Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type. II. The <Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">N</Emphasis>−1</Subscript> Case: First Steps

This is the second part of a series of papers concerning Hilbert-Schmidt integral operators acting on the Hilbert spaces associated with elliptic Calogero-Moser type Hamiltonians. We present an explicit diagonalization of special Hilbert-Schmidt operators arising in the free A _N−1 case, and a spectral structure analysis of the commuting family of Hilbert-Schmidt operators associated with the general A _N−1 case.     

Discussion notes on “Wettability conundrum: Discrepancies of soft contact lens performance <Emphasis Type="Italic">in vitro</Emphasis> and <Emphasis Type="Italic">in vivo</Emphasis>”, by T.F. Svitova &; M.C. Lin

Comments are provided for [1].     

Structural and magnetic properties of Fe<Subscript>7−<Emphasis Type="Italic">n</Emphasis></Subscript>Pt<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> with <Emphasis Type="Italic">n</Emphasis> = 0, 1, 2, . . . 7, bimetallic clusters

An exhaustive study of the structural and magnetic properties of Fe_7?n Pt _n with n = 0, 1, 2, …7, bimetallic clusters is presented. Based on ab initio density functional theory that includes spin-orbit coupling (SOC) and graph theory, the ground state geometry, the local chemical order, and the orbital and spin magnetic moments are calculated. We show how the systems evolves from the 3-d Fe to the quasi-planar Pt clusters. These calculations show that SOC are necessary to describe correctly the composition dependence of the binding energy of these nanoalloys. We observe that the ground state geometries on the Fe rich side resemble the fcc structure adopted by bulk samples. Furthermore, we observe how the spin and orbital magnetic moments depend on the chemical concentration and chemical order. Based on these results, we estimated the magnetic anisotropy energy and found that the largest values correspond to some of the most symmetric structures, Fe₅Pt₂ and FePt₆. To determine the degree of non-collinearity, we define an index that shows that in FePt₆ the total magnetic moments, on each atom, are the less collinear.     

Reply to: “Comment on: ‘Exposed-key weakness of αη’ [Phys. Lett. A 370 (2007) 131]” [Phys. Lett. A 372 (2008) 7091]

We present simulations countering the claims in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091] that the approximation given in [C. Ahn, K. Birnbaum, Phys. Lett. A 370 (2007) 131, quant-ph/0612058] for the eavesdropper's entropy on the encrypted key cannot be valid, and additionally discuss ways in which our views on security requirements differ from those given in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091].     

Reply to the Comment by F. Kožíšek et al. on “Evidence for the existence of stable-water-clusters at room temperature and normal pressure” [Phys. Lett. A 373 (2009) 3872]

After discussing various points raised in a recent comment by F. Ko?íšek et al., who claim that our Letter “Evidence for the existence of stable-water-clusters at room temperature and normal pressure” (Phys. Lett. A 373 (2009) 3872) is unclear and the evidence is scant, we conclude that their arguments are wrong.     

Superparamagnetic properties of <Emphasis Type="Italic">γ</Emphasis>-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> particles: Mössbauer spectroscopy and d.c. magnetic measurements

Particles of Fe oxide were prepared by chemical coprecipitation and their sizes were shown by TEM and confirmed by XRD to be in the range of 5 nm. The Mössbauer spectra at 120K clearly indicated the absence of magnetite and presence of the maghemite (γ-Fe₂O₃) phase.We studied the transition of the system to superparamagnetic behaviour, which strongly depends on the relevant time window amounting to ～ 10^?7 s for Mössbauer spectroscopy of ⁵⁷Fe and units of seconds for d.c. magnetic measurements. From the temperature dependences of magnetic moments of zero-field-cooled (ZFC)) and field-cooled (FC) samples, the distributions of blocking temperatures were determined. The comparison of the transition temperatures derived from these two types of measurements gave an independent estimate for the pre-exponential factor and the energy barrier and thus magnetocrystalline anisotropy in an order-of-magnitude agreement with the published data for bulk γ-Fe₂O₃.     

On the Non-Lorentz-Invariance of <Emphasis Type="SmallCaps">M.W. Evans’</Emphasis><Emphasis Type="Italic">O</Emphasis>(3)-Symmetry Law

In 1992 M.W. Evans proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. Evans has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published a proof of the Lorentz invariance of O(3) symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant.     

从J.H. Schön的科学不端行为探讨防范对策

20世纪末和21世纪初世界科学行为的上空出现了三朵乌云,第一朵是科学前沿的原创活动中出现了实验数据的作假和虚构现象,严格地说出现了行为严重的科学不端事件;第二朵是一般科技研究人员中产生了为数不算少的范围不同的抄袭甚至剽窃的严重问题;第三朵是在研究生的习作和学位论文中出现了将互联网上的信息、资料和国内外披露或发表的论文片断予以摘引、拼凑或连接而构成"论文"的屡见不鲜的情况.这些利用信息技术和设施发展不平衡的背景,以授其奸的科学不端行为,严重违犯了国际科学界长期形成的周知科学准则和科学精神,引起了舆论的普遍贬斥和指责.文章仅就普世关注的、关系到近年来世界科学发展和影响最大的事件--舍恩(J. Hendrick Schn)博士的不端科学行为,作为一个案例予以分析."麻雀虽小,五脏俱全",通过这个分析可以从中得出一些对科学不端行为的防范和决策等有益的启示.     

The Boundary Control Approach to the Titchmarsh-Weyl <Emphasis Type="Italic">m</Emphasis>–Function. I. The Response Operator and the <Emphasis Type="Italic">A</Emphasis>–Amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? _x ²  + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.     

On the Lippmann-Schwinger equation in Liouville space. Π&#x030A; subdynamics

We study some aspects of the Lippmann-Schwinger equation in Liouville space: The relation between the Møller approach and Π&#x030A; subdynamics, the obtention of H-invariants from the corresponding H₀-invariants and the derivation of kinetic equations.     

Reply to: “Comment on: ‘Spherical Kadomtsev–Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation’ ” [Phys. Lett. A 361 (2007) 520]

Dusty plasmas exist almost everywhere in the Universe and relevant nonlinear studies are encouragingly going to non-planar geometry. On our recent construction of a spherical Kadomtsev–Petviashvili model for the dust-ion-acoustic waves in a cosmic dusty plasma [B. Tian, Y.-T. Gao, Phys. Lett. A 340 (2005) 243], Hong [W.P. Hong, Phys. Lett. A (2006), doi:10.1016/j.physleta.2006.11.021, in press] comments that certain interesting coordinate transformations exist, with presentation of a transformed equation (TE) and nebulon solutions. In this Reply, we point out that the TE is valuable to the studies on both cosmic plasmas and applied mathematics. We obtain an auto-Bäcklund transformation on the TE and more general nebulons. With series of pictures, we discuss nebulon structures out of the TE, and address that there are cosmic plasma systems for which the TE is valid. We remove a constraint set in that Comment so that the TE can be useful for the Saturn-F-ring-typed dusty plasmas as well.     

Review of AdS/CFT Integrability,Chapter II.2: Quantum Strings in AdS<Subscript>5</Subscript> × S<Superscript>5</Superscript>

We review the semiclassical analysis of strings in AdS₅ × S⁵ with a focus on the relationship to the underlying integrable structures. We discuss the perturbative calculation of energies for strings with large charges, using the folded string spinning in AdS₃ ? AdS₅ as our main example. Furthermore, we review the perturbative light-cone quantisation of the string theory and the calculation of the worldsheet S-matrix.     

Tendencies toward nematic order in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+δ</Subscript>: Uniform distortion <Emphasis Type="Italic">vs.</Emphasis> incipient charge stripes

Recent neutron scattering and transport data obtained on underdoped YBa₂Cu₃O_6+δ, with strong signatures of rotation symmetry breaking at low temperatures, point toward electron-nematic order in the charge sector. Such order may originate from a uniform distortion with d-wave symmetry or as a precursor of a uni-directional stripe phase. Here, we discuss whether the neutron scattering data can be linked to incipient charge stripes. We employ and extend a phenomenological model for collective spin and charge fluctuations and analyze the resulting spin excitation spectrum under the influence of lattice anisotropies. Our results show that the experimentally observed temperature-dependent magnetic incommensurability is compatible with a scenario of incipient stripes, the temperature dependence being due to the temperature variation of both strength and correlation length of the charge stripes. Finally, we propose further experiments to distinguish the possible theoretical scenarios.     

Comment on: “Exposed-key weakness of αη” [Phys. Lett. A 370 (2007) 131]

We show that the insecurity claim of the αη cryptosystem made by C. Ahn and K. Birnbaum in [C. Ahn, K. Birnbaum, Phys. Lett. A 370 (2007) 131] under heterodyne attack is based on invalid extrapolations of Shannon's random cipher analysis and on an invalid statistical independence assumption. We show, both for standard ciphers and αη, that expressions of the kind given by Ahn and Birnbaum can at best be interpreted as security lower bounds.     

Addendum to: “Geometrical and topological aspects of electrostatics on Riemannian manifolds” [J. Geom. Phys. 57 (8) (2007) 1679–1696]

In this note we discuss and solve several open problems posed in our recent paper “Geometrical and topological aspects of electrostatics on Riemannian manifolds”, also published in this journal. Some minor mistakes therein are corrected as well.