Spectral Analysis of Biorthogonal Expansions of Functions, and Exponential Series

Abstract

Measurements of the temperature-dependent resistivity of high-mobility GaAs/GaAlAs heterojunctions are used to measure the effective mass of Composite Fermions (CF). The CF effective mass is found to increase approximately linearly with the effective field B * up to effective fields of 14 T. Data from all fractions around ν = 1/2 are unified by the single parameter B * for samples studied over a wide range of temperature. The energy gap is found to increase as √ B * at high fields. Hydrostatic pressure is used to reduce the value of the electron g-factor, and this is shown to have a large effect on the relative strengths of different fractions. By 13.4 kbar, where the Zeeman energy is only 1/4 of its value at 0 bar, fractions with odd numerators are found to be strongly suppressed, and new features with even numerators appear. The energy gaps measured for 5/3 as a function of carrier density and pressure are consistent with a g-factor equal to the bulk value enhanced by a factor of two due to exchange interactions.

To the Question of a Multipoint Mixed Boundary Value Problem for a Wave Equation

“…which is the Riesz basis in 0, (see [1]). Here is a multiplicity of the corresponding eigenvalue for all ∈ .…”

“…Since is defined on ∞, ∞ , then we can always to continue functions and outside of the segment 0, . From [1] Bekbolat Bayan -Doctorate, аl-Farabi Kazakh National University, Almaty, Kazakhstan.…”

Спектральное Разложение Модельных Операторов В Пространствах Де Бранжа

“…В случае экспонент теорема 2.2 эквивалентна критерию полноты Б. Я. Лeвина (см. [15]), а теорема 2.6 впервые доказана в [20]. В случае Λ = Λ + теорема 2.8 для семейств экспонент впервые доказана Б. С. Павловым (см.…”