Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Computational (DFT) and Experimental (NMR) Study of the Chelation of an Iridium Hyperpolarization Transfer Catalyst by Amino Acids

Non-hydrogenative Para-Hydrogen Induced Hyperpolarization (nhPHIP) is a Nuclear Magnetic Resonance (NMR) hyperpolarization technique which has experimentally been used to analyze complex biological samples containing amino acids using the Ir-IMes hyperpolarization transfer catalyst. A computational study based on Density Function Theory (DFT) was performed on all relevant stereoisomers of [Ir(H)₂(IMes)(AA)(Py)] (with AA=glycine, alanine, valine; Py=pyridine), for which R/S chirality and orientation of the amino acid chelation (C/A) were considered. A total of 30 structures were calculated comprising of 6 stereoisomers for achiral glycine, and 12 stereoisomers for each of the chiral amino acids. The abundances derived from the DFT energies confirmed the trends observed in thermal (non-hyperpolarized) NMR experiments. Additionally, theoretical calculations of electronic (Wiberg bond indices, Natural Bond Orders, Frontier Orbital Analysis), bond dissociation energies, transition states, and activation energies related to interconversion between binding modes, and steric factors (Solid angle) were performed to provide detailed explanations for NMR experimental observations.     

The Steady-State ALTADENA RASER Generates Continuous NMR Signals**

A RASER (Radio Amplification by Stimulated Emission of Radiation) facilitates the study of nonlinear phenomena, as well as the determination of NMR parameters with high precision. To achieve maximum sensitivity in the desired operating mode, it is crucial to control the RASER over long periods of time. So far, this was only possible at ultra-low magnetic fields. Here, we introduce a way to control the operating regime of a RASER at a magnetic field of 1.45 T. We employ a continuous-flow RASER, pumped by PHIP (ParaHydrogen Induced Polarization). The hydrogenation of vinyl acetate (VA) with parahydrogen provides the required negative polarization on the methyl group of the product ethyl acetate (EA). The protons within the methyl group, separated by a 7 Hz J-coupling, are RASER active. This system demonstrates five RASER phenomena: inequivalent and equivalent amplitudes in the “normal NMR mode”, period doublings, frequency combs, and chaos. The experiments match with simulations based on a theoretical model of two nonlinear-coupled RASER modes. We predict the RASER regime at set conditions and visualize the prediction in a bifurcation diagram.     

Partitions of natural numbers with the same representation functions

For a set A of nonnegative integers the representation functions R₂(A,n), R₃(A,n) are defined as the number of solutions of the equation n=a+a^′,a,a^′∈A with a<a^′, a?a^′, respectively. Let D(0)=0 and let D(a) denote the number of ones in the binary representation of a. Let A₀ be the set of all nonnegative integers a with even D(a) and A₁ be the set of all nonnegative integers a with odd D(a). In this paper we show that (a) if R₂(A,n)=R₂(N?A,n) for all n?2N−1, then R₂(A,n)=R₂(N?A,n)?1 for all n?12N²−10N−2 except for A=A₀ or A=A₁; (b) if R₃(A,n)=R₃(N?A,n) for all n?2N−1, then R₃(A,n)=R₃(N?A,n)?1 for all n?12N²+2N. Several problems are posed in this paper.     

Generalized gluing for Einstein constraint equations

In this paper we construct a family of new (topologically distinct) solutions to the Einstein constraint equations by performing the generalized connected sum (or fiber sum) of two known compact m-dimensional constant mean curvature solutions (M ₁, g ₁, Π₁) and (M ₂, g ₂,Π₂) along a common isometrically embedded k-dimensional sub-manifold (K, g _K ). Away from the gluing locus the metric and the second fundamental form of the new solutions can be chosen as close as desired to the ones of the original solutions. The proof is essentially based on the conformal method and the geometric construction produces a polyneck between M ₁ and M ₂ whose metric is modeled fiber-wise (i. e. along the slices of the normal fiber bundle of K) around a Schwarzschild metric; for these reasons the codimension n : =  m − k of K in M ₁ and M ₂ is required to be  ≥  3. In this sense our result is a generalization of the Isenberg–Mazzeo–Pollack gluing, which works for connected sum at points and in dimension 3. The solutions we obtain for the Einstein constraint equations can be used to produce new short time vacuum solutions of the Einstein system on a Lorentzian (m + 1)-dimensional manifold, as guaranteed by a well known result of Choquet-Bruhat.     

On the number of unique expansions in non-integer bases

Let q>1 be a real number and let m=m(q) be the largest integer smaller than q. It is well known that each number can be written as with integer coefficients 0?ci<q. If q is a non-integer, then almost every x∈Jq has continuum many expansions of this form. In this note we consider some properties of the set Uq consisting of numbers x∈Jq having a unique representation of this form. More specifically, we compare the size of the sets Uq and Ur for values q and r satisfying 1<q<r and m(q)=m(r).     

Inverse cyclotomic polynomials

Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x)=(xn−1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n<561 all coefficients of Ψn(x) are ?1 in absolute value. We establish various properties of the coefficients of Ψn(x), especially focusing on the easiest non-trivial case where n is composed of 3 distinct odd primes.     

Hydrodynamic cavitation coupled with zero-valent iron produces radical sulfate radicals by sulfite activation to degrade direct red 83

In the present research, hydrodynamic cavitation (HC) and zero-valent iron (ZVI) were used to generate sulfate radicals through sulfite activation as a new source of sulfate for the efficient degradation of Direct Red 83 (DR83). A systematic analysis was carried out to examine the effects of operational parameters, including the pH of the solution, the doses of ZVI and sulfite salts, and the composition of the mixed media. Based on the results, the degradation efficiency of HC/ZVI/sulfite is highly dependent upon the pH of the solution and the dosage of both ZVI and sulfite. Degradation efficiency decreased significantly with increasing solution pH due to a lower corrosion rate for ZVI at high pH. The corrosion rate of ZVI can be accelerated by releasing Fe²⁺ ions in an acid medium, reducing the concentration of radicals generated even though ZVI is solid/originally non-soluble in water. The degradation efficiency of the HC/ZVI/sulfite process (95.54 % + 2.87%) was found to be significantly higher under optimal conditions than either of the individual processes (<6% for ZVI and sulfite and 68.21±3.41% for HC). Based on the first-order kinetic model, the HC/ZVI/sulfite process has the highest degradation constant of 0.035±0.002 min⁻¹. The contribution of radicals to the degradation of DR83 by the HC/ZVI/sulfite process was 78.92%, while the contribution of SO₄^•− and ^•OH radicals was 51.57% and 48.43%, respectively. In the presence of HCO₃⁻ and CO₃²⁻ ions, DR83 degradation is retarded, whereas SO₄²⁻ and Cl⁻ ions promote degradation. To summarise, the HC/ZVI/sulfite treatment can be viewed as an innovative and promising method of treating recalcitrant textile wastewater.     

Complete hypersurfaces immersed in a semi-Riemannian warped product

The aim of this paper is to study the uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm and such that its fiber has constant sectional curvature. By using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds and supposing a natural comparison inequality between the r-th mean curvatures of the hypersurface and that ones of the slices of the region where the hypersurface is contained, we are able to prove that a such hypersurface must be, in fact, a slice.