$$L^2_f$$ L f 2 -harmonic 1-forms on smooth metric measure spaces with positive $$\lambda _1(\Delta _f)$$ λ 1 ( Δ f )

In this paper, we study vanishing and splitting results on a complete smooth metric measure space \((M^n,g,\mathrm {e}^{-f}\mathrm {d}v)\) with various negative m-Bakry-Émery Ricci curvature lower bounds in terms of the first eigenvalue \(\lambda _1(\Delta _f)\) of the weighted Laplacian \(\Delta _f\), i.e., \(\mathrm {Ric}_{m,n}\ge -a\lambda _1(\Delta _f)-b\) for \(0<a\le \dfrac{m}{m-1}, b\ge 0\). In particular, we consider three main cases for different a and b with or without conditions on \(\lambda _1(\Delta _f)\). These results are extensions of Dung and Vieira, and weighted generalizations of Li-Wang, Dung-Sung, and Vieira.

     

Synthesis and luminescence properties of hybrid systems based on liquid crystal terbium(ІІІ) and europium(ІІІ) complexes

Russian Journal of General Chemistry - Hybrid liquid crystal systems with different ratios of the components have been prepared on the basis of 5,5′-di(heptadecyl)-2,2′-bipyridine...     

Photoelastic analysis of edge residual stresses in glass by the automated tint plate method

Experimental Techniques - The analysis of residual stress in glass is usually carried out by means of photoelastic methods. This article considers the automation of the white light photoelastic...