In this paper, we prove new pinching theorems for the first eigenvalue λ1(M) of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for λ1(M) in terms of higher order mean curvatures Hk. We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost isometric to a standard sphere. Moreover, as a...

In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space X is z-embedded in every larger Tychonoff space if and only if X is almost compact or Lindelöf. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.

In mammals, GRF and pituitary adenylate cyclase-activating polypeptide (PACAP) are encoded in separate genes. We report here that in the salmon a 4.5-kilobase gene contains five exons that encode the biologically active part of the GRF-like peptide (amino acids 1-32) on exon 4 and PACAP on exon 5. Analysis of two fish messenger RNAs reveals that a long precursor containing GRF and PACAP and a s...

BACKGROUND Because an excessive use of activator (formaldehyde + glutaraldehyde) is supposed to be responsible for later adverse events after the use of gelatin resorcin formalin (GRF) glue in surgery for acute aortic dissection, we have tried to use a minimum dose of activator when the GRF glue was applied. We compare our midterm surgical results for acute aortic dissection with and without th...

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎.