Esscher transform

In actuarial science, the Esscher transform (Gerber & Shiu 1994) is a transform that takes a probability density f(x) and transforms it to a new probability density f(x; h) with a parameter h. It was introduced by F. Esscher in 1932 (Esscher 1932).

Let f(x) be a probability density. Its Esscher transform is defined as

More generally, if μ is a probability measure, the Esscher transform of μ is a new probability measure E_h(μ) which has density

with respect to μ.

 Sumber : http://en.wikipedia.org/wiki/Esscher_transform

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Discrete Chebyshev transform

In applied mathematics, the discrete Chebyshev transform (DCT), named after Pafnuty Chebyshev, is one of either of two main varieties of DCTs: the discrete Chebyshev transform on the 'roots' grid of the Chebyshev polynomials of the first kind , and the discrete Chebyshev transform on the 'extrema' grid of the Chebyshev polynomials of the first kind.

The discrete chebyshev transform of u(x) at the points  is given by:

where:

where  and  otherwise.

Using the definition of ,

and its inverse transform:

(This so happens to the standard Chebyshev series evaluated on the roots grid.)

This can readily be obtained by manipulating the input arguments to a discrete cosine transform.

Sumber : http://en.wikipedia.org/wiki/Discrete_Chebyshev_transform

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Bessel function

Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are the canonical solutions y(x) of Bessel's differential equation

for an arbitrary complex number α (the order of the Bessel function). The most important cases are for α an integer or half-integer.

Although α and −α produce the same differential equation for real α, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α. Bessel functions are also known as cylinder functions or the cylindrical harmonics because they appear in the solution toLaplace's equation in cylindrical coordinates.

Sumber : http://en.wikipedia.org/wiki/Bessel_function

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Anscombe transform

In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely used in photon-limited imaging (astronomy, X-ray) where images naturally follow the Poisson law. The Anscombe transform is usually used to pre-process the data in order to make thestandard deviation approximately constant. Then denoising algorithms designed for the framework of additive white Gaussian noise are used; the final estimate is then obtained by applying an inverse Anscombe transformation to the denoised data.

For the Poisson distribution the mean  and variance  are not independent: . The Anscombe transform^[1]

aims at transforming the data so that the variance is set approximately 1 whatever the mean. It transforms Poissonian data  (with mean ) to approximately Gaussian data of mean  and standard deviation 1. This approximation is valid provided that  is larger than 4.^{[citation needed]}

Sumber : http://en.wikipedia.org/wiki/Anscombe_transform

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Airy zeta function

In mathematics, the Airy zeta function, studied by Crandall (1996), is a function analogous to the Riemann zeta function and related to the zeros of the Airy function.

The Airy function

is positive for positive x, but oscillates for negative values of x; the sequence of values of x for which Ai(x) = 0, sorted by their absolute values, are called the Airy zeros and are denoted a₁, a₂, ...

The Airy zeta function is the function defined from this sequence of zeros by the series

This series converges when the real part of s is greater than 3/2, and may be extended by analytic continuation to other values of s.

Sumber : http://en.wikipedia.org/wiki/Airy_zeta_function

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Airy function

This article is about the Airy special function. For the Airy stress function employed in solid mechanics, see Stress functions.

In the physical sciences, the Airy function Ai(x) is a special function named after the British astronomer George Biddell Airy (1801–92). The function Ai(x) and the related functionBi(x), which is also called the Airy function, but sometimes referred to as the Bairy function, are solutions to the differential equation

known as the Airy equation or the Stokes equation. This is the simplest second-order linear differential equation with a turning point (a point where the character of the solutions changes from oscillatory to exponential).

The Airy function is the solution to Schrödinger's equation for a particle confined within a triangular potential well and for a particle in a one-dimensional constant force field. For the same reason, it also serves to provide uniform semiclassical approximations near a turning point in the WKB method, when the potential may be locally approximated by a linear function of position. The triangular potential well solution is directly relevant for the understanding of many semiconductor devices.

The Airy function also underlies the form of the intensity near an optical directional caustic, such as that of the rainbow. Historically, this was the mathematical problem that led Airy to develop this special function. The Airy function is also important in microscopy and astronomy; it describes the pattern, due to diffraction and interference, produced by a point source of light (one which is smaller than the resolution limit of a microscope or telescope).

Sumber : http://en.wikipedia.org/wiki/Airy_function

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Tranformasi Abel

For summation transformation, see summation by parts.

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by:

Assuming f(r) drops to zero more quickly than 1/r, the inverse Abel transform is given by

In image analysis, the forward Abel transform is used to project an optically thin, axially symmetric emission function onto a plane, and the reverse Abel transform is used to calculate the emission function given a projection (i.e. a scan or a photograph) of that emission function.

In absorption spectroscopy of cylindrical flames or plumes, the forward Abel transform is the integrated absorbance along a ray with closest distance y from the center of the flame, while the inverse Abel transform gives the local absorption coefficient at a distance r from the center. Abel transform is limited to applications with axially symmetric geometries. For more general asymmetrical cases, more general-oriented reconstruction algorithms such as Algebraic Reconstruction Technique (ART), Maximum Likelihood Expectation Maximization (MLEM), Filtered Back-Projection (FBP) algorithms should be employed.

In recent years, the inverse Abel transformation (and its variants) has become the cornerstone of data analysis in photofragment-ion imaging and photoelectron imaging. Among recent most notable extensions of inverse Abel transformation are the Onion Peeling and BAsis Set Expansion (BASEX) methods of photoelectron and photoion image analysis.

sumber : http://en.wikipedia.org/wiki/Abel_transform

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Program Konversi Kilobyte ke Megabyte dan GigaByte

 

/*

 * To change this template, choose Tools | Templates

 * and open the template in the editor.

 */

package athir;

import javax.swing.JOptionPane;

/**

 *

 * @author NAHWU

 */

public class KonversiByte {

    public static void main(String[] args) {

        // TODO code application logic here

        String input;   //input adalah variabel bertipedata string

        long kb;        //kb adalah variabel bertipedata longint

        long mb;        //mb adalah variabel bertipedata longint

        long gb;        //gb adalah variabel bertipedata longint

        long sisa;      //sisa adalah variabel bertipedata longint

        long nilai;     //nilai adalah variabel bertipedata longint

       

        input = JOptionPane.showInputDialog("Masukkan Nilai Konversi : ");

        // menampilkan input dialog dan menyimpan data yang dimasukkan kedalam varibel input

        nilai = Integer.parseInt(input);  //mengkonversi nilai string ke nilai integer

       

        gb = nilai / 1048576;   // nilai dibagi 1048576 disimpan ke variable gb

        sisa = nilai % 1048576; // nilai sisa pembagian 1048576 disimpan ke variable sisa

        mb = sisa / 1024;       // sisa dibagi 1024 disimpan ke variable mb

        kb = sisa % 1024;        // sisa sisa pembagian 1024 disimpan ke variable kb

       

        JOptionPane.showMessageDialog(null,"Hasil Konversi Dari " + nilai + " kb adalah  => " + gb + " Gb " + mb + " Mb " + kb + " kb ");

        // menampilkan pesan hasil konversi dan menampilkan nilai dari viriabel nilai,gb,mb dan kb

    }

}

Menampilkan input dialog dan memberi nilai yang akan dionversi

Menampilkan pesan hasil dari konversi nilai dari input dialog diatas

semoga bermanfaat :)

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