We show that the third eigenvalue of Neumann Laplacian in hyperbolic space is maximal for disjoint union two geodesic balls, among domains given volume. This extends a recent result by Bucur and Henrot Euclidean space, while providing new proof key step their argument

There is a slight disparity in smooth ergodic theory, between Pesin theory and the Pugh-Shub partially hyperbolic theory. Both theories assume a weakened form of hyperbolicity and conclude ergodicity. While the two theories have considerable overlap, Pesin theory assumes a C hypothesis, whereas the Pugh-Shub stable ergodicity theorem assumes a C hypothesis. The purpose of this paper is to close...

We study two classes of sigmoids: the simple sigmoids, defined to be odd, asymptotically bounded, completely monotone functions in one variable, and the hyperbolic sigmoids, a proper subset of simple sigmoids and a natural generalization of the hyperbolic tangent. We obtain a complete characterization for the inverses of hyperbolic sigmoids using Euler's incomplete beta functions, and describe ...

We look at periodic Jacobi matrices on trees. provide upper and lower bounds the gap of such operators analogous to well known in spectrum Laplacian half-plane with hyperbolic metric. make some conjectures about antibound states an interesting observation for what [3] calls rg-model.

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. in fact, they both fail to represent proper unloading slopes during cyclic loading. to overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. in this regard, various classes of plastic-damage models have...

in recent decades artificial neural networks (anns) have shown great ability in modeling and forecasting non-linear and non-stationary time series and in most of the cases especially in prediction of phenomena have showed very good performance. this paper presents the application of artificial neural networks to predict drought in yazd meteorological station. in this research, different archite...

If the smooth vector fields X1,…,Xm and their commutators span tangent space at every point in Ω⊆RN for any fixed m≤N, then we establish full interior regularity theory of quasi-linear equations ∑i=1mXi⁎Ai(X1u,…,Xmu)=0 with p-Laplacian type growth condition. In other words, show that a weak solution equation is locally C1,α.