This chapter gives an overview of the proposed study. To define the illicit material detection problem, in Section 2.1, the types of illicit materials are first introduced. The environment in which these illicit materials need to be detected is also carefully described. In Section 2.2, x-ray physics is discussed in detail. In Section 2.3, the principle of illicit material detection using x-ray ...

Experiments were conducted at the Horticulture Research Farm of Horticulture Department, Bangabandhu Sheikh Mujibur Rahman Agricultural University (BSMRAU), Salna, Gazipur during December, 2007 to May, 2009 to investigate the effect of bulb cutting and potting media on propagation of hippeastrum. The bulb cutting significantly influenced all the parameters except days required to first leaf eme...

where j Z s  are i.i.d. B(1,p) r.v’s. The remainder of the paper is organized as follows. In Section 2 we obtain the characteristic function of X and give an interpretation for the variable X. In Section 3 we derive the distribution function of X and prove some of its properties. In Section 4 we discuss the existence of the density function. In Section 5 distribution of sum of a finite number ...

Kato established higher local reciprocity map (see section 5 and [K1, Th. 2 of §6] (two-dimensional case), [K2, Th. II], [K3, §4]) using in particular this theorem. In this section we deduce the reciprocity map for higher local fields from this theorem and Bloch–Kato’s theorem of section 4. Our approach which uses generalized class formations simplifies Kato’s original argument. We use the nota...

Given a closed ideal I in a C-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism α : A → M(I) and a map L : J → A with some properties, based on [3] and [9] we define a C-algebra O(A,α, L) which we call the Crossed Product by a Partial Endomorphism. In the second section we introduce the Crossed Product by a Partial Endomorphism O(X,α, L) induced by a local homeomorphism σ : ...

First, we summarize definitions and related theorems of asymptotic statistics in Section A. We prove Theorems in Section B. Lastly, Section C contains additional simulation results. A Asymptotic Statistics We summarize some results of asymptotic statistics from (Serfling, 1980). Let X1, X2, . . . and X be random variables on a probability space (Ω,A, P ). We say that Xn converges in probability...

In section 1.1 we detail the experimental setup used at the SXR beamline of the Linac Coherent Light Source. This is followed by section 1.2 detailing the sample preparation and the x-ray characterization performed at beamline 13-3 of the Stanford Synchrotron Radiation Lightsource. In section 1.3 we detail how spin sensitivity is achieved in resonant x-ray scattering and subsequently in section...

In section 1, we define the abelian groups Ak(X) in a manner analagous to the homology groups Hk(X) by considering cycles of subvarieties modulo rational equivalence. In section 2, we construct, for any Cartier divisor D on X and subvariety V ⊂ X, an intersection class D · [V ] ∈ Ak−1(|D|∩|V |) and state its basic properties. Bezout’s theorem follows easily. In section 3, we discuss the centerp...

This section is devoted to the discussion of two fundamental (partial) differential equations, that arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous state Markov processes, we introduce the forward and backward equation, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples ...

After revisiting some practical problems of numerical methods by playing with models introduced in Chapter 2, we will investigate the two most important properties of numerical algorithms—stability and accuracy. This is done most easily in the context of the simplest numerical method, i.e., the explicit Euler method (Section 5.2). The problem of solving stiff differential equations is addressed...