On the abelianizations of congruence subgroups of Aut(<Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript>)

Let F _n be the free group of rank n, and let Aut⁺(F _n ) be its special automorphism group. For an epimorphism π : F _n → G of the free group F _n onto a finite group G we call the standard congruence subgroup of Aut⁺(F _n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ⁺(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ⁺(G, π) ≤ Aut⁺(F ₂) has infinite abelianization.     

Topological entropy of formal languages

We introduce the notion of topological entropy of a formal language as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill–Nerode congruence relation, we are able to compute the topological entropies of certain example languages. Those examples suggest that the notion of a “simple” formal language coincides with the language having zero entropy.     

Pleine fidélité sans structure de Frobenius et isocristaux partiellement surconvergents

Soit _boxclose{\mathcal V} un anneau de valuation discrète complet d’inégales caractéristiques (0, p), de corps résiduel parfait k, de corps des fractions K. Soient X une variété sur k, Y un ouvert de X. Nous prolongeons le théorème de pleine fidélité de Kedlaya de la manière suivante (en effet, nous ne supposons pas Y lisse): le foncteur canonique F\text-Isoc ^f (Y,X/K) ? F\text-Isoc ^f (Y,Y/K) {F\text{-}\mathrm{Isoc} ^{\dag} (Y,X/K) \to F\text{-}\mathrm{Isoc} ^{\dag} (Y,Y/K) } est pleinement fidèle. Supposons à présent Y lisse. Nous construisons la catégorie Isoc ^ff (Y,X/K){\mathrm{Isoc} ^{\dag\dag} (Y,X/K) } des isocristaux partiellement surcohérents sur (Y, X) dont les objets sont certains D{\mathcal D} -modules arithmétiques. De plus, nous vérifions l’équivalence de catégories sp _(Y,X),+: Isoc ^f (Y,X/K) @ Isoc ^ff (Y,X/K){{\rm sp} _{(Y,X),+}: \mathrm{Isoc} ^{\dag} (Y,X/K) \cong \mathrm{Isoc} ^{\dag\dag} (Y,X/K)} .     

Relaxation mechanisms of multi-quantum coherences in the Zeeman structure of atomic Cs trapped in solid He

This paper extends our previous work on near-degenerate magnetic resonance transitions in alkali ground states involving the simultaneous absorption of multiple radio-frequency quanta. New experimental results with an improved spectral resolution were obtained with cesium atoms trapped in the cubic phase of a helium crystal. The main objective of the paper is a theoretical study of the influence of stochastic perturbations of given multipole orders on the various multi-photon coherences. Algebraic and numerical results for perturbations of both dipolar and quadrupolar symmetry are presented. The present experimental resolution does not yet allow us to distinguish between these two most likely relaxation mechanisms. Nonetheless, the experimental spectra are very well described when allowing in the calculations for a magnetic field inhomogeneity of 2×10^-5. PACS 76.70.Hb; 32.80.Wr; 32.30.Dx; 32.60.+i     

Does polynomial parallel volume imply convexity?

For a non-empty compact set A^d, d2, and r0, let Ar denote the set of points whose distance from A is r at the most. It is well-known that the volume, V_d(A_r), of A_r is a polynomial of degree d in the parameter r if A is convex. We pursue the reverse question and ask whether A is necessarily convex if V_d(A_r) is a polynomial in r. An affirmative answer is given in dimension d=2, counterexamples are provided for d3. A positive resolution of the question in all dimensions is obtained if the assumption of a polynomial parallel volume is strengthened to the validity of a (polynomial) local Steiner formula. Mathematics Subject Classification (2000):52A38, 28A75, 52A22, 53C65     

An error analysis of the dynamic mode decomposition

Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and temporal dynamics of coherent structures in experimental fluid flows. To aid interpretation of experimental data, error-bars on the measured growth rates are needed. In this article, we undertake a massively parallel error analysis of the DMD algorithm using synthetic waveforms that are shown to be representative of the canonical instabilities observed in shear flows. We show that the waveform of the instability has a marked impact on the error of the measured growth rate. Sawtooth and square waves may have an order of magnitude larger error than sine waves under the same conditions. We also show that the effects of data quantity and quality are of critical importance in determining the error in the growth or decay rate, and that the effect of the key parametric variables are modulated by the growth rate itself. We further demonstrate methods by which ensemble and orthogonal data may be introduced to improve the noise response. With regard for the important variables, precise measurement of the growth rates of instabilities may be supplemented with an accurately estimated uncertainty. This opens many new possibilities for the measurement of coherent structure in shear flows.     

LaB6场发射尖锥的场发射特性研究

报道了六硼化镧（LaB6）场发射尖锥的场发射性能。采用电化学腐蚀方法制作了LaB6场发射尖锥,并在10-2～10-7 Pa 的宽真空度范围内对单尖LaB6场发射二极管的发射特性进行了测试。发现残余气体电离产生的离子轰击对LaB6场发射阴极尖锥表面起到了离子清洗作用,使LaB6场发射尖锥在低真空工作后发射电流大幅度提高。离子轰击是一种适用于LaB6场发射阴极的激活处理方法。     

Voltammetric cadmium(II) sensor based on a fluorine doped tin oxide electrode modified with polyamide 6/chitosan electrospun nanofibers and gold nanoparticles

The authors have developed an electrochemical sensor for cadmium(II) that is based on the use of a conventional fluorine doped tin oxide (FTO) electrode modified with polymeric electrospun nanofibers consisting of polyamide 6 (PA6) and chitosan which were further modified with gold nanoparticles (AuNPs). The materials were characterized by infrared spectroscopy, thermal analysis (DSC and TGA), and scanning electron microscopy. The modified electrode was applied to the detection of Cd(II) by square wave voltammetry. Response is linear in the 25 to 75 μg ? L^?1 Cd(II) concentration range, with a detection limit of 0.88 μg ? L^?1. The relative standard deviations are 4.6% and 8.2% for intra- and inter-electrode measurements, respectively. Mercury(II), lead(II), and copper(II) did not significantly interfere.

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Graphical abstract The sensing platform developed can detect cadmium(II) with a detection limit of 0.88 μg L^?1, with no significant interference by mercury(II) and lead(II).

     

Dynamics of Team Member Replacements from Complex Systems Theory

Simulations based on the NK model are carried out to address team member replacements that follow tweaking (i.e., gradual changes) of the strategy of the team leader. For simple teams in which the team members do not interact, team member replacements occur independently. However, for teams in which team members interact with other team members, team member replacements occur as cascades. In these cascades, the replacement of one team member triggers the replacement of another, which triggers the replacement of yet another, and so on. These cascades of team member replacements are largest for teams with intermediate complexity, in which each member interacts with between and of the other team members. The cascades are roughly independent of team size, and so smaller teams are more volatile in that the cascades affect a larger fraction of the team.Daniel J. Lacks is the C. Benson Branch Professor of Chemical Engineering at CaseWestern Reserve University. Prof. Lacks received his B.S. in chemical engineering from Cornell University in 1987, and his Ph.D. in chemistry from Harvard University in 1992. Following a postdoctoral fellowship at MIT from 1993–1994, Prof. Lacks was on the faculty of the chemical engineering department at Tulane University from 1994–2003. Prof. Lacks joined the faculty at Case in 2003. His research interests involve the simulation of nonequilibrium processes, ranging from physical processes such as fluid flow and fracture in glasses, to nonphysical processes such as biological evolution and chemical process optimization.