Warm tachyon inflation and swampland criteria

In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.     

Quartic Thue equations

We will give upper bounds upon the number of integral solutions to binary quartic Thue equations. We will also study the geometric properties of a specific family of binary quartic Thue equations to establish sharper upper bounds.     

On the Littlewood cyclotomic polynomials

In this article, we study the cyclotomic polynomials of degree N−1 with coefficients restricted to the set {+1,−1}. By a cyclotomic polynomial we mean any monic polynomial with integer coefficients and all roots of modulus 1. By a careful analysis of the effect of Graeffe's root squaring algorithm on cyclotomic polynomials, P. Borwein and K.K. Choi gave a complete characterization of all cyclotomic polynomials with odd coefficients. They also proved that a polynomial p(x) with coefficients ±1 of even degree N−1 is cyclotomic if and only if p(x)=±Φp₁(±x)Φp₂(±xp₁)?Φpr(±xp₁p₂?pr−1), where N=p₁p₂?pr and the pi are primes, not necessarily distinct. Here is the pth cyclotomic polynomial. Based on substantial computation, they also conjectured that this characterization also holds for polynomials of odd degree with ±1 coefficients. We consider the conjecture for odd degree here. Using Ramanujan's sums, we solve the problem for some special cases. We prove that the conjecture is true for polynomials of degree α²pβ−1 with odd prime p or separable polynomials of any odd degree.     

Involutions on certain Banach algebras related to locally compact groups

Let \(\mathcal{{A}}\) be a Banach algebra and let \(\mathcal{{X}}\) be an introverted closed subspace of \(\mathcal{{A}}^*\) . Here, we give necessary and sufficient conditions for that the dual algebra \(\mathcal{{X}}^*\) of \(\mathcal{{X}}\) or the topological centers \({\mathfrak {Z}}_t^{(1)}(\mathcal{{X}}^{*})\) and \({\mathfrak {Z}}_t^{(2)}(\mathcal{{X}}^{*})\) of \(\mathcal{{X}}^*\) are Banach \(*\) -algebras. We finally apply these results to the Banach space \(L_0^\infty (G)\) of all equivalence classes of essentially bounded functions vanishing at infinity on a locally compact group \(G\) .     

Thue’s inequalities and the hypergeometric method

We establish upper bounds for the number of primitive integer solutions to inequalities of the shape \(0<|F(x, y)| \le h\), where \(F(x , y) =(\alpha x + \beta y)^r -(\gamma x + \delta y)^r \in \mathbb {Z}[x ,y]\), \(\alpha \), \(\beta \), \(\gamma \) and \(\delta \) are algebraic constants with \(\alpha \delta -\beta \gamma \ne 0\), and \(r \ge 5\) and h are integers. As an important application, we pay special attention to binomial Thue’s inequalities \(|ax^r - by^r| \le c\). The proofs are based on the hypergeometric method of Thue and Siegel and its refinement by Evertse.     

Copper(II) and nickel(II) complexes of tetradentate Schiff base ligand: UV-Vis and FT-IR spectra and DFT calculation of electronic,vibrational and nonlinear optical properties

The experimental fourier transform infrared (FT-IR) and ultraviolet-visible (UV-Vis) spectra of copper(II) and nickel(II) complexes of the deprotonated tetradentate Schiff base ligand N,N′-bis(2-hydroxybenzylidene)-2,2-dimethyl-1,3-propanediamine (H₂L) are compared with their corresponding theoretical ones. The applied theoretical method is based on the density functional theory and time-dependent density functional theory at the UPBE0/PBE0 levels using Def2-TZVP basis set. The computational optimised geometric parameters of the complexes are in good agreement with their corresponding experimental data. The FT-IR and UV-Vis spectra of the complexes were reproduced on the basis of their optimised structures. The vibrational assignments of some fundamental modes of the complexes are performed. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies are calculated. The analyses of the calculated electronic absorption spectra of the complexes are carried out to elucidate the electronic transitions assignments and their characters. Second-order nonlinear optical property of the complexes is evaluated by the above-mentioned theoretical method that implies much greater values for the complexes in comparison with the corresponding value of urea.     

Monte Carlo Simulation of a Segmented Detector for Low-Energy Electron Antineutrinos

Detection of low-energy electron antineutrinos is of importance for several purposes, such as ex-vessel reactor monitoring, neutrino oscillation studies, etc. The inverse beta decay (IBD) is the interaction that is responsible for detection mechanism in (organic) plastic scintillation detectors. Here, a detailed study will be presented dealing with the radiation and optical transport simulation of a typical segmented antineutrino detector withMonte Carlo method using MCNPX and FLUKA codes. This study shows different aspects of the detector, benefiting from inherent capabilities of the Monte Carlo simulation codes.     

Folate-Targeted Curcumin-Loaded Niosomes for Site-Specific Delivery in Breast Cancer Treatment: In Silico and In Vitro Study

As the most common cancer in women, efforts have been made to develop novel nanomedicine-based therapeutics for breast cancer. In the present study, the in silico curcumin (Cur) properties were investigated, and we found some important drawbacks of Cur. To enhance cancer therapeutics of Cur, three different nonionic surfactants (span 20, 60, and 80) were used to prepare various Cur-loaded niosomes (Nio-Cur). Then, fabricated Nio-Cur were decorated with folic acid (FA) and polyethylene glycol (PEG) for breast cancer suppression. For PEG-FA@Nio-Cur, the gene expression levels of Bax and p53 were higher compared to free drug and Nio-Cur. With PEG-FA-decorated Nio-Cur, levels of Bcl2 were lower than the free drug and Nio-Cur. When MCF7 and 4T1 cell uptake tests of PEG-FA@Nio-Cur and Nio-Cur were investigated, the results showed that the PEG-FA-modified niosomes exhibited the most preponderant endocytosis. In vitro experiments demonstrate that PEG-FA@Nio-Cur is a promising strategy for the delivery of Cur in breast cancer therapy. Breast cancer cells absorbed the prepared nanoformulations and exhibited sustained drug release characteristics.     

Strongly amenable involutive representations of involutive Banach algebras

Let \(\mathfrak{A }\) be a Banach \(*\) -algebra and let \(\varphi \) be a nonzero self-adjoint character on \(\mathfrak{A }\) . For a   \(*\) -representation \(\pi \) of \(\mathfrak{A }\) on a Hilbert space \(\mathcal{H }\) , we introduce and study strong \(\varphi \) -amenability of \(\pi \) in terms of certain states on the von Neumann algebra of bounded operators on \(\mathcal{H }\) . We then give some characterizations of this notion in terms of certain positive functionals on \(\mathfrak{A }\) . We finally investigate some hereditary properties of strong \(\varphi \) -amenability of Banach algebras.