University of Science and Technology of China A dissertation for doctor s degree An Example of USTC Thesis Template for Bachelor, Master and Doctor Author: Zeping Li Speciality: Mathematics and Applied Mathematics Supervisors: Prof. Luogeng Hua, Prof. Xuesen Qian Finished time: June 2, 2018
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ABSTRACT ABSTRACT This is a sample document of USTC thesis L A TEX template for bachelor, master and doctor. The template is created by zepinglee and seisman, which orignate from the template created by ywg. The template meets the equirements of USTC theiss writing standards. This document will show the usage of basic commands provided by L A TEX and some features provided by the template. For more information, please refer to the template document ustcthesis.pdf. Key Words: University of Science and Technology of China (USTC); Thesis; L A TEX Template; Bachelor; Master; PhD II
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2 2 2.1 upright e i d arg max arg min \eu \iu \diff \argmax \argmin e iπ + 1 = 0 (2.1) d 2 u dt 2 = f(x) dx (2.2) arg min f(x) (2.3) x 2.2 2.1 If the integral of function f is measurable and non-negative, we define its (extended) Lebesgue integral by f = sup g g, (2.4) where the supremum is taken over all measurable functions g such that 0 g f, and where g is bounded and supported on a set of finite measure. 2.1 are given by Simple examples of functions on R d that are integrable (or non-integrable) x a if x 1, f a (x) = (2.5) 0 if x > 1. 1 F a (x) = 1 + x a, all x Rd. (2.6) Then f a is integrable exactly when a < d, while F a is integrable exactly when a > d. 2
2.1 (Fatou) 2 Suppose {f n } is a sequence of measurable functions with f n 0. If lim n f n (x) = f(x) for a.e. x, then f lim inf n f n. (2.7) We do not exclude the cases f =, or lim inf n f n =. 2.2 Suppose f is a non-negative measurable function, and {f n } a sequence of non-negative measurable functions with f n (x) f(x) and f n (x) f(x) for almost every x. Then lim n f n = f. (2.8) 2.3 Suppose f is integrable on R d. Then for every ϵ > 0: i. There exists a set of finite measure B (a ball, for example) such that B c f < ϵ. (2.9) ii. There is a δ > 0 such that f < ϵ whenever m(e) < δ. (2.10) 2.4 E Suppose {f n } is a sequence of measurable functions such that f n (x) f(x) a.e. x, as n tends to infinity. If f n (x) g(x), where g is integrable, then f n f 0 as n, (2.11) and consequently f n f as n. (2.12) Trivial. 2.3 Axiom of choice Suppose E is a set and E α is a collection of non-empty subsets of E. Then there is a function α x α (a choice function ) such that x α E α, for all α. (2.13) Observation 1 Suppose a partially ordered set P has the property that every chain has an upper bound in P. Then the set P contains at least one maximal element. A concise proof Obvious. 3
3 3 3.1 3.1 3.1 macos Windows TeX TeX Live MacTeX MikTeX 3.2 longtable 3.2 3.2 4
3 3.2 3.3 3.1 3.1 3.1 arxiv TEX 3.4 algorithm2e listings 5
3 Data: this text Result: how to write algorithm with L A TEX2e 1 initialization; 2 while not at end of this document do 3 read current; 4 if understand then 5 go to next section; 6 current section becomes this one; 7 else 8 go back to the beginning of current section; 9 end 10 end 3.1: 1 6
4 4 4.1 4.1.1. \cite{knuth86a} [1] \citet{knuth86a} Knuth [1] \citet[chap.~2]{knuth86a} Knuth [1]chap. 2 \citep{knuth86a} [1] \citep[chap.~2]{knuth86a} [1]chap. 2 \citep[see][]{knuth86a} see [1] \citep[see][chap.~2]{knuth86a} see [1]chap. 2 \citet*{knuth86a} Knuth [1] \citep*{knuth86a} [1] \citet{knuth86a,tlc2} Knuth [1], Mittelbach et al. [2] \citep{knuth86a,tlc2} [1,2] \cite{knuth86a,knuth84} [1,3] \citet{knuth86a,knuth84} Knuth [1,3] \citep{knuth86a,knuth84} [1,3] \cite{knuth86a,knuth84,tlc2} [1 3] 4.1.2. \cite{knuth86a} [1] \citet{knuth86a} Knuth [1] \citet[chap.~2]{knuth86a} Knuth [1] chap. 2 \citep{knuth86a} [1] \citep[chap.~2]{knuth86a} [1] chap. 2 \citep[see][]{knuth86a} [see 1] \citep[see][chap.~2]{knuth86a} [see 1] chap. 2 \citet*{knuth86a} Knuth [1] \citep*{knuth86a} [1] 7
4 \citet{knuth86a,tlc2} Knuth [1], Mittelbach et al. [2] \citep{knuth86a,tlc2} [1, 2] \cite{knuth86a,knuth84} [1, 3] \citet{knuth86a,knuth84} Knuth [1, 3] \citep{knuth86a,knuth84} [1, 3] \cite{knuth86a,knuth84,tlc2} [1 3] 4.2 - \cite{knuth86a} Knuth (1986) \citet{knuth86a} Knuth (1986) \citet[chap.~2]{knuth86a} Knuth (1986) chap. 2 \citep{knuth86a} (Knuth, 1986) \citep[chap.~2]{knuth86a} (Knuth, 1986) chap. 2 \citep[see][]{knuth86a} (see Knuth, 1986) \citep[see][chap.~2]{knuth86a} (see Knuth, 1986) chap. 2 \citet*{knuth86a} Knuth (1986) \citep*{knuth86a} (Knuth, 1986) \citet{knuth86a,tlc2} Knuth (1986); Mittelbach et al. (2004) \citep{knuth86a,tlc2} (Knuth, 1986; Mittelbach et al., 2004) \cite{knuth86a,knuth84} Knuth (1986, 1984) \citet{knuth86a,knuth84} Knuth (1986, 1984) \citep{knuth86a,knuth84} (Knuth, 1986, 1984) 4.3 \citealt{tlc2} Mittelbach et al. 2004 \citealt*{tlc2} Mittelbach, Goossens, Braams, and Carlisle 2004 \citealp{tlc2} Mittelbach et al., 2004 \citealp*{tlc2} Mittelbach, Goossens, Braams, and Carlisle, 2004 \citealp{tlc2,knuth86a} Knuth, 1986; Mittelbach et al., 2004 pg. 32 \citealp[pg.~32]{tlc2} Mittelbach et al., 2004 \citenum{tlc2} 2 \citetext{priv.\ comm.} (priv. comm.) 8
4 \citeauthor{tlc2} Mittelbach et al. \citeauthor*{tlc2} Mittelbach, Goossens, Braams, and Carlisle \citeyear{tlc2} 2004 \citeyearpar{tlc2} 2004 9
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