Meir–Keeler-type conditions in abstract metric spaces

Various Meir–Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenovi?, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38–50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.     

Soy-oil-based segmented polyurethanes

Segmented polyurethanes were prepared from soy polyol, diphenyl methane diisocyanate (MDI), and ethylene glycol or butane diol as chain extenders. Samples were prepared with true hard-segment concentrations (HSC) of about 0, 10, and 40%. Both the soft MDI–polyol and hard MDI/diol segments are glassy at room temperature. These samples were also crosslinked through the polyfunctional polyol soft segment. Partial crystallinity and phase separation were detected in samples with 40% HSC, on the basis of DSC data. Small-angle X-ray scattering shows the existence of phase separation with domain sizes of about 10 nm in the 40% HSC samples, but not in the others. The distribution of domain sizes is considerably broader for the ethylene-glycol extended system compared with that for the butane-diol case. Although the presence of hard segments lowers the crosslink density, samples with higher HSC had higher glass transition temperatures, higher strengths, higher moduli, lower swelling, lower elongation at break, and lower impact strengths. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3178–3190, 2005     

$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.     

The role of guaiacyl moiety in free radical scavenging by 3,5-dihydroxy-4-methoxybenzyl alcohol: thermodynamics of 3H+/3e− mechanisms

ABSTRACT

Participation of guaiacyl moiety of 3,5-dihydroxy-4-methoxybenzyl alcohol (DHMBA) in inactivation of free radicals was investigated using the DFT method. The thermodynamics of triple (3H⁺/3e^?) free radical scavenging mechanisms was investigated. The Gibbs free energies of reactions of inactivation of selected 10 free radicals indicate DHMBA as a potent scavenger. Obtained results allow us to suggest that the contribution of guaiacyl moiety to antioxidant activity of phenolic compounds should be taken into account, what has been scarcely considered until now.     

Coherent Vortex Structures and 3D Enstrophy Cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities – ${\frac{1}{2}}$ -Hölder coherence of the vorticity direction – coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.     

Improved Thermoelectric Properties of SrTiO3 via (La,Dy and N) Co-Doping: DFT Approach

This work considers the enhancement of the thermoelectric figure of merit, ZT, of SrTiO₃ (STO) semiconductors by (La, Dy and N) co-doping. We have focused on SrTiO₃ because it is a semiconductor with a high Seebeck coefficient compared to that of metals. It is expected that SrTiO₃ can provide a high power factor, because the capability of converting heat into electricity is proportional to the Seebeck coefficient squared. This research aims to improve the thermoelectric performance of SrTiO₃ by replacing host atoms by La, Dy and N atoms based on a theoretical approach performed with the Vienna Ab Initio Simulation Package (VASP) code. Here, undoped SrTiO₃, Sr_0.875La_0.125TiO₃, Sr_0.875Dy_0.125TiO₃, SrTiO_2.958N_0.042, Sr_0.750La_0.125Dy_0.125TiO₃ and Sr_0.875La_0.125TiO_2.958N_0.042 are studied to investigate the influence of La, Dy and N doping on the thermoelectric properties of the SrTiO₃ semiconductor. The undoped and La-, Dy- and N-doped STO structures are optimized. Next, the density of states (DOS), band structures, Seebeck coefficient, electrical conductivity per relaxation time, thermal conductivity per relaxation time and figure of merit (ZT) of all the doped systems are studied. From first-principles calculations, STO exhibits a high Seebeck coefficient and high figure of merit. However, metal and nonmetal doping, i.e., (La, N) co-doping, can generate a figure of merit higher than that of undoped STO. Interestingly, La, Dy and N doping can significantly shift the Fermi level and change the DOS of SrTiO₃ around the Fermi level, leading to very different thermoelectric properties than those of undoped SrTiO₃. All doped systems considered here show greater electrical conductivity per relaxation time than undoped STO. In particular, (La, N) co-doped STO exhibits the highest ZT of 0.79 at 300 K, and still a high value of 0.77 at 1000 K, as well as high electrical conductivity per relaxation time. This renders it a viable candidate for high-temperature applications.     

Space-Time Localization of a Class of Geometric Criteria for Preventing Blow-up in the 3D NSE

A class of local (in the space-time) conditions on the vorticity directions implying local regularity of weak solutions to the 3D Navier-Stokes equations is established. In all the preceding results, the relevant geometric conditions, although being local in nature, have been assumed uniformly throughout the spatial regions of high vorticity magnitude, and uniformly in time. In addition, similar results are obtained assuming a less restrictive integral condition on the vorticity directions.     

Frobenius Problem and dead ends in integers

Let a and b be positive and relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley graph) with respect to this property. In addition, for given integers a and b, we explicitly describe all such elements in Z. Finally, we show that Z has only finitely many dead ends with respect to any finite symmetric generating set. In Appendix A we show that every finitely generated group has a generating set with respect to which dead ends exist.     

Sub-Coulomb deuteron break-up and the neutron-nucleus interaction

Low-energy deuteron break-up on heavy nuclei is treated paying special attention to the neutron-nucleus interaction. The neutron-nucleus elastic scattering phase shift, the only quantity through which the neutron-nucleus interaction enters into our calculations, is split into an energy-averaged part described by the optical model and a fluctuating part. Some calculations are given in order to illustrate the effects of the neutron-nucleus interaction, along with a comparison with recent experimental results, which shows very good agreement.