On the multilinear restriction and Kakeya conjectures

We prove d-linear analogues of the classical restriction and Kakeya conjectures in R ^d . Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians, closely related to heat flow. We conclude by giving some applications to the corresponding variable-coefficient problems and the so-called “joints” problem, as well as presenting some n-linear analogues for n < d.     

Weighted Hardy inequalities for decreasing sequences and functions

We obtain a complete characterization of the weights for which Hardy's inequality holds on the cone of non-increasing sequences. Our proofs translate immediately to the analogous inequality for non-increasing functions, thereby also completing the investigation in that direction. As an application of our results we characterize the boundedness of the Hardy-Littlewood maximal operator on Lorentz sequence spaces.     

On Tzitzéica Vortex Streets and Their Reciprocals in Subsonic Gas Dynamics

Hydrodynamic vortex street solutions are generated based on an elliptic Tzitzéica model. A multiparameter class of reciprocal transformations is coupled with the action of a Bäcklund transformation to construct compressible vortex solutions of breather type valid in subsonic flow régimes of a generalized Kármán–Tsien gas.     

Holey self-orthogonal Latin squares with symmetric orthogonal mates

We improve the existence results for holey self-orthogonal Latin squares with symmetric orthogonal mates (HSOLSSOMs) and show that the necessary conditions for the existence of a HSOLSSOM of typeh ⁿ are also sufficient with at most 28 pairs (h, n) of possible exceptions. Research supported in part by NSERC Grant A-5320 for the first author, NSF Grants CCR-9504205 and CCR-9357851 for the second author, and NSFC Grant 19231060-2 for the third author.     

Intrinsic ultraviolet luminescence from Lu2O3, Lu2SiO5 and Lu2SiO5:Ce

Radioluminescence and thermally stimulated luminescence measurements on Lu₂O₃, Lu₂SiO₅ (LSO) and Lu₂SiO₅:Ce³⁺ (LSO:Ce) reveal the presence of intrinsic ultraviolet luminescence bands. Characteristic emission with maximum at 256 nm occurs in each specimen and is attributed to radiative recombination of self-trapped excitons. Thermal quenching of this band obeys the Mott-Seitz relation yielding quenching energies 24, 38 and 13 meV for Lu₂O₃, LSO and LSO:Ce, respectively. A second intrinsic band appears at 315 nm in LSO and LSO:Ce, and at 368 nm in Lu₂O₃. Quenching curves for these bands show an initial increase in peak intensity followed by a decrease. Similarity in spectral peak position and quenching behavior indicate that this band has a common origin in each of the samples and is attributed to radiative recombination of self-trapped holes, in agreement with previous work on similar specimens. Comparison of glow curves and emission spectra show that the lowest temperature glow peaks in each specimen are associated with thermal decay of self-trapped excitons and self-trapped holes. Interplay between the intrinsic defects and extrinsic Ce³⁺ emission in LSO:Ce is strongly indicated.     

InSb epilayers on GaAs(100) for spintronic and magneto-resistive sensor applications

Both magneto-resistive sensors and spintronic hybrid semiconductor devices require thin epitaxial layers of high-mobility InSb. Here we study unintentionally doped InSb epilayers grown on semi-insulating GaAs(100) substrates by molecular-beam epitaxy. We have introduced an initial low-temperature growth step extending the work that the NTT group reported in 2000. We find significant improvement in the room temperature mobility for epilayer thickness between 60 and 300 nm. The importance of the initial growth step to the epilayer mobility performance is discussed.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Renormalization group approach to 1D cellular automata with large updating neighborhoods

We study self‐similarity in one‐dimensional probabilistic cellular automata (PCA) by applying a real‐space renormalization technique to PCA with increasingly large updating neighborhoods. By studying the flow about the critical point of the renormalization, we may produce estimates of the spatial scaling properties of critical PCA. We find that agreement between our estimates and experimental values are improved by resolving correlations between larger blocks of spins, although this is not sufficient to converge to experimental values. However, applying the technique to PCA with larger neighborhoods, and, therefore, more renormalization parameters, results in further improvement. Our most refined estimate produces a spatial scaling exponent, found at the critical point of the five‐neighbor PCA, of ν = 1.056 which should be compared to the experimental value of ν = 1.097. © 2014 Wiley Periodicals, Inc. Complexity 21: 206–213, 2015     

Synthesis,physical properties,and structure of TIPS-difuranoacenes

The synthesis, physical properties, and structure of triisopropylsilylethynyltetracenodifuran (2) and pentacenodifuran (3) derivatives were reported. There showed high stability in solution in the dark, yet decomposed under light. Single crystal of pentacenodifuran was analyzed by X-ray diffraction analysis, and showed one dimensional packing array along the c-axis. The molecules were stacked with a 3.30 Å interlayer distance. The crystals exhibited a high thermal stability under an ambient condition.