Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

Newton's method and periodic solutions of nonlinear wave equations

We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity

We study translation surfaces with rich groups of affine diffeomorphisms—“prelattice” surfaces. These include the lattice translation surfaces studied by W. Veech. We show that there exist prelattice but nonlattice translation surfaces. We characterize arithmetic surfaces among prelattice surfaces by the infinite cardinality of their set of points periodic under affine diffeomorphisms. We give examples of translation surfaces whose periodic points and Weierstrass points coincide.     

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm that is constant in a neighbourhood of zero.      

An intelligent decomposition of pairwise comparison matrices for large-scale decisions

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.     

Noncovalent Interaction of Graphene with Heterocyclic Compounds: Benzene,Imidazole, Tetracene,and Imidazophenazines

Noncovalent functionalization of graphene with organic molecules offers a direct route to multifunctional modification of this nanomaterial, leading to its various possible practical applications. In this work, the structures of hybrids formed by linear heterocyclic compounds such as imidazophenazine (F1) and its derivatives (F2‐F4) with graphene and the corresponding interaction energies are studied by using the DFT method. Special attention is paid to the hybrids where the attached molecule is located along the graphene zigzag ( G_ZZ) and armchair ( G_AC ) directions. The interaction energies corresponding to the graphene hybrids of the F1‐F4 compounds for the two directions are found to be distinct, while tetracene (being a symmetrical molecule) shows a small difference between these binding energies. It is found that the back‐side CH₃ and CF₃ groups have an important influence on the arrangements of F1 derivatives on graphene and on their binding energies. The contribution of the CF₃ group to the total binding energy of the F3 molecule with graphene is the largest (3.4 kcal mol^?1) (the G_ZZ direction) while the CH₃ group increases this energy of F2 only by 2.0 kcal mol^?1 (the G_AC direction). It is shown that replacing the carbons with other atoms or adding a back‐side group enables one to vary the polarizability of graphene.     

The phytochemical analysis and antioxidant activity assessment of orange peel (Citrus sinensis) cultivated in Greece-Crete indicates a new commercial source of hesperidin

The flavonoid content of several methanolic extract fractions of Navel orange peel (flavedo and albedo of Citrus sinensis) cultivated in Crete (Greece) was first analysed phytochemically and then assessed for its antioxidant activity in vitro. The chemical structures of the constituents fractionated were originally determined by comparing their retention times and the obtained UV spectral data with the available bibliographic data and further verified by detailed LC-DAD-MS (ESI+) analysis. The main flavonoid groups found within the fractions examined were polymethoxylated flavones, O-glycosylated flavones, C-glycosylated flavones, O-glycosylated flavonols, O-glycosylated flavanones and phenolic acids along with their ester derivatives. In addition, the quantitative HPLC analysis confirmed that hesperidin is the major flavonoid glycoside found in the orange peel. Interestingly enough, its quantity at 48 mg/g of dry peel permits the commercial use of orange peel as a source for the production of hesperidin. The antioxidant activity of the orange peel methanolic extract fractions was evaluated by applying two complementary methodologies, DPPH(*) assay and the Co(II)/EDTA-induced luminol chemiluminescence approach. Overall, the results have shown that orange peel methanolic extracts possess moderate antioxidant activity as compared with the activity seen in tests where the corresponding aglycones, diosmetin and hesperetin were assessed in different ratios.     

Ligand-free nickel catalyzed perfluoroalkylation of arenes and heteroarenes

We describe a “ligand-free” Ni-catalyzed perfluoroalkylation of heteroarenes to produce a diverse array of trfiluoromethyl, pentafluoroethyl and heptafluoropropyl adducts. Catalysis proceeds at room temperature via a radical pathway. The catalytic protocol is distinguished by its simplicity, and its wide scope demonstrates the potential in the late-stage functionalization of drug analogues and peptides.

A ligand-free, room temperature, Ni-catalyzed perfluoroalkylation of heteroarenes produced a diverse array of polyfluorinated adducts; potential in the late-stage functionalization of drugs and peptides is also demonstrated.