Беларусы ў творах Міхала К. Паўлікоўскага

Belarusians in Michał K. Pawlikowski’s novels, essays and articles are the subjects of research by the author of this article. Michał K. Pawlikowski (1893–1972) was a Polish writer who spent his childhood and youth in eastern Belarus. He immigrated to America for thelast thirty years of his life where he dealt with literature. In Poland his Works were unknown. His novels and essays have been published for ten years. Since then,, the author has been researching Pawlikowski’s work. As an anthropologist, he notices many interesting things in it. Literary anthropology is also interested in the descriptions of various nations. Pawlikowski’s Works also contains descriptions of Belarusians. The author found them and put them in order. It was not easy, because there are very few references to Belarusians which are scattered in various works by the writer. Pawlikowski sees mainly pasants in Belarus. He is fascinated by their language and culture. He hardly notices their national aspirations. However, he notes that they live in harmony with the Poles. нак, што беларусы жылі ў згодзе з палякамі.Przedmiotem badań autora artykułu są Białorusini w powieściach, esejach i artykułach Michała K. Pawlikowskiego. Pawlikowski był polskim pisarzem, który dzieciństwo i młodość przeżył na ziemiach wschodniej Białorusi. Ostatnie trzydzieści lat swego życia był emigrantem i mieszkał w Ameryce. Tam zajmował się literaturą. W Polsce jego utwory nie były znane. Jego powieści i eseje wydaje się tu od dziesięciu lat. Autor od tego czasu prowadzi badania nad twórczością Pawlikowskiego. Jako antropolog zauważa w niej wiele ciekawych rzeczy. An­tropologia literatury interesuje się także opisami różnych ludów. W utworach Pawlikowskiego znajdują się między innymi opisy Białorusinów. Autor je wyszukał i uporządkował. To zajęcie nie było łatwe, bo niewielkie wzmianki o Białorusinach są rozproszone w różnych pracach pisa­rza. Pawlikowski w Białorusinach widzi głównie chłopów. Jest on zafascynowany ich językiem i kulturą. W małym stopniu dostrzega ich aspiracje narodowe. Zauważa jednak, że zgodnie żyli z Polakami.У артыкуле разглядаюцца вобразы беларусаў у аповесцях, эсэ і артыкулах Міхала К. Паўлікоўскага – польскага пісьменніка, дзяцінства і маладосць якога прайшлі на землях усходняй Беларусі. Апошнія трыццаць гадоў свайго жыцця ён правёў у Амерыцы, дзе займаўся літаратурнай творчасцю. У Польшчы творы пісьменніка былі невядомыя, яго аповесці і эсэ пачалі выдавацца тут дзесяць гадоў назад. З гэтага часу аўтар артыкула займаецца даследаваннем творчасці Паўлікоўскага. Як антраполаг заўважае ў ёй шмат цікавых рэчаў. Антрапалогія літаратуры цікавіцца апісаннем розных народаў. У творах Паўлікоўскага ёсць між іншым апісанні беларусаў, якія даследчык знайшоў і сістэматызаваў. Гэта была нялёгкая задача, бо невялікія згадкі пра беларусаў раскіданыя па розных творах пісьменніка. Паўлікоўскага бачыць беларусаў у першую чаргу як сялян. Ён захапляецца іх мовай і культурай. У меншай ступені заўважае ён іх нацыянальныя памкненні. Адзначае, аднак, што беларусы жылі ў згодзе з палякамі

Trylogia Sylwestra Chęcińskiego

Sylwester Chęciński is famous polish director. He made three great films: “Sami swoi” (1967), “Nie ma mocnych” (1974), “Kochaj albo rzuć” (1967). This is trilogy about Pawlaks and Karguls, two family from little village from West Poland. Their history is a part of polish history. Films about Pawlaks and Karguls became a polish national myth

Direct sums and the Szlenk index

For $\alpha$ an ordinal and $1<p<\infty$, we determine a necessary and sufficient condition for an $\ell_p$-direct sum of operators to have Szlenk index not exceeding $\omega^\alpha$. It follows from our results that the Szlenk index of an $\ell_p$-direct sum of operators is determined in a natural way by the behaviour of the $\epsilon$-Szlenk indices of its summands. Our methods give similar results for $c_0$-direct sums.Comment: The proof of Proposition~2.4 has changed, with some of the arguments transferred to the proof of an added-in lemma, Lemma~2.8. Changes have been made to the Applications sectio

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

The symmetric Radon-Nikod\'ym property for tensor norms

We introduce the symmetric-Radon-Nikod\'ym property (sRN property) for finitely generated s-tensor norms $\beta$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $\beta$ is a projective s-tensor norm with the sRN property, then for every Asplund space $E$, the canonical map $\widetilde{\otimes}_{\beta}^{n,s} E' \to \Big(\widetilde{\otimes}_{\beta'}^{n,s} E \Big)'$ is a metric surjection. This can be rephrased as the isometric isomorphism $\mathcal{Q}^{min}(E) = \mathcal{Q}(E)$ for certain polynomial ideal \Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikod\'{y}m properties of different tensor products. Similar results for full tensor products are also given. As an application, results concerning the ideal of $n$-homogeneous extendible polynomials are obtained, as well as a new proof of the well known isometric isomorphism between nuclear and integral polynomials on Asplund spaces.Comment: 17 page

On the Bohnenblust-Hille inequality and a variant of Littlewood's 4/3 inequality

The search for sharp constants for inequalities of the type Littlewood's 4/3 and Bohnenblust-Hille, besides its pure mathematical interest, has shown unexpected applications in many different fields, such as Analytic Number Theory, Quantum Information Theory, or (for instance) in deep results on the $n$-dimensional Bohr radius. The recent estimates obtained for the multilinear Bohnenblust-Hille inequality (in the case of real scalars) have been recently used, as a crucial step, by A. Montanaro in order to solve problems in the theory of quantum XOR games. Here, among other results, we obtain new upper bounds for the Bohnenblust-Hille constants in the case of complex scalars. For bilinear forms, we obtain the optimal constants of variants of Littlewood's 4/3 inequality (in the case of real scalars) when the exponent 4/3 is replaced by any $r\geq4/3.$ As a consequence of our estimates we show that the optimal constants for the real case are always strictly greater than the constants for the complex case

Operators whose dual has non-separable range

Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.Comment: 20 pages, no figure

Banach spaces of universal disposition

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\u{\i} space $\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\mathfrak F$ of finite dimensional spaces), or the Kubis space $\mathcal K$ (under {\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\sf CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties

On the nontrivial projection problem

The Nontrivial Projection Problem asks whether every finite-dimensional normed space of dimension greater than one admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension greater than one) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true "up to a logarithmic factor."Comment: 17 page