualizing and morphological process. A Biomimetic Structural Form is a flow system whose different forces and functions tend to be “better”, more "fit", to “survive”, and to be efficient. Through geometry and function—the two aspects of knowledge extracted from nature—the attributes of the Biomimetic Structural Form are formulated. Vital Sustainability is the survival level of sustainability in natural systems through which a system enhances the performance of its internal working and its interaction with the external environment. A Biomimetic Structural Form, in this context, is a medium for evolving tall architecture to emulate natural models in their ways of coexistence with the environment. As an integral part of this article, the sustainable super tall building 3Ts is discussed as a case study of applying Biomimetic Structural Form.   

Keywords: biomimicry, design in nature, high-rise buildings, sustainability, structural form, tall architecture, vital sustainability

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: Donglan Zha, Jiansong Si

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Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: bias of technical change, CES production function, elasticity of substitution, energy input

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Shatha S. Alhily

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The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

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Authors: H. Ozbasaran

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Lateral torsional buckling is a global stability loss which should be considered in the design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice. Such equations can be obtained by using energy method. Unfortunately, this method has a vital drawback. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. The accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties, and loading case, the hardest step is to determine a proper mode function. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for the concentrated load at the free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: buckling mode, cantilever, lateral-torsional buckling, I-beam

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Authors: Dwi Retno Sri Ambarwati

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Recently, the traditional architecture were getting lost, replaced by modern architecture. The existence of many traditional houses often changing the function and change the values in an effort to adjust to the modern lifestyle, whereas the spiritual background of traditional architectural design is very specific and be the basis for consideration in the construction of the building, both in terms of determining the location of the building, the direction toward building, the spatial pattern and organization of space, zoning, hierarchical space, building form, ornamentation, the selection of building materials, and so on. The changes in function and form will transformed the spiritual values contained in it, because the architecture affects human behavior and reflects the culture. The traditional architecture views the architecture as a concept that has different tendencies in terms of orientation, shape, and attitude toward nature that tends to harmony with the social environment and local culture. The concept of the spirit of place made the architecture looks familiar, not arrogant and give a positive value to the surrounding environment. Every culture has a traditional architecture that full of spiritual values, although in the simplest form. Humans can learn about human values and local wisdom through the positive values that contained in traditional architecture, the desire to balance themselves with nature and the environment, not overbearing, strict adherence to the prevailing norms, openness in public life and intimacy family life that form a harmonious in life. The great and the wise value of traditional architecture should be revived in modern architecture that tends to ignore the spiritual values and more concerned with the functional and aesthetic pleasure, by combining the noble values of traditional architecture into modern architecture.

Keywords: architecture, combining noble values, local wisdom, traditional architecture

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Authors: Hisham Arab Alkabeya, A. M. Hughes, J. Adams

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Background: People with Rheumatoid Arthritis (RA) continue to experience problems with hand function despite new drug advances and targeted medical treatment. Consequently, it is important to identify the factors that influence the impact of RA disease on hand function. This systematic review identified observational studies that reported factors that influenced the impact of RA on hand function. Methods: MEDLINE, EMBASE, CINAL, AMED, PsychINFO, and Web of Science database were searched from January 1990 up to March 2017. Full-text articles published in English that described factors related to hand functional disability in people with RA were selected following predetermined inclusion and exclusion criteria. Pertinent data were thoroughly extracted and documented using a pre-designed data extraction form by the lead author, and cross-checked by the review team for completion and accuracy. Factors related to hand function were classified under the domains of the International Classification of Functioning, Disability, and Health (ICF) framework and health-related factors. Three reviewers independently assessed the methodological quality of the included articles using the quality of cross-sectional studies (AXIS) tool. Factors related to hand function that was investigated in two or more studies were explored using a best-evidence synthesis. Results: Twenty articles form 19 studies met the inclusion criteria from 1,271 citations; all presented cross-sectional data (five high quality and 15 low quality studies), resulting in at best limited evidence in the best-evidence synthesis. For the factors classified under the ICF domains, the best-evidence synthesis indicates that there was a range of body structure and function factors that were related with hand functional disability. However, key factors were hand strength, disease activity, and pain intensity. Low functional status (physical, emotional and social) level was found to be related with limited hand function. For personal factors, there is limited evidence that gender is not related with hand function; whereas, conflicting evidence was found regarding the relationship between age and hand function. In the domain of environmental factors, there was limited evidence that work activity was not related with hand function. Regarding health-related factors, there was limited evidence that the level of the rheumatoid factor (RF) was not related to hand function. Finally, conflicting evidence was found regarding the relationship between hand function and disease duration and general health status. Conclusion: Studies focused on body structure and function factors, highlighting a lack of investigation into personal and environmental factors when considering the impact of RA on hand function. The level of evidence which exists was limited, but identified that modifiable factors such as grip or pinch strength, disease activity and pain are the most influential factors on hand function in people with RA. The review findings suggest that important personal and environmental factors that impact on hand function in people with RA are not yet considered or reported in clinical research. Well-designed longitudinal, preferably cohort, studies are now needed to better understand the causality between personal and environmental factors and hand functional disability in people with RA.

Keywords: factors, hand function, rheumatoid arthritis, systematic review

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Authors: Ayman Baklizi

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This paper discusses the problem of testing hypotheses about the lifetime distributions of a matched pair based on censored data. A distribution free test based on a runs statistic is proposed. Its null distribution and power function are found in a simple convenient form. Some properties of the test statistic and its power function are studied.

Keywords: censored data, distribution free, matched pair, runs statistics

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Authors: Warda Nasir, M. N. S. Qureshi

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Whistler waves are right handed circularly polarized waves and are frequently observed in space plasmas. The Low frequency branch of the Whistler waves having frequencies nearly around 100 Hz, known as Lion roars, are frequently observed in magnetosheath. Another feature of the magnetosheath is the observations of flat top electron distributions with single as well as two electron populations. In the past, lion roars were studied by employing kinetic model using classical bi-Maxwellian distribution function, however, could not be justified both on quantitatively as well as qualitatively grounds. We studied Whistler waves by employing kinetic model using non-Maxwellian distribution function such as the generalized (r,q) distribution function which is the generalized form of kappa and Maxwellian distribution functions by employing kinetic theory with single or two electron populations. We compare our results with the Cluster observations and found good quantitative and qualitative agreement between them. At times when lion roars are observed (not observed) in the data and bi-Maxwellian could not provide the sufficient growth (damping) rates, we showed that when generalized (r,q) distribution function is employed, the resulted growth (damping) rates exactly match the observations.

Keywords: kinetic model, whistler waves, non-maxwellian distribution function, space plasmas

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Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

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Authors: Hamza Zidoum

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This paper investigates the impact of human genetic variation on the function of human proteins using machine-learning algorithms. Single-Nucleotide Polymorphism represents the most common form of human genome variation. We focus on the single amino-acid polymorphism located in the coding region as they can affect the protein function leading to pathologic phenotypic change. We use several supervised Machine Learning methods to identify structural properties correlated with increased risk of the missense mutation being damaging. SVM associated with Principal Component Analysis give the best performance.

Keywords: single-nucleotide polymorphism, machine learning, feature selection, SVM

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Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

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Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: graphic parameterization, green building design, mathematical model, plane form

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Dení Stincer Gómez, Zuraya Monroy Nasr

Abstract:

Pedagogy of science historically has given priority to teaching strategies that mobilize the cognitive mechanisms leaving out emotional. Modern epistemology, cognitive psychology and psychoanalysis begin to argue and prove that emotions are relevant epistemological functions. They are 1) the selection function: that allows the perception and reason choose, to multiple alternative explanation of a particular fact, those are relevant and discard those that are not, 2) heuristic function: that is related to the activation cognitive processes that are effective in the process of knowing; and 3) the function that called carrier content: on the latter it arises that emotions give the material reasoning that later transformed into linguistic propositions. According to these hypotheses, scientific knowledge seems to come from emotions that meet these functions. In this paper I argue that science education should start from the presence of certain emotions in the learner if it is to form citizens with scientific or cultural future scientists.

Keywords: epistemic emotions, science education, formation of citizens and scientists., philosophy of emotions

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Authors: Damir Latypov

Abstract:

A closed-form solution for 4-D double surface integrals arising in boundary integrals equations of a potential theory is obtained for arbitrary coplanar polygonal surfaces. The solution method is based on the construction of exact differential forms followed by the application of Stokes' theorem for each surface integral. As a result, the 4-D double surface integral is reduced to a 2-D double line integral. By an appropriate change of variables, the integrand is transformed into a separable function of integration variables. The closed-form solutions to the corresponding 1-D integrals are readily available in the integration tables. Previously closed-form solutions were known only for the case of coincident triangle surfaces and coplanar rectangles. Solutions for these cases were obtained by surface-specific ad-hoc methods, while the present method is general. The method also works for non-polygonal surfaces. As an example, we compute in closed form the 4-D integral for the case of coincident surfaces in the shape of a circular disk. For an arbitrarily shaped surface, the proposed method provides an efficient quadrature rule. Extensions of the method for non-coplanar surfaces and other than 1/R integral kernels are also discussed.

Keywords: boundary integral equations, differential forms, integration, stokes' theorem

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