Search results for: Steady state solution

Authors: Azelin Mohamed Noor, Abd Mutalib Embong, Muhamad Ridhuan Tony Lim Abdullah

Abstract:

After the Terengganu state government decided to give a boost in teaching and learning through the allocation of free ebooks to all Primary five and six students; it was time to examine the presence of e-books in the classrooms. A survey was conducted on 101 students to determine how they felt about using the e-book and their experiences. It was discovered that a majority of these students liked using the e-book. However, although they had little problems using the e-book and the e-book helped to lighten the schoolbags, these new-age textbooks were not fully utilized. It is implied that perhaps the school administrators, teachers and students may not be able to overcome the unfamiliar characteristics of the e-book and its limitations.

Keywords: E-books, students, classroom, limitations

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4222

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1485

Authors: Gabi N. Nehme

Abstract:

The reduction of phosphorus and sulfur in engine oil are the main topics of this paper. Very reproducible boundary lubrication tests were conducted as part of Design of Experiment software (DOE) to study the behavior of fluorinated catalyst iron fluoride (FeF3), and polutetrafluoroethylene or Teflon (PTFE) in developing environmentally friendly (reduced P and S) anti-wear additives for future engine oil formulations. Multi-component Chevron fully formulated oil (GF3) and Chevron plain oil were used with the addition of PTFE and catalyst to characterize and analyze their performance. Lower phosphorus blends were the goal of the model solution. Experiments indicated that new sub-micron FeF3 catalyst played an important role in preventing breakdown of the tribofilm.

Keywords: Wear, SEM, EDS, friction, lubricants.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1986

Authors: Nien-Zheng Yew, Kung-Ming Tiong, Su-Ting Yong

Abstract:

Number Link is a Japanese logic puzzle where pairs of same numbers are connected using lines. Number Link can be regarded as a dynamic multiple travelers, multiple entries and exits maze, where the walls and passages are dynamically changing as the travelers move. In this paper, we apply the Tremaux’s algorithm to solve Number Link puzzles of size 8x8, 10x10 and 15x20. The algorithm works well and produces a solution for puzzles of size 8x8 and 10x10. However, solving a puzzle of size 15x20 requires high computer processing power and is time consuming.

Keywords: Number Link, maze, puzzle, Tremaux’s algorithm

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4027

Authors: R. Saini, R. Lal

Abstract:

The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: Bilinear thickness, generalized differential quadrature (GDQ), non-homogeneous, Rectangular.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2471

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

Abstract:

In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1161

Authors: R. Kongnuy, P. Pongsumpun

Abstract:

We used mathematical model to study the transmission of dengue disease. The model is developed in which the human population is separated into two populations, pregnant and non-pregnant humans. The dynamical analysis method is used for analyzing this modified model. Two equilibrium states are found and the conditions for stability of theses two equilibrium states are established. Numerical results are shown for each equilibrium state. The basic reproduction numbers are found and they are compared by using numerical simulations.

Keywords: Basic reproductive number, dengue disease, equilibrium states, pregnancy.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1593

Authors: S.M. Sarwarul Islam Rizvi, Zinat Sultana, Bo Sun, Md. Washiqul Islam

Abstract:

In a very simple form a Mobile Agent is an independent piece of code that has mobility and autonomy behavior. One of the main advantages of using Mobile Agent in a network is - it reduces network traffic load. In an, ad hoc network Mobile Agent can be used to protect the network by using agent based IDS or IPS. Besides, to deploy dynamic software in the network or to retrieve information from network nodes Mobile Agent can be useful. But in an ad hoc network the Mobile Agent itself needs some security. Security services should be guaranteed both for Mobile Agent and for Agent Server. In this paper to protect the Mobile Agent and Agent Server in an ad hoc network we have proposed a solution which is based on Threshold Cryptography, a new vibe in the cryptographic world where trust is distributed among multiple nodes in the network.

Keywords: Ad hoc network, Mobile Agent, Security, Threats, Threshold Cryptography.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1967

Authors: V. Kahya, A. Birinci, R. Erdol

Abstract:

A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.

Keywords: Frictionless contact, Initial separation, Orthotropicmaterial, Singular integral equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1812

Authors: Pavol Tanuska, Pavel Vazan, Michal Kebisek, Dominika Jurovata

Abstract:

The paper gives the results of the project that was oriented on the usage of knowledge discoveries from production systems for needs of the hierarchical process control. One of the main project goals was the proposal of knowledge discovery model for process control. Specifics data mining methods and techniques was used for defined problems of the process control. The gained knowledge was used on the real production system thus the proposed solution has been verified. The paper documents how is possible to apply the new discovery knowledge to use in the real hierarchical process control. There are specified the opportunities for application of the proposed knowledge discovery model for hierarchical process control.

Keywords: Hierarchical process control, knowledge discovery from databases, neural network.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1775

Authors: Mpho A. Mbeo, Patient Rambe

Abstract:

The 13th year of the Central University of Technology, Free State’s (CUT) transition from a vocational and professional training orientation institution (i.e. a technikon) into a university with a strong research focus has neither been a smooth nor an easy one. At the heart of this transition was the need to transform the psychological faculties of academic and research staffs compliment who were accustomed to training graduates for industrial placement. The lack of a research culture that fully embraces the strong solid ethos of conducting cutting-edge research needs to be addressed. The induction and socialisation of academic staff into the development and execution of cutting-edge research also required the provision of research support and the creation of a conducive academic environment for research, both for emerging and non-research active academics. Drawing on ten cases, consisting of four heads of departments, three seasoned researchers, and three novice researchers, this study explores the challenges faced in establishing a strong research culture at the university. Furthermore, it gives an account of the extent to which the current research interventions have addressed the perceivably “missing research culture”, and the implications of these interventions for knowledge management. Evidence suggests that the capability of an ideal institutional research environment, consisting of mentorship of novice researchers by seasoned researchers, balanced effort into teaching and research responsibilities, should be supported by strong research-oriented leadership. Furthermore, recruitment of research passionate staff, adoption of a salary structure that encourages the retention of excellent scholars should be matched by a coherent research incentive culture to growth research publication outputs. This is critical for building new knowledge and entrenching knowledge management founded on communities of practice and scholarly networking through the documentation and communication of research findings. The study concludes that the multiple policy documents set for the different domains of research may be creating pressure on researchers to engage research activities and increase output at the expense of research quality.

Keywords: Central University of Technology, performance, publication, research culture, university.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 330

Authors: Vishnu Pratap Singh Kirar

Abstract:

In the cloud computing hierarchy IaaS is the lowest layer, all other layers are built over it. Thus it is the most important layer of cloud and requisite more importance. Along with advantages IaaS faces some serious security related issue. Mainly Security focuses on Integrity, confidentiality and availability. Cloud computing facilitate to share the resources inside as well as outside of the cloud. On the other hand, cloud still not in the state to provide surety to 100% data security. Cloud provider must ensure that end user/client get a Quality of Service. In this report we describe possible aspects of cloud related security.

Keywords: Cloud Computing, Cloud Networking, IaaS, PaaS, SaaS, Cloud Security.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2244

Authors: M. Zielina, W. Dabrowski, E. Radziszewska-Zielina

Abstract:

Several different cements have been tested to evaluate their potential to leach calcium, chromium and aluminum ions in soft water environment. The research allows comparing some different cements in order to the potential risk of water contamination. This can be done only in the same environment. To reach the results in reasonable short time intervals and to make heavy metals measurements with high accuracy, demineralized water was used. In this case the conditions of experiments are far away from the water supply practice, but short time experiments and measurably high concentrations of elements in the water solution are an important advantage. Moreover leaching mechanisms can be recognized, our experiments reported here refer to this kind of cements evaluation.

Keywords: Concrete corrosion, hydrogen sulfide, odors, reinforced concrete sewers, sewerage.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3343

Authors: Sangsuree Vasupongayya, Kittisak Keawneam, Kittipong Sengloilaun, Patt Emmawat

Abstract:

Library management systems are commonly used in all educational related institutes. Many commercial products are available. However, many institutions may not be able to afford the cost of using commercial products. Therefore, an alternative solution in such situations would be open source software. This paper is focusing on reviewing open source library management system packages currently available. The review will focus on the abilities to perform four basic components which are traditional services, interlibrary load management, managing electronic materials and basic common management system such as security, alert system and statistical reports. In addition, environment, basic requirement and supporting aspects of each open source package are also mentioned.

Keywords: open source, library management, review.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7352

Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2002

Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2482

Authors: Wen-Bao Qiao, Jean-Charles Créput

Abstract:

To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: Doubly linked list, parallel 2-opt, tour division, GPU.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1223

Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1498

Authors: Tomáš Bakalár, Milan Búgel, Henrieta Pavolová

Abstract:

This study deals with evaluation of influence of salinity (NaCl) onto equilibrium of Cu and Ni removal from aqueous solutions by natural sorbent – zeolite. Equilibrium data were obtained by batch experiments. The salinity of the aqueous solution was influenced by dissolving NaCl in distilled water. It was studied in the range of NaCl concentrations from 1 g.l-1 to 100g.l-1. For Cu sorption there is a significant influence of salinity. The maximum capacity of zeolite for Cu was decreasing with growing concentration of NaCl. For Ni sorption there is not so significant influence of salinity as for Cu. The maximum capacity of zeolite for Ni was slightly decreasing with growing concentration of NaCl.

Keywords: Cu, Ni, sorption, zeolite.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1302

Authors: Xuan Qi, Changzhi Zhao

Abstract:

In this paper, a uniform calculus-based approach for synthesizing monitors checking correctness properties specified by a large variety of logics at runtime is provided, including future and past time logics, interval logics, state machine and parameterized temporal logics. We present a calculus mechanism to synthesize monitors from the logical specification for the incremental analysis of execution traces during test and real run. The monitor detects both good and bad prefix of a particular kind, namely those that are informative for the property under investigation. We elaborate the procedure of calculus as monitors.

Keywords: calculus, eagle logic, monitor synthesis, runtime verification

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1258

Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

Abstract:

In this paper, we consider a drift flux mixture model of the blood flow. The mixture consists of gas phase which is carbon dioxide and liquid phase which is an aqueous carbon dioxide solution. This model was used to determine the distributions of the mixture velocity, the mixture pressure, and the carbon dioxide pressure. These theoretical data are used to determine a measurement method of mean gas pressure through the determination of radial velocity distribution. This method can be applicable in experimental domain.

Keywords: Mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1248

Authors: G. B. Hong, H. W. Chen

Abstract:

Liquid-Liquid Equilibrium (LLE) data are measured for the ternary mixtures of water + 1-butanol + butyl acetate and quaternary mixtures of water + 1-butanol + butyl acetate + glycerol at atmospheric pressure at 313.15 K. In addition, isothermal vapor–liquid–liquid equilibrium (VLLE) data are determined experimentally at 333.15 K. The region of heterogeneity is found to increase as the hydrophilic agent (glycerol) is introduced into the aqueous mixtures. The experimental data are correlated with the NRTL model. The predicted results from the solution model with the model parameters determined from the constituent binaries are also compared with the experimental values.

Keywords: LLE, VLLE, hydrophilic agent, NRTL.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1284

Authors: Luka Pavlič, Marjan Heričko

Abstract:

E-services have significantly changed the way of doing business in recent years. We can, however, observe poor use of these services. There is a large gap between supply and actual eservices usage. This is why we started a project to provide an environment that will encourage the use of e-services. We believe that only providing e-service does not automatically mean consumers would use them. This paper shows the origins of our project and its current position. We discuss the decision of using semantic web technologies and their potential to improve e-services usage. We also present current knowledge base and its real-world classification. In the paper, we discuss further work to be done in the project. Current state of the project is promising.

Keywords: E-Services, E-Services Repository, Ontologies, Semantic Web

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1400

Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2098

Authors: Arthur David Snider, Laiq Azam

Abstract:

The classic problem of recovering arbitrary values of a band-limited signal from its samples has an added complication in software radio applications; namely, the resampling calculations inevitably fold aliases of the analog signal back into the original bandwidth. The phenomenon is quantified by the spur-free dynamic range. We demonstrate how a novel application of the Remez (Parks- McClellan) algorithm permits optimal signal recovery and SFDR, far surpassing state-of-the-art resamplers.

Keywords: Sampling methods, Signal sampling, Digital radio, Digital-analog conversion.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1406

Authors: A. Rouili

Abstract:

Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0.5 to 0.7 ensure in most case the stability requirements, however, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.

Keywords: Cantilever wall, proportioning, numerical analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9436

Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1833

Authors: Nikola Karanovic, Aleksandar Djuric

Abstract:

This paper introduces a method of calculating the quantities of construction materials and construction waste on site in city of Novi Sad. In buildings is about 40% of the total weight of materials that are in circulation in the world economic space. The best solution for this waste is to be stored at source, at the point of generation. There are several treatment options for this type of waste, reduction at source, reuse, recycling. Beside its negative effects on the environment, construction waste can be and resource. Novi Sad is divided in 16 single family resident zones and 10 multi family resident zones. For every zone of the city, quantities of used construction materials and construction waste were obtained. Rational use of natural resources is an essential factor in applying the principles of development with savings.

Keywords: Construction materials, Construction waste, Novi Sad, Recycling

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1654

Authors: Raphael Zanella

Abstract:

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

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 352

Authors: Wen Po Cheng, Chi Hua Fu, Ping Hung Chen, Ruey Fang Yu

Abstract:

Recovering resources from water purification sludge (WPS) have been gradually stipulated in environmental protection laws and regulations in many nations. Hence, reusing the WPS is becoming an important topic, and recovering alum from WPS is one of the many practical alternatives. Most previous research efforts have been conducted on studying the amphoteric characteristic of aluminum hydroxide for investigating the optimum pH range to dissolve the Al(III) species from WPS, but it has been lack of reaction kinetics or mechanisms related discussion. Therefore, in this investigation, water purification sludge (WPS) solution was broken by ultrasound to make particle size of reactants smaller, specific surface area larger. According to the reaction kinetics, these phenomena let the dissolved aluminum salt quantity increased and the reaction rate go faster.

Keywords: Aluminum, Acidification, Sludge, Recovery.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1716