The primary reasons for conducting fundamental research are satisfying curiosity, acquiring knowledge, and achieving understanding. Here we develop why we believe it is essential to promote basic ecological research, despite increased impetus for ecologists to conduct and present their research in the light of potential applications. This includes the understanding of our environment, for intel...

There are several examples of heuristic rules first proposed from empirical observation, which eventually earned physicochemical validity after the fundamental derivation of a posteriori. This may be the case of Sherwood’s plot – for which a sound rationalization from first principles, entailing enthalpy and mass balances, is provided here; it applies to (fine) chemicals undergoing concentr...

We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group G can be utilized to simplify its solution. We prove, that for a G-invariant maximum lifetime problem there exists a G-invariant solution. Constrains which follow from the G-inv...

We construct fundamental domains for arithmetic subgroups of Γ = GL2(Fq [t]). Given ∆ ⊇ Γ(a) we construct a contracted form T of the Bruhat-Tits tree T and a fundamental domain F of ∆ acting on T. We define a lift of F to F ⊂ T called the “bipartite” lift. We show that F is a fundamental domain of ∆ acting on T precisely when F is “∆-compressed.”

In this paper we study the Casimir force for a piston configuration in R 3 with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is " free to move " along a transverse dimension to the curved one and in the other case the piston " moves " along the curved one. We find that the Casimir force has opposite sig...

Hyperbolic space groups are isometry groups, acting discontinuously on the hyperbolic 3-space with compact fundamental domain. One possibility to classify them is to look for fundamental domains of these groups. Here are considered supergroups for four series of groups with simplicial fundamental domains. Considered simplices, denoted in [9] by T19, T46, T59, belong to family F12, while T31 bel...

Hecke proved analytically that when h > 2 or when h = 2 CDS (m/q), q E Z, q > 3, then B(h) = (7: Im I > 0, / Re 7 1 < h/2, [ 7 j > 1) is a fundamental region for the group G(h) = (SA , T), where S,+ : 7 --f 7 + X and T: 7 ---t -l/~. He also showed that B(A) fails to be a fundamental region for all other A > 0 by proving that G(X) is not discontinuous. We give an elementary proof of these facts ...

The most secure type of grasp of a frictionless woorkpiece is the form-closure grasp. However, task constraints may make achieving form-closure impossible or undesirable. In this case, one needs to employ a force-closure 1 grasp. In this paper, we study the subclass of force-closure grasps known as second-order stable grasps, which typically have a small number of contacts. We derive conditions...