Let X be a set of n Boolean variables and denote by C(X) the set of all 3lauses overX, i.e. the set of all 8 n3 possible disjun tions of three distin t, nonomplementary literals from variables in X. Let F (n;m) be a random 3-SAT formula formed by sele ting, with repla ement, m lauses uniformly at random from C(X) and taking their onjun tion. The satis ability threshold onje ture asserts that th...

This paper is concerned with the existence of ground states for a class Kirchhoff type equations in R3 combined power nonlinearities ?a+b?R3|?u(x)|2?u=?u+|u|p?2u+u5 restriction ?R3u2=c2 Sobolev critical case 2* = 6 and proves that problem has state solution (uc,?c)?S(c)×R any c > 0, a, b 143?p<6, where S(c)=u?H1(R3):?R3u2=c2.

Hindbrain neural crest cells adjacent to rhombomeres 2 (r2), r4 and r6 migrate in a segmental pattern, toward the first, second and third branchial arches, respectively. Although all rhombomeres generate neural crest cells, those arising from r3 and r5 deviate rostrally and caudally (J. Sechrist, G. Serbedzija, T. Scherson, S. Fraser and M. Bronner-Fraser (1993) Development 118, 691-703). We ha...

In Arabidopsis, a MYB-bHLH-WD40 (MBW) transcriptional activator complex activates the homeodomain protein gene GLABRA2 (GL2), leading to the promotion of trichome formation and inhibition of root hair formation. The same MBW complex also activates single-repeat R3 MYB genes. R3 MYBs in turn, play a negative feedback role by competing with R2R3 MYB proteins for binding bHLH proteins, thus blocki...

The receptor for hyaluronic acid-mediated motility (RHAMM/CD168) has been described as a leukemia-associated antigen. To define T-cell epitopes of RHAMM/CD168 toward specific immunotherapies for acute myeloid leukemia (AML), 10 potential HLA-A2-binding RHAMM/CD168 peptides (R1 to R10) were synthesized based on computer algorithms and screened by enzyme-linked immunospot (ELISPOT) analysis using...

We show that the intersection of three subgroups in a free group is related to the computation of the third homotopy group π3. This generalizes a result of Gutierrez-Ratcliffe who relate the intersection of two subgroups with the computation of π2. Let K be a twodimensional CW-complex with subcomplexes K1,K2,K3 such that K = K1 ∪ K2 ∪ K3 and K1 ∩ K2 ∩ K3 is the 1-skeleton K of K. We construct a...

For simplicity, we adopt the following convention: D is a set, x, x0, y, y0, z, z0, r, s, t are real numbers, p, a, u, u0 are elements of R3, f , f1, f2, f3, g are partial functions from R3 to R, R is a rest, and L is a linear function. We now state three propositions: (1) dom proj(1, 3) = R3 and rng proj(1, 3) = R and for all elements x, y, z of R holds (proj(1, 3))(〈x, y, z〉) = x. (2) dom pro...

In this paper we find a ground state solution for the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. where V is a possibly singular potential and 3 < p < 5.