Let q(r) , r = |x| , x ∈ R3 , be a real-valued square-integrable compactly supported function, and [0, a] be the smallest interval containing the support of q(r) . Let A(α′, α) = A(α′ · α) be the corresponding scattering amplitude at a fixed positive energy, k2 = 1 . Let δ` be the phase shifts at k = 1 . It is proved that lim `→∞ ( 2`+ 1 e |δ`| 1 2` ) = a , provided that q(r) does not change si...

In this paper we analyze the behavior of solutions of reaction-diffusion equations with nonlinear boundary conditions of the type (1.1). We show that if f(x, u) = −β0u and g(x, u) = uq in a neighborhood of a point x0 ∈ ΓN , then i) for the case q > 1, if p + 1 < 2q or if p + 1 = 2q and β0 < q, then blow up in finite time at x0 occurs. ii) for the case p > 1 if p + 1 > 2q or if p + 1 = 2q and β0...

Let f and g be two smooth vector fields on a manifold M . Given a submanifold S of M , we study the local structure of time-optimal trajectories for the single-input control-affine system q̇ = f(q) + ug(q) with the initial condition q(0) ∈ S. When the codimension s of S in M is small (s ≤ 4) and the system has a small codimension singularity at a point q0 ∈ S, we prove that all timeoptimal traje...

Q is any quasivariety. A congruence relation 0 on a member A of Q is a Q-congruence if A/0 G Q. The set CouqA. of all Qcongruences is closed under arbitrary intersection and hence forms a complete lattice Cong A. Q. is relatively congruence-distributive if ConjA is distributive for every A e Q.. Relatively congruence-distributive quasivarieties occur naturally in the theory of abstract data typ...

Following the recent theory of $f(Q)$ gravity, we continue to investigate possible existence wormhole geometries, where $Q$ is non-metricity scalar. Recently, scalar and corresponding field equations have been studied for some spherically symmetric configurations in [ Phys. Lett. B 821, 136612 (2021) Rev. D 103, 124001 ]. One can note that are different these two studies. [Phys. (2021)], system...

Let G = (V, E) be a simple graph with vertex set V (G) = {v1, v2, . . . , vn} and edge set E(G). In this paper, first some sharp upper and lower bounds on the largest and least eigenvalues of graphs are given when vertices are removed. Some conjectures in [M. Aouchiche. Comparaison Automatisée d’Invariants en Théorie des Graphes. Ph.D. Thesis, École Polytechnique de Montréal, February 2006.] an...

Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which the...

Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...

Changes in specific tRNA isoacceptors during Friend leukemia cell (F.L.C.) erythroid differentiation have been found to be concomitant with differences in the extent of the Q-base modification in certain species of tRNA. Transfer RNA was isolated from F.L.C. cultures after 0, 36, 48, 72, and 96 hr of DMSO induced differentiation. Changes in 17 isoacceptors of tRNAasn, tRNAasp, tRNAhis and tRNAt...