The role of alkane coordination in C–H bond cleavage at a Pt(II) center

The rates of CFormula H bond activation for various alkanes by [(N–N)Pt(Me)(TFEd3)]+ (N Formula N = ArFormula NFormula C(Me)Formula C(Me)Formula NFormula Ar; Ar = 3,5-di-tert-butylphenyl; TFE-d3 = CF3CD2OD) were studied. Both linear and cyclic alkanes give the corresponding alkene-hydride cation [(N–N)Pt(H)(alkene)]+ via (i) rate determining alkane coordination to form a CFormula H {sigma} complex, (ii) oxidative cleavage of the coordinated CFormula H bond to give a platinum(IV) alkyl-methyl-hydride intermediate, (iii) reductive coupling to generate a methane {sigma} complex, (iv) dissociation of methane, and (v) beta-H elimination to form the observed product. Second-order rate constants for cycloalkane activation (CnH2n), are proportional to the size of the ring (k ~ n). For cyclohexane, the deuterium kinetic isotope effect (kH/kD) of 1.28 (5) is consistent with the proposed rate determining alkane coordination to form a CFormula H {sigma} complex. Statistical scrambling of the five hydrogens of the Pt-methyl and the coordinated methylene unit, via rapid, reversible steps ii and iii, and interchange of geminal CFormula H bonds of the methane and cyclohexane CFormula H {sigma} adducts, is observed before loss of methane

Constructions of regular algebras Lpw(G)L_p^w(G)

Criterion of (Shilov) regularity for weighted algebras $L_1^w(G)$ on a locally compact abelian group $G$ is known by works of Beurling (1949) and Domar (1956). In the present paper this criterion is extended to translation invariant weighted algebras $L_p^w(G)$ with $p>1$. Regular algebras $L_p^w(G)$ are constructed on any sigma-compact abelian group $G$. It was proved earlier by the author that sigma-compactness is necessary (in the abelian case) for the existence of weighted algebras $L_p^w(G)$ with $p>1$.Comment: Submitted to Mat. Sborni

High frequency magnetic oscillations of the organic metal θ\theta-(ET)4_4ZnBr4_4(C6_6H4_4Cl2_2) in pulsed magnetic field of up to 81 T

De Haas-van Alphen oscillations of the organic metal $\theta$-(ET)$_4$ZnBr$_4$(C$_6$H$_4$Cl$_2$) are studied in pulsed magnetic fields up to 81 T. The long decay time of the pulse allows determining reliable field-dependent amplitudes of Fourier components with frequencies up to several kiloteslas. The Fourier spectrum is in agreement with the model of a linear chain of coupled orbits. In this model, all the observed frequencies are linear combinations of the frequency linked to the basic orbit $\alpha$ and to the magnetic-breakdown orbit $\beta$.Comment: 6 pages, 4 figure

Морфология и экологические особенности Sparganium × longifolium (Typhaceae) в центре Европейской части России

The increasing impact of anthropogenic factors and climate change affect the growth of a number of taxa of hybrid nature. These taxa are widespread among various taxonomic groups of aquatic and semi-aquatic plants. The genus Sparganium L. В is not an exception. In that regard, the aim of this study is to conduct biomorphological investigation of Sparganium × longifolium Turcz. ex Ledeb., evaluate qualitative and quantitative criteria for the hybrid similarities and differences with its parental species, as well as to analyze data on its habitat characteristics. Samples were collected in 2014–2016 from waterbodies in European Russia (Tver and Yaroslavl oblasts). In the study on biomorphology of S. × longifolium we used live and fixed materials, as well as herbarium funds of IBIW, MXA and MW. To establish and specify taxonomic features of the hybrid under study, indicating to its similarity with a certain ancestral species, our data on the morphology and ecology of S. emersum Rehm. and S. gramineum Georgi. are used. During field studies, the type of water object where the hybrid was detected, ecological characteristics of its habitat (type of soil, depth, water temperature and pH) are determined; the list of taxa which enter into the cenosis composition is compiled. The biomorphological investigation of S. × longifolium shows that by life form this hybrid, as well as its parental species, is a vegetative-mobile evidently-polycentric annual or biennial plant of vegetative origin with a racemose root system. The following should be attributed to the characteristic features justifying the hybrid origin of S. × longifolium: 1) a wider, slightly carinated lamina (as in S. emersum); 2) a branched inflorescence (as in S. gramineum); 3) the lower covering leaf of inflorescence, often exceeding the total length of the latter; 4) fruits with a straight (as in S. emersum) as well as bent (as in S. gramineum) style. Interestingly, some populations of S. × longifolium are rich in terate forms that can be explained by back crossing with one of the parental species or pleiotropic mutation(s). It is established that S. × longifolium is not widespread in European Russia, is a typically freshwater species, occurring in the littoral zone of mesotrophic and dystrophic waterbodies (usually in lakes of glacier origin). At present, its appearance in lake ecosystems is due to accelerated eutrophication caused by increasing human activities. Perhaps earlier this hybrid formation occurred in peripheral zones of the range of S. gramineum under cyclic climate changes. Observations suggest that S. × longifolium exceeds S. gramineum in ecological potential. At the same time, habitat features of the latter have an effect on the hybrid’s distribution potential (limitation of habitat spectrum), which is hardly exceeds S. emersum in its ecological and coenotic characteristics. 154   На основе современных подходов к анализу жизненных форм рассмотрена морфология вегетативной и генеративной сферы Sparangium × longifolium Turcz. ex Ledeb. (S. emersum Rehm. × S. gramineum Georgi). По жизненной форме S. × longifolium, как и его родительские виды, представляет собой вегетативно-подвижный явнополицентрический малолетник вегетативного происхождения с кистевидной корневой системой. В работе установлен промежуточный характер конкретных признаков гибрида, либо смещение того или иного признака в сторону одного из родительских видов. К характерным особенностям, подтверждающим гибридное происхождение S. × longifolium, следует отнести: 1) наличие более широкой, слегка килеватой листовой пластинки (как у S. emersum); 2) наличие разветвленного соцветия (как у S. gramineum); 3) нижний кроющий лист соцветия, часто превышающий общую длину последнего; 4) наличие плодов как с прямым (как у S. emersum), так и с загнутым (как у S. gramineum) столбиком. Отдельные популяции S. × longifolium изобилуют тератными формами, которые могут быть объяснены наличием возвратного скрещивания, либо мутации(й) с плейотропным проявлением. Анализ пыльцы гибрида на жизнеспособность показал преобладание стерильной пыльцы над фертильной. Установлено, что S. × longifolium – малораспространенный на территории Европейской части России – типично пресноводный вид, встречающийся в прибрежной зоне мезотрофных и дистрофных водных объектов (обычно в озерах ледникового происхождения). Появление популяций гибрида в озерах обусловлено их стремительной эвтрофикацией в результате антропогенной деятельности. Ранее образование этого гибрида, вероятно, происходило в периферийных частях ареала S. gramineum при циклических изменениях климата. Вместе с тем, особенности местообитания последнего накладывают «отпечаток» на потенциал распространения гибрида (ограниченность спектра местообитаний), который вряд ли может превзойти по своим эколого-ценотическим характеристикам S. emersum.&nbsp

Quantum oscillations in the linear chain of coupled orbits: the organic metal with two cation layers theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2))

Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linear chain of coupled two-dimensional (2D) orbits (Pippard's model) are derived systematically taking into account the chemical potential oscillations in magnetic field. Although corrective terms are observed, basic (alpha) and magnetic breakdown-induced (beta and 2beta - alpha) orbits can be accounted for by the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models in the explored field and temperature ranges. In contrast, the 'forbidden orbit' beta - alpha amplitude is described by a non-LK equation involving a product of two classical orbit amplitudes. Furthermore, strongly non-monotonic field and temperature dependence may be observed for the second harmonics of basic frequencies such as 2alpha and the magnetic breakdown orbit beta + alpha, depending on the value of the spin damping factors. These features are in agreement with the dHvA oscillation spectra of the strongly 2D organic metal theta- theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2)).Comment: to be published in Europhysics Letters (2012

Differential Form Valued Forms and Distributional Electromagnetic Sources

Properties of a fundamental double-form of bi-degree $(p,p)$ for $p\ge 0$ are reviewed in order to establish a distributional framework for analysing equations of the form $$\Delta \Phi + \lambda^2 \Phi = {\cal S}$$ where $\Delta$ is the Hodge-de Rham operator on $p-$forms $\Phi$ on ${\bf R}^3$. Particular attention is devoted to singular distributional solutions that arise when the source ${\cal S}$ is a singular $p-$form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in ${\bf R}^3$ is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time dependent sources of certain physical attributes, such as electric charge, electric current and polarization or magnetization, are concentrated on localized regions in space.Comment: 40 page

Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1...1], [21...1], [31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.Comment: 14 pages, LaTeX, replaced due to a LaTex erro

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Relative luminosity measurement of the LHC with the ATLAS forward calorimeter

In this paper it is shown that a measurement of the relative luminosity changes at the LHC may be obtained by analysing the currents drawn from the high voltage power supplies of the electromagnetic section of the forward calorimeter of the ATLAS detector. The method was verified with a reproduction of a small section of the ATLAS forward calorimeter using proton beams of known beam energies and variable intensities at the U-70 accelerator at IHEP in Protvino, Russia. The experimental setup and the data taking during a test beam run in April 2008 are described in detail. A comparison of the measured high voltage currents with reference measurements from beam intensity monitors shows a linear dependence on the beam intensity. The non-linearities are measured to be less than 0.5 % combining statistical and systematic uncertainties.Comment: 16 page