A note on the refinement of Hermite-Hadamard inequality

In this paper, we give the sharper bounds for the mean value of a convex function using dyadic decomposition. Our result is related with classical Hermite-Hadamard inequality. Moreover, using the result, we can determine the maximum error before calculating the numerical (trapezoidal) integral of the convex function.

Sistem Pengenalan Pembicara dengan Metode Wavelet-MCFF dan Pengklasifikasi Hidden Markov Models (HMM)

<p class="Abstrak">Penelitian pengolahan sinyal digital yang berfokus pada pengenalan pembicara telah dimulai sejak beberapa dekade yang lalu, dan telah menghasilkan banyak metode-metode pengenalan pembicara. Di antara algoritma pembentukan koefisien ciri yang telah dikembangkan tersebut, ada dua algoritma yang dapat memberikan akurasi yang tinggi jika diterapkan pada sistem, yaitu <em>Mel Frequency Cepstral Coefficient</em> (MFCC) dan <em>Wavelet</em>. Penelitian ini bertujuan untuk menguji dan memilih kanal terbaik dari proses <em>wavelet</em>-MFCC yang dapat dijadikan sebagai koefisien ciri baru untuk diterapkan pada sistem pengenal pembicara. Koefisien ciri baru tersebut kemudian disebut dengan koefisien ciri <em>Wavelet</em>-MFCC. Kofisien ini dibentuk dari merubah kanal hasil dekomposisi <em>wavelet</em>, yaitu kanal aproksimasi (cA), kanal detail (cD), dan penggabungannya (cAcD), menjadi koefisien MFCC. Metode dekomposisi <em>wavelet</em> yang digunakan adalah metode <em>dyadic</em> dengan menerapkan <em>level</em> dekomposisi <em>level</em> 1 dan <em>level</em> 2. Setiap koefisien ciri kemudian menjadi inputan pada sistem pengklasifikasi <em>Hidden Markov Models</em> (HMM). Keluaran dari HMM kemudian dihitung akurasinya dan dianalisis. Dari pengujian yang dilakukan, diperoleh bahwa kanal detail (cD) sebagai ciri dapat memberikan akurasi yang sama dengan menggunakan kanal gabungan (cAcD) dan lebih tinggi dari kanal aproksimasi (cA), dengan akurasi sebesar 95%. Hal ini menunjukkan bahwa, kanal detail pada dekomposisi <em>level</em> 1 menyimpan ciri suara dari setiap pembicara sehingga sudah cukup untuk dijadikan sebagai koefisien ciri. Maka, penggunaan dekomposisi <em>level</em> 1 dan kanal detail cD sebagai ciri <em>Wavelet</em>-<em>MFCC</em> pada sistem pengenalan pembicara dapat meringankan dan mempercepat proses komputasi.</p><p class="Abstrak"> </p><p class="Abstrak"><em><strong>Abstract</strong></em></p><p class="Abstract"><em>Research in digital signal that focused on speaker recognition has begun since decades ago, and has resulted many speaker recognition methods. there are two algorithms that can provide high accuracy in recognition system, which are Mel Frequency Cepstral Coefficient (MFCC) and Wavelet. the aims of this study is to examine and chose the best channel from wavelet-MFCC process that can be used as new feature coefficient, then called as Wavelet-MFCC features coefficient. The coefficient is built by converting the wavelet decomposition channels, which are approximation (cA), detail (cD), and its combination (cAcD), into the MFCC coefficient. Wavelet dyadic decomposition with level 1 and level 2 of decomposition is applied. Each feature coefficient acts as an input to the HMM classifier. The accuracy of the HMM output is calculated, then analyzed. The obtained results show that the detail chanel (cD) achieve equal accuracy as the combination chanel (cAcD), and higher accuracy compared to aproximation channel (cA), with accuracy 95%. Thus, it can be conclude that the detail channel on level 1 decomposition contains features of each speaker's. Then, cD is enough to be used as a Wavelet-MFCC feature. Thus, its implementation in the SRS can ease and speed up the computing process.</em></p><p class="Abstrak"><em><strong><br /></strong></em></p>

Restriction for Surfaces with Linear Height below 2

This chapter studies the case where hsubscript lin(φ‎) < 2. It first performs a dyadic decomposition of a domain introduced in the previous chapter and the corresponding measure dμ‎superscript Greek small letter rho1. Next, given a measure dν‎ₖ, the chapter performs yet another Littlewood–Paley decomposition. Since the decay of the Fourier transforms of these measures is strongly nonisotropic, as a last step this chapter performs a dyadic decomposition in each of the frequency variables ζ‎₁, ζ‎₂, and ζ‎₃ dual to x₁, x₂, and x₃. In the end, a few cases in which this chapter is unable to sum the operator norms remain open, to be dealt with in the next chapter.

The Case When hlin(φ‎) ≥ 2: Preparatory Results

This chapter turns to the case where hsubscript lin(φ‎) ≥ 2. In a first step, the chapter performs a decomposition of the remaining piece Ssubscript Greek small letter psi of the surface S. Then, in the domains Dₗ the chapter once again applies dyadic decomposition techniques in combination with rescaling arguments, making use of the dilations associated with the weight κ‎ₗ. But serious new problems arise, caused by the nonlinear change from the coordinates (x₁, x₂) to the adapted coordinates (y₁, y₂). Therefore, the chapter takes a closer look at the domain Dsubscript pr and devises a further decomposition of the domain Dsubscript pr into various subdomains of “type” Dsubscript (l) and Esubscript (l).

An Automated Kinematic Analysis Tool for Computationally Synthesizing Planar Mechanisms

This paper presents an implementation of kinematic analysis to evaluate planar mechanisms for use in an automated design process. The existing software available for kinematic analysis require the user to manually input the mechanism for analysis. But in order to computationally synthesize planar mechanisms, it is important to automatically define the boundary conditions and adjust the necessary parameters to evaluate the kinematics of the mechanism in consideration. Currently, there are no kinematic analysis tools available that can be integrated with a design generation tool. One of the reasons is the absence of a method which not only solves the kinematics reliably but is also applicable to generalized n-bar mechanisms. The authors have implemented the instant center method for solving velocities, the vector polygon approach for solving accelerations and the dyadic decomposition method for solving positions. This implementation operates on n-bar mechanisms consisting of four-bar loops and one-degree of freedom on revolute (R), prismatic (P) and revolute-prismatic (R-P) joints. The developed method takes advantage of the concepts in object oriented programming as well as a unique representation based on graph-grammar formalism. This paper describes the methodology used for generalizing kinematic analysis for integration with a concept generator along with examples to validate the implementation.

Discrete quadratic estimates and holomorphic functional calculi in Banach spaces

We develop a discrete version of the weak quadratic estimates for operators of type w explained by Cowling, Doust, McIntosh and Yagi, and show that analogous theorems hold. The method is direct and can be generalised to the case of finding necessary and sufficient conditions for an operator T to have a bounded functional calculus on a domain which touches σ(T) nontangentially at several points. For operators on Lp, 1 < p < ∞, it follows that T has a bounded functional calculus if and only if T satisfies discrete quadratic estimates. Using this, one easily obtains Albrecht's extension to a joint functional calculus for several commuting operators. In Hilbert space the methods show that an operator with a bounded functional calculus has a uniformly bounded matricial functional calculus.The basic idea is to take a dyadic decomposition of the boundary of a sector Sv. Then on the kth ingerval consider an orthonormal sequence of polynomials . For h ∈ H∞(Sν), estimates for the uniform norm of h on a smaller sector Sμ are obtained from the coefficients akj = (h, ek, j). These estimates are then used to prove the theorems.