Search results for: Distortion Theorem

Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

Abstract:

Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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Authors: Yasuhito Tanaka

Abstract:

We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.

Keywords: Maximum theorem, Constructive mathematics, Sequentially locally at most one maximum.

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Authors: K. Kalaiselvan, A. Elango

Abstract:

In general, it is desirable to finish the weld quickly, before a large volume of surrounding metal heats up and expands. The welding process used, type, welding current and speed of travel, thus, affect the degree of shrinkage and distortion of a weldment. The use of mechanized welding equipment reduces welding time, metal affected zone and consequently distortion. This article helps to define what weld distortion is and then provide a practical understanding of the causes of distortion, effects of shrinkage in butt joint welded assemblies using TI6AL4VA and Aluminium AA2024 alloy sheet. The beam offset position to the joint interface towards titanium and aluminium side. The factors affecting distortion during welding is also given. Test results reveal that welding speed is the significant parameter to decide the extent of distortion. Also welding from Al side reduces the distortion while Ti side increases the distortion.

Keywords: Nd:YAG Pulsed laser welding, Titanium/Aluminium thin sheet butt joint, distortion.

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Authors: Bahareh Babaei, Hadi Bahrami Ehsan, Reza Reza-zadeh, Hossien Kaviani

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Judgment is affected by many agents and distortion in this assessment is unpreventable. Personality dimensions are among those factors that interfere with the distortion. In this research, the relations between personality dimensions of subject and his judgment on friends- personality dimensions is investigated. One-hundred friend couples completed both NEO Five Factor Inventory (NEOFFI) and Ahvaz Reality Distortion Inventory (ARDI) to make judgments about themselves and their friends. Observations show that judge-s Agreement and Neuroticism dimensions are impressed by reality distortion. On the other hand, this reality distortion interferes with one-s evaluation of his friend-s Agreement, Neuroticism, and Conscientiousness dimensions. Conscientiousness with suppressive effect on judge-s other dimensions plays the irrelevant role on personality judgment. Therefore, observer-rating tools which are used as a conventional criterion seem to be not valid because of the reality distortion due to judge-s personality dimensions.

Keywords: Personality dimensions, reality distortion, judgmental accuracy.

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Authors: Jose William Porras Ferreira

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This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: Christian Bräuer-Burchardt, Peter Kühmstedt, Gunther Notni

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A new hybrid method to realise high-precision distortion determination for optical ultra-precision 3D measurement systems based on stereo cameras using active light projection is introduced. It consists of two phases: the basic distortion determination and the refinement. The refinement phase of the procedure uses a plane surface and projected fringe patterns as calibration tools to determine simultaneously the distortion of both cameras within an iterative procedure. The new technique may be performed in the state of the device “ready for measurement" which avoids errors by a later adjustment. A considerable reduction of distortion errors is achieved and leads to considerable improvements of the accuracy of 3D measurements, especially in the precise measurement of smooth surfaces.

Keywords: 3D Surface Measurement, Fringe Projection, Lens Distortion, Stereo.

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Authors: A. Alghanim, J. Benedikt, P. J. Tasker

Abstract:

The increasing demand for higher data rates in wireless communication systems has led to the more effective and efficient use of all allocated frequency bands. In order to use the whole bandwidth at maximum efficiency, one needs to have RF power amplifiers with a higher linear level and memory-less performance. This is considered to be a major challenge to circuit designers. In this thesis the linearity and memory are studied and examined via the behavior of the intermodulation distortion (IMD). A major source of the in-band distortion can be shown to be influenced by the out-of-band impedances presented at either the input or the output of the device, especially those impedances terminated the low frequency (IF) components. Thus, in order to regulate the in-band distortion, the out of-band distortion must be controllable. These investigations are performed on a 12W LDMOS device characterised at 2.1 GHz within a purpose built, high-power measurement system.

Keywords: Low Frequency Memory, IntermodulationDistortion (IMD).

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Authors: Adil AL-Rammahi

Abstract:

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

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

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Authors: Benshi Zhu

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In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

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Authors: Yasuhito Tanaka

Abstract:

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.

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Authors: Joy Jo-Yi Chang, Justie Su-Tzu Juan

Abstract:

Visual secret sharing (VSS) was proposed by Naor and Shamir in 1995. Visual secret sharing schemes encode a secret image into two or more share images, and single share image can’t obtain any information about the secret image. When superimposes the shares, it can restore the secret by human vision. Due to the traditional VSS have some problems like pixel expansion and the cost of sophisticated. And this method only can encode one secret image. The schemes of encrypting more secret images by random grids into two shares were proposed by Chen et al. in 2008. But when those restored secret images have much distortion, those schemes are almost limited in decoding. In the other words, if there is too much distortion, we can’t encrypt too much information. So, if we can adjust distortion to very small, we can encrypt more secret images. In this paper, four new algorithms which based on Chang et al.’s scheme be held in 2010 are proposed. First algorithm can adjust distortion to very small. Second algorithm distributes the distortion into two restored secret images. Third algorithm achieves no distortion for special secret images. Fourth algorithm encrypts three secret images, which not only retain the advantage of VSS but also improve on the problems of decoding.

Keywords: Visual cryptography, visual secret sharing, random grids, multiple, secret image sharing

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Authors: K. Kalaiselvan, A. Elango

Abstract:

To achieve reliable welds with minimum distortion for the fabrication of components in aerospace industry laser beam welding is attempted. Laser welding can provide a significant benefit for the welding of Titanium and Aluminium thin sheet alloys of its precision and rapid processing capability. For laser welding, pulse shape, energy, duration, repetition rate and peak power are the most important parameters that influence directly the quality of welds. In this experimental work for joining 1mm thick TI6AL4V and AA2024 alloy and JK600 Nd:YAG pulsed laser units used. The distortions at different welding power and speed of titanium and aluminium thin sheet alloys are investigated. Test results reveal that increase in welding speed increases distortion in weldment

Keywords: Laser Beam Welding, Titanium, Aluminium alloy sheets and distortion.

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge Transformation.

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Authors: Mohammed Golam Sarwer, Lai Man Po, Kai Guo, Q.M. Jonathan Wu

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In H.264/AVC video encoding, rate-distortion optimization for mode selection plays a significant role to achieve outstanding performance in compression efficiency and video quality. However, this mode selection process also makes the encoding process extremely complex, especially in the computation of the ratedistortion cost function, which includes the computations of the sum of squared difference (SSD) between the original and reconstructed image blocks and context-based entropy coding of the block. In this paper, a transform-domain rate-distortion optimization accelerator based on fast SSD (FSSD) and VLC-based rate estimation algorithm is proposed. This algorithm could significantly simplify the hardware architecture for the rate-distortion cost computation with only ignorable performance degradation. An efficient hardware structure for implementing the proposed transform-domain rate-distortion optimization accelerator is also proposed. Simulation results demonstrated that the proposed algorithm reduces about 47% of total encoding time with negligible degradation of coding performance. The proposed method can be easily applied to many mobile video application areas such as a digital camera and a DMB (Digital Multimedia Broadcasting) phone.

Keywords: Context-adaptive variable length coding (CAVLC), H.264/AVC, rate-distortion optimization (RDO), sum of squareddifference (SSD).

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Authors: Say Wei Foo, Qi Dong

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A novel robust audio watermarking scheme is proposed in this paper. In the proposed scheme, the host audio signals are segmented into frames. Two consecutive frames are assessed if they are suitable to represent a watermark bit. If so, frequency transform is performed on these two frames. The compressionexpansion technique is adopted to generate distortion over the two frames. The distortion is used to represent one watermark bit. Psychoacoustic model is applied to calculate local auditory mask to ensure that the distortion is not audible. The watermarking schemes using mono and stereo audio signals are designed differently. The correlation-based detection method is used to detect the distortion and extract embedded watermark bits. The experimental results show that the quality degradation caused by the embedded watermarks is perceptually transparent and the proposed schemes are very robust against different types of attacks.

Keywords: Audio watermarking, Compression-expansion, Stereo signals, Robustness.

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

Abstract:

In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: Labiba Gilani, Asifullah Khan, Anwar M. Mirza

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This paper introduces a technique of distortion estimation in image watermarking using Genetic Programming (GP). The distortion is estimated by considering the problem of obtaining a distorted watermarked signal from the original watermarked signal as a function regression problem. This function regression problem is solved using GP, where the original watermarked signal is considered as an independent variable. GP-based distortion estimation scheme is checked for Gaussian attack and Jpeg compression attack. We have used Gaussian attacks of different strengths by changing the standard deviation. JPEG compression attack is also varied by adding various distortions. Experimental results demonstrate that the proposed technique is able to detect the watermark even in the case of strong distortions and is more robust against attacks.

Keywords: Blind Watermarking, Genetic Programming (GP), Fitness Function, Discrete Cosine Transform (DCT).

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Authors: Menglong Su, Shaoyun Shi, Qing Xu

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In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

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In the present paper, we obtain a sandwich-type theorem. As applications of our main result, we discuss the univalence and starlikeness of analytic functions in terms of certain differential subordinations and differential inequalities.

Keywords: Univalent function, Starlike function, Differential subordination, Differential superordination.

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Authors: Yilun Shang

Abstract:

Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.

Keywords: central limit theorem, martingale difference sequence, backward martingale.

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Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu

Abstract:

Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC_4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC₃ cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC_4,6 cryptosystem than LUC₃ and LUC cryptosystems. Current study concludes that LUC_4,6 cryptosystem is more secure than LUC and LUC₃ cryptosystems in sustaining against Lenstra’s attack.

Keywords: Lucas sequence, Dickson Polynomial, faulty signature, corresponding signature, congruence.

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Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy

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The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.

Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.

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Authors: Khalid M. Aamir, Mohammad A. Maud

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Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: Hassan Noori, Abdolali Basiri, Sajjad Rahmany

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In this paper we will introduce a brief introduction to theory of Gr¨obner bases and some applications of Gr¨obner bases to graph coloring problem, automatic geometric theorem proving and cryptography.

Keywords: Gr¨obner bases, Application of Gr¨obner bases, Automatic Geometric Theorem Proving, Graph Coloring, Cryptography.

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Authors: Maharavo Randrianarivony

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The objective is to split a simply connected polygon into a set of convex quadrilaterals without inserting new boundary nodes. The presented approach consists in repeatedly removing quadrilaterals from the polygon. Theoretical results pertaining to quadrangulation of simply connected polygons are derived from the usual 2-ear theorem. It produces a quadrangulation technique with O(n) number of quadrilaterals. The theoretical methodology is supplemented by practical results and CAD surface segmentation.

Keywords: Quadrangulation, simply connected, two-ear theorem.

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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Authors: Ibrahim El rube'

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In this paper, a method for matching image segments using triangle-based (geometrical) regions is proposed. Triangular regions are formed from triples of vertex points obtained from a keypoint detector (SIFT). However, triangle regions are subject to noise and distortion around the edges and vertices (especially acute angles). Therefore, these triangles are expanded into parallelogramshaped regions. The extracted image segments inherit an important triangle property; the invariance to affine distortion. Given two images, matching corresponding regions is conducted by computing the relative affine matrix, rectifying one of the regions w.r.t. the other one, then calculating the similarity between the reference and rectified region. The experimental tests show the efficiency and robustness of the proposed algorithm against geometrical distortion.

Keywords: Image matching, key point detection, affine invariant, triangle-shaped segments.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim

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Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.

Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation

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Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman

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Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.

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