Search results for: stochastic differential equation

Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

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In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

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Authors: Lukumba Phiri, Simon Tembo, Kumbuso Joshua Nyoni

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In Zambia recent initiatives by various power operators like ZESCO, CEC, and consumers like the mines to upgrade power systems into smart grids target an even tighter integration with information technologies to enable the integration of renewable energy sources, local and bulk generation, and demand response. Thus, for the reliable operation of smart grids, its information infrastructure must be secure and reliable in the face of both failures and cyberattacks. Due to the nature of the systems, ICS/SCADA cybersecurity and governance face additional challenges compared to the corporate networks, and critical systems may be left exposed. There exist control frameworks internationally such as the NIST framework, however, there are generic and do not meet the domain-specific needs of the SCADA systems. Zambia is also lagging in cybersecurity awareness and adoption, therefore there is a concern about securing ICS controlling key infrastructure critical to the Zambian economy as there are few known facts about the true posture. In this paper, we introduce a stochastic Edged-based Anomaly Detection for SCADA systems (SEADS) framework for threat modeling and risk assessment. SEADS enables the calculation of steady-steady probabilities that are further applied to establish metrics like system availability, maintainability, and reliability.

Keywords: anomaly, availability, detection, edge, maintainability, reliability, stochastic

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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: Razyeh Behbahani, Martin L. Plumer, Ivan Saika-Voivod

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Micromagnetic simulations based on the stochastic Landau-Lifshitz-Gilbert equation are used to calculate dynamic magnetic hysteresis loops relevant to magnetic hyperthermia applications. With the goal to effectively simulate room-temperature loops for large iron-oxide based systems at relatively slow sweep rates on the order of 1 Oe/ns or less, a coarse-graining scheme is proposed and tested. The scheme is derived from a previously developed renormalization-group approach. Loops associated with nanorods, used as building blocks for larger nanoparticles that were employed in preclinical trials (Dennis et al., 2009 Nanotechnology 20 395103), serve as the model test system. The scaling algorithm is shown to produce nearly identical loops over several decades in the model grain sizes. Sweep-rate scaling involving the damping constant alpha is also demonstrated.

Keywords: coarse-graining, hyperthermia, hysteresis loops, micromagnetic simulations

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Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: Raheela Akhtar, Zafar Iqbal Chaudhary, Yongqun Oliver He, Muhammad Younus, Aftab Ahmad Anjum

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Brucella abortus is an intracellular pathogen affecting macrophages. Macrophages release some components such as lysozymes (LZ), reactive oxygen species (ROS) and reactive nitrite intermediates (RNI) which are important tools against intracellular survival of Brucella. The antibrucella activity of bovine and murine macrophages was compared following stimulation with Brucella abortus lipopolysaccharides. Our results revealed that murine macrophages were ten times more potent to produce antibrucella components than bovine macrophages. The differential production of these components explained the differential Brucella killing ability of these species that was measured in terms of intramacrophagic survival of Brucella in murine and bovine macrophages.

Keywords: bovine macrophages, Brucella abortus, cell stimulation, cytokines, Murine macrophages

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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: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

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Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I₁, I₂, … I_n at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: multi-temporal satellite image, urban growth, non-stationary, stochastic model

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Authors: H. N. Cheung

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Self-compassion encourages one to accept oneself, reduce self-criticism and self-judgment, and see one’s shortcomings and setbacks in a balanced view. Adolescent self-compassion is a crucial protective factor against mental illness. It is, however, affected by gender. Given the scarcity of self-compassion scales for adolescents, the current study evaluates the Self-Compassion Scale for Youth (SCS-Y) in a large cross-cultural sample and investigates how the subscales of SCS-Y relate to the dimensions of depressive symptoms across gender. Through the internet-based Qualtrics, a total of 2881 teenagers aged 12 to 18 years were recruited from Hong Kong (HK), China, and the United Kingdom. A Multiple Indicator Multiple Cause (MIMIC) model was used to evaluate measurement invariance of the SCS-Y, and differential item functioning (DIF) was checked across gender. Upon the establishment of the best model, a multigroup structural equation model (SEM) was built between factors of SCS-Y and Multidimensional depression assessment scale (MDAS) which assesses four dimensions of depressive symptoms (emotional, cognitive, somatic and interpersonal). The SCS-Y was shown to have good reliability and validity. The MIMIC model produced a good model fit for a hypothetical six-factor model (CFI = 0.980; TLI = 0.974; RMSEA = 0.038) and no item was flagged for DIF across gender. A gender difference was observed between SCS-Y factors and depression dimensions. Conclusions: The SCS-Y exhibits good psychometric characteristics, including measurement invariance across gender. The study also highlights the gender difference between self-compassion factors and depression dimensions.

Keywords: self compassion, gender, depression, structural equation modelling, MIMIC model

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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: 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: Renjie Liu, Junshuai Xue, Jiajia Yao, Guanlin Wu, Zumao L, Xueyan Yang, Fang Liu, Zhuang Guo

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Here, we report the study of the performance of AlN/GaN bipolar resonance tunneling diodes (BRTDs) using numerical simulations. The I-V characteristics of BRTDs show double negative differential resistance regions, which exhibit similar peak current density and peak-to-valley current ratio (PVCR). Investigations show that the PVCR can approach 4.6 for the first and 5.75 for the second negative resistance region. The appearance of the two negative differential resistance regions is realized by changing the collector material of conventional GaN RTD to P-doped GaN. As the bias increases, holes in the P-region and electrons in the N-region undergo resonant tunneling, respectively, resulting in two negative resistance regions. The appearance of two negative resistance regions benefits from the high AlN barrier and the precise regulation of the potential well thickness. This result shows the promise of GaN BRTDs in the development of multi-valued logic circuits.

Keywords: GaN bipolar resonant tunneling diode, double negative differential resistance regions, peak to valley current ratio, multi-valued logic

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Authors: Ali Vaezi, Jyotirmoy Dalal, Manish Verma

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The railroad is one of the primary transportation modes for hazardous materials (hazmat) shipments in North America. Installing an emergency response network capable of providing a commensurate response is one of the primary levers to contain (or mitigate) the adverse consequences from rail hazmat incidents. To this end, we propose a two-stage stochastic program to determine the location of and equipment packages to be stockpiled at each response facility. The raw input data collected from publicly available reports were processed, fed into the proposed optimization program, and then tested on a realistic railroad network in Ontario (Canada). From the resulting analyses, we conclude that the decisions based only on empirical datasets would undermine the effectiveness of the resulting network; coverage can be improved by redistributing equipment in the network, purchasing equipment with higher containment capacity, and making use of a disutility multiplier factor.

Keywords: hazmat, rail network, stochastic programming, emergency response

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Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

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The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: fractional model predictive control, fractional order systems, thermal system, predictive control

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Ibrahim Baba

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The work examines the nature and causes of differential politics in Africa with particular reference to the sub-Saharan region of the continent. It also among other objectives provides alternative panacea to gender discrimination in African politics and offers solutions on how to promote political inclusion of all citizens in respect of gender differences in Africa. The work is conducted using library base documentation analysis.

Keywords: gender, political, participation, differential politics, sub-Saharan Africa

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Authors: Hui-Yun Cao, Hai-Qing Zhou

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The high precision measurements and experiments play more and more important roles in particle physics and atomic physics. To analyse the precise experimental data sets, the corresponding precise and reliable theoretical calculations are necessary. Until now, the form factors of elemental constituents such as pion and proton are still attractive issues in current Quantum Chromodynamics (QCD). In this work, the two-photon-exchange (TPE) effects in ep→enπ⁺ at small -t are discussed within a hadronic model. Under the pion dominance approximation and the limit mₑ→0, the TPE contribution to the amplitude can be described by a scalar function. We calculate TPE contributions to the amplitude, and the unpolarized differential cross section with the only elastic intermediate state is considered. The results show that the TPE corrections to the unpolarized differential cross section are about from -4% to -20% at Q²=1-1.6 GeV². After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections σ(L,T,LT,TT). We find that the TPE corrections (at Q²=1-1.6 GeV²) to σL are about from -10% to -30%, to σT are about 20%, and to σ(LT,TT) are much larger. By these analyses, we conclude that the TPE contributions in ep→enπ⁺ at small -t are important to extract the separated cross sections σ(L,T,LT,TT) and the electromagnetic form factor of π⁺ in the experimental analysis.

Keywords: differential cross section, form factor, hadronic, two-photon

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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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: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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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: Mansour H. Alkmim, Adriano T. Fabro, Marcus V. G. De Morais

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In this paper, a global direct search optimization algorithm to reduce vibration of a tuned liquid column damper (TLCD), a class of passive structural control device, is presented. The objective is to find optimized parameters for the TLCD under stochastic load from different wind power spectral density. A verification is made considering the analytical solution of an undamped primary system under white noise excitation. Finally, a numerical example considering a simplified wind turbine model is given to illustrate the efficacy of the TLCD. Results from the random vibration analysis are shown for four types of random excitation wind model where the response PSDs obtained showed good vibration attenuation.

Keywords: generalized pattern search, parameter optimization, random vibration analysis, vibration suppression

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Authors: Tefera Kebede Leyu

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The purpose of this study was to estimate the impact of LIVES project participation on the level of technical efficiency of farm households in three regions of Ethiopia. We used household-level data gathered by IRLI between February and April 2014 for the year 2013(retroactive). Data on 1,905 (754 intervention and 1, 151 control groups) sample households were analyzed using STATA software package version 14. Efforts were made to combine stochastic frontier modeling with impact evaluation methodology using the Heckman (1979) two-stage model to deal with possible selectivity bias arising from unobservable characteristics in the stochastic frontier model. Results indicate that farmers in the two groups are not efficient and operate below their potential frontiers i.e., there is a potential to increase crop productivity through efficiency improvements in both groups. In addition, the empirical results revealed selection bias in both groups of farmers confirming the justification for the use of selection bias corrected stochastic frontier model. It was also found that intervention farmers achieved higher technical efficiency scores than the control group of farmers. Furthermore, the selectivity bias-corrected model showed a different technical efficiency score for the intervention farmers while it more or less remained the same for that of control group farmers. However, the control group of farmers shows a higher dispersion as measured by the coefficient of variation compared to the intervention counterparts. Among the explanatory variables, the study found that farmer’s age (proxy to farm experience), land certification, frequency of visit to improved seed center, farmer’s education and row planting are important contributing factors for participation decisions and hence technical efficiency of farmers in the study areas. We recommend that policies targeting the design of development intervention programs in the agricultural sector focus more on providing farmers with on-farm visits by extension workers, provision of credit services, establishment of farmers’ training centers and adoption of modern farm technologies. Finally, we recommend further research to deal with this kind of methodological framework using a panel data set to test whether technical efficiency starts to increase or decrease with the length of time that farmers participate in development programs.

Keywords: impact evaluation, efficiency analysis and selection bias, stochastic frontier model, Heckman-two step

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Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

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Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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Authors: Azizul Baten, Kamrul Hossain, Abdullah-Al-Zabir

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The objective of this study is to develop an appropriate stochastic frontier secondary schools efficiency model by ICT Intervention and to examine the impact of ICT challenges on secondary schools efficiency in the Sylhet division in Bangladesh using stochastic frontier analysis. The Translog stochastic frontier model was found an appropriate than the Cobb-Douglas model in secondary schools efficiency by ICT Intervention. Based on the results of the Cobb-Douglas model, it is found that the coefficient of the number of teachers, the number of students, and teaching ability had a positive effect on increasing the level of efficiency. It indicated that these are related to technical efficiency. In the case of inefficiency effects for both Cobb-Douglas and Translog models, the coefficient of the ICT lab decreased secondary school inefficiency, but the online class in school was found to increase the level of inefficiency. The coefficients of teacher’s preference for ICT tools like multimedia projectors played a contributor role in decreasing the secondary school inefficiency in the Sylhet division of Bangladesh. The interaction effects of the number of teachers and the classrooms, and the number of students and the number of classrooms, the number of students and teaching ability, and the classrooms and teaching ability of the teachers were recorded with the positive values and these have a positive impact on increasing the secondary school efficiency. The overall mean efficiency of urban secondary schools was found at 84.66% for the Translog model, while it was 83.63% for the Cobb-Douglas model. The overall mean efficiency of rural secondary schools was found at 80.98% for the Translog model, while it was 81.24% for the Cobb-Douglas model. So, the urban secondary schools performed better than the rural secondary schools in the Sylhet division. It is observed from the results of the Tobit model that the teacher-student ratio had a positive influence on secondary school efficiency. The teaching experiences of those who have 1 to 5 years and 10 years above, MPO type school, conventional teaching method have had a negative and significant influence on secondary school efficiency. The estimated value of σ-square (0.0625) was different from Zero, indicating a good fit. The value of γ (0.9872) was recorded as positive and it can be interpreted as follows: 98.72 percent of random variation around in secondary school outcomes due to inefficiency.

Keywords: efficiency, secondary schools, ICT, stochastic frontier analysis

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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: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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