We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are independent from the spectral parameter. For such operators we prove a representation for the heat kernel as a sum over all walks with given initial and terminal edges. Using this representation a trac...

Synaptic transmission is a critical mechanism for transferring information from the nervous system to the body. Environmental stress, such as extreme temperature, can disrupt synaptic transmission and result in death. Previous work on larval Drosophila has shown that prior heat-shock exposure protects synaptic transmission against failure during subsequent thermal stress. This induced thermopro...

In this article we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation [16], by showing that the solution to this approximation approaches the fundamental solution of the heat equation at a sub-optimal rate. The result is valid in particular for the central differences scheme approximation of the heat equation, a property which to our knowl...

Studies on the durability and dimensional stability of a series of hardwoods and softwoods after thermal modification in vegetable oils and in steam atmospheres have been performed. Mass loss after exposure to Coniophora puteana (BAM Ebw.15) for 16 weeks was very low for European birch, European aspen, Norway spruce, and Scots pine thermally modified in a linseed oil product with preservative (...

Bending property of Ti-Ni alloy dental castings was evaluated in comparison with that of Co-Cr alloy in a cantilever test. Heat treatment effect on the bending property was also investigated in relation to phase transformation. Ti-50.85Ni (mol%) alloy was used, and the shape of bending test specimens was half-rounded in cross section, 2.0mm in diameter. The bending test was carried out at 310K....