Homogeneous Instantons in Bigravity

We study homogeneous gravitational instantons, conventionally called the Hawking-Moss (HM) instantons, in bigravity theory. The HM instantons describe the amplitude of quantum tunneling from a false vacuum to the true vacuum. Corrections to General Relativity (GR) are found in a closed form. Using the result, we discuss the following two issues: reduction to the de Rham-Gabadadze-Tolley (dRGT) massive gravity and the possibility of preference for a large $e$-folding number in the context of the Hartle-Hawking (HH) no-boundary proposal. In particular, concerning the dRGT limit, it is found that the tunneling through the so-called self-accelerating branch is exponentially suppressed relative to the normal branch, and the probability becomes zero in the dRGT limit. As far as HM instantons are concerned, this could imply that the reduction from bigravity to the dRGT massive gravity is ill-defined.Comment: 20 pages, 2 figures, comments and references adde

The Laplacian Eigenvalues and Invariants of Graphs

In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.Comment: 10 pages,Filomat, 201

Reduced glutamine synthetase activity alters the fecundity of female Bactrocera dorsalis (Hendel)

Glutamine synthetase (GS) is a key enzyme in glutamine synthesis and is associated with multiple physiological processes in insects, such as embryonic development, heat shock response, and fecundity regulation. However, little is known about the influence of GS on female fecundity in the oriental fruit fly, Bactrocera dorsalis. Based on the cloning of BdGSs, mitochondrial BdGSm and cytoplasmic BdGSc, we determined their expressions in the tissues of adult B. dorsalis. BdGSm was highly expressed in the fat body, while BdGSc was highly expressed in the head and midgut. Gene silencing by RNA interference against two BdGSs isoforms suppressed target gene expression at the transcriptional level, leading to a reduced ovarian size and lower egg production. The specific inhibitor L-methionine S-sulfoximine suppressed enzyme activity, but only the gene expression of BdGSm was suppressed. A similar phenotype of delayed ovarian development occurred in the inhibitor bioassay. Significantly lower expression of vitellogenin and vitellogenin receptor was observed when GS enzyme activity was suppressed. These data illustrate the effects of two GS genes on adult fecundity by regulating vitellogenin synthesis in different ways