We use the following standard terminology. We denote by Denjoy domain an open subset Ω of the complex plane C whose complement E := C \ Ω, where C := C ∪ {∞}, is a subset of R := R ∪ {∞}, where R is the real axis (see [13]). Throughout the paper we rely on the following assumption. Each point of E (including the point at infinity) is regular for the Dirichlet problem in Ω. Denote by P∞ = P∞(Ω) ...

Genetically driven alterations in the complement of retinal photopigments are fundamental steps in the evolution of vision. We sought to determine how a newly added photopigment might impact vision by studying a transgenic mouse that expresses a human cone photopigment. Electroretinogram (ERG) measurements indicate that the added pigment works well, significantly changing spectral sensitivity w...

Spectral tuning of visual pigments is typically accomplished through changes in opsin amino acid sequence. Within a given opsin class, changes at a few key sites control wavelength specificity. To investigate known differences in the visual pigment spectral sensitivity of the Lake Malawi cichlids, Metriaclima zebra (368, 488, and 533 nm) and Dimidiochromis compressiceps (447, 536, and 569 nm), ...

Behavioral discrimination tests and electroretinogram (ERG) flicker photometry were used to measure spectral sensitivity and to define the spectral mechanisms of the guinea pig (Cavia porcellus). Results from these 2 approaches converge to indicate that guinea pig retinas contain rods with peak sensitivity of about 494 nm and 2 classes of cone having peak sensitivities of about 429 nm and 529 n...

Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection. Such games can be formulated as the search for sections to the complement of a coverage region in a Euclidean space over a timeline. Prior results give homological criteria for evasion in the general case that are not necessary and sufficient. This paper provides a necessary and sufficient positive coho...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...