The multicolor Ramsey number rk(C4) is the smallest integer n for which any k-coloring of the edges of the complete graph Kn must produce a monochromatic 4-cycle. In [6] and [3] it was proved that rk(C4) ≥ k2−k+2 for k − 1 being a prime power. In this note we establish rk(C4) ≥ k2 + 2 for k being an odd prime power. ( Journal of Combinatorial Theory, Series B 79, 172–176 (2000))

We investigate the question of whether one can characterize complexity classes in terms of efficient reducibility to the set of Kolmogorov-random strings RK. We show that this question is dependent on the choice of universal machine in the definition of Kolmogorov complexity. We show for a broad class of reductions that the sets reducible to RK have very low computational complexity. Further, w...

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring Rk,s = F42k [u1, . . . , us]/〈u 2 1 − u1, . . . , u 2 s − us〉. We define an automorphism θ over Rk,s which helps us both finding the idempotent decomposition of Rk,s and solving the reversibility problem via skew cyclic codes. Moreover, we introduce a generaliz...

Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...

PURPOSE To demonstrate that the crucial elements responsible for the spatial and temporal expression patterns of rhodopsin kinase (Rk) are contained within a narrow conserved segment immediately flanking the Rk transcription start sites. METHODS Sequences upstream of the mouse Rk gene were compared to the human sequence to identify areas of conservation. Transgenic mice carrying a segment of ...

Rhodopsin kinase (RK), a specialized G-protein-coupled receptor kinase expressed in retina, is involved in quenching of light-induced signal transduction in photoreceptors. The role of RK in recovery after photoactivation has been explored in vitro and in vivo experimentally but has not been specifically defined in humans. We investigated the effects on human vision of a mutation in the RK gene...

Structure–function studies of rhodopsin kinase (RK; EC 2.7.1.125) require a variety of mutants. Therefore, there is need for a suitable system for the expression of RK mutant genes. Here we report on a study of expression of the RK gene in baculovirus-infected Sf21 cells and characterization of the enzyme produced as purified to near homogeneity. Particular attention has been paid to the posttr...

This paper deals with periodic solutions of the Hamilton equation ẋ(t) = J∇xH(x(t), λ), where H ∈ C2,0(R2n × Rk,R) and λ ∈ Rk is a parameter. Theorems on global bifurcation of solutions with periods 2π j , j ∈ N, from a stationary point (x0, λ0) ∈ R2n × Rk are proved. ∇xH(x0, λ0) can be singular. However, it is assumed that the local topological degree of ∇xH(·, λ0) at x0 is nonzero. For system...

The retinal S-antigen (S-Ag) has been shown to induce uveitis effectively in subhuman primates, and lymphocytes from patients with certain uveitic conditions show cell-mediated responses to this antigen. Rhodopsin kinase (RK), an enzyme probably unique to the mammalian eye, is reported here to resemble the retinal S-Ag in its capacity to induce uveitis in experimental animals. A histological co...

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storag...