2,763 research outputs found

    [[alternative]]Liouville Theory(1850-1990)

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    [[abstract]]本文主要從歷史的角度來看Liouville定理。所謂Liouville定理是指 n3n\geq 3維的保角變換,其實就是Mobius變換。 變換x=(x1,x2,...,xn)y=(y1,y2,...,yn)x=(x^1,x^2,...,x^n) \rightarrow y=(y^1,y^2,...,y^n) 稱為保角是指dy=λ(x)dx|dy|=\lambda(x)|dx|,其中λ0\lambda \geq 0。 令dx=(dx1,dx2,...,dxn)dx=(dx^1,dx^2,...,dx^n)dy=(dy1,dy2,...,dyn) dy=(dy^1,dy^2,...,dy^n)代入,有 (dy1)2+(dy2)2+...+(dyn)2=λ2(x)[(dx1)2+(dx2)2+...+(dxn)2](dy^1)^2+(dy^2)^2+...+(dy^n)^2=\lambda^2(x)[(dx^1)^2+(dx^2)^2+...+(dx^n)^2]AL(n,n)A\in L(\Re^n,\Re^n)使得:(dy1,dy2,...,dyn)=A(dx1,dx2,...,dxn)(dy^1,dy^2,...,dy^n)=A(dx^1,dx^2,...,dx^n),則 AA=Inλ2(x)A^*A=I_n \lambda^2(x)det(A)=λ(x)0det(A)=\lambda(x) \geq 0。 Liouville定理最先是Liouville於1850發表於法文期刊Application de l\'analyse[L]上, 他考慮三維Euclid空間變換(x,y,z)(ζ,η,ξ)(x,y,z) \rightarrow (\zeta,\eta,\xi),若變換滿足下列方程: dζ2+dη2+dξ2=λ2(dx2+dy2+dz2)d\zeta^2+d\eta^2+d\xi^2 = \lambda^2(dx^2+dy^2+dz^2) 其中λ=λ(x,y,z)0\lambda=\lambda(x,y,z) \geq 0。Liouville證明其實λ\lambda只會滿足下列情況: (1)\lambda=\mbox{常數;}(2)\lambda=\frac{c}{x^2+y^2+z^2} \mbox{。} \begin{flushleft} 原先預想λ\lambda可能很複雜,但是最後總能簡化成上面非常簡單的型式。由此可解得滿足該變換條件只有是Mobius變換。 \end{flushleft} 在Liouville之後,許多人嘗試放寬限制,使得用最少的條件,我們照樣可以得到同樣的好結果。 到目前為止,所得到的最好結果是Gehring[G2]於1961年所給出的,之後的只作稍微的修正如[R3][Bo]。 本文中給出最近1990年[AVV]用擬保角得到的最新知識,給出較為簡潔的證明。

    Polymeric micelles and the Dy-166/Ho-166 generator: A study of the loading mechanism of Dy/Dy-166 and Ho-166 into PCL-b-PEO polymeric micelles for imaging and cancer treatment

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    A radioisotope used in radionuclide therapy is Holmium-166 (Ho-166). The treatment effectiveness of Ho-166 could be improved by the use of a so called in vivo Dysprosium-166(Dy-166)/Ho-166 generator. The application of this generator is hindered by an effect called internal conversion (IC). This affect can arise after the decay of Dy-166 to Ho-166, which can cause separation of Ho-166 from its carrier.Polymeric micelles might form a solution in the application of the Dy-166/Ho-166 generator in radionuclide therapy. The main goal of this thesis was to investigate and understand the loading mechanism of metallic species and polymeric micelles with a focus on the loading of Dy/Dy-166 and Ho-166. It was found that it was not effective to load metallic species (Dy/Dy-166) as free ions or as solid precipitates. Loading metallic species as aqueous hydroxides showed to be crucial for achieving a good loading and high stability. The second goal was to study if polymeric micelles were able to retain Ho-166 inside their core under the effects of internal conversion. No additional losses of Ho-166 were found when Dy/Dy-166 and Ho-166 were loaded into the micelles. It was concluded that the PCL-PEO micelles prevented the loss of Ho-166 under internal conversion effects.Applied Science

    Anisotropic magnetization and resistivity of single crystalline RNi1-xBi2 +/- y (R = La-Nd, Sm, Gd-Dy)

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    We present a detailed study of RNi1−xBi2±y (R = La–Nd, Sm, Gd–Dy) single crystals by measurements of stoichiometry and temperature dependent magnetic susceptibility, magnetization, and electrical resistivity. This series forms with partial Ni occupancy, 0.72 ⩽ (1−x) ⩽ 0.84, as well as a variable Bi occupancy, 1.76 ⩽ (2±y) ⩽ 2.14. For R = Ce–Nd, Gd–Dy, the RNi1−xBi2±y compounds show local-moment like behavior and order antiferromagnetically at low temperatures. Determination of anisotropies as well as antiferromagnetic ordering temperatures for RNi1−xBi2±y (R = Ce–Nd, Sm, Gd–Dy) have been made. Crystalline samples from this family exhibit minority, second phase superconductivity at low temperatures, which can be associated with Ni–Bi and Bi contamination. No evidence of bulk superconductivity has been observed.This is a manuscript of an article published as Lin, Xiao, Warren E. Straszheim, Sergey L. Bud’ko, and Paul C. Canfield. "Anisotropic magnetization and resistivity of single crystalline RNi1− xBi2±y (R= La–Nd, Sm, Gd–Dy)." Journal of Alloys and Compounds 554 (2013): 304-311. DOI: 10.1016/j.jallcom.2012.11.138. Posted with permission.</p

    [[alternative]]The Study of Improving Chinese Input Methods and The Implementation of NTNU-Master Input Method

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    [[abstract]]Chinese Character Input on computers is the basic ability in the east, especially in Taiwan, Hong Kong and China. If someone can input Chinese characters quickly, then he can improve his ability in using computers to do many things. In this study, we stand on some famous input methods, like ChangJie, and other input methods based on ChangJie’s method. We try to develop some techniques, such as rearranging the ChangJie alphabets, encoding the characters with 3 codes, reducing the numbers of strokes using space bar, etc. We compare our results with ChangJie and Dy-Sin-Cang-Jie by statistical techniques in typing lots of articles. We named this method as NTNU-Master input method. The basic concept was originally designed by Dr. Shun-Shii Lin. This study is the first one to implement the system and analyze it. After some experiments, we get some encouraging results. Successfully, we are able to reduce the average number of strokes for typing Chinese characters.

    beta-delayed proton decays and spin assignments for Tb-140, Dy-141 and Dy-143

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    The proton-rich isotopes Tb-140 and Dy-141 were produced via the fusion evaporation reaction Ca-40+ Cd-106. Their beta-delayed proton decays were studied by p-gamma coincidence in combination with a He-jet tape transport system, and half-lives, proton energy spectra, gamma-transitions following the proton emission, as well as beta-delayed proton branching ratios to the low-lying states in the grand-daughter nuclei were determined. Comparing the experimental data with statistical model calculations, the ground-state spins of Tb-140 and Dy-141 were found to be consistent with 7 and 9/2, respectively. The configuration-constrained nuclear potential energy surfaces (NPES) of Tb-140 and Dy-141 were calculated using the Woods-Saxon-Strutinsky method, which suggest the ground-state spins and parities of Tb-140 and Dy-141 to be 7(+) and 9/2(-), respectively. In addition, the configuration-constrained NPES of Dy-143 were calculated, which predict a 1/2(+) ground state and a 11/2(-) isomer with excitation energy of 198 keV. These findings are consistent with our previous experimental data on Dy-143 reported in Eur. Phys. J. A 16, 347 (2003).Physics, NuclearPhysics, Particles &amp; FieldsSCI(E)3ARTICLE137-402

    Study on W-Mo-Dy Multi-Elements Diffusion Layer

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    W-Mo-Dy and W-Mo permeation were carried out on the 20 steel by plasma surface metallurgy technology. The microstructure, cross-section morphology ,distribution of alloy element and phase structure of diffusion layer were tested and observed. The results showed that: thickness of alloy layer was 128μm, 108μm, there is a dividing line between the diffusion layer and the substrate, indicating that the permeation process follow with reaction-diffusion phenomena; Compared with W-Mo diffusion layer,the grain size of W-Mo-Dy diffusion layer were fine grain;The basic phase composition of W-Mo-Dy diffusion layer were solid solution of (W, Mo, Dy) in Fe, Dy2O3and a small quantity of Dy Fe10Mo2; The basic phase composition of W-Mo diffusion layer was solid solution of (W, Mo) in Fe.The surface alloy contents of W-Mo-Dy diffusion layer were 4.81%, 9.99%, 4.4% (wt%), which of W-Mo diffusion layer were 3.04%, 7.68% (wt%);Heavy rare earth (Dy)has a significant penetration and improved the organizations of diffusion layer.</jats:p

    Linker molecules between laminins and dystroglycan ameliorate laminin-alpha2-deficient muscular dystrophy at all disease stages

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    Mutations in laminin-alpha2 cause a severe congenital muscular dystrophy, called MDC1A. The two main receptors that interact with laminin-alpha2 are dystroglycan and alpha7beta1 integrin. We have previously shown in mouse models for MDC1A that muscle-specific overexpression of a miniaturized form of agrin (mini-agrin), which binds to dystroglycan but not to alpha7beta1 integrin, substantially ameliorates the disease (Moll, J., P. Barzaghi, S. Lin, G. Bezakova, H. Lochmuller, E. Engvall, U. Muller, and M.A. Ruegg. 2001. Nature. 413:302-307; Bentzinger, C.F., P. Barzaghi, S. Lin, and M.A. Ruegg. 2005. Matrix Biol. 24:326-332.). Now we show that late-onset expression of mini-agrin still prolongs life span and improves overall health, although not to the same extent as early expression. Furthermore, a chimeric protein containing the dystroglycan-binding domain of perlecan has the same activities as mini-agrin in ameliorating the disease. Finally, expression of full-length agrin also slows down the disease. These experiments are conceptual proof that linking the basement membrane to dystroglycan by specifically designed molecules or by endogenous ligands, could be a means to counteract MDC1A at a progressed stage of the disease, and thus opens new possibilities for the development of treatment options for this muscular dystrophy
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