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Because P is symmetric positive de nite, there exists orthonormal matrix U and positive de nite diagonal matrix such that P = U 2 U The units of the diagonal elements of = diag([ 1 , 2 , 3 ]) are meters To simplify the analysis, we introduce a new random variable v = Sw where S = 1 U The covariance matrix for v is the identity matrix which is shown as follows: E vv = E Sww S = SPS = 1 U = I Therefore, v N (0, I) The probability density function for v is pv = 1 (2 )

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PDF : https://www.e-iceblue.com/Introduce/ pdf -for- net -introduce.html; considered also using Word via COM automation to open and save to pdf  ...

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Free .NET Word API - CodePlex Archive
CodePlex Archive Open Source Project Archive ... NET, WinForms and Web Service) and it supports in C# , VB. ... Word 2007, Word 2010, Word 2013) to commonly used file format, such as RTF, TXT, HTML, PDF , XPS, EPUB and Image etc.

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The components of the vector v are independent and identically distributed with variance equal to one The components of v are dimensionless Given the previous de nitions and a positive scalar c, we have the following relationships P rob{ v c} = P rob{w S Sw c2 } = P rob{w P 1 w c2 } We will nd the value of c such that the sphere in the v coordinates with radius c contains 50% of the v samples In the w coordinates the region expected to contain 50% of the w samples will be the ellipsoid

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Convert PDF to Word Using C# - C# Corner
Jul 13, 2015 · Convert PDF to Word Using C# The first step will be to get the PdfBox package using the Nuget Package Manager. Now, import the following DLLs into your .cs file: The third step will be to install the DocX NuGet Package from the NuGet Package Manager: Let's read a PDF file and try to get the text from it.

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Piezoelectric Crystals Pieces of quartz, when cut into thin wafers and subjected to voltages, will vibrate at high frequencies Because of the physical dimensions of such a piezoelectric crystal, these vibrations occur at a precise frequency fo, and also at whole-number multiples of fo These multiples, 2fo, 3fo, 4fo, and so on, are called harmonic frequencies or simply harmonics The frequency fo is called the fundamental frequency or simply the fundamental The fundamental, fo, is defined as the lowest frequency at which resonance occurs Quartz crystals can be made to act like LC circuits in electronic devices A crystal exhibits an impedance that varies with frequency The reactance is zero at fo and the harmonic frequencies Cavities Lengths of metal tubing, cut to specific dimensions, exhibit resonance at very high, ultrahigh, and microwave radio frequencies They work in much the same way as musical instruments resonate with sound waves But the waves are electromagnetic, rather than acoustic Such cavities, also called cavity resonators, have reasonable physical dimensions at frequencies above about 150 MHz Below this frequency, a cavity can be made to work, but it is long and unwieldy Like crystals, cavities resonate at a fundamental frequency fo, and also at harmonic frequencies Sections of Transmission Line When a transmission line is cut to 1 4 wavelength, or to any whole-number multiple of this, it behaves as a resonant circuit The most common length for a transmission-line resonator is a 1 4 wavelength Such a piece of transmission line is called a quarter-wave section When a quarter-wave section is short-circuited at the far end, it acts like a parallel-resonant LC circuit, and has a high resistive impedance at the resonant frequency fo When it is open at the far end, it acts as a series-resonant LC circuit, and has a low resistive impedance at fo In effect, a quarterwave section converts an ac short circuit into an ac open circuit and vice versa, at a specific frequency fo The length of a quarter-wave section depends on the desired fo It also depends on how fast the electromagnetic energy travels along the line This speed is specified in terms of a velocity factor, abbreviated v The value of v is given as a fraction of the speed of light Typical transmission lines have velocity factors ranging from about 066 to 095 (or 66 percent to 95 percent) This factor is provided by the manufacturers of prefabricated lines such as coaxial cable If the frequency in megahertz is fo and the velocity factor of a line is v, then the length L ft of a quarter-wave section of transmission line, in feet, is given by this formula:.

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w R3 w P 1 w c2 Because w = U v and U is an orthonormal matrix, the columns of U de ne the principle axes of the ellipsoid and the diagonal elements of de ne the elongation of the ellipsoidal axes For example, if U = [u1 , u2 , u3 ] where ui is the i-th column of U, then a unit vector along the i-th coordinate axis of the v reference frame transforms to the vector ( i ui ) in the w reference frame The probability that v falls in the region v c can be derived as P rob{ v c} =

L ft = 246v/fo The length Lm in meters is given by this: L m = 750v/fo We use L here to stand for length, not inductance !

= = = =

1 (2 ) 1 (2 ) 2

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How to convert PDF to Doc in C#, VB.NET - E-Iceblue
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