<p>Denna rapport behandlar det animationsarbete som jag gått igenom för att försöka skapa så trovärdiga och dynamiska animationer som möjligt till spelet Colosseum: Code of Hammurabi och dess nya omarbetade stridssystem. Jag har utgått från ett relativt sparsmakat designdokument som i princip bara förklarar kortfattat hur spelmekaniken ska fungera på en grundläggande nivå samt en animationslista på animationer som ska finnas i spelet. Spelet ska i slutändan innehålla 3 olika vapenstilar men på grund av tidsbrist har jag valt att fokusera på en av dess, nämligen kampstilen för strid med tvåhandssvärd. Först har jag analyserat det gamla stridssystemet för att ha en grund att stå på, för att bland annat se vilka brister mitt tidigare arbete präglats av. Utifrån diverse referenser som behandlar medeltida stridkonst inom nyss nämnda kampstil har jag hämtat det mesta av inspirationen och följaktligen kryddat dessa jordnära anvisningar med mina egna idéer samt ett antal fightingspel med spektakulära kontexter och även försökt dra nytta av det material som finns i kampsportsfilmer. Mycket av arbetet har cirkulerat kring att lära sig hur animationer implementeras i ett stridssystem och vilka tekniska samt programmerarmässiga relationer man måste ta hänsyn till. Jag har även försökt ha Disneys 12 animationsprinciper i bakhuvudet för att ha en teoretisk källa till hur animation ska se ut och fungera.</p>

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Order picking is an essential part of order processing in warehousing and distribution operations and can be performed using manual, automated, or semi-automated systems. This thesis analyzes two automated systems, which include carousel and AS/RS (automated storage and retrieval system). The main goal of this research is to develop mathematical models to compare the performance of both systems under random and class-based storage assignments. Simulation models are used to validate the reliability of mathematical models. The outputs of mathematical and simulation models are consistent indicating carousel system with class-based assignment has the highest throughput. Economic analysis is used to estimate the payback periods required to convert from manual to AS/RS and carousel systems. The economic analysis shows that converting from manual to AS/RS with class-based assignment has the shortest payback period.

No description available.

In this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries. / text

Huang Liren. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 96). / Abstract --- p.1 / Introduction --- p.2 / References --- p.5 / Chapter Chapter 1. --- Some elementary results in nonsmooth analysis and optimization --- p.6 / Chapter 1. --- "Some properties for ""lim sup"" and ""lim inf""" --- p.6 / Chapter 2. --- The directional derivative of the sup-type function --- p.8 / Chapter 3. --- Some results in nonsmooth analysis and optimization --- p.12 / References --- p.19 / Chapter Chapter 2. --- On generalized second-order derivatives and Taylor expansions in nonsmooth optimization --- p.20 / Chapter 1. --- Introduction --- p.20 / Chapter 2. --- "Dini-directional derivatives, Clark's directional derivatives and generalized second-order directional derivatives" --- p.20 / Chapter 3. --- On Cominetti and Correa's conjecture --- p.28 / Chapter 4. --- Generalized second-order Taylor expansion --- p.36 / Chapter 5. --- Detailed proof of Theorem 2.4.2 --- p.40 / Chapter 6. --- Corollaries of Theorem 2.4.2 and Theorem 2.4.3 --- p.43 / Chapter 7. --- Some applications in optimization --- p.46 / Ref erences --- p.51 / Chapter Chapter 3. --- Second-order necessary and sufficient conditions in nonsmooth optimization --- p.53 / Chapter 1. --- Introduction --- p.53 / Chapter 2. --- Second-order necessary and sufficient conditions without constraint --- p.56 / Chapter 3. --- Second-order necessary conditions with constrains --- p.66 / Chapter 4. --- Sufficient conditions theorem with constraints --- p.77 / References --- p.87 / Appendix --- p.89 / References --- p.96

by Ki-sing Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 30.

在這篇論文中，我們將會首先討論什麼概率測度μ 上的L²空間會存在指數型正交基(exponential orthonormal basis) ，而μ 則稱為一個譜測度若指數型正交基存在。這個問題源於1974年的Fuglede猜想和Jorgensen與Pedersen對分形譜測度存在性的研究。我們有興趣理解怎麼樣的測度會是譜測度，而對於沒有指數型正交基的測度，我們則探討它們會否存在更廣義且在Fourier分析中常用的指數型基，如Riesz基或Fourier框架(Fourier frame) 。 / 我們知道一個測度可以唯一分解成離散、奇異和絶對連續三部份。我們首先証明譜測度肯定是純型(pure type) 。若測度是絶對連續，我們對有Fourier框架的測度的密度給出一個完全的刻直到。這個結果對研究Gabor框架的問題都有幫助。對於離散且只有有限個非零質量原子的測度，我們証明它們全都都有Riesz基。在最困難作出一般討論的奇異測度中，我們透過譜測度與離散測度的卷積找出了有Riesz基但沒有指數型正交基的奇異測度。我們進而探討自彷函數送代系統(affine IFSs) ，我們証明到如果一個自彷函數送代系統是測度分離且有Fourier框架，那麼它在每一個函數的概率權都是一樣的。我們亦証明了Laba-Wang猜想在絶對連續的自相似測度上是正確的。這些結果都表示了一個有Fourier框架的測度都應該在其支撐上有一定的均勻性。 / 在論文的第二部分我們會探討自彷tile其Fourier變換的零點集。在自彷tile的研究中，其中一個基本問題就是刻劃其數字集(digit set)使得那自彷函數送代系統的不變集能以平移密鋪空間。透過Kenyon條件，我們可將這個問題轉化成理解Fourier變換的零點集。男一方面，指數型正交基的存在性亦需要我們探討Fourier變換的零點集，而自彷tile 的Fourier變換是可以明確寫出來的。這使自彷tile成為一個很好去研究tilings和譜測度相互關係的好例子。 / 我們利用了分圓多項式(cyclotomic polynomials)對一維自彷tile的零點集進行了一個詳細的研究。從這裡我們把tile的數字集寫成某些分圓多項式的乘積。這個乘積亦可以一個樹上的切集(blocking)表示出來。這個表示亦把tile數字集的乘積形式(product-forms) 一般化成高階乘積形式。我們証明了在任何維數的tile數字集都是整數tile(即它們能平移密鋪整數集Z) 。這個結果讓我們能使用Coven和Meyerowitz所提出的整數tile分解方法，來使tile數字集完整刻劃成高階模乘積形式(high order modulo product-forms) 當數字集的數目為p[superscript α]q而p，q則是質數。由於我們對零點集亦完全清楚，這對在自彷tile上尋找完備的指數型正交基提供了一個新的方向。 / In this thesis, we will first consider when a probability measure μ admits an exponential orthonormal basis on its L² space (μ is called spectral measures).This problem originates from the conjecture of Fuglede in 1974, and the discovery of Jorgensen and Pedersen that some fractal measures also admit exponential orthonormal bases, but some do not. It generates a lot of interest in understand- ing what kind of measures are spectral measures. For those measures failing to have exponential orthonormal bases, it is interesting to know whether such mea- sures still have Riesz bases and Fourier frames, which are generalized concepts of orthonormal bases with wide range of uses in Fourier analysis. / It is well-known that a measure has a unique decomposition as the discrete, singular and absolutely continuous parts. We first show that spectral measures must be of pure type. If the measure is absolutely continuous, we completely classify the class of densities of the measures with Fourier frames. This result has new applications to topics in applied harmonic analysis, like the Gabor analysis. For the discrete measures with finite number of atoms, we show that they all have Riesz bases. For the case of singular measure, which is the most difficult one, we show that there exist measures with Riesz bases but not orthonormal bases by considering convolution between spectral measures and discrete measures. We then investigate affine iterated function systems (IFSs), we show that if an IFS has measure disjoint condition and admits a Fourier frame, then the probability weights are all equal. Moreover, we also show that the Łaba-Wang conjecture is true if the self-similar measure is absolutely continuous. These results indicate that measures with Fourier frames must have certain kind of uniformity on the support. / In the second part of the thesis we study the zero sets of Fourier transform of self-affine tiles. One of the fundamental problems in self-affine tiles is to classify the digit sets so that the attractors form tiles. This problem can be turned to study the zeros of the Fourier transform via the Kenyon criterion. On the other hand, existence of exponential orthonormal bases requires us to know the zero sets of the Fourier transform. Self-affine tiles are translational tiles arising from IFSs with its Fourier transform written explicitly. It therefore serves as an ideal place to investigate the relation of tilings and spectral measures. / We carry out a detail study in the zero sets of the one-dimensional tiles using cyclotomic polynomials. From this we characterize the tile digit sets through some product of cyclotomic polynomials represented in terms of a blocking in a tree, which is a generalization of the product-form to higher order. We show that tile digit sets in any dimension are integer tiles. This result allows us to use the decomposition method of integer tiles by Coven and Meyerowitz to provide the explicit classification of the tile digit sets in terms of the higher order modulo product-forms when number of the digits is p[superscript α]q, p, q are primes. Since the zero sets are completely known, this provides us a new approach to study the existence of complete orthogonal exponentials in the self-affine tiles on R¹. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lai, Chun Kit. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 128-135). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.9 / Chapter 1.1 --- Background and Motivations --- p.9 / Chapter 1.2 --- Results on spectral measures --- p.13 / Chapter 1.3 --- Results on self-affine tiles --- p.16 / Chapter 2 --- Fourier Frames: Absolutely Continuous Measures --- p.21 / Chapter 2.1 --- Beurling densities --- p.22 / Chapter 2.2 --- Law of pure type --- p.28 / Chapter 2.3 --- Absolutely continuous F-spectral measures --- p.31 / Chapter 2.3.1 --- Proof by Beurling densities --- p.32 / Chapter 2.3.2 --- Proof by translational absolute continuity --- p.35 / Chapter 2.4 --- Applications to applied harmonic analysis --- p.40 / Chapter 2.5 --- Remarks and open questions --- p.42 / Chapter 3 --- Fourier Frames: Discrete and Singular Measures --- p.45 / Chapter 3.1 --- Discrete measures --- p.46 / Chapter 3.2 --- Convolutions with discrete measures --- p.50 / Chapter 3.3 --- Self-affine measures --- p.56 / Chapter 3.4 --- Iterated function systems on R¹ --- p.65 / Chapter 3.5 --- Concluding remarks --- p.70 / Chapter 4 --- Spectral structure of tile digit sets --- p.74 / Chapter 4.1 --- Preliminaries --- p.76 / Chapter 4.2 --- Modulo product-forms --- p.81 / Chapter 4.3 --- Higher order product-forms --- p.86 / Chapter 4.4 --- Φ-tree, blocking and kernel polynomials --- p.90 / Chapter 5 --- Classifications of tile digit sets --- p.101 / Chapter 5.1 --- Tile digit sets --- p.101 / Chapter 5.2 --- The p[superscript α]q[superscript β] integer tiles --- p.105 / Chapter 5.3 --- Tile digit sets for b = p[superscript α]q --- p.112 / Chapter 5.4 --- Self-similar measures: Absolute continuity --- p.122 / Chapter 5.5 --- Remarks --- p.126

這篇論文的目的是討論下述半線性橢圓方程的穩定解。 / -Δu = f (u) in Ω, / 這裡Ω是R{U+207F}中的光滑區域。對於非線性項f (u) = / [附圖]. / 我們得到了關於穩定解的Liouville-type結果。對於帶有更一般非線性項的半線性橢圓方程，在二到四維的情況下，我們得到一個關於穩定解的先驗估計。 / 最後，在維數很大的情形下，我們具體的給出一個關於以下雙調和方程的指數P的上界P，使得當P滿足 <1 P < Pc ‘下述雙調和方程不存在穩定解。 / Δ²u=u{U+1D56}, u>0 in R{U+207F} / The main aim of this thesis is to review recent results on stable solutions to the following semilinear elliptic equation / -Δu = f (u) in Ω, / where Ω ⊆ R{U+207F}.For the special case f (u) = / [With mathematic formula]. / For the general nonlinearity f in a bounded domain, we obtain a priori estimate for the stable solution when 2 ≤ n ≤ 4 / Finally, we give a explicit bound on the exponent for the nonexistence of stable solutions to the following biharmonic problem in large dimensions. / Δ²u=u{U+1D56}, u>0 in R{U+207F} / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yang, Wen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 66-69). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- On the Lane-Emden equation --- p.12 / Chapter 2.1 --- On stable solutions to the Lane-Emden equation --- p.12 / Chapter 2.2 --- On nite Morse index solutions to the Lane-Emden equation --- p.19 / Chapter 3 --- On general semilinear elliptic equation --- p.28 / Chapter 4 --- On the biharmonic equation --- p.44 / Chapter 4.1 --- The rst part of the proof of Theorem 1.6 --- p.44 / Chapter 4.2 --- The second part of the proof of Theorem 1.6 --- p.54 / Bibliography --- p.66

Leung, Cheung Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Introduction --- p.6 / Chapter 1 --- Preliminaries --- p.7 / Chapter 1.1 --- Locally compact groups and unitary representations --- p.7 / Chapter 1.2 --- Positive definite functions --- p.10 / Chapter 1.3 --- Affine isometric actions of groups --- p.23 / Chapter 1.4 --- Ultraproducts --- p.29 / Chapter 2 --- Amenability --- p.33 / Chapter 2.1 --- Reiter's property --- p.33 / Chapter 2.2 --- Fφlner's property --- p.41 / Chapter 3 --- Kazhdan's Property (T) --- p.43 / Chapter 3.1 --- Definition and basic properties --- p.43 / Chapter 3.2 --- Property (FH) --- p.51 / Chapter 3.3 --- Spectral criterion for Property (T) --- p.56 / Chapter 3.4 --- Property (T) for SL3(Z) --- p.60 / Chapter 3.5 --- Expanders --- p.72 / Approximation Properties of Groups --- p.5 / Chapter 4 --- Haagerup Property --- p.74 / Chapter 4.1 --- Equivalent formulations of Haagerup Property --- p.74 / Chapter 4.2 --- Trees and wall structures --- p.82 / Bibliography --- p.85