Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

On the determination of the potential function from given orbits

The paper deals with the problem of finding the field of force that generates a given (N ? 1)-parametric family of orbits for a mechanical system with N degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the theorem enunciated by Joukovski in 1890, solve the inverse Stäckel problem and solve the problem of constructing the potential-energy function U that is capable of generating a bi-parametric family of orbits for a particle in space. We determine the equations for the sought-for function U and show that on the basis of these equations we can define a system of two linear partial differential equations with respect to U which contains as a particular case the Szebehely equation. We solve completely a special case of the inverse dynamics problem of constructing U that generates a given family of conics known as Bertrand’s problem. At the end we establish the relation between Bertrand’s problem and the solutions to the Heun differential equation. We illustrate our results by several examples.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

Modular forms and effective Diophantine approximation

After the work of G. Frey, it is known that an appropriate bound for the Faltings height of elliptic curves in terms of the conductor (Frey?s height conjecture) would give a version of the ABC conjecture. In this paper we prove a partial result towards Frey?s height conjecture which applies to all elliptic curves over $\mathbb{Q}$, not only Frey curves. Our bound is completely effective and the technique is based in the theory of modular forms. As a consequence, we prove effective explicit bounds towards the ABC conjecture of similar strength to what can be obtained by linear forms in logarithms, without using the latter technique. The main application is a new effective proof of the finiteness of solutions to the S-unit equation (that is, S-integral points of ${\mathbb{P}}^1?\{0,1,\infty \}$), with a completely explicit and effective bound, without using any variant of Baker?s theory or the Thue–Bombieri method.     

High resolution emission spectroscopy of the AП-XΣ (red) system of CN

The emission spectra of the A²П-X²Σ⁺ (red) system of ¹²C¹⁴N have been reinvestigated in the 3500-22 000 cm⁻¹ region at high resolution using a Fourier transform spectrometer. In total, spectra of 63 bands involving vibrational levels up to v′ = 22 of the A²П state and v″ = 12 of the X²Σ⁺ ground state have been measured and rotationally analyzed providing an improved set of spectroscopic constants. The present measurements of the Δv = −2 sequence bands of ¹²C¹⁴N and those of ¹³C¹⁴N from Ram et al. (2010) [36] allow for a much improved identification of these two isotopologues in the near infrared spectra of carbon stars.     

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Elusive Double Perovskite Iodides: Structural,Optical, and Magnetic Properties

Halide double perovskites [A₂M^IM^IIIX₆] are an important class of materials that have garnered substantial interest as non-toxic alternatives to conventional lead iodide perovskites for optoelectronic applications. While numerous studies have examined chloride and bromide double perovskites, reports of iodide double perovskites are rare, and their definitive structural characterization has not been reported. Predictive models have aided us here in the synthesis and characterization of five iodide double perovskites of general formula Cs₂NaLnI₆ (Ln=Ce, Nd, Gd, Tb, Dy). The complete crystal structures, structural phase transitions, optical, photoluminescent, and magnetic properties of these compounds are reported.     

Development of a highly sensitive imaged cIEF immunoassay for studying AAV capsid protein charge heterogeneity

Post-translational modifications (PTMs) of adeno-associated virus (AAV) capsid proteins tune and regulate the AAV infective life cycle, which can impact the safety and efficacy of AAV gene therapy products. Many of these PTMs induce changes in protein charge heterogeneity, including deamidation, oxidation, glycation, and glycosylation. To characterize the charge heterogeneity of a protein, imaged capillary isoelectric focusing (icIEF) has become the gold standard method. We have previously reported an icIEF method with native fluorescence detection for denatured AAV capsid protein charge heterogeneity analysis. Although well suited for final products, the method does not have sufficient sensitivity for upstream, low-concentration AAV samples, and lacks the specificity for capsid protein detection in complex samples like cell culture supernatants and cell lysates. In contrast, the combination of icIEF, protein capture, and immunodetection affords significantly higher sensitivity and specificity, addressing the challenges of the icIEF method. By leveraging different primary antibodies, the icIEF immunoassay provides additional selectivity and affords a detailed characterization of individual AAV capsid proteins. In this study, we describe an icIEF immunoassay method for AAV analysis that is 90 times more sensitive than native fluorescence icIEF. This icIEF immunoassay provides AAV stability monitoring, where changes in individual capsid protein charge heterogeneity can be observed in response to heat stress. When applied to different AAV serotypes, this method also provides serotype identity with reproducible quantification of VP protein peak areas and apparent isoelectric point (pI). Overall, the described icIEF immunoassay is a sensitive, reproducible, quantitative, specific, and selective tool that can be used across the AAV biomanufacturing process, especially in upstream process development where complex sample types are often encountered.     

Isotope dilution-thermal ionisation mass spectrometric analysis for tin in a fly ash material

Isotope dilution-thermal ionisation mass spectrometry (ID-TIMS) analysis has been applied to the determination of tin in a fly ash sample supplied by the EC Joint Research Centre (Ispra, Italy). The proposed procedure includes the silica gel/phosphoric acid technique for tin thermal ionisation activation and a strict heating protocol for isotope ratio measurements. Instrumental mass discrimination factor has been previously determined measuring a natural tin standard solution. Spike solution has been prepared from ¹¹²Sn-enriched metal and quantified by reverse isotope dilution analysis. Two sample aliquots were spiked and tin was extracted with 4.5 M HCl during 25 min ultrasound exposure time. Due to the complex matrix of this fly ash material, a two-step purification stage using ion-exchange chromatography was required prior TIMS analysis. Obtained results for the two sample-spike blends (10.11 ± 0.55 and 10.50 ± 0.64 μmol g⁻¹) are comparable, both value and uncertainty. Also a good reproducibility is observed between measurements. The proposed ID-TIMS procedure, as a primary method and due to the lack of fly ash reference materials certified for tin content, can be used to validate more routine methodologies applied to tin determination in this kind of samples.