Anomalous hydrodynamics in two dimensions

A new approach is presented to discuss two-dimensional hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. Also, a connection between response parameters and anomaly coefficients is discussed. These are new results which, in the absence of the gauge sector, reproduce the results found by the gradient expansion approach.     

Magnetic behaviour of AuFe and NiMo alloys

We study the electronic structure and a mean-field phase analysis based on the pair–pair energies derived from first-principles electronic structure calculations of AuFe and NiMo alloys. We have used the tight-binding linear muffin-tin orbitals-based augmented space recursion (TB-LMTO-ASR) method to do so. We investigate different behaviours of the two alloy systems by mapping the problems onto equivalent Ising models and then discuss the magnetic phase diagrams using the calculated pair energies. All three phases: paramagnetic, random ferromagnetic and spin glass, have been studied.     

Experimental study of the <Emphasis Type="Italic">πh</Emphasis><Subscript>11/2</Subscript> band in <Superscript>113</Superscript>Sb

In the present work, the excited states of ¹¹³Sb were populated in the ¹⁰⁰Mo(²⁰Ne, p6n) reaction at a beam energy of 136 MeV. States only up to 59/2⁻ were observed in the ΔJ = 2 band. Mean lifetimes for the five states (from 4460 to 7998 keV) were measured for the first time using Doppler shift attenuation method. An upper limit of the lifetime (0.14 ps) was estimated for the 9061 keV, 47/2⁻ state. The B(E2) values, derived from the present lifetime results, correspond to a large quadrupole deformation of β ₂ = 0.32. The observed reduction in the experimental B(E2) values for the 918.4 keV (spin 39/2⁻ → 35/2⁻) and 985 keV (spin 43/2⁻ → 39/2⁻) transitions may be interpreted as due to the proton alignement in the g _7/2 orbital. The dynamic moment of inertia was observed to be about half of the rigid body value at the highest observed frequency.     

Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number

In this paper we find a new lower bound on the number of imaginary quadratic extensions of the function field $\mathbb{F}_{q}(x)$ whose class groups have elements of a fixed odd order. More precisely, for q, a power of an odd prime, and g a fixed odd positive integer ≥?3, we show that for every ε?>?0, there are $\gg q^{L(\frac{1}{2}+\frac{3}{2(g+1)}-\epsilon)}$ polynomials $f \in \mathbb{F}_{q}[x]$ with $\deg f=L$ , for which the class group of the quadratic extension $\mathbb{F}_{q}(x, \sqrt{f})$ has an element of order g. This sharpens the previous lower bound $q^{L(\frac{1}{2}+\frac{1}{g})}$ of Ram Murty. Our result is a function field analogue which is similar to a result of Soundararajan for number fields.     

A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs

Characteristic polynomial coefficients of three classes of graph, namely L_n + n(p), C_n + n(p) and K _1,n-1 + n(p), which are known to have reciprocal pairs of eigenvalues, have been shown to be generated by simple manipulation of the Pascal's triangle.     

Kinetics and Mechanism of Oxidation of 2‐Mercaptoethanol by the Heteropolyoxovanadate [MnV13O38]7−

In aqueous acetate buffer (pH 3.25 – 4.30) 2‐mercaptoethanol is oxidized to 2‐hydroxyethyldisulfide by 13‐vanadomanganate(IV) (1). Each mole of 1 consumes 15 mol of 2‐mercaptoethanol, and in this process all of their V^VO₆ units (in total 13 in number) are reduced to VO²⁺ in a multistep process. In the first step, 1 is converted to a one‐electron–reduced product ( 2) , comparable to heteropolyblue. Its kinetics has been measured for the first time. The extra electron in 2 is most possibly trapped (in electron paramagnetic resonance spectroscopic timescale) on the 13th vanadium atom, which shares one oxygen with the central Mn^IV atom in 1 . Complex 2 being metastable in the studied pH range decompose further into smaller oligomers, which are further reduced to free vanadyl ions. We found that in the presence of ≥10 fold [2‐mercaptoethanol] over [ 1 ], the kinetics of the first step is first order with respect to [ 1 ], [2‐mercaptoethanol], and [H+]. Monoprotonated 1 seems kinetically more active than 1 . A plausible mechanism has been suggested.     

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx) ^α (and (Δt) ^α ) with 0 < α < 1; called as ‘fractional differentials’. For arbitrarily small Δx and Δt (tending towards zero), these ‘fractional’ differentials are greater than Δx (and Δt), i.e. (Δx) ^α > Δx and (Δt) ^α > Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.     

B s data at Tevatron and possible new physics

The new physics (NP) is parametrized with four model-independent quantities: the magnitudes and phases of the dispersive part M ₁₂ and the absorptive part ??₁₂ of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables ??M _s, ????_s, the mixing phase $\beta_\mathrm{s}^{J/\psi\phi}$ and $A^b_{\rm sl}$ . This formalism is extended to include charge-parity-time reversal (CPT) violation, and it is shown that CPT violation by itself, or even in the presence of CPT-conserving NP without an absorptive part, helps only marginally in the simultaneous resolution of these anomalies.