Search results for: log skew normal approximation

Authors: Bader Alruwaili, Surajit Ray

Abstract:

Finite mixtures are a flexible and powerful tool that can be used for univariate and multivariate distributions, and a wide range of research analysis has been conducted based on the multivariate normal mixture and multivariate of a t-mixture. Determining the number of modes is an important activity that, in turn, allows one to determine the number of homogeneous groups in a population. Our work currently being carried out relates to the study of the modality of the skew normal distribution in the univariate and multivariate cases. For the skew normal distribution, the aims are associated with studying the modality of the skew normal distribution and providing the ridgeline, the ridgeline elevation function, the $\Pi$ function, and the curvature function, and this will be conducive to an exploration of the number and location of mode when mixing the two components of skew normal distribution. The subsequent objective is to apply these results to the application of real world data sets, such as flow cytometry data.

Keywords: mode, modality, multivariate skew normal, finite mixture, number of mode

Procedia PDF Downloads 459

Authors: Marwane Ben Hcine, Ridha Bouallegue

Abstract:

The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.

Keywords: LTE, OFDMA, effective SINR, log skew normal approximation

Procedia PDF Downloads 331

Authors: Eusebio Jr. Lina, Ederlina Nocon

Abstract:

Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

Procedia PDF Downloads 299

Authors: Ahmad Moussavi

Abstract:

In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

Procedia PDF Downloads 135

Authors: Jing Li, Xiuli Li

Abstract:

This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= F_q+uF_q+…+u^k-1F_q, where q is a prime power. A Gray map ɸ from R to F_q and a Gray map ɸ' from Rⁿ to Fⁿ_q are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over F_q, and they still keep the dual relation.

Keywords: skew cyclic code, gray map, automorphism, cyclic code

Procedia PDF Downloads 260

Authors: M. T. Alodat

Abstract:

In this paper, we propose a generalization to the Gaussian process regression(GPR) model called the extended skew Gaussian process for regression(ESGPr) model. The ESGPR model works better than the GPR model when the errors are skewed. We derive the predictive distribution for the ESGPR model at a new input. Also we apply the ESGPR model to FOREX data and we find that it fits the Forex data better than the GPR model.

Keywords: extended skew normal distribution, Gaussian process for regression, predictive distribution, ESGPr model

Procedia PDF Downloads 518

Authors: M. T. Alodat

Abstract:

In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions.

Keywords: normal distribution, moments, Fisher information, symmetric distributions

Procedia PDF Downloads 625

Authors: Iman Mohseni

Abstract:

Current studies indicate that neglecting the effect of intermediate diaphragms might lead to highly conservative values for bending moment distribution factors and result in non-economic designs for skew bridges. This paper reports on a parametric study performed on 160 prototypes of straight and skew concrete multicell box-girder bridges. The obtained results were used to develop practical expressions to account for the diaphragm effects on American Association of State Highway and Transportation Officials formulas for live load distribution factors. It was observed that decks with internal transverse diaphragms perpendicular to the longitudinal webs are the best arrangement for load distribution in skew bridges.

Keywords: box bridges, truck, distribution factor, diaphragm

Procedia PDF Downloads 344

Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

Abstract:

This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components, as well as the introduction of the bars skew, in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars is neglected.

Keywords: modeling, MWFA, skew effect, squirrel cage induction motor, spectral domain

Procedia PDF Downloads 404

Authors: Bernardo C. P. Albuquerque, Darym J. F. Campos

Abstract:

Increasing our ability to solve complex engineering problems is directly related to the processing capacity of computers. By means of such equipments, one is able to fast and accurately run numerical algorithms. Besides the increasing interest in numerical simulations, probabilistic approaches are also of great importance. This way, statistical tools have shown their relevance to the modelling of practical engineering problems. In general, statistical approaches to such problems consider that the random variables involved follow a normal distribution. This assumption tends to provide incorrect results when skew data is present since normal distributions are symmetric about their means. Thus, in order to visualize and quantify this aspect, 9 statistical distributions (symmetric and skew) have been considered to model a hypothetical slope stability problem. The data modeled is the friction angle of a superficial soil in Brasilia, Brazil. Despite the apparent universality, the normal distribution did not qualify as the best fit. In the present effort, data obtained in consolidated-drained triaxial tests and saturated direct shear tests have been modeled and used to analytically derive the probability density function (PDF) of the safety factor of a hypothetical slope based on Mohr-Coulomb rupture criterion. Therefore, based on this analysis, it is possible to explicitly derive the failure probability considering the friction angle as a random variable. Furthermore, it is possible to compare the stability analysis when the friction angle is modelled as a Dagum distribution (distribution that presented the best fit to the histogram) and as a Normal distribution. This comparison leads to relevant differences when analyzed in light of the risk management.

Keywords: statistical slope stability analysis, skew distributions, probability of failure, functions of random variables

Procedia PDF Downloads 305

Authors: Yungtai Lo

Abstract:

Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

Procedia PDF Downloads 319

Authors: Kayode A. Olaniyi, Olabanji F. Omotoye, Adeola A. Ogunleye

Abstract:

The skew detection and correction form an important part of digital document analysis. This is because uncompensated skew can deteriorate document features and can complicate further document image processing steps. Efficient text document analysis and digitization can rarely be achieved when a document is skewed even at a small angle. Once the documents have been digitized through the scanning system and binarization also achieved, document skew correction is required before further image analysis. Research efforts have been put in this area with algorithms developed to eliminate document skew. Skew angle correction algorithms can be compared based on performance criteria. Most important performance criteria are accuracy of skew angle detection, range of skew angle for detection, speed of processing the image, computational complexity and consequently memory space used. The standard Hough Transform has successfully been implemented for text documentation skew angle estimation application. However, the standard Hough Transform algorithm level of accuracy depends largely on how much fine the step size for the angle used. This consequently consumes more time and memory space for increase accuracy and, especially where number of pixels is considerable large. Whenever the Hough transform is used, there is always a tradeoff between accuracy and speed. So a more efficient solution is needed that optimizes space as well as time. In this paper, an improved Hough transform (HT) technique that optimizes space as well as time to robustly detect document skew is presented. The modified algorithm of Hough Transform presents solution to the contradiction between the memory space, running time and accuracy. Our algorithm starts with the first step of angle estimation accurate up to zero decimal place using the standard Hough Transform algorithm achieving minimal running time and space but lacks relative accuracy. Then to increase accuracy, suppose estimated angle found using the basic Hough algorithm is x degree, we then run again basic algorithm from range between ±x degrees with accuracy of one decimal place. Same process is iterated till level of desired accuracy is achieved. The procedure of our skew estimation and correction algorithm of text images is implemented using MATLAB. The memory space estimation and process time are also tabulated with skew angle assumption of within 00 and 450. The simulation results which is demonstrated in Matlab show the high performance of our algorithms with less computational time and memory space used in detecting document skew for a variety of documents with different levels of complexity.

Keywords: hough-transform, skew-detection, skew-angle, skew-correction, text-document

Procedia PDF Downloads 123

Authors: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

Procedia PDF Downloads 644

Authors: Raymond Yudhi Purba, Levy Olivia Nur, Radial Anwar

Abstract:

This research presents the design and measurement of a skew planar wheel antenna that is used to visualize the first person view perspective of unmanned aerial vehicles. The antenna has been designed using CST Studio Suite 2019 to have voltage standing wave ratio (VSWR) ≤ 2, return loss ≤ -10 dB, bandwidth ≥ 100 MHz to covering outdoor access point band from 5.725 to 5.825 GHz, omnidirectional radiation pattern, and elliptical polarization. Dimensions of skew planar wheel antenna have been modified using parameter sweep technique to provide good performances. The simulation results provide VSWR 1.231, return loss -19.693 dB, bandwidth 828.8 MHz, gain 3.292 dB, and axial ratio 9.229 dB. Meanwhile, the measurement results provide VSWR 1.237, return loss -19.476 dB, bandwidth 790.5 MHz, gain 3.2034 dB, and axial ratio 4.12 dB.

Keywords: skew planar wheel, cloverleaf, first-person view, unmanned aerial vehicle, parameter sweep

Procedia PDF Downloads 182

Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol

Procedia PDF Downloads 180

Authors: N. Guruprasad

Abstract:

This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

Procedia PDF Downloads 494

Authors: Panagiotis Lemonakis, Nikolaos Moisiadis, Andromachi Gkoutzini, George Kaliabetsos, Nikos Eliou

Abstract:

The proper surface water drainage not only affects vehicle movement dynamics but also increases the likelihood of an accident due to the fact that inadequate drainage is associated with potential hydroplaning and splash and spray driving conditions. Nine solutions have been proposed to address hydroplaning in sections with inadequate drainage, e.g., augmented superelevation and longitudinal rates, reduction of runoff length, and skew superelevation. The latter has been extensively implemented in highways recently, enhancing the safety level in the applied road segments in regards to the effective drainage of the rainwater. However, the concept of the skew superelevation has raised concerns regarding the driver’s comfort when traveling over skew superelevation sections, particularly at high speeds. These concerns alleviated through the concept of the round-up skew superelevation, which reduces both the lateral and the vertical acceleration imposed to the drivers and hence, improves comfort and traffic safety. Various research studies aimed at investigating driving comfort by evaluating the lateral and vertical accelerations sustained by the road users and vehicles. These studies focused on the influence of the skew superelevation to passenger cars, buses and trucks, and the drivers themselves, traveling at a certain range of speeds either below or above the design speed. The outcome of these investigations which based on the use of simulations, revealed that the imposed accelerations did not exceed the statutory thresholds even when the travelling speed was significantly greater than the design speed. Nevertheless, the effect of the skew superelevation to other vehicle types for instance, motorcycles, has not been investigated so far. The present research study aims to bridge this gap by investigating the impact of skew superelevation on the motorcycle rider’s comfort. Power two-wheeler riders are susceptible to any changes on the pavement surface and therefore a comparison between the traditional superelevation practice and the skew superelevation concept is of paramount importance. The methodology based on the utilization of sophisticated software in order to design the model of the road for several values of the longitudinal slope. Based on the values of the slopes and the use of a mathematical equation, the accelerations imposed on the wheel of the motorcycle were calculated. Due to the fact that the final aim of the study is the influence of the skew superelevation to the rider, it was deemed necessary to convey the calculated accelerations from the wheel to the rider. That was accomplished by implementing the quarter car suspension model adjusted to the features of two-wheeler vehicles. Finally, the accelerations derived from this process evaluated according to specific thresholds originated from the International Organization for Standardization, which correspond to certain levels of comfort. The most important conclusion drawn is that the comfort of the riders is not dependent on the form of road gradient to a great extent due to the fact that the vertical acceleration imposed to the riders took similar values regardless of the value of the longitudinal slope.

Keywords: acceleration, comfort, motorcycle, safety, skew superelevation

Procedia PDF Downloads 128

Authors: Wesam Ali

Abstract:

This paper provides useful guidelines to the circuit designers on the magnitude of fabrication errors in multilayer millimeter-wave components that are acceptable and presents data not previously reported in the literature. A particularly significant error that was quantified was that of skew between conductors on different layers, where it was found that a skew angle of only 0.1° resulted in very significant changes in bandwidth and insertion loss. The work was supported by a detailed investigation on a 35GHz, multilayer edge-coupled band-pass filter, which was fabricated on alumina substrates using photoimageable thick film process.

Keywords: fabrication errors, multilayer, high frequency band, photoimagable technology

Procedia PDF Downloads 442

Authors: M. Qamarul Islam, Ergun Dogan, Mehmet Yazici

Abstract:

There is a growing body of evidence that non-normal data is more prevalent in nature than the normal one. Examples can be quoted from, but not restricted to, the areas of Economics, Finance and Actuarial Science. The non-normality considered here is expressed in terms of fat-tailedness and asymmetry of the relevant distribution. In this study a skew t distribution that can be used to model a data that exhibit inherent non-normal behavior is considered. This distribution has tails fatter than a normal distribution and it also exhibits skewness. Although maximum likelihood estimates can be obtained by solving iteratively the likelihood equations that are non-linear in form, this can be problematic in terms of convergence and in many other respects as well. Therefore, it is preferred to use the method of modified maximum likelihood in which the likelihood estimates are derived by expressing the intractable non-linear likelihood equations in terms of standardized ordered variates and replacing the intractable terms by their linear approximations obtained from the first two terms of a Taylor series expansion about the quantiles of the distribution. These estimates, called modified maximum likelihood estimates, are obtained in closed form. Hence, they are easy to compute and to manipulate analytically. In fact the modified maximum likelihood estimates are equivalent to maximum likelihood estimates, asymptotically. Even in small samples the modified maximum likelihood estimates are found to be approximately the same as maximum likelihood estimates that are obtained iteratively. It is shown in this study that the modified maximum likelihood estimates are not only unbiased but substantially more efficient than the commonly used moment estimates or the least square estimates that are known to be biased and inefficient in such cases. Furthermore, in conventional regression analysis, it is assumed that the error terms are distributed normally and, hence, the well-known least square method is considered to be a suitable and preferred method for making the relevant statistical inferences. However, a number of empirical researches have shown that non-normal errors are more prevalent. Even transforming and/or filtering techniques may not produce normally distributed residuals. Here, a study is done for multiple linear regression models with random error having non-normal pattern. Through an extensive simulation it is shown that the modified maximum likelihood estimates of regression parameters are plausibly robust to the distributional assumptions and to various data anomalies as compared to the widely used least square estimates. Relevant tests of hypothesis are developed and are explored for desirable properties in terms of their size and power. The tests based upon modified maximum likelihood estimates are found to be substantially more powerful than the tests based upon least square estimates. Several examples are provided from the areas of Economics and Finance where such distributions are interpretable in terms of efficient market hypothesis with respect to asset pricing, portfolio selection, risk measurement and capital allocation, etc.

Keywords: least square estimates, linear regression, maximum likelihood estimates, modified maximum likelihood method, non-normality, robustness

Procedia PDF Downloads 377

Authors: Betty Johanna Garzon Rozo, Jonathan Crook, Fernando Moreira

Abstract:

Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation.

Keywords: operational risk, loss distribution approach, extreme value theory, copulas

Procedia PDF Downloads 556

Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

Procedia PDF Downloads 164

Authors: Valeria Bondarenko

Abstract:

In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

Procedia PDF Downloads 341

Authors: Smita Sonker, Uaday Singh

Abstract:

Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

Procedia PDF Downloads 442

Authors: N. Lebga, Kh. Bouamama, K. Kassali

Abstract:

We report first-principles calculation results on the structural and elastic properties of ZnS x Se1−x alloy for which we employed the virtual crystal approximation provided with the ABINIT program. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation, we made a comparative study between the numerical results obtained from ab-initio calculation using ABINIT or Wien2k within the Density Functional Theory framework with either Local Density Approximation or Generalized Gradient approximation and the pseudo-potential plane-wave method with the Hartwigzen Goedecker Hutter scheme potentials. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x. The variation of the elastic constants is also numerically studied and the phase transformations are discussed in relation to the mechanical stability criteria.

Keywords: density functional theory, elastic properties, ZnS, ZnSe,

Procedia PDF Downloads 545

Authors: Anusuya Ghosh, Vishnu Narayanan

Abstract:

The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming.

Keywords: semidefinite programming, semidefinite representable set, compactly semidefinite representable set, approximation

Procedia PDF Downloads 352

Authors: Tulin Coskun

Abstract:

We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

Procedia PDF Downloads 312

Authors: Hare Krishna Nigam

Abstract:

In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained.

Keywords: Degree of approximation, (E, q)(C, 2) means, Fourier series, Lebesgue integral, Lip (alpha, r)class, W(L(r), xi(t))class of functions

Procedia PDF Downloads 482

Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

Procedia PDF Downloads 64

Authors: Kejal Khatri, Vishnu Narayan Mishra

Abstract:

We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

Procedia PDF Downloads 378

Authors: Serge B. Provost, Yishan Zhang

Abstract:

A moment-based adjustment to the saddlepoint approximation is introduced in the context of density estimation. First applied to univariate distributions, this methodology is extended to the bivariate case. It then entails estimating the density function associated with each marginal distribution by means of the saddlepoint approximation and applying a bivariate adjustment to the product of the resulting density estimates. The connection to the distribution of empirical copulas will be pointed out. As well, a novel approach is proposed for estimating the support of distribution. As these results solely rely on sample moments and empirical cumulant-generating functions, they are particularly well suited for modeling massive data sets. Several illustrative applications will be presented.

Keywords: empirical cumulant-generating function, endpoints identification, saddlepoint approximation, sample moments, density estimation

Procedia PDF Downloads 124