We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere. 1. Harmonic morphisms Harmonic maps φ : (M, g) → (N, h) between two smooth Riemannian manifolds are critical points of the energy functional E(φ,Ω) = 1 2 ∫ Ω |dφ| dvg for any compact domain Ω ⊆...

p53-Based cyclotherapy is proving to be a promising approach to palliate undesired effects of chemotherapy in patients with tumours carrying p53 mutations. For example, pre-treatment of cell cultures with Nutlin-3, a highly-selective inhibitor of the p53-mdm2 interaction, has been successfully used as a cytostatic agent to protect normal cells, but not p53-defective cells, from subsequent treat...

Protection against harmful chemical compounds is a major social concern, especially warfare agents (CWAs) that are easy to synthesize and can cause mass casualties. The metal oxides with large surface area, porous structures, number of active sites have shown outstanding performance for the adsorption decontamination CWAs. However, single-component show lower degradation rate agents. Here, we d...

We present the structure of the human Aurora B kinase domain in complex with the C-terminal Aurora-binding region of human INCENP and the Aurora kinase inhibitor VX-680. The structure unexpectedly reveals a dimeric arrangement of the Aurora B:INCENP complex, which was confirmed to exist in solution by analytical ultracentrifugation. The dimerization involves a domain swap of the activation loop...

A vertex set X of a digraph D = (V, A) is a kernel if X is independent (i.e., all pairs of distinct vertices of X are non-adjacent) and for every v ∈ V − X there exists x ∈ X such that vx ∈ A. A vertex set X of a digraph D = (V, A) is a quasi-kernel if X is independent and for every v ∈ V − X there exist w ∈ V − X, x ∈ X such that either vx ∈ A or vw, wx ∈ A. In 1994, Chvátal and Lovász proved ...

We compute the decay of the autocorrelation function of the observable |vx| in the Sinai billiard and of the observable vx in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disks is centered inside a unit square. The asymptotic decay is found to be C(t) ∼ c(R)/t. An explicit expression is given for the prefact...

The present work aims to determine the solution f : R2 → R of the equation f(ux − vy, uy − vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) for all x, y, u, v ∈ R without any regularity assumption. The solution of the functional equation f(ux+ vy, uy− vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) is also determined. The methods of solution of these equations are simple and elementary. These two equations ...

Let G be a semisimple connected linear Lie group, w, a finite-dimensional irreducible representation of G, tr2 an infinite-dimensional irreducible representation of G which has a nontrivial extension with w,. We study the category of all Harish-Chandra modules whose composition factors are equivalent to w, and Introduction. In a series of articles [5]-[8], I. M. Gelfand, Graev and Ponomarev cla...

Objective. To study the clinical manifestations of W1282R variant, functional activity cystic fibrosis transmembrane conductance regulator (CFTR) channel, and effectiveness CFTR modulator therapy in patients with variant. Materials methods included medical records, intestinal current measurement method (ICM) organoids (IO). Results. The c.3844T>C (p.Trp1282Arg, W1282R) variant refers to miss...