Large Deviations for Random Trees

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.     

Oscillation criteria for second-order nonlinear differential equations with damping

For a second-order nonlinear differential equation with a damping term, we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades. Two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations, and both sets of oscillation criteria established in the paper are of independent interest. Several examples are provided to illustrate the relevance of the new theorems.     

Decision Making Times in Mean-Field Dynamic Ising Model

We consider a dynamic mean-field ferromagnetic model in the low-temperature regime in the neighborhood of the zero magnetization state. We study the random time it takes for the system to make a decision, i.e., to exit the neighborhood of the unstable equilibrium and approach one of the two stable equilibrium points. We prove a limit theorem for the distribution of this random time in the thermodynamic limit.     

Multifrequency tapered plasmonic nanoantennas

We suggest a multifrequency Yagi–Uda-type nanoantenna loaded with an array of tapered plasmonic nanorods. The arrays of director nanorods can be used for the excitation of the nanoantenna by emitters matched spectrally with their resonant frequency and placed in their near-field region. An overlap of multifrequency operating bands of the nanoantenna provides novel opportunities for broadband operation, and the same nanoantenna architecture can be employed both as a transmitter and/or as a receiver, thus being useful for broadband wireless communication.     

Symmetry analysis of the bidimensional Lane–Emden systems

We carry out a complete group classification of the nonlinear Lane–Emden systems in dimension two. The Noether symmetries are found and their corresponding conservation laws are established.     

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Numerical Algorithms - An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in $\mathbb {R}^{d} (d \geq 1)$ ....     

Fidelity evaluation of metallic luster in six-band high-dynamic-range imaging

This paper presents subjective evaluation results for images reproducing metallic luster. The images were produced by a six-band high-dynamic-range imaging technique, which provides high color fidelity and the capability of various tone mapping operations. The preferences for images produced by four kinds of tone mapping operations were evaluated by means of a paired comparison method under the conditions that observers could or could not refer to real scenes. The evaluation results indicated that preferences for images depend on tone mapping operations, especially for objects that have the luster changing over a large area with moderately high intensity. In addition, when referring to a real scene, the spatially varying tone compression, which reproduces the color and complex characteristics of metallic luster, was significantly preferable to the tone mappings by other approaches. Without a real scene, the preference was also strong for images produced by simply saturating pixel values at highlights.     

Chiral ion pairs in catalysis: lithium salts of chiral metallocomplex anions as catalysts for asymmetric C–C bond formation

A series of Co(III) anionic complexes of Schiff bases obtained from substituted salicylaldehydes and optically active amino acids has been synthesized. The ion pairing of these anions to a lithium cation can be used to induce asymmetry into lithium-catalyzed trimethylsilylcyanation of aldehydes and Michael reactions. The influence of the temperature, solvent polarity and structural modification of the chiral anion on the enantioselectivity of the catalysis has been investigated.