Search results for: orthogonal functions

Authors: Luiz F. J. Maia

Abstract:

This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Alcardo Alex Barakabitze, Saddam Aziz, Muhammad Zubair

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The Orthogonal Frequency Division Multiplexing (OFDM) is a special form of multicarrier transmission that splits the total transmission bandwidth into a number of orthogonal and non-overlapping subcarriers and transmit the collection of bits called symbols in parallel using these subcarriers. In this paper, we explore the Peak to Average Power Reduction (PAPR) problem in OFDM systems. We provide the performance analysis of CCDF and BER through MATLAB simulations.

Keywords: bit error ratio (BER), OFDM, peak to average power reduction (PAPR), sub-carriers

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Ping Bo, Meng Yunshan

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Satellite-derived sea surface temperature (SST) is a key parameter for many operational and scientific applications. However, the disadvantage of SST data is a high percentage of missing data which is mainly caused by cloud coverage. Data Interpolating Empirical Orthogonal Function (DINEOF) algorithm is an EOF-based technique for reconstructing the missing data and has been widely used in oceanographic field. The reconstruction of SST images within a long time series using DINEOF can cause large discontinuities and one solution for this problem is to filter the temporal covariance matrix to reduce the spurious variability. Based on the previous researches, an algorithm is presented in this paper to improve the temporal correlations in EOF expansion. Similar with the previous researches, a filter, such as Laplacian filter, is implemented on the temporal covariance matrix, but the temporal relationship between two consecutive images which is used in the filter is considered in the presented algorithm, for example, two images in the same season are more likely correlated than those in the different seasons, hence the latter one is less weighted in the filter. The presented approach is tested for the monthly nighttime 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder SST for the long-term period spanning from 1989 to 2006. The results obtained from the presented algorithm are compared to those from the original DINEOF algorithm without filtering and from the DINEOF algorithm with filtering but without taking temporal relationship into account.

Keywords: data interpolating empirical orthogonal function, image reconstruction, sea surface temperature, temporal filter

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Authors: Keunhong Chae, Seokho Yoon

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We address a new integer frequency offset (IFO) estimation scheme with an aid of a pilot for orthogonal frequency division multiplexing systems. After correlating each continual pilot with a predetermined scattered pilot, the correlation value is again correlated to alleviate the influence of the timing offset. From numerical results, it is demonstrated that the influence of the timing offset on the IFO estimation is significantly decreased.

Keywords: estimation, integer frequency offset, OFDM, timing offset

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Theena Thayalan, K. N. Ramesh Babu

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Machining induced residual stress (RS) is one of the most important surface integrity parameters that characterize the near surface layer of a mechanical component, which plays a crucial role in controlling the performance, especially its fatigue life. Since experimental determination of RS is expensive and time consuming, it would be of great benefit if they could be predicted. In such case, it would be possible to select the cutting parameters required to produce a favorable RS profile. In the present study, an effort has been made to develop a 'two dimensional finite element model (FEM)' to simulate orthogonal cutting process and to predict surface and sub-surface RS using the commercial FEA software DEFORM-2D. The developed finite element model has been validated through experimental investigation of RS. In the experimentation, the orthogonal cutting tests were carried out on AISI 4340 by varying the cutting speed (VC) and uncut chip thickness (f) at three levels and the surface & sub-surface RS has been measured using XRD and Electro polishing techniques. The comparison showed that the RS obtained using developed numerical model is in reasonable agreement with that of experimental data.

Keywords: FEM, machining, residual stress, XRF

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Ying-Pin Chang

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This paper presents a method for combining a particle swarm optimization with nonlinear time-varying evolution and orthogonal arrays (PSO-NTVEOA) in the planning of harmonic filters for the high speed railway traction system with specially connected transformers in unbalanced three-phase power systems. The objective is to minimize the cost of the filter, the filters loss, the total harmonic distortion of currents and voltages at each bus simultaneously. An orthogonal array is first conducted to obtain the initial solution set. The set is then treated as the initial training sample. Next, the PSO-NTVEOA method parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates the full factorial experiments. This PSO-NTVEOA method is then applied to design optimal harmonic filters in Taiwan High Speed Rail (THSR) traction system, where both rectifiers and inverters with IGBT are used. From the results of the illustrative examples, the feasibility of the PSO-NTVEOA to design an optimal passive harmonic filter of THSR system is verified and the design approach can greatly reduce the harmonic distortion. Three design schemes are compared that V-V connection suppressing the 3rd order harmonic, and Scott and Le Blanc connection for the harmonic improvement is better than the V-V connection.

Keywords: harmonic filters, particle swarm optimization, nonlinear time-varying evolution, orthogonal arrays, specially connected transformers

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

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Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals.

Keywords: compressed sensing, lest support orthogonal matching pursuit, partial knowing support, restricted isometry property, signal reconstruction

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Authors: Keunhong Chae, Seokho Yoon

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We propose a code acquisition scheme called improved multiple-shift (IMS) for optical code division multiple access systems, where the optical orthogonal code is used instead of the pseudo noise code. Although the IMS algorithm has a similar process to that of the conventional MS algorithm, it has a better code acquisition performance than the conventional MS algorithm. We analyze the code acquisition performance of the IMS algorithm and compare the code acquisition performances of the MS and the IMS algorithms in single-user and multi-user environments.

Keywords: code acquisition, optical CDMA, optical orthogonal code, serial algorithm

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Authors: Manikandakumar Shunmugavel, Ashwin Polishetty, Moshe Goldberg, Junior Nomani, Guy Littlefair

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Selective laser melting (SLM), a promising additive manufacturing (AM) technology, has a huge potential in the fabrication of Ti-6Al-4V near-net shape components. However, poor surface finish of the components fabricated from this technology requires secondary machining to achieve the desired accuracy and tolerance. Therefore, a systematic understanding of the machinability of SLM fabricated Ti-6Al-4V components is paramount to improve the productivity and product quality. Considering the significance of machining in SLM fabricated Ti-6Al-4V components, this research aim is to study the influence of build orientation on machinability characteristics by performing low speed orthogonal cutting tests. In addition, the machinability of SLM fabricated Ti-6Al-4V is compared with conventionally produced wrought Ti-6Al-4V to understand the influence of SLM technology on machining. This paper is an attempt to provide evidence to the hypothesis associated that build orientation influences cutting forces, chip formation and surface integrity during orthogonal cutting of SLM Ti-6Al-4V samples. Results obtained from the low speed orthogonal cutting tests highlight the practical importance of microstructure and build orientation on machinability of SLM Ti-6Al-4V.

Keywords: additive manufacturing, build orientation, machinability, titanium alloys (Ti-6Al-4V)

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Kyo Jin An, Bukyo Seo, Young-Chul Park

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The current trend in car market is increase of parts of automobile and weight in vehicle. It comes from improvement of vehicle performance. Outer tie rod is a part of component of steering system and it is lighter than the others. But, weight lightening is still required for improvement of car mileage. So, we have presented a model of aluminized outer tie rod, but the process of fabrication has to be checked to manufacture the product. Therefore, we have anticipated forming load, die stress and abrasion to use the program of forging interpretation in the part of hot forging process of outer tie rod in this study. Also, we have implemented the experiments design to use the table of orthogonal arrays to reduce the forming load.

Keywords: forming load, hot forging, orthogonal array, outer tie rod (OTR), multi–step forging

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Authors: Kassim A. Jassim

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In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

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Authors: Sriram Venkatesh, V. Murali Mohan, T. V. Karthikeyan

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The main advantage of multi-directionally reinforced composites is the freedom to orient selected fibre types and hence derives the benefits of varying fibre volume fractions and there by accommodate the design loads of the final structure of composites. This technology provides the means to produce tailored composites with desired properties. Due to the high level of fibre integrity with through thickness reinforcement those composites are expected to exhibit superior load bearing characteristics with capability to carry load even after noticeable and apparent fracture. However a survey of published literature indicates inadequacy in the design and test data base for the complete characterization of the multidirectional composites. In this paper the research objective is focused on the development and testing of 4-D orthogonal composites with different preform configurations and resin systems. A preform is the skeleton 4D reinforced composite other than the matrix. In 4-D preforms fibre bundles are oriented in three directions at 1200 with respect to each other and they are on orthogonal plane with the fibre in 4th direction. This paper addresses the various types of 4-D composite manufacturing processes and the mechanical test methods followed for the material characterization. A composite analysis is also made, experiments on course and fine woven preforms are conducted and the findings of test results are discussed in this paper. The interpretations of the test results reveal several useful and interesting features. This should pave the way for more widespread use of the perform configurations for allied applications.

Keywords: multi-directionally reinforced composites, 4-D orthogonal preform, course weave, fine weave, fibre bundle spools, unit cell, fibre architecture, fibre volume fraction, fibre distribution

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Authors: Linyu Wang, Furui Huo, Jianhong Xiang

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The Doppler shift generated by high-speed movement and multipath effects in the channel are the main reasons for the generation of a time-frequency doubly-selective (DS) channel. There is severe inter-carrier interference (ICI) in the DS channel. Channel estimation for an orthogonal frequency division multiplexing (OFDM) system over a DS channel is very difficult. The simultaneous orthogonal matching pursuit algorithm under distributed compressive sensing theory (DCS-SOMP) has been used in channel estimation for OFDM systems over DS channels. However, the reconstruction accuracy of the DCS-SOMP algorithm is not high enough in the low SNR stage. To solve this problem, in this paper, we propose an improved DCS-SOMP algorithm based on the inner product difference comparison operation (DCS-DCSOMP). The reconstruction accuracy is improved by increasing the number of candidate indexes and designing the comparison conditions of inner product difference. We combine the DCS-DCSOMP algorithm with the basis expansion model (BEM) to reduce the complexity of channel estimation. Simulation results show the effectiveness of the proposed algorithm and its advantages over other algorithms.

Keywords: OFDM, doubly selective, channel estimation, compressed sensing

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Fariha Asif

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The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others.

Keywords: methodology, functions, teaching, ESP

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Cherifi Abdelhamid

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In optical communication systems, OFDM has received increased attention as a means to overcome various limitations of optical transmission systems such as modal dispersion, relative intensity noise, chromatic dispersion, polarization mode dispersion and self-phase modulation. The multipath dispersion limits the maximum transmission data rates. In this paper we investigate OFDM system where multipath induced intersymbol interference (ISI) is reduced and we increase the number of users by combining OFDM system with OCDMA system using direct detection Incorporate OOC (orthogonal optical code) for minimize a bit error rate.

Keywords: OFDM, OCDMA, OOC (orthogonal optical code), (ISI), prim codes (Pc)

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: NFV, resource allocation, virtual routing function, minimum power consumption

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Keunhong Chae, Seokho Yoon

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We address the integer frequency offset (IFO) estimation under the influence of the timing offset (TO) in orthogonal frequency division multiplexing (OFDM) systems. Incorporating the IFO and TO into the symbol set used to represent the received OFDM symbol, we investigate the influence of the TO on the IFO, and then, propose a combining method between two consecutive OFDM correlations, reducing the influence. The proposed scheme has almost the same complexity as that of the conventional schemes, whereas it does not need the TO knowledge contrary to the conventional schemes. From numerical results it is confirmed that the proposed scheme is insensitive to the TO, consequently, yielding an improvement of the IFO estimation performance over the conventional schemes when the TO exists.

Keywords: estimation, integer frequency offset, OFDM, timing offset

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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