High-cycle thermal fatigue arising from turbulent mixing of non-isothermal flows is a key issue associated with the life management and extension of nuclear power plants. The induced thermal loads and damage are not fully understood yet. With the aim of acquiring extensive data sets for the validation of codes modeling thermal mixing at reactor conditions, thermocouples recorded temperature time series at the inner surface of a vertical annular volume where turbulent mixing occurred. There, a stream at either 333 K or 423 K flowed upwards and mixed with two streams at 549 K. Pressure was set at 72E5 Pa. The annular volume was formed between two coaxial stainless-steel tubes. Since the thermocouples could only cover limited areas of the mixing region, the inner tube to which they were soldered was lifted, lowered, and rotated around its axis, to extend the measurement region both axially and azimuthally. Trends, which stemmed from the variation of the experimental boundary conditions over time, were subtracted from the inner-surface temperature time series collected. An estimator assessing intensity and inhomogeneity of the mixing process in the annulus was also computed. In addition, a frequency analysis of the detrended inner-surface temperature time series was performed. In the cases examined, frequencies between 0.03 Hz and 0.10 Hz were detected in the subregion where mixing inhomogeneity peaked. The uncertainty affecting such measurements was then estimated. Furthermore, a preliminary assessment of the radial heat flux at the inner surface was conducted. / <p>QC 20161116</p>

In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field.

Since their discovery in the early 1950's, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in Rn, but very little is known about the l2(Z) case or the l2(Zd) case. We establish some basic Gabor frame theory for l2(Z) and then generalize to the l2(Zd) case.

<p>We derive new combinatorail formulas for vector-valued weight functions for the evolution modules over the Yangians Y (gln). We obtain them using the Nested Algebraic Bethe ansatz method.</p> <p>We also describe the asymptotic behavior of the radial solutions of the negative tt∗ equation via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method.</p>

yes / The orthocomplemented modular lattice of subspaces L[H(d)] , of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)] ). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H1,H2) , which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H1),P(H2) , to the subspaces H 1, H 2. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.

No / Extensive research has been performed to investigate effective techniques, including advanced sensors and new monitoring methods, to develop reliable condition monitoring systems for industrial applications. One promising approach to develop effective monitoring methods is the application of time-frequency analysis techniques to extract the crucial characteristics of the sensor signals. This paper investigates the effectiveness of a new time-frequency analysis method based on Empirical Model Decomposition and Hilbert transform for analyzing the nonstationary cutting force signal of the machining process. The advantage of EMD is its ability to adaptively decompose an arbitrary complicated time series into a set of components, called intrinsic mode functions (IMFs), which has particular physical meaning. By decomposing the time series into IMFs, it is flexible to perform the Hilbert transform to calculate the instantaneous frequencies and to generate effective time-frequency distributions called Hilbert spectra. Two effective approaches have been proposed in this paper for the effective detection of tool breakage. One approach is to identify the tool breakage in the Hilbert spectrum, and the other is to detect the tool breakage by means of the energies of the characteristic IMFs associated with characteristic frequencies of the milling process. The effectiveness of the proposed methods has been demonstrated by considerable experimental results. Experimental results show that (1) the relative significance of the energies associated with the characteristic frequencies of milling process in the Hilbert spectra indicates effectively the occurrence of tool breakage; (2) the IMFs are able to adaptively separate the characteristic frequencies. When tool breakage occurs the energies of the associated characteristic IMFs change in opposite directions, which is different from the effect of changes of the cutting conditions e.g. the depth of cut and spindle speed. Consequently, the proposed approach is not only able to effectively capture the significant information reflecting the tool condition, but also reduces the sensitivity to the effect of various uncertainties, and thus has good potential for industrial applications.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24387号 / 理博第4886号 / 新制||理||1699(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)教授 森脇 淳, 教授 雪江 明彦, 教授 吉川 謙一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Polyominoes are two-dimensional objects obtained by joining edge by edge squares of same size. Originally, polyominoes appeared in mathematical recreations, but it turned out that they have applications in various fields, for example, theoretical physics and bio-informatics. Among the most popular topics in combinatorics related to polyominoes one finds enumerating polyominoes of given size, including the asymptotic growth of the numbers of polyominoes, tiling problems, and reconstruction of polyominoes. Recently Qureshi introduced a binomial ideal induced by the geometry of a given polyomino, called polyomino ideal, and its related algebra. From that moment different authors studied algebraic properties and invariants related to this ideal, such as primality, Gröbner bases, Gorensteinnes and Castelnuovo-Mumford regularity. In this thesis, we provide an overview on the results that we obtained about polyomino ideals and its related algebra. In the first part of the thesis, we discuss questions about the primality and the Gröbner bases of the polyomino ideal. In the second part of the thesis, we talk over the Castelnuovo-Mumford regularity, Hilbert series, and Gorensteinnes of the polyomino ideal and its coordinate ring.

Mutually unbiased bases is an important topic in the recent quantum system researches. Although there is much work in this area, many problems related to mutually unbiased bases are still open. For example, constructing a complete set of mutually unbiased bases in the Hilbert spaces with composite dimensions has not been achieved yet. This thesis defines a weaker concept than mutually unbiased bases in the Hilbert spaces with composite dimensions. We call this concept, weak mutually unbiased bases. There is a duality between such bases and the geometry of the phase space Zd × Zd, where d is the phase space dimension. To show this duality we study the properties of lines through the origin in Zd × Zd, then we explain the correspondence between the properties of these lines and the properties of the weak mutually unbiased bases. We give an explicit construction of a complete set of weak mutually unbiased bases in the Hilbert space Hd, where d is odd and d = p1p2; p1, p2 are prime numbers. We apply the concept of weak mutually unbiased bases in the context of quantum tomography and quantum cryptography. / Egyptian government.

Research has shown that a frame for an n-dimensional real Hilbert space offers phase retrieval if and only if it has the complement property. There is a geometric characterization of general frames, the Han-Larson-Naimark Dilation Theorem, which gives us the necessary and sufficient conditions required to dilate a frame for an n-dimensional Hilbert space to a frame for a Hilbert space of higher dimension k. However, a frame having the complement property in an n-dimensional real Hilbert space does not ensure that its dilation will offer phase retrieval. In this thesis, we will explore and provide what necessary and sufficient conditions must be satisfied to dilate a phase retrieval frame for an n-dimensional real Hilbert space to a phase retrieval frame for a k-dimensional real Hilbert.