Finite pseudocomplemented lattices: The spectra and the Glivenko congruence

Recently, Gr?tzer, Gunderson and Quackenbush have characterized the spectra of finite pseudocomplemented lattices, solving a problem raised by G. Gr?tzer in his first monograph on lattice theory from 1971. In this note we discuss the tight connection between the spectra and the Glivenko congruence of finite pseudocomplemented lattices.     

An extension of the SCP-integral with a relaxed integration by parts formula

An integral more general than the SCP-integral is introduced, and among other properties, it is proved that iff is integrable in this sense with its second primitive ACG* and ifG is the indefinite integral of a functiong of bounded variation, thenfG is also integrable in this sense and the integration by parts formula holds. The integration by parts formula for the SCP-integral is also proved wheng is of bounded variation. This advances the existing result when, in addition,g is also continuous.     

Приближение функций многих переменных классов H p Ω полиномами по системе Хаара

In the paper, problems of approximation of functions indicated in the title are studied in the case when a majorant of their mixed modulus of continuity is given. Two forms of approximation (linear and nonlinear) are considered: the classical linear approximation by polynomials with respect to the Haar system when the indices lie in hyperbolic crosses; and the best M-term approximation by polynomials also with respect to the Haar system. For the corresponding quantities, exact estimates are obtained as to their order of magnitude.     

О структуре множеств расходимости рядов Ф урье-Уолша

It is proved that each set ofG _δ type on the dyadic groupG is the set of unbounded divergence of some Fourier-Walsh-Lebesgue series. There exists such a functionf(x)∈C(G) that the set of divergence of its Fourier-Walsh series possesses the following properties: ¦E¦=0,E∈G _δσ,E?F _σ,E∈G _δ, andE cannot be represented neither in the formE=(E₀N₁)∪N₂, whereE ₀∈G _δ andN ₁,N ₂ are countable, nor in the formE=(E⁰P₁), whereE ⁰∈F _σ, |E ⁰|=0, andP ₁,P ₂ are of the first category onG.     

О распаде твердых растворов KCl-NaClAbout Decay of Solid Solutions KCl-NaCl

Lattice parameter of KCl, NaCl and 10 solid solutions of these salts within the temperature range of 20 – 780 °C has been measured. The whole equilibrium decay curve of solid solutions KCl - NaCl has been obtained. It has been shown, that rectilinear diameter rule and empirical rule of constancy of molal volumes sum at conjugate points on the decay curve are well kept for the curve.     

On local summability of Riesz potentials in the case Reα>0

The rangeI ^α (L _p ) of the Riesz potential operator, defined in the sense of distributions in the casep≥n/α, is shown to consist of regular distributions. Moreover, it is shown thatI ^α (L _p ) ?L _p ^loc (R ⁿ ) for all 1≤p<∞ and 0<α<∞. The distribution space used is that of Lizorkin, which is invariant with respect to the Riesz operator.     

A theorem concerning approximation on the sphere

Рассматривается тео рема типа Джексона и е е обращение на единичной сфереσ _n ?1≡σ пространстваR ⁿ . Сфери ческий сдвигS _y f(μ) фун кцииf(μ)∈L _p (σ), 1≦p≦∞, определяе тся как среднее значениеf(μ′) на «окружности»μ μ′=cosγ, μ,μ′∈σ. Для того, чтобы при 2k>г-2?>0 выполнялось нер авенство $$\left\| {(S_\gamma - E)^k D^\varrho f} \right\|L_p \left( \sigma \right) \leqq M\gamma ^{r - 2\varrho } $$ (гдеE — единичный опер атор, D - оператор Лапласа—Бельтрами) н еобходимо и достаточ но, чтобы наилучшее приб лижение функциf в мет рикеL _p (σ) полиномами порядкаv по сферическим гармоникам подчинял ось оценке $$E_v \left( f \right)_p \leqq \frac{K}{{v^r }} \left( {v = 1, 2, \ldots } \right).$$ Полное доказательст во дано приp=2.     

Some inequalities for Franklin series

Обозначим через {f _k (t)} _k=0 ^∞ систему Франклина на отрезке [0, 1]. Доказано, чт о еслиg∈L(0,1), то $$mes\{ t:|\sum\limits_{\kappa = 0}^\infty {\varepsilon _\kappa a_\kappa (g)f_\kappa (t)| > y} \} \leqq \frac{B}{y}\int\limits_0^1 {|g(t)|dt} $$      

ИССЛЕДОВАНИЕ НЕКОТО РЫХ СЛОЖНЫХ ПОЛУПРОВОДНИКОВЫХ Т ВДРДЫХ РАСТВОРОВ И СОЕДИНЕНИЙ НА ОСНОВ Е ИНДИЯ

A(III)B(V)-A₂(III)B₃(VI) - , , , In₂S₃, In₂Se₃ In₂Te₃, . , , : InP-In₂Se₃ — 50% , InAs-In₂Se₃ — 60% , InAs-In₂Te₃ — — . . , A(III)B(V). - - In₄SbTe₃, 6,12₈ Å. , .

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Investigation of some complex semi-conducting solid solutions and compounds on the basis of indium

In order to determine the possibility of preparing solid solutions on the principle of heterovalent substitution between semi-conducting compounds with undefective and defective structures A(III) B(V)-A₂(III) B₃(VI) systems on the basis of indium-indium phosphide, indium arsenide and indium antimonide on the one hand and In₂S₃, In₂Se₃ and In₂Te₃ on the other, are investigated.It was found by means of X-ray structure analysis and thermal and metallographical examinations that immediately after the synthesis, solid solutions with the structure of zinc blende are created in the following systems: InP-In₂Se₃ — in the range of 50% concentration of the initial compounds, InAs-In₂Se₃ — in the range of 60% concentration of the initial compounds, InAs-In₂Te₃ — unlimited solid solutions.Certain electric properties of the alloys within the range of existence of the solid solutions were measured.Regarding the rest of the systems, observable solubility is either completely missing or is limited within a narrow region near the compounds of the A(III) B(V)-type.In the indium-antimony-tellurium system a new compound, with empirical formula In₄SbTe₃ was discovered which showed an NaCl-type structure and lattice parameter equal to 6·12₈ Å. Preliminary study of the electrical characteristics concerning this compound leads to the conclusion that it possesses semi-conducting properties.