Search results for: Late solution

Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

Abstract:

In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2317

Authors: Intan Waheedah Othman, Maslinawati Mohamad, Azizah Abdullah

Abstract:

Cooperative organizations in Malaysia are going through a phase of rapid growth. They are seen by the government as another crucial vehicle to drive and boost up the country-s economical development and growth. Hence, the issue of cooperative governance is of great importance. Unlike literatures on corporate governance for public listed companies-, literatures on governance for social enterprises, in particular the cooperative organizations are still at the early stage in Malaysia and very scant in number. This paper will look into current practices as well as issues and challenges related to cooperative governance. The need for a better solution towards forming best practices of cooperative governance framework appears imperative in deterring cases of mismanagement and fraud.

Keywords: Cooperative, Governance, Issues, Malaysia.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4978

Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1436

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1679

Authors: Seung Pil Pack

Abstract:

Carbonic anhydrases (CAs) has been focused as biological catalysis for CO2 sequestration process because it can catalyze the conversion of CO2 to bicarbonate. Here, codon-optimized sequence of α type-CA cloned from Duneliala species. (DsCAopt) was constructed, expressed, and characterized. The expression level in E. coli BL21(DE3) was better for codon-optimized DsCAopt than intact sequence of DsCAopt. DsCAopt enzyme shows high-stability at pH 7.6/10.0. In final, we demonstrated that in the Ca2+ solution, DsCAopt enzyme can catalyze well the conversion of CO2 to CaCO3, as the calcite form.

Keywords: Carbonic anhydrase, Codon-optimization, Duneliala species, CO2 sequestration

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1645

Authors: O. Wright, N. Perkins, M. Donn, M. Halstead

Abstract:

This research responded to anecdotal evidence that suggested inefficiencies within the Architect and Acoustician relationship may lead to ineffective acoustic design decisions.  The acoustician spoken to believed that he was approached too late in the design phase. The approached architect valued acoustical qualities, yet, struggled to interpret common measurement parameters. The preliminary investigation of these opinions indicated a gap in the current New Zealand Architectural discourse and currently informs the creation of a 2016 Master of Architecture (Prof) thesis research. Little meaningful information about acoustic intervention in the early design phase could be found from past literature. In the information that was sourced, authors focus on software as an incorporation tool without investigating why the flaws in the relationship originally exist. To further explore this relationship, a survey was designed. It underwent three phases to ensure its consistency, and was delivered to a group of 51 acousticians from one international Acoustics company. The results were then separated between New Zealand and off-shore to identify trends. The survey results suggest that 75% of acousticians meet the architect less than 5 times per project. Instead of regular contact, a mediated method is adopted though a mix of telecommunication and written reports. Acousticians tend to be introduced later into New Zealand building project than the corresponding off-shore building. This delay corresponds to an increase in remedial action for each of the building types in the survey except Auditoria and Office Buildings. 31 participants have had their specifications challenged by an architect. Furthermore, 71% of the acousticians believe that architects do not have the knowledge to understand why the acoustic specifications are in place. The issues raised in this investigation align to the colloquial evidence expressed by the two consultants. It identifies a larger gap in the industry were acoustics is remedially treated rather than identified as a possible design driver. Further research through design is suggested to understand the role of acoustics within architectural design and potential tools for its inclusion during, not after, the design process.

Keywords: Architectural acoustics, early-design, interdisciplinary communication, remedial response.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1436

Authors: Rimmy Yadav, Avtar Singh

Abstract:

Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in finding excellent solution to finding shortest path during communication link failure.

Keywords: Ant colony optimization, link failure, prim’s algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2182

Authors: Diana M.L. Wong

Abstract:

This paper presents an integrated case based and rule based reasoning method for car faulty diagnosis. The reasoning method is done through extracting the past cases from the Proton Service Center while comparing with the preset rules to deduce a diagnosis/solution to a car service case. New cases will be stored to the knowledge base. The test cases examples illustrate the effectiveness of the proposed integrated reasoning. It has proven accuracy of similar reasoning if carried out by a service advisor from the service center.

Keywords: component; case based reasoning (CBR), rule basedreasoning (RBR), decision support systems, diagnosis tool.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1924

Authors: Ahmad M. Shafiee, Mehrdad Montazeri, Mahdi Nikdast

Abstract:

Every day human life experiences new equipments more automatic and with more abilities. So the need for faster processors doesn-t seem to finish. Despite new architectures and higher frequencies, a single processor is not adequate for many applications. Parallel processing and networks are previous solutions for this problem. The new solution to put a network of resources on a chip is called NOC (network on a chip). The more usual topology for NOC is mesh topology. There are several routing algorithms suitable for this topology such as XY, fully adaptive, etc. In this paper we have suggested a new algorithm named Intermittent X, Y (IX/Y). We have developed the new algorithm in simulation environment to compare delay and power consumption with elders' algorithms.

Keywords: Computer architecture, parallel computing, NOC, routing algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1677

Authors: Fuyang Peng, Bo Deng, Chao Qi

Abstract:

This paper presents the design and implementation of CASTE, a Cloud-based automatic software test environment. We first present the architecture of CASTE, then the main packages and classes of it are described in detail. CASTE is built upon a private Infrastructure as a Service platform. Through concentrated resource management of virtualized testing environment and automatic execution control of test scripts, we get a better solution to the testing resource utilization and test automation problem. Experiments on CASTE give very appealing results.

Keywords: Software testing, test environment, test script, cloud computing, IaaS, test automation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2176

Authors: Ivica Martinjak, Mario-Osvin Pavcevic

Abstract:

When trying to enumerate all BIBD-s for given parameters, their natural solution space appears to be huge and grows extremely with the number of points of the design. Therefore, constructive enumerations are often carried out by assuming additional constraints on design-s structure, automorphisms being mostly used ones. It remains a hard task to construct designs with trivial automorphism group – those with no additional symmetry – although it is believed that most of the BIBD-s belong to that case. In this paper, very many new designs with parameters 2-(13, 5, 5), 2-(16, 6, 5) and 2-(21, 6, 4) are constructed, assuming an action of an automorphism of order 3. Even more, it was possible to construct millions of such designs with no non-trivial automorphisms.

Keywords: BIBD, incidence matrix, automorphism group, tactical decomposition, deterministic algorithm.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318

Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1478

Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 756

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Keywords: Food chain system, periodic solution, time scales, coincidence degree.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8469

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1413

Authors: Swathi Ganesan, Nalinda Somasiri, Rebecca Jeyavadhanam, Gayathri Karthick

Abstract:

The COVID-19 crisis presents a substantial and critical hazard to worldwide health. Since the occurrence of the disease in late January 2020 in the UK, the number of infected people confirmed to acquire the illness has increased tremendously across the country, and the number of individuals affected is undoubtedly considerably high. The purpose of this research is to figure out a predictive machine learning (ML) archetypal that could forecast the COVID-19 cases within the UK. This study concentrates on the statistical data collected from 31st January 2020 to 31st March 2021 in the United Kingdom. Information on total COVID-19 cases registered, new cases encountered on a daily basis, total death registered, and patients’ death per day due to Coronavirus is collected from World Health Organization (WHO). Data preprocessing is carried out to identify any missing values, outliers, or anomalies in the dataset. The data are split into 8:2 ratio for training and testing purposes to forecast future new COVID-19 cases. Support Vector Machine (SVM), Random Forest (RF), and linear regression (LR) algorithms are chosen to study the model performance in the prediction of new COVID-19 cases. From the evaluation metrics such as r-squared value and mean squared error, the statistical performance of the model in predicting the new COVID-19 cases is evaluated. RF outperformed the other two ML algorithms with a training accuracy of 99.47% and testing accuracy of 98.26% when n = 30. The mean square error obtained for RF is 4.05e11, which is lesser compared to the other predictive models used for this study. From the experimental analysis, RF algorithm can perform more effectively and efficiently in predicting the new COVID-19 cases, which could help the health sector to take relevant control measures for the spread of the virus.

Keywords: COVID-19, machine learning, supervised learning, unsupervised learning, linear regression, support vector machine, random forest.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 170

Authors: J. Cecrdle

Abstract:

This paper deals with the whirl flutter of the turboprop aircraft structures. It is focused on the influence of the blade lift span-wise distribution on the whirl flutter stability. Firstly it gives the overall theoretical background of the whirl flutter phenomenon. After that the propeller blade forces solution and the options of the blade lift modeling are described. The problem is demonstrated on the example of a twin turboprop aircraft structure. There are evaluated the influences with respect to the propeller aerodynamic derivatives and finally the influences to the whirl flutter speed and the whirl flutter margin respectively.

Keywords: Aeroelasticity, flutter, propeller blade force, whirl flutter.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2328

Authors: Adil AL-Rammahi

Abstract:

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2488

Authors: I. López , J. Garay, R. Carreño, Z. Varga

Abstract:

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. The method is illustrated with a trophic chain of resource – producer – primary consumer type and a numerical example is also presented.

Keywords: Monitoring, observer system, trophic chain

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1431

Authors: Radek Fisera, Petr Stluka

Abstract:

This paper describes a methodology for remote performance monitoring of retail refrigeration systems. The proposed framework starts with monitoring of the whole refrigeration circuit which allows detecting deviations from expected behavior caused by various faults and degradations. The subsequent diagnostics methods drill down deeper in the equipment hierarchy to more specifically determine root causes. An important feature of the proposed concept is that it does not require any additional sensors, and thus, the performance monitoring solution can be deployed at a low installation cost. Moreover only a minimum of contextual information is required, which also substantially reduces time and cost of the deployment process.

Keywords: Condition monitoring, energy baselining, fault detection and diagnostics, commercial refrigeration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2879

Authors: Nerey H. Mvungi, Mosses Makoko

Abstract:

In today-s highly globalised and competitive world access to information plays key role in having an upper hand between business rivals. Hence, proper protection of such crucial resource is core to any modern business. Implementing a successful information security system is basically centered around three pillars; technical solution involving both software and hardware, information security controls to translate the policies and procedure in the system and the people to implement. This paper shows that a lot needs to be done for countries adapting information technology to process, store and distribute information to secure adequately such core resource.

Keywords: security, information systems, controls, technology, practices.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2611

Authors: Yi-Fan Zhu, Wei Zhang, Xuan Zhou, Qun Li, Yong-Lin Lei

Abstract:

The quick training algorithms and accurate solution procedure for incremental learning aim at improving the efficiency of training of SVR, whereas there are some disadvantages for them, i.e. the nonconvergence of the formers for changeable training set and the inefficiency of the latter for a massive dataset. In order to handle the problems, a new training algorithm for a changeable training set, named Approximation Incremental Training Algorithm (AITA), was proposed. This paper explored the reason of nonconvergence theoretically and discussed the realization of AITA, and finally demonstrated the benefits of AITA both on precision and efficiency.

Keywords: support vector regression, incremental learning, changeable training set, quick training algorithm, accurate solutionprocedure

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1483

Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 749

Authors: Sudarat Jiamyangyuen, Tipawan Thongsook, Riantong Singanusong, Chanida Saengtubtim

Abstract:

Rice bran is normally used as a raw material for rice bran oil production or sold as feed with a low price. Conventionally, the protein in defatted rice bran was extracted using alkaline extraction and acid precipitation, which involves in chemical usage and lowering some nutritious component. This study was conducted in order to extract of rice bran protein concentrate (RBPC) from defatted rice bran using enzymes and employing polysaccharides in a precipitating step. The properties of RBPC obtained will be compared to those of a control sample extracted using a conventional method. The results showed that extraction of protein from rice bran using enzymes exhibited the higher protein recovery compared to that extraction with alkaline. The extraction conditions using alcalase 2% (v/w) at 50 C, pH 9.5 gave the highest protein (2.44%) and yield (32.09%) in extracted solution compared to other enzymes. Rice bran protein concentrate powder prepared by a precipitation step using alginate (protein in solution: alginate 1:0.016) exhibited the highest protein (27.55%) and yield (6.84%). Precipitation using alginate was better than that of acid. RBPC extracted with alkaline (ALK) or enzyme alcalase (ALC), then precipitated with alginate (AL) (samples RBP-ALK-AL and RBP-ALC-AL) yielded the precipitation rate of 75% and 91.30%, respectively. Therefore, protein precipitation using alginate was then selected. Amino acid profile of control sample, and sample precipitated with alginate, as compared to casein and soy protein isolated, showed that control sample showed the highest content among all sample. Functional property study of RBP showed that the highest nitrogen solubility occurred in pH 8-10. There was no statically significant between emulsion capacity and emulsion stability of control and sample precipitated by alginate. However, control sample showed a higher of foaming capacity and foaming stability compared to those of sample precipitated with alginate. The finding was successful in terms of minimizing chemicals used in extraction and precipitation steps in preparation of rice bran protein concentrate. This research involves in a production of value-added product in which the double amount of protein (28%) compared to original amount (14%) contained in rice bran could be beneficial in terms of adding to food products e.g. healthy drink with high protein and fiber. In addition, the basic knowledge of functional property of rice bran protein concentrate was obtained, which can be used to appropriately select the application of this value-added product from rice bran.

Keywords: Alginate, carrageenan, rice bran, rice bran protein.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2665

Authors: Shashikant R. Kuchekar, Haribhau R. Aher, Priti M. Dhage

Abstract:

The removal vanadium from aqueous solution using natural exchanger was investigated. The effects of pH, contact time and exchanger dose were studied at ambient temperature (25 ⁰C ± 2 ⁰C). The equilibrium process was described by the Langmuir isotherm model with adsorption capacity for vanadium. The natural exchanger i.e. tamarindus seeds powder was treated with formaldehyde and sulpuric acid to increase the adsorptivity of metals. The maximum exchange level was attained as 80.1% at pH 3 with exchanger dose 5 g and contact time 60 min. Method is applied for removal of vanadium from industrial effluents.

Keywords: Industrial effluent, natural ion exchange, Tamarindus indica, vanadium.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 733

Authors: Jinfeng Wang, Yang Liu, Hong Li

Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2136

Authors: Dezhi Liu Guiyuan Yang Wei Zhang

Abstract:

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1286

Authors: Dmitry D. Zakharov

Abstract:

The theoretical prediction of the acoustical polarization effects in the heterogeneous composites, made of thick elastic solids with thin nematic films, is presented. The numericalanalytical solution to the problem of the different wave propagation exhibits some new physical effects in the low frequency domain: the appearance of the critical frequency and the existence of the narrow transition zone where the wave rapidly changes its speed. The associated wave attenuation is highly perturbed in this zone. We also show the possible appearance of the critical frequencies where the attenuation changes the sign. The numerical results of parametrical analysis are presented and discussed.

Keywords: Surface wave, guided wave, heterogeneous composite, nematic coating.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1361

Authors: Zdeňka Dostálová, David Matoušek, Bohumil Brtnik

Abstract:

As there are also graph methods of circuit analysis in addition to algebraic methods, it is, in theory, clearly possible to carry out an analysis of a whole switched circuit in two-phase switching exclusively by the graph method as well. This article deals with two methods of full-graph solving of switched circuits: by transformation graphs and by two-graphs. It deals with the circuit switched capacitors and the switched current, too. All methods are presented in an equally detailed steps to be able to compare.

Keywords: Switched capacitors of two phases, switched currents of two phases, transformation graph, two-graph, Mason's formula, voltage transfer, summary graph.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1312

Authors: Emin Özyılmaz

Abstract:

In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.

Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1467