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E-BEAM LITHOGRAPHY
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The presentation of spectral regions may be in terms of wavelength as metres or sub-multiples of a metre. The following units are commonly encountered in spectroscopy: 1 A = 10 10 m 1 nm = 10 9 m 1 m = 10 6 m
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Figure 7.25. Topology of a neural network
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EXAMPLE 13.2 Determine m so that Ma Mt in magnitude. Solution: We set 1 jMa j Mt2 Mt m Hence, m Mt 13:5-16
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Let s request this page again and observe the change in the resulting page. Figure 5.8 displays the output of the include directive after the changes in meeting.html.
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It should be noted that any bond with a nonzero coupon would have a duration gure less than its actual maturity, whereas a zerocoupon bond s duration and maturity will be the same. Quality. Credit quality ratings refer to the ability of the issuer to make payments of interest and principal on loan securities such as bonds or notes. The credit quality of an issuer could be thought of as the probability that the issuer will default. Credit quality is measured by rating agencies such as Standard & Poor s and Moody s. Credit ratings can broadly be classi ed as: (1) investment grade (highest quality); (2) non investment grade (mid-to-low quality, commonly referred to as high yield debt); and (3) speculative (securities of rms that have defaulted on their debt, commonly referred to as distressed debt). A good working knowledge of the three bond measures de ned can aid the investment manager analyst in the evaluation of xed income managers, but the body of knowledge needed to properly assess xed income managers and put their track records and investment processes in perspective is far more expansive. As the previous section states, this book is not a tutorial on the assets classes reviewed within. Instead, it is assumed that the reader has the basic knowledge to understand the securities discussed. In this section, we are discussing bonds, so I make the assumption that you, the reader, already possess a basic understanding of xed income instruments. While the underlying fundamental characteristics may be different, the formulas, methods and analytical techniques remain the same. When analyzing a xed income portfolio, we look to see if the portfolio is concentrated in any broad categories, such as investment type (U.S. Treasuries, corporate bonds, investment-grade bonds, non-investment-grade bonds, etc.). When looking at a portfolio s duration, it is important to assess the underlying risk based on our initial risk assumptions and, if appropriate, compared to some benchmark. For example, a xed income portfolio with a signi cantly higher exposure to zero-coupon bonds than its peers or relevant benchmarks should be viewed as potentially carrying with it heightened interest rate risk. Contrast that portfolio example with a portfolio of high-grade corporate and Treasury bonds with maturities on a par with the rst example. Assuming no derivatives are being used to hedge out interest rate risk, the second portfolio would likely exhibit less interest rate risk
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64 Up/Down Market Analysis
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BASIC INEQUALITIES FOR GAUSSIAN PROCESSES
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0.6 Index 0.4 0.2
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5 6 7 8 9
DIFFRACTIVE OPTICS II
line having C -paths and satisfying the nondegeneracy condition Var(X(t)) > 0 for every t [0, T ], all the moments of crossings of any level are nite. Rice formulas for random elds are considered in 6. Proofs are new and self-contained except for the aforementioned co-area formula. In all cases, formulas for the moments of weighted (or marked ) crossings are stated and proved. They are used in the sequel for various applications and, moreover, are important by themselves. 4 consists of two parts. In Sections 4.1 to 4.3, X is a Gaussian process de ned on a bounded interval of the real line, and some initial estimates for P(M > u) are given, based on computations of the rst two moments of the number of crossings. In Sections 4.4 and 4.5, two statistical applications are considered: the rst to genomics and the second to statistical inference on mixtures of populations. The common feature of these two applications is that the relevant statistic for hypothesis testing is the maximum of a certain Gaussian process, so that the calculation of its distribution appears to be naturally related to the methods in the earlier sections. 5 establishes a bridge between the distribution of the maximum on an interval of a one-parameter process and the factorial moments of up-crossings of the paths. The main result is the general formula (5.2), which expresses the tail of the distribution of the maximum as the sum of a series (the Rice series) de ned in terms of certain factorial moments of the up-crossings of the given process. Rice series have been used for a long time with the aim of computing the distribution of the maximum of some special one-parameter Gaussian processes: as, for example, in the work of Miroshin (1974). The main point in Theorems 5.1, 5.6, and 5.7 is that they provide general suf cient conditions to compute or approximate the distribution of the maximum. Even though some of the theoretical results are valid for non-Gaussian processes, if one wishes to apply them in speci c cases, it becomes dif cult to compute the factorial moments of up-crossings for non-Gaussian processes. An interesting feature of the Rice series is its enveloping property: replacing the total sum of the series by partial sums gives upper and lower bounds for the distribution of the maximum, and a fortiori, the error when one replaces the total sum by a partial sum is bounded by the absolute value of the last term computed. This allows one to calculate the distribution of the maximum with some ef ciency. We have included a comparison with the computation based on Monte Carlo simulation of the paths of the process. However, in various situations, more ef cient methods exist; they are considered in 9. In Section 7.1 we prove a general formula for the density of the probability distribution of the maximum which is valid for a large class of random elds. This is used in Section 7.2 to give strong results on the regularity of the distribution of a one-parameter Gaussian process; as an example, if the paths are of class C and the joint law of the process and its derivatives is nondegenerate (in the sense speci ed in the text), the distribution of the maximum is also of class C . When it comes to random elds, the situation is more complicated and the known results are essentially weaker, as one can see in Section 7.3.
4. Declare a variable called interestAmount to hold the value of the calculated interest and initialize it to 0.0. 5. Use the init() method to create and initialize the ORB (each server is required to have one). The init() method has two parameters, the first of which is the command line argument for the main method, and the second of which contains application specific properties (which is a Property object). For this example, assume that you do not have application specific properties that is, pass null for that parameter. In some situations, the first parameter of the method may also be null.
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