Superheating behavior in a breakdown reactor

Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule

“…Both the potential V (ξ) and its Fourier transform V (ξ) must have a branching of the form |x| = x 2 1 + x 2 2 + x 2 3 . It is even possible that this condition is unnecessary for the results presented below, but it appears in a wide variety of other problems and is profoundly significant for analytic continuation (see, e.g., [15]). This means that the potential V (r) essentially depends on the first degree of the radius r and its Fourier transform has the same property in relation to |p|.…”

Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide

“…In addition, it was shown in [7] that the eigenvalue of problem (2) in the critical case η 0 = 0 can either be absent or appear in the interval (0, π 2 ) depending on the profile function H in formula (1).…”

“…The discrete spectrum in problem (2) under study in waveguide (1) was studied in [6], where it was verified that under the condition η 0 = π 2 R H(x 1 ) dx 1 < 0 ( 8 ) stating that a perturbation of the waveguide decreases its volume, the interval (0, π 2 ) is free of the spectrum of the problem but contains a unique point…”

“…The asymptotic expansions of the eigenvalues below the threshold λ † = π 2 of the continuous spectrum were sought and studied in numerous publications. In [2]- [5], the existence of an eigenvalue λ ε < λ † for slightly bent waveguides was proved, and its asymptotic expansion was constructed. In [6]- [11], planar and multidimensional waveguides with regular and singular local perturbations of the boundary were considered, different conditions for the existence and absence of the discrete spectrum were obtained, and asymptotic expansions were constructed.…”

“…It is well known (see, e.g., [1]) that the continuous spectrum of problem (2) occupies the ray [π 2 , +∞) divided into intervals of constant multiplicity by the thresholds π 2 n 2 , n ∈ N = {1, 2, 3, . .…”