京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22823号 / 理博第4633号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 矢野 孝次, 教授 泉 正己, 教授 日野 正訓 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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This work deals with the identification of a remote computer by monitoring TCP timestamps of the tracked device. It is possible to determine computer's clock skew from these timestamps as the clock skew is unique for every device. We are able to differentiate devices even though they have changed location, network address or connection type. Passive data capturing ensures that the identification process is invisible to the fingerprinted computer. It is necessary that the network communication of fingerprinted computer is visible to the observing device. We are able to utilise only TCP traffic with timestamps enabled.

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Short span bridges are commonly used throughout the United States to span small waterways and highway overpasses. New technologies in the civil engineering industry have aided in the creation of many unique designs of these short span highway bridges in efforts to decrease construction cost, decrease maintenance costs, increase efficiency, increase constructability, and increase safety. Three innovative systems, the Integral Abutment Bridge, “Bridge-in-a-Backpack”, and the Folded Plate Girder bridge will be analyzed to study how the bridges behave under various types of loading. Detailed finite element models were created for integral abutment bridges of varying geometry. These models are used to study how the live load distribution transversely across the bridge is effected by varying geometric properties and varying modeling techniques. These models will also be used to determine live load distribution factors for the integral abutment bridges and compare them to current American Association of State Highway and Transportation Officials specifications. The “Bridge-in-a-Backpack” and the Folded Plate Girder bridges were each constructed with a variety of instruments to measure the bridge movements. Readings from these instruments are used to determine the bridge response under various loading conditions. Bridges were analyzed during their construction process, during static live load testing, and during long term seasonal changes. The results from these studies will aid in the refinement of these innovative designs.

In this paper we study a dynamical system given by a variant of the classic skew-shifts on the torus $S^1\times S^1$. Our map is defined based on $T(x,y) = (x+\omega,x+f(y))$, where $\omega$ is Diophatine, $f$ is an orientation-preserving circle diffeomorphism. We show that for our specific type of $f$, there exist 2 maps from the torus to itself whose graphs are $T$-invariant. Moreover, one of the graphs attracts (Lebesgue) almost every point in the torus. The results are robust under a small $C^1$ perturbation on the second coordinate. / I denna artikel studerar vi ett dynamiskt system som ges av en variant av de klassiska skevskiftningarna på torus $S^1\ gånger S^1$. Vår karta är definierad utifrån $T(x,y) = (x+\omega,x+f(y))$, där $\omega$ är diofatin, $f$ är en orienteringsbevarande cirkeldiffeomorfism. Vi visar att för vår specifika typ av $f$ finns det 2 kartor från torus till sig själv vars grafer är $T$-invarianta. Dessutom lockar en av graferna (Lebesgue) nästan varje punkt i torus. Resultaten är robusta under en liten $C^1$ störning på den andra koordinaten.

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Finite element analysis depends greatly upon a high-quality mesh to be able to provide reasonably accurate answers to engineering problems. Models that need to be analyzed using finite element analysis are becoming increasingly more complex, and correspondingly harder to mesh with good quality. Skew is one quality metric which can cause problems with finite element analyses. This thesis explains how skew is calculated, discusses two common sources of skew: multiply-linked surfaces with interval constraints, and biased edge meshes. Two methods of lessening skew in surface meshes are then presented: the skew control algorithm, and the curve morphing algorithm. These algorithms are discussed in detail, with representative graphics. Examples which demonstrate the skew which arises from the above-mentioned sources are presented. These models are then subjected to the algorithms discussed in the thesis, and a comparison of the skew measure for each example is presented. Finally, areas of possible future work are presented and the possible detrimental effects that the skew control algorithm can exert on the quality metrics of aspect ration and mesh size gradation are discussed.

Accounting for seismic forces and thermal expansion in bridge design requires an accurate passive force versus backwall deflection relationship. Current design codes make no allowances for skew effects on the development of the passive force. However, small-scale experimental results and available numerical models indicate that there is a significant reduction in peak passive force as skew angle increases for plane-strain cases. To further explore this issue large-scale field tests were conducted at skew angles of 0°, 15°, and 30° with unconfined backfill geometry. The abutment backwall was 11 feet (3.35-m) wide by 5.5 feet (1.68-m) high, and backfill material consisted of dense compacted sand. The peak passive force for the 15° and 30° tests was found to be 73% and 58%, respectively, of the peak passive force for the 0° test which is in good agreement with the small-scale laboratory tests and numerical model results. However, the small differences may suggest that backfill properties (e.g. geometry and density) may have some slight effect on the reduction in peak passive force with respect to skew angle. Longitudinal displacement of the backfill at the peak passive force was found to be approximately 3% of the backfill height for all field tests and is consistent with previously reported values for large-scale passive force-deflection tests, though skew angle may slightly reduce the deflection necessary to reach backfill failure. The backfill failure mechanism appears to transition from a log spiral type failure mechanism where Prandtl and Rankine failure zones develop at low skew angles, to a failure mechanism where a Prandtl failure zone does not develop as skew angle increases.

The Hochschild cohomology of an associative algebra records information about the deformations of that algebra, and hence the first step toward understanding its deformations is an examination of the Hochschild cohomology. In this dissertation, we use techniques from homological algebra, invariant theory, and combinatorics to analyze the Hochschild cohomology of skew group algebras arising from finite cyclic groups acting on polynomial rings over fields of arbitrary characteristic. These algebras are the natural semidirect product of the group ring with the polynomial ring. Many families of algebras arise as deformations of skew group algebras, such as symplectic reflection algebras and rational Cherednik algebras. We give an explicit description of the Hochschild cohomology governing graded deformations of skew group algebras for cyclic groups acting on polynomial rings. For skew group algebras, a description of the Hochschild cohomology is known in the nonmodular setting (i.e., when the characteristic of the field and the order of the group are coprime). However, in the modular setting (i.e., when the characteristic of the field divides the order of the group), much less is known, as techniques commonly used in the nonmodular setting are not available.