Superficies de Bézier en el Espacio de Lorentz-Minkowski

El objetivo principal de este trabajo es estudiar qué cambios experimenta la geometría diferencial de las superficies de Bézier al ser introducidas en el espacio de Lorentz-Minkowski. Específicamente se estudiarán resultados relacionados con el área de las superficies para poder tratar el Problema de Plateau-Bézier en estas condiciones. Para ello reuniremos una serie de condiciones sobre las redes de puntos que nos permitirán acotar las áreas de las superficies con un borde fijo.The main objective of this work is to study how changes the differential geometry of Bézier surfaces when they are studied in Lorentz-Minkowski space. Results about the area of the surfaces will be studied specifically in order to deal with the Plateau-Bézier problem in this particular conditions. We will gather a number of conditions over the control points which will allow us to delimit the area value of prescribed border surfaces.Universidad de Sevilla. Grado en Matemática

The Constructability of the Cheops Pyramid

Abstract The aim of this paper is to forecast the methodology by which Cheops Pyramid as a historic building was built, based on notions of modular patterns discovered within the following planar illustrations, starting at the apex and descending to its grand base. Some of Cheops’ heritage in terms of form and function has existed for millennia, as its mark was recapped with a front line that was constructed thousands of years before. Such a voyage through the missing captures of the building techniques wouldn’t have occurred without the incidental outcome that resulted from overlaying the various pixelated plans of block arrangements on the floor maps of Cheops. This building is believed to exhibit norms similar to those governing the balance between matter and void in the universe. By assessing this historical masonry structure of Giza, we have come to find some regulatory approaches concerning how to asses the construction of such a building by predicting their interiors, spatial definitions, customs, and layouts. As there are no major records of their plans, the best practice anticipated in this paper is to modularize the figurative appearance of such buildings, by imitating themes of the repetitive patterns of past regional Egyptian architecture seen as pixels. This led to the fundamental solution to such a dilemma in building construction. Keywords: Cheops, Pyramid, Balance, Historical Building

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.This research work has received funding from the project PDE-GIR (Partial Differential Equations for Geometric modelling, Image processing, and shape Reconstruction) of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 778035, the Spanish Ministry of Economy and Competitiveness (Computer Science National Program) under Grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE), and the project #JU12, jointly supported by public body SODERCAN of the Regional Government of Cantabria and European Funds FEDER (SODERCAN/FEDER UE). We also thank Toho University, Nihon University, and the Symmetry 2018, 10, 58 23 of 25 University of Cantabria for their support to conduct this research wor

Modelling, analysis and feedback control design for upright standing sways

Human body upright standing is inherently unstable, and as a bipedal creature, the body can implement several functions such as upright standing, walking and running, with the help of the central nervous system. Understanding the stability control of the human body during upright standing is important for prosthetic design and joint prostheses, walking restoration, diagnosis of nervous system diseases. Also, it is essential to anthropology, clinical research, aerospace science and kinesiology.Therefore, the objective of this work is to model the musculoskeletal system of human upright standing posture for analysis and control design of body sway. An asymmetric Gaussian function is proposed to model the force-length relationship and compared with other existing force-length models. By using least square curve fitting tools with a set of rabbit experimental data, and simulated data that represent sarcomere of the frog. Also, the implicit and explicit ordinary differential equations, are used to model muscle-tendon unit and compare the simulation results in term of singularity.In addition to, the equilibrium analysis is used to determine sway ranges during upright standing, and the equilibrium points can be used to linearize the model for feedback control design and stability analysis of the musculoskeletal system. Furthermore, a switching function is designed to model the intermittent activity of the MG muscle, where the parameters are optimised using the centre of gravity and electromyography data with Genetic Algorithm tool. The musculoskeletal system of the human body is modelled as a single inverted pendulum, which rotates around the ankle joint, in the sagittal plane only. The calf muscles especially the medial gastrocnemius activated intermittently, and soleus activated continuously are included in the model of the musculoskeletal system. The developed musculoskeletal system model is linearized in order to have clear stability analysis using Routh-Hurwitz stability criterion and eigenvalue analysis.The results show that the musculoskeletal system cannot be stabilised at the upright standing without feeding back angular velocity. The equilibrium analysis reveals how the sway range (sway points) depends on the used anatomical and anthropometry data. Finally, the stability analysis shows that during forwarding sway the calf muscles are shortening paradoxically and lengthening during backwards sway, which supports some existing experimental results. The model-based analysis which used in modelling the body upright standing, will help in analysis and understands the dynamics of the body during upright standing. Also, it assists in medical research, in clinical diagnostics and application

Micro-scale continuous and discrete numerical models for nonlinear analysis of masonry shear walls

A novel damage mechanics-based continuous micro-model for the analysis of masonry-walls is presented and compared with other two well-known discrete micro-models. The discrete micro-models discretize masonry micro-structure with nonlinear interfaces for mortar-joints, and continuum elements for units. The proposed continuous micro-model discretizes both units and mortar-joints with continuum elements, making use of a tension/compression damage model, here refined to properly reproduce the nonlinear response under shear and to control the dilatancy. The three investigated models are validated against experimental results. They all prove to be similarly effective, with the proposed model being less time-consuming, due to the efficient format of the damage model. Critical issues for these types of micro-models are analysed carefully, such as the accuracy in predicting the failure load and collapse mechanism, the computational efficiency and the level of approximation given by a 2D plane-stress assumption.Peer ReviewedPostprint (author's final draft

A Software Engineered Voice-Enabled Job Recruitment Portal System

The inability of job seekers to get timely job information regarding the status of the application submitted via conventional job portal system which is usually dependent on accessibility to the Internet has made so many job applicants to lose their placements. Worse still, the epileptic services offered by Internet Service Providers and the poor infrastructures in most developing countries have greatly hindered the expected benefits from Internet usage. These have led to cases of online vacancies notifications unattended to simply because a job seeker is neither aware nor has access to the Internet. With an increasing patronage of mobile phones, a self-service job vacancy notification with audio functionality or an automated job vacancy notification to all qualified job seekers through mobile phones will simply provide a solution to these challenges. In this paper, we present a Voice-enabled Job Recruitment Portal (JRP) System. The system is accessed through two interfaces – the voice user’s interface (VUI) and web interface. The VUI was developed using VoiceXML and the web interface using PHP, and both interfaces integrated with Apache and MySQL as the middleware and back-end component respectively. The JRP proposed in this paper takes the hassle of job hunting from job seekers, provides job status information in real-time to the job seeker and offers other benefits such as, cost, effectiveness, speed, accuracy, ease of documentation, convenience and better logistics to the employer in seeking the right candidate for a job