[en] The Maxwell algebra, an enlargement of Poincaré algebra by Abelian tensorial generators, can be obtained in arbitrary dimension D by the suitable contraction of O(D-1,1)⊕O(D-1,2) (Lorentz algebra ⊕ AdS algebra). We recall that in D=4 the Lorentz algebra O(3,1) is described by the realification Sp_R(2|C) of complex algebra Sp(2|C)≃Sl(2|C) and O(3,2)≃Sp(4). We study various D=4N-extended Maxwell superalgebras obtained by the contractions of real superalgebras OSp_R(2N-k;2|C)⊕OSp(k;4) (k=0,1,2,…,2N); (extended Lorentz superalgebra ⊕ extended AdS superalgebra). If N=1 (k=0,1,2) one arrives at three different versions of simple Maxwell superalgebra. For any fixed N we get 2N different superextensions of Maxwell algebra with n-extended Poincaré superalgebras (1⩽n⩽N) and the internal symmetry sectors obtained by suitable contractions of the real algebra O_R(2N-k|C)⊕O(k). Finally the comments on possible applications of Maxwell superalgebras are presented.

[en] This paper presents a comprehensive study of the boundedness, global asymptotic stability and periodic character for positive solutions of a higher-order difference equation of interest.

[en] We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions and obtain an asymptotic expansion of its exact expression for large M and N

[en] We prove an asymptotic formula for the distribution of primes among the denominators of the approximants for almost all real numbers

No abstract available

[en] A fast approach is described for determination of the normalized parameter of the failure flow for recoverable objects. It is shown that the asymptotic values of the parameter are reached in a very short period. This conclusion allows to consider the failure flow stationary in the reliability analysis and to use the asymptotic value ω-tilde for the whole period

[en] Results on nodal properties of L² solutions of two-dimensional Schroedinger equations obtained in a previous paper are refined. The generally unbounded nodal set of ψ is investigated for r → ∞ and shown that in this limit the nodal set consists of non-intersecting nodal lines which look asymptotically either like straight lines or like branches of parabolas. (G.Q.)

[en] Let Ω_R=RⁿB_R where n≥3 and B_R{x is an element of Rⁿ:|x|≤R}. We investigate the asymptotics of real valued solutions ψ is an element of L²(Ω_R) of the Schroedinger equation (-Δ+V-E)ψ=0, where E<0 and V(x)→0 for |x|→∞ : Let D denote an unbounded nodal domain of ψ(i.e. a component of Ω_R {x:ψ(x)=0}) and let S(r)={y is an element of S^n-1:ry is an element of D} with S^n-1 the unit sphere in Rⁿ. Under suitable assumptions on V it is shown that for some γ>0 lim inf_r→∞r^γ∫_S(r)ψ²dσ/ ∫_S^n-1ψ²dσ >0 and lim inf_r→∞ln(Volume(D intersection B_r))/lnr≥(n+1)/2. Results of this type are already non trivial for radial problems with ψ satisfying non radial boundary conditions on ∂Ω_R or for exited states of the Hydrogen atom if one considers linear combinations of different l-waves. 25 refs. (Author)

[en] The discrete ergodic method is used to find a complete solution of the problem of the asymptotic behaviour of the number of representations of integers by an arbitrary integral isotropic ternary quadratic form both over regions on the corresponding surface and over the residue classes of a given modulus

No abstract available