Interpolation of nonlinear maps

Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\subseteq X_0$ with norms satisfying $\|x\|_{X_0} \le c\|x\|_{X_1}$ for some $c > 0$. For any $0<\theta <1$, denote by $X_\theta = [X_0, X_1]_\theta$ and $Y_\theta = [Y_0, Y_1]_\theta$ the complex interpolation spaces and by $B(r, X_\theta)$, $0 \le \theta \le 1,$ the open ball of radius $r>0$ in $X_\theta$, centered at zero. Then for any analytic map $\Phi: B(r, X_0) \to Y_0+ Y_1$ such that $\Phi: B(r, X_0)\to Y_0$ and $\Phi: B(c^{-1}r, X_1)\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respectively, the restriction of $\Phi$ to $B(c^{-\theta}r, X_\theta)$, $0 < \theta < 1,$ is shown to be a map with values in $Y_\theta$ which is analytic and bounded by $M_0^{1-\theta} M_1^\theta$

Advantages of the using of batch action butter maker on small productivity enterprises

The development of nuclear fusion as an alternative energy source requires the research on magnetically confined, high temperature plasmas. In particular, the quantification of plasma flows in the domain near exposed material surfaces of the plasma container by computer simulations is of key importance, both for guiding interpretation of present fusion experiments and for aiding the ongoing design activities for large future devices such as ITER, W7-X or the DEMO reactor. There is a large number of computational issues related to the physics of hot, fully ionized and magnetized plasmas near surfaces of the vacuum chamber. This thesis is dedicated to one particular such challenge, namely the numerical quantification of self-consistent kinetic neutral gas and plasma fluid flows in very complex 3D (partially chaotic) magnetic fields, in the absence of any common symmetries for plasma and neutral gas dynamics. Such magnetic field configurations are e.g. generated by externally applied magnetic perturbations at the plasma edge, and are of great interest for the control of particle and energy exhausts. In the present thesis the 3D edge plasma and neutral particle transport code EMC3-EIRENE is applied to two distinct configurations of open chaotic magnetic system: at the TEXTOR and DIII-D tokamaks. Improvements of the edge transport model and extensions of the transport code are presented, which have allowed such simulations for the first time for 3D scenarios at DIII-D with ITER similar plasmas. A strong 3D effect of the chaotic magnetic field on the DIII-D edge plasma is found and analyzed in detail. It is found that a pronounced striation pattern of target particle and heat fluxes at DIII-D can only be obtained up to a certain upper limiting level of anomalous cross-field transport. Hence, in comparison to experimental data, these findings allow to narrow down the range of this model parameter. One particular interest at TEXTOR is the achievement of a regime with reduced particle and heat fluxes towards the divertor target within a 3D perturbed boundary, the so called helical divertor configuration. It is shown in this thesis that plasma states, which are both consistent with the limited experimental data and show transition to reduced particle and heat fluxes, can indeed be observed in numerical simulations of the TEXTOR helical divertor. This is, however, at the expense of also reduced upstream temperatures, which might not be consistent with an advanced tokamak operation (in which the hottest possible confined plasma periphery should be combined with the coldest possible plasma-wall contact zone)

Interpolation of nonlinear maps

Let (X 0, X 1) and (Y 0, Y 1) be complex Banach couples and assume that X 1 ⊆ X 0 with norms satisfying ‖x‖X 0 ≤ c‖x‖X 1 for some c > 0. For any 0 0 in X θ centered at zero. Then, for any analytic map Φ: B(r, X 0) → Y 0 + Y 1 such that Φ: B(r, X 0) → Y 0 and Φ: B(c −1 r, X 1) → Y 1 are continuous and bounded by constants M 0 and M 1, respectively, the restriction of Φ to B(c −θ r, X χ ), 0 < θ < 1, is shown to be a map with values in Y θ which is analytic and bounded by M 0 1 − θ M 1 θ

Historians in dialogue: experience in implementing the project “Memory of the Great Patriotic war: directions, trends, practices of memorialization in Belarus and Russia”

In May 2020 have passed 75 years since the end of the Great Patriotic War. The further the history of this fateful conflict for all mankind goes into the past, the more acute and politicized is the confrontation of different approaches to interpreting the causes and results of the war, preserving the memory of the war and its heroes. The surge of neo-Nazism in modern Europe, the destruction of monuments to soldiers of the Second World War in a number of countries of the post-Soviet space, attempts to revise the role of individuals in the history of the war prompt modern researchers to revert to the problems of preserving the collective historical memory of the Past, the formation of the historical consciousness of young people. In what forms and with what expressive means should the memory of the war be broadcast today? How to convey to the younger generation, far from the realities of that time, the scale and tragedy of the event that put the world on the brink of disaster? The article presents the interim results of the Russian-Belarusian project “Remembrance of the Great Patriotic War: directions, trends, memorialization practices in Belarus and Russia”. The authors proceed from the fact that at the present stage, when there is a generational change in the Belarusian and Russian society and the problem of alienating the collective memory from the events of the war is becoming more acute, the task of finding new forms of perpetuating the memory of the Great Patriotic War is becoming ever more urgent, more and more significant is the dialogue between representatives of the scientific and educational community. A study of state policy to preserve the historical memory of the Great Patriotic War and the practice of memorialization of the events of 1941-1945 in a comparative retrospective, it is aimed at identifying those key mechanisms that are of particular importance for the formation of memory of significant events of the Past.В мае 2020 г. исполняется 75 лет с момента окончания Великой Отечественной войны. Чем дальше в прошлое уходит история этого судьбоносного для всего человечества конфликта, тем более острым и политизированным становится противостояние разных подходов к интерпретации причин и итогов войны, сохранению памяти о войне и ее героях. Всплеск неонацизма в современной Европе, уничтожение памятников солдатам Второй мировой войны в ряде стран постсоветского пространства, попытки пересмотра роли отдельных личностей в истории войны побуждают современных исследователей вновь обращаться к проблемам сохранения коллективной исторической памяти о событиях прошлого, формирования исторического сознания молодежи. В каких формах и с помощью каких выразительных средств должна транслироваться сегодня память о войне? Как передать подрастающему поколению, далекому от реалий того времени, масштаб и трагизм события, поставившего мир на грань катастрофы? В статье представлены промежуточные итоги реализации российско-белорусского проекта «Память о Великой Отечественной войне: направления, тенденции, практики мемориализации в Беларуси и России». Авторы исходят из того, что на современном этапе, когда в белорусском и российском обществе происходит смена поколений и проблема отчуждения коллективной памяти от событий войны становится все более острой, как никогда ранее становится актуальной задача поиска новых форм увековечения памяти о Великой Отечественной войне, все более значимым является диалог между представителями научно-образовательного сообщества. Методологической основой исследования является концепция исторической памяти. Исследование государственной политики по сохранению исторической памяти о Великой Отечественной войне и практик мемориализации событий 1941-1945 гг. в сравнительной ретроспективе направлено на выявление тех ключевых механизмов, которые имеют особое значение для формирования памяти о значимых событиях прошлого

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Антидіабетичні властивості лікарських рослин, поширених на території України

The article presents the results of studies of the effects of some Ukrainian medicinal plants aqueous extracts on blood glucose concentration in healthy rats in dynamics of glucose tolerance test. The results indicate that under these conditions the most pronounced antihyperglycemic effect had the common bean (P. vulgaris) pods extract. The extracts from garlic seed (A. sativum) and wild strawberry (F. vesca) had less pronounced effect. None of antihyperglycemic effect has been observed under the influence of extracts from milk thistle (S. marianum), stinging nettle (U. dioica) and bilberry (V. myrtillus).В статье представлены результаты исследования влияния водных экстрактов некоторых представителей лекарственных растений Украины на динамику изменения концентрации глюкозы в крови здоровых крыс в условиях теста толерантности к глюкозе. Полученные результаты свидетельствуют, что при данных условиях наиболее выраженное антигипергликемическое действие имел экстракт створок бобов фасоли обыкновенной (P. vulgaris), менее выраженное действие имели экстракты чеснока посевного (A. sativum) и земляники лесной (F. vesca). Не было установлено антигипергликемического эффекта в условиях влияния экстрактов расторопши пятнистой (S. marianum), крапивы двудомной (U. dioica) и черники обыкновенной (V. myrtillus).У статті представлені результати дослідження впливу водних екстрактів деяких представників лікарських рослин України на динаміку зміни концентрації глюкози у крові здорових щурів за умов тесту толерантності до глюкози. Отримані результати свідчать, що за даних умов найбільш виражену антигіперглікемічну дію мав екстракт стулок бобів квасолі звичайної (P. vulgaris), менш виражену дію мали екстракти часнику посівного (A. sativum) та суниці лісової (F. vesca). Не було встановлено антигіперглікемічного ефекту за умов впливу екстрактів розторопші плямистої (S. marianum), кропиви дводомної (U. dioica) та чорниці звичайної (V. myrtillus)

A priori estimates for the Hill and Dirac operators

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps \g_n,n\ge 1 with length |\g_n|\ge 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if \m_n^\pm are the effective masses associated with the gap \g_n=(\l_n^-,\l_n^+), then |\m_n^-+\m_n^+|\le C|\g_n|^2n^{-4} for some constant $C=C(q)$ and any $n\ge 1$. In order prove these results we use the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator. That makes possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory. Then the proof is based on the analysis of the conformal mapping and the identities. Moreover, we obtain the similar estimates for the Dirac operator