Asymmetry and structural information in preferential attachment graphs

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd?s‐Rényi graphs are typically asymmetric, real networks are highly symmetric. So a natural question is whether preferential attachment graphs, where in each step a new node with m edges is added, exhibit any symmetry. In recent work it was proved that preferential attachment graphs are symmetric for m = 1, and there is some nonnegligible probability of symmetry for m = 2. It was conjectured that these graphs are asymmetric when m ≥ 3. We settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. To do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. These results have further implications for information theoretic problems of interest on preferential attachment graphs.     

The Occurrence and Biological Activity of Tormentic Acid—A Review

This review focuses on the natural sources and pharmacological activity of tormentic acid (TA; 2α,3β,19α-trihydroxyurs-2-en-28-oic acid). The current knowledge of its occurrence in various plant species and families is summarized. Biological activity (e.g., anti-inflammatory, antidiabetic, antihyperlipidemic, hepatoprotective, cardioprotective, neuroprotective, anti-cancer, anti-osteoarthritic, antinociceptive, antioxidative, anti-melanogenic, cytotoxic, antimicrobial, and antiparasitic) confirmed in in vitro and in vivo studies is compiled and described. Biochemical mechanisms affected by TA are indicated. Moreover, issues related to the biotechnological methods of production, effective eluents, and TA derivatives are presented.     

Equation of state of CaMnO3: a combined experimental and computational study

Elastic properties of CaMnO₃ are of primary importance in the science and technology of CaMnO₃-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K ₀, of 1734(96) kbar was obtained after fitting parameters to the third-order Birch–Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.     

Plasmonic enhancement of blue emission from ZnO nanorods grown on the anodic aluminum oxide (AAO) template

Luminescent properties of ZnO nanorods covered with Ag nanoparticles are examined. Nanorods were synthesized on AAO templates using Atomic Layer Deposition (ALD) technique. Two types of the samples were prepared with different arrangement of ZnO nanorods and doping conditions. Nanorods of the second type were codoped with Al, to stimulate defect-related emissions. The ZnO material fills heterogeneously the interior of the AAO nanopores and has hexagonal, wurtzite structure. Both types of structures exhibit a broad defect-related emission at about 440 nm, most probably related to recombination at zinc interstitial (Zn_i) defects. This emission in samples with a random distribution of ZnO:Al nanorods and finer Ag nanoparticles is enhanced by factor of ～2.5 upon Ag deposition. The so-obtained material is interesting from the point of view of its application in blue range emitting diodes.     

The 2:1 cocrystal of benzamide and penta­fluoro­benzoic acid

The crystal structure of the title compound, benzamide–2,3,4,5,6‐penta­fluoro­benzoic acid (2/1), 2C₇H₇NO·C₇HF₅O₂, consists of centrosymmetric hexa­meric supermolecules composed of four amide and two carboxylic acid mol­ecules connected via O—H⋯O and N—H⋯O hydrogen bonds. No phen­yl–perfluoro­phenyl π–π stacking inter­actions are observed in this cocrystal.     

Systems of Inclusions Involving Fredholm Operators of Nonnegative Index and Nonconvex-Valued Maps

We study the existence of solutions to a system of two inclusions involving Fredholm operators of nonnegative (Fredholm) index and the so-called c-admissible maps: upper semicontinuous maps with values being continuous images of cell-like sets. The presented approach resembles the substitution technique, i.e. applies the so-called solution map. The appearance of the ‘dimension defect’ reflecting the nonnegativity of Fredholm indices requires the use of algebraic tools based on the cohomotopy theory, different from the usual homological ones present in the fixed point theory. An application to boundary value problems is provided as well as the brief exposition of basic facts from the cohomotopy theory. Mathematics Subject Classifications (2000) 47H04, 47A53, 55M20, 55Q55, 34A60.     

Global existence to a three‐dimensional non‐linear thermoelasticity system arising in shape memory materials

This paper is concerned with the unique global solvability of a three‐dimensional (3‐D) non‐linear thermoelasticity system arising from the study of shape memory materials. The system consists of the coupled evolutionary problems of viscoelasticity with non‐convex elastic energy and non‐linear heat conduction with mechanical dissipation. The present paper extends the previous 2‐D existence result of the authors Reference [1] to 3‐D case. This goal is achieved by means of the Leray–Schauder fixed point theorem using technique based on energy arguments and DeGiorgi method. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiple Gradient TLC and Densitometric Analysis of p-Coumaric Acid in Some Medicinal Plants from the Family Solanaceae

JPC – Journal of Planar Chromatography – Modern TLC -     

Effective High‐Pressure Cleavage of Sterically Hindered Steroid Esters

A simple and effective method to deprotect of sterically hindered steroid esters is described. Deprotection was carried out in MeOH in the presence of a catalytic amount of Et₃N under high‐pressure conditions. Enzymatic, anionite, and high‐pressure methods are compared.