Stability and vibrational spectra of toroidal isomers of C 240

To study the thermodynamic and mechanical stability of toroidal isomers of C ₂₄₀, we use a semi-empirical tight-binding theory and calculate their electronic structure, cohesive energy and vibrational spectra within the harmonic approximation. From these, we deduce their free energy at temperatures up to 1500K. The results are also compared to the isomer with icosahedral symmetry. Finally, we discuss within this approach, their stability and abundance.     

High-pressure phases of hydrogen cyanide: formation of hydrogenated carbon nitride polymers and layers and their electronic properties

We have performed a set of first-principles simulations to consider the possible phase transitions in molecular crystals of HCN under high pressure. Our calculations reveal several transition paths from the orthorhombic phase to tetragonal and then to triclinic phases. The transitions from the orthorhombic to the tetragonal phases are of the second order, whereas those from the tetragonal to the triclinic phases turn out to be of the first-order type and characterized by an abrupt decrease in volume. Our calculations show that, by adjustment of the temperature and pressure of the HCN molecular crystal, novel layered and polymeric crystals with insulating, semiconducting or metallic properties can be found. Based on our simulation results, two different crystal formation mechanisms are deduced. The stabilities of the predicted structures at ambient pressure are further assessed by performing phonon or MD simulations. In addition, the electron transport properties of the predicted polymers are obtained using the non-equilibrium Green's function technique combined with density functional theory. The results show that the polymers have metallic-like I-V characteristics.     

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 \(G\) .     

Prediction of the penetrated rust into the microcracks of concrete caused by reinforcement corrosion

Consider a steel-rust-concrete composite consisting of a circular cylindrical concrete cover and a coaxial uniformly corroding steel reinforcement. Prediction of the amount of rust penetrated into the microcracks of concrete cover from a set of data measured at the surface of the concrete is of particular interest. The steel is assumed to be linear isotropic and rust follows a power law stress–strain relation. For the concrete, anisotropic behavior and post-cracking softening model is employed. The formulations lead to a nonlinear boundary value problem which is solved analytically. A key parameter β, defined as the ratio of the volume of corrosion products inside the cracks to the volume of the cracks, is calculated. With some efforts, this parameter is also extracted from the available theoretical and experimental studies for the purpose of comparison. The effects of the mechanical properties of rust and concrete on β is addressed.     

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.     

Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects

The potential application of SWCNTs as mass nanosensors is examined for a wide range of boundary conditions. The SWCNT is modeled via nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The added nano-objects are considered as rigid solids, which are attached to the SWCNT. The mass weight and rotary inertial effects of such nanoparticles are appropriately incorporated into the nonlocal equations of motion of each model. The discrete governing equation pertinent to each model is obtained using an effective meshless technique. The key factor in design of a mass nanosensor is to determine the amount of frequency shift due to the added nanoparticles. Through an inclusive parametric study, the roles of slenderness ratio of the SWCNT, small-scale parameter, mass weight, number of the attached nanoparticles, and the boundary conditions of the SWCNT on the frequency shift ratio of the first flexural vibration mode of the SWCNT as a mass sensor are also discussed.     

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.     

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.