Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system.     

Correlation for the fin Nusselt number of natural convective heat sinks with vertically oriented plate-fins

In this paper, a correlation for estimating the fin Nusselt number of natural convective heat sinks with vertically oriented plate-fins is suggested. For this purpose, extensive experimental investigations are performed for various channel widths, heights and input powers. A numerical simulation is conducted by using a commercial tool to verify the present experimental results and examine fluid flow and heat transfer characteristics of a natural convective heat sink. By comparison of the present study and the previous studies, it is shown that the present correlation is widely applicable for Elenbaas numbers between 0.5 and 2 × 10⁶ and is more accurate than previous correlations. Based on an asymptotic approach, it is found that the optimal channel width is independent of the heat sink height but dependent of the heat sink length, the difference between the heat sink base and the ambient temperatures, and fluid property.     

Syntomic regulators and special values of p-adic L-functions

In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map, and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters. Oblatum 14-V-96 & 9-X-97     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Finding more perfect matchings in leapfrog fullerenes

We use some recent results on the existence of long cycles in leapfrog fullerenes to establish new exponential lower bounds on the number of perfect matchings in such graphs. The new bounds are expressed in terms of Fibonacci numbers.     

A [Cyclentetrakis(methylene)]tetrakis[2‐hydroxybenzamide] Ligand That Complexes and Sensitizes Lanthanide(III) Ions

The synthesis of the cyclen derivative H₄ L ¹ ?2 HBr containing four 2‐hydroxybenzamide groups is described. The spectroscopic properties of the Ln^III conplexes of L ¹ (Ln=Gd, Tb, Yb, and Eu) reveal changes of the UV/VIS‐absorption, circular‐dichroism‐absorption, luminescence, and circularly polarized luminescence spectra. It is shown that at least two metal‐complex species are present in solution, whose relative amounts are pH dependent. At pH>8.0, an intense long‐lived emission is observed (for [Tb L ¹ ] and [Yb L ¹ ]), while at pH<8.0, a weaker, shorter‐lived species predominates. Unconventional Ln^III emitters (Pr, Nd, Sm, Dy, and Tm) were sensitized in basic solution, both in the VIS and in the near‐IR, to measure the emission of these ions.     

Catalytic one-pot synthesis of [5.5.5.6]fenestrane systems via a dicobalt octacarbonyl-catalyzed tandem cycloaddition of dienediynes

Catalytic one-pot synthesis of fenestrane derivatives from dienediynes was developed: fenestranes were synthesized in high yields by a dicobalt octacarbonyl-catalyzed tandem cycloaddition of dienediynes.     

Charge and spin structure in of YBa(2)Cu(3)O(6.35)

Neutron scattering has been used to measure the charge and spin structure in the highly underdoped superconductor YBa(2)Cu(3)O(6.35). Incommensurate static charge ordering is found that remains at high temperatures. The magnetic pattern is complex with a resonance and incommensurate structure observed at low temperatures. The results clarify the role of striped phases in YBa(2)Cu(3)O(6+x) superconductors.