Iwasawa Theory of Quadratic Twists of X_0(49)

The field K=Q((-7)(1/2)) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X_0(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X_0(49)by the quadratic extension K(M1/2)/K, where M is any square free element of O with M ≡1 mod 4 and(M, 7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F_∞ = K(E_(p∞)),where E_(p∞) denotes the group of p~∞-division points on E. Moreover, writing B for the twist of X_0(49)by K((-7)(1/4))/K, our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z_2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper.     

Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

Periodic solutions of Wick-type stochastic Korteweg–de Vries equations

Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform is implemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.     

Quasar polarization with ultralight (pseudo-)scalars

Recently, it was shown that the absence of circular polarization of visible light from quasars severely constrains the interpretation of axion-like particles (ALPs) as a solution for the generation of linear polarization. Furthermore, the new observation of linear polarization in radio wavelength from quasars, similar to the earlier observation performed in the optical bands, makes the ALPs scenario inconsistent with at least one of the two observations. In this study, we extend this scenario by including more scalars. We find that the effects from scalar and pseudoscalar neutralize each other, thereby suppressing the circular polarization, while preserving consistent linear polarization, as observed in both the visible and radio wave bands.     

The Structure of the Solution Set for Periodic Oscillations in a Suspension Bridge Model

Numerical results are reported for the computation of periodicsolution paths for a suspension bridge model represented bythe equation. u_n + EIu_xxxx + u_t, + Ku⁺ = W(^x) + sin x sin µt. with hinged-end boundary conditions, as the forcing amplitude and frequency µ are varied. The term Ku⁺ models the factthat there is restoring force due to the cables only when theyare being stretched. It is found that an S-shaped curve is obtainedwhen the displacement amplitudes are plotted against the forcingamplitudes for some frequency regimes. As a two-parameter problem,it appears that the solution set resembles a cusp-like surfacewith the singular point near linear resonance. While the effectof strengthening the cable (i.e. increasing K) will enhancethe occurrence of the multiple solutions, the effect of increasingthe damping coefficient gives the opposite effect.     

Rapid Preparation of Monolithic Columns for Capillary Electrochromatography Separation

Sol-gel technology can provide a versatile approach to the synthesis of organic polymers and organic-inorganic hybrid materials applied in HPLC, micro-HPLC and capillary electrochromatography (CEC)1. It can take place under extraordinarily mild thermal co…     

EXPERIMENTAL STUDY ON THE VORTEX-INDUCED VIBRATION OF TOWED PIPES

We experimentally attempted to understand the vibration characteristics of a flexible pipe excited by vortex shedding. This has been extensively studied in the previous decades (for example, see Sarpkaya 1979 Journal of Applied Mechanics46, 241-258; Price et al. 1989 Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague-March 19 -23, 447-454; Yoerger et al. 1991 Journal of Offshore Mechanics and Arctic Engineering, Transaction of Engineers113, 117-127; Grosenbaugh et al. 1991Journal of Offshore Mechanics and Arctic Engineering, Transaction of Engineers113 , 199-204; Brika and Laneville 1992 Journal of Fluid Mechanics250, 481-508; Chakrabarti et al. 1993 Ocean Engineering20, 135-162; Jong 1983 Ph.D. Dissertation, Department of Ocean Engineering, M. I. T.; Kimet al. 1986 Journal of Energy Resources Technology, Transactions of American Society of Mechanical Engineers108, 77-83). However, there are still areas that need more study. One of them is the relation between spatial characteristics of a flow-induced vibrating pipe, such as its length, the distribution of wave number, and frequency responses. A non-linear mechanism between the responses of in-line and cross-flow directions is also an area of interest, if the pipe is relatively long so that structural modal density is reasonably high. In order to investigate such areas, two kinds of instrumented pipe were designed. The instrumented pipes, of which the lengths are equally 6 m, are wound with rubber and silicon tape in different ways, having different vortex-shedding conditions. One has uniform cross-section of diameter of 26·7 mm, and the other has equally spaced four sub-sections, which are composed of different diameters of 75·9, 61·1, 45·6 and 26·7 mm. Both pipes are towed in a water tank (200 m×16 m×7 m) so that they experienced different vortex-shedding excitations. Various measures were obtained from the towing experiment, including frequency responses, the time-domain tracing of in-line and cross-flow responses, and Wigner-Ville distributions. The experimental results analyzed by using these measures exhibit several valuable features. One of them is that the natural frequencies and their corresponding strain mode shapes dominate the strain response of the uniform pipe. However for those of non-uniform pipe, the responses are more likely local and many modes participate in it.     

一种支链含有螺吡喃和查尔酮双光功能基团的复合高分子材料光致变色性能研究

合成了两种支链含有光致变色的螺吡喃结构的复合高分子材料, 观察了光激发下材料的光致变色动力学过程. 一种高分子材料为丙烯酸甲脂(MMA)和丙烯酸-螺吡喃单体(MMA-Spiropyran)的共聚物, 另一种是丙烯酸-查尔酮单体(MMA-Chalcone)和丙烯酸-螺吡喃单体的共聚物. 利用紫外-可见光谱仪对合成的复合高分子材料的光敏性能进行了考察, 从研究中发现, 材料的光致聚合过程对其光致变色显色体稳定性的影响.     

FLOW CHARACTERISTICS AROUND AN INCLINED ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an inclined elliptic cylinder located near a flat plate were investigated experimentally. The axis ratio of the elliptic cylinder was AR=2. The pressure distributions along the surface of the cylinder and the flat plate were measured by varying the angle of attack of the elliptic cylinder. The velocity profiles behind the cylinder were measured using hot-wire anemometry. When the angle of attack varies, the peak pressure location on the windward cylinder surface moves towards the rear edge of the cylinder, while that on the leeward surface moves towards the front edge of the cylinder. The vortex-shedding frequency also gradually decreases, defining a critical angle of attack for each gap ratio. The location of the minimum pressure on the flat plate surface moves downstream for positive angles of attack, while it moves upstream for negative angles of attack. Negative angles of attack cause a greater disturbance in the boundary layer near the wall compared to positive angles of attack. This shows that the separated wall shear layer from the boundary layer and the lower shear layer of the cylinder wake are strongly merged compared to other cases.     

Steady-state solution for electroplating

At steady state, electroplating processes are governed by thedimensionless equations where d_i, e_i, and u_i arerespectively the diffusion coefficient, charge, and concentrationof the ith species. The extra electroneutrality condition will determine the electric potential. This system of nonlinear differential equations is subjectto the nonlinear boundary conditions modelling the actual electrodekinetics. The authors prove the existence of the solution andconstruct a computational algorithm. Numerical experiments areperformed on practical data.