Nonlinearizability of the Iwasawa Poisson Lie structure

We show that Lu and Weinstein's Iwasawa Poisson Lie structure on a simple compact Lie group K is not linearizable when K is not SU(2).Chercheur qualifié au FNRS. Research partially supported by EEC contract SC1-0105-C.     

Wigner rotations and Iwasawa decompositions in polarization optics

Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.     

Iwasawa factorization of the pseudo-orthogonal groupSO(5, 1) and its corresponding Lie algebraso(5, 1)

We carry out a structural analysis of the Lie group SO(5, 1) by obtaining its Iwasawa factorization. The Iwasawa factorization at the Lie algebra level is also obtained.     

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian. We consider symmetric scalar manifolds in ��‐extended supergravity in various space‐time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits‐Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space‐time dimension of the theory. These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions.     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．     

On the predictability of the positions of the convergence zones in the ocean

The disagreement between the experimental and calculated positions of the first convergence zone are known from many publications. The most probable cause for such a disagreement, namely, the incorrect specification of the input data for the calculations, is considered. The lack of simultaneity between the hydrological surveys of the region and the acoustic experiments is emphasized. The experimental data obtained by the author in five ocean regions are presented. These data characterize the diurnal variability of the distance from the source to the nearest boundary of the convergence zone. The relations proposed by different researchers for calculating the sound speed from the temperature, salinity, and hydrostatic pressure are analyzed. It is shown that these relations lead to a substantial difference in the estimated depth dependence of the hydrostatic gradient of the sound speed. The position of the first convergence zone is calculated for the propagation conditions determined by vertical temperature and salinity profiles with the subsequent recalculation of these profiles into sound speed profiles by using eight different formulas known from the literature. It is shown that different formulas lead to different values of the distance to the first zone; this difference is substantially greater than that between the calculations and experiment. The necessity of improving the recalculation relations in view of the experimental data on sound propagation in natural oceanic waveguides, including the data on the actual positions of the convergence zones, is emphasized.     

Dependence of the Intensity of the Spectral Lines and the Composition of the Sample and the Plasma Parameters of the Unipolar Arc

The investigation was made of the dependence of the intensity of Tl, Ga, Mo, Mg, Mn, Sn, Bi, Ni, Zn, Pt and Au spectral lines and the plasma parameters (temperature T, electron concentration n_e, degree of 6 ionnization α) from concentration of lithium additive.     

Extracting the wavefunction of the LSP at the LHC

We consider associated production of squarks and gluinos with the lightest supersymmetric particle (LSP), or states nearly degenerate in mass with it. Though sub-dominant to pair production of color SU(3)-charged superpartners, these processes are directly sensitive to the wavefunction composition of the lightest neutralinos. Exploiting event-shape variables - including some introduced here for the first time - we are able to identify the composition of the LSP by selecting events involving a single high-pT jet recoiling against missing transverse energy. We illustrate the proposed technique on a set of benchmark cases and propose methods for applying these results in more realistic experimental environments.     

On the calculation of the bremsstrahlung in the region of the plasma frequency

On the basis of the classical theory of radiation produced in incomplete Coulomb interaction, a formula is derived for the coefficient of the bremsstrahlung of fully ionized plasma. In the region of rectilinear approximation a comparison is made with the results of the quantum formula derived from the Born approximation. Furthermore, the influence of dispersion upon the emission coefficient is taken into account; some relations for the region of dispersion are given.     

On the Question of the Source of the Apokamp

Technical Physics - The object of this work is the apokamp—a new type of plasma jet, which is formed from a bright offshoot emerging at the bending point of a channel of a high-voltage...     

Set the controls for the heart of the Sun

In this paper we describe experiments conducted with high-power lasers that are attempting to replicate, for a very short time and in miniature, conditions found in the Sun. Experiments to date have reached conditions in the outer part of the Sun. To reach the Sun's centre requires compression of material to very much greater than solid density and heating to over ten million degrees. To achieve this, a new class of experiments and a new generation of high-power lasers are required.     

From the Solution of the Tsarev System to the Solution of the Whitham Equations

We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries.     

Contributions of the cornea and the lens to the aberrations of the human eye

The relative contributions of optical aberrations of the cornea and the crystalline lens to the final image quality of the human eye were studied. The aberrations of the entire eye were obtained from pairs of double-pass retinal images, and the aberrations of the cornea were obtained from videokeratographic data. Third-order spherical aberration and coma were significantly larger for the cornea than for the complete eye, indicating a significant role of the lens in compensating for corneal aberrations. In a second experiment retinal images were recorded in an eye before and after we neutralized the aberrations of the cornea by having the subjects wear swimming goggles filled with saline water, providing a direct estimate of the optical performance of the crystalline lens.     

干涉仪系统传递函数测量及影响因素的分析

波前功率谱密度(PSD)被用于评价惯性约束聚变(ICF)激光驱动器光学元件中频段的波前误差。干涉仪对PSD较高空间频率分量的测量存在失真效应,可通过干涉仪系统传递函数(STF)的检测标定来获得真实的波前PSD分布。采用台阶板位相比较法测得大口径菲索相移干涉仪检测系统在透射和反射检测情形下的传递函数。对传递函数测试算法进行了比较分析,明确了干涉仪系统zoom倍率的改变等因素对传递函数测量的影响,为波前PSD的准确检测奠定了基础。