The existence of multiple solutions for a class of fourth-order elliptic equation with respect to the generalized asymptotically linear conditions is established by using the minimax method and Morse theory.

We prove that a morphism h over a two-letter alphabet {a, b} is overlap-free, i.e., maps overlap-free words into overlap-free words, iff the word h(abbabaab) is overlap-free. As a consequence, we obtain a simple proof of the fact that the only infinite overlap-free words that can be obtained by iterating a morphism are the Thue-Morse sequence and its opposite. RLsumP Nous prouvons qu’un morphis...

In this work, we design a nearly linear time discrete Morse theory based algorithm for computing homology groups of 2-manifolds, thereby establishing the fact that computing homology groups of 2-manifolds is remarkably easy. Unlike previous algorithms of similar flavor, our method works with coefficients from arbitrary abelian groups. Another advantage of our method lies in the fact that our al...

The collection, processing and certification of a new sediment Standard Reference Material (SRM), SRM 2704, is described. Collected from the bottom of the Buffalo River in New York State during the fall of 1986, SRM 2704 is certified for 25 elements with information provided on another 22 elements. Improvements in analytical methods as well as the application of well-defined quality-control pro...

The landscape of translational research has been shifting toward drug combination therapies. Pairing of drugs allows for more types of drug interaction with cells. In order to accurately and comprehensively assess combinational drug efficacy, analytical methods capable of recognizing these alternative reactions will be required to prioritize those drug candidates having better chances of delive...

We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can...

A developing country like India encounters challenges like exponential increase in population and rising per capita energy consumption which demands an optimum usage of available energy resources. Currently the energy demands are mostly met by non renewable energy sources, a system that puts a tremendous pressure on the economy and causes a serious threat to the environment, flora and fauna. He...