Hamilton算子和R3中相似运动

四元数是一个可除环·　它可表达为R3中通过原点的平面中的四元数乘积的域·　利用Hamilton算子,定义了在该平面上的相似运动,并讨论了这些运动的新特性·     

1H NMR studies of U(IV)-1,2-cyclohexane(dinitrilo)-N,N,N′,N′-tetraacetic acid complexes

¹H NMR spectrum of a U(IV)-trans-1,2-cyclohexane(dinitrilo)-N,N,N′,N′-tetraacetic acid (CyDTA) complex (prepared by dissolving U(IV)(Cy     

Об одной теореме И. И. П ривалова

Let G be a finite Jordan domain,f(z)=u(z)+iv(z) an analytic function inG. Connections between smoothness of the functionu(z) on dG and smoothness of the functionf(z) on ¯G are obtained. In these results the regionG is assumed to satisfy the condition

Коэффициенты рядов Ф урье и класс Липшица

We generalize and sharpen certain results concerning Fourier series from the Lipschitz class. In particular, for sinnx we prove the following: Let ¦b_n¦n^–2L(n) where L(x) is a continuous and slowly oscillating function. Then

MB 45型卤素水分测定仪快速测定面粉中水分

水分含量是面粉的一个重要质量指标，对维持和调节其正常呼吸、色、香、味、型有重要作用，关系到面粉的生产和储藏。面粉的安全水分要求在13％左右。加工时水分太低磨出面粉色泽欠佳、麸量明显增加，同时麸量中含粉也明显增多。如水分太高，面粉色泽白、麸量少，但对储存不利，易发热、发霉、变质、生虫，从而缩短了面粉的可食用期限。因此，面粉中水分含量关系到面粉的质量、贮存、可食用期限等方面。     

The metric projection on the classH(Ω) satisfies Lipschitz condition

Устанавливается лиш шщивость и односторо нняя дифференцируемость метрической проекции $$P_H^t :x \to P_H^t \left( x \right) = \left\{ {y \in H: \parallel x - y\parallel \leqq t + \varrho \left( {x, H} \right)} \right\}, t \geqq 0$$ на класс из пространстваB(Q) огр аниченных на множест веQ функцийx c нормой ∥x∥=sup {∣x(q)∣:q∈Q}, гдеΩ—метрика наQ. В частн ости, дляy _i ∈B(Q),t _i ≧0, метрикΩ _i и \(P_i = P_{H(\Omega _i )}^{t_i } \left( {y_i } \right), i = 1, 2\) доказано неравенство $$h\left( {P_1 , P_2 } \right) \leqq \frac{3}{2}\mathop {\sup }\limits_{q_1 , q_2 \in Q} \left| {\Omega _1 \left( {q_1 , q_2 } \right) - \Omega _2 \left( {q_1 , q_2 } \right)} \right| + 2\parallel y_1 - y_2 \parallel + 1\left| {t_1 - t_2 } \right|,$$ гдеh — расстояние Хау сдорфа. Константы 3/2, 2, 1 в э том неравенстве неулучш аемы.     

Paзлoжeниe пo 1Z для чapтpи-фoкoвcкoй и кoppeляциoннoй энepгии, peлятивиcтcкич пoпpaвoк, дипoльнoгo мaтpичнoгo элeмeнтa

Energies and dipole matrix elements have been calculated for He, Li, Be, B, C, N, O, F, and Ne-like ions (configurations 1s²2sⁿ¹2pⁿ²?1s²2s^n1?12pⁿ²⁺¹). The Hartree-Fock energy, the correlation energy, and relativistic corrections were taken into account. Relativistic corrections were obtained by computing the entire quantity H_B. Numerical results are presented for energies of the terms in the form

$\text{E=E}{}_0\text{Z}{}^2\text{+ ΔE}{}_1\text{Z + ΔE}{}_2\text{+}\text{1}\text{Z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{Z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{Z}{}^3\text{)}$

, and for the fine structure of the terms in the form

$\text{〈1s}{}^2\text{2s}{}^{\mathrm{n1}}\text{2p}{}^{\mathrm{n2}}\text{LSJ|H}{}_{\mathrm{Б}}\text{|1s}{}^2\text{2s}{}^{\mathrm{n1\prime }}\text{2p}{}^{\mathrm{n2\prime }}\text{L′S′J〉=(?1)}{}^{\mathrm{L+S\prime +J}}\text{LSJ}\text{S′L′1}\text{×}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{[E}{}^{\mathrm{(0)}}\text{(Z ? B)+}\text{E}{}_{\mathrm{c0}}\text{]+(?1)}{}^{\mathrm{L\; +\; S\prime \; +\; J}}\text{LSJ}\text{S′L′2}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{E}{}_{\mathrm{cc}}$

. Dipole matrix elements are required for calculation of oscillator strengths or transition probabilities. For the dipole matrix elements, two terms of the expansion in $\text{1}\text{Z}$ have been obtained. Numerical results are presented in the form P(a, a′) = (a/Z)[1 + (τ/Z)].     

О НАИлУЧшЕМ ОДНОстОР ОННЕМ пРИБлИжЕНИИ цЕ лыМИ ФУНкцИьМИ

Let $$W_1 (G) = \{ x = G*y:y\varepsilon L_1 ,\parallel y\parallel _1 \leqq 1\} (L_1 = L_1 (R^1 ))$$ and $$W_1^0 (G) = \{ x = G*y\varepsilon W_1 (G), y \bot 1\} .$$ For each even functionG(t) (¦G^(v)(t)¦≦/(1+t²), v=0,1,...; t?R¹) such that its Fourier transformg(t) is 4 times monotonous on [λ, ∞) and tends to zero ast→∞, exact estimates of the best one-sided approximations by entire functions of exponential type≦σ (σ≧λ) are calculated for the classesW ₁ (G) andW ₁ ⁰ (G) inL ₁-metric.