# Artykuły naukowe (WMiI)

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Item Performance of Selected Models for Predicting Malignancy in Ovarian Tumors in Relation to the Degree of Diagnostic Uncertainty by Subjective Assessment With Ultrasound(Journal of Ultrasound in Medicine vol 39, pp. 939-947, 2020) Szubert, Sebastian; Szpurek, Dariusz; Wójtowicz, Andrzej; Żywica, Patryk; Stukan, Maciej; Sajdak, Stefan; Jabłoński, Sławomir; Wicherek, Łukasz; Moszyński, RafałShow more Objectives The study's main aim was to evaluate the relationship between the performance of predictive models for differential diagnoses of ovarian tumors and levels of diagnostic confidence in subjective assessment (SA) with ultrasound. The second aim was to identify the parameters that differentiate between malignant and benign tumors among tumors initially diagnosed as uncertain by SA. Methods The study included 250 (55%) benign ovarian masses and 201 (45%) malignant tumors. According to ultrasound findings, the tumors were divided into 6 groups: certainly benign, probably benign, uncertain but benign, uncertain but malignant, probably malignant, and certainly malignant. The performance of the risk of malignancy index, International Ovarian Tumor Analysis assessment of different neoplasias in the adnexa model, and International Ovarian Tumor Analysis logistic regression model 2 was analyzed in subgroups as follows: SA-certain tumors (including certainly benign and certainly malignant) versus SA-probable tumors (probably benign and probably malignant) versus SA-uncertain tumors (uncertain but benign and uncertain but malignant). Results We found a progressive decrease in the performance of all models in association with the increased uncertainty in SA. The areas under the receiver operating characteristic curve for the risk of malignancy index, logistic regression model 2, and assessment of different neoplasias in the adnexa model decreased between the SA-certain and SA-uncertain groups by 20%, 28%, and 20%, respectively. The presence of solid parts and a high color score were the discriminatory features between uncertain but benign and uncertain but malignant tumors. Conclusions Studies are needed that focus on the subgroup of ovarian tumors that are difficult to classify by SA. In cases of uncertain tumors by SA, the presence of solid components or a high color score should prompt a gynecologic oncology clinic referral.Show more Item Descriptive Topology in non-Archimedean Function Spaces Cp(X, K). Part I(2012) Śliwa, Wiesław; Kąkol, JerzyShow more Let $K$ be a non-archimedean field and let $X$ be an ultraregular space. We study the non-archimedean locally convex space $C_p(X;K)$ of all $K$-valued continuous functions on $X$ endowed with the pointwise topology. We show that $K$ is spherically complete if and only if every polar metrizable locally convex space $E$ over $K$ is weakly angelic. This extends a result of Kiyosawa - Schikhof for polar Banach spaces. For any compact ultraregular space $X$ we prove that $C_p(X;K)$ is Frechet-Urysohn if and only if $X$ is scattered (a non-archimedean variant of Gerlits - Pytkeev's result). If $K$ is locally compact we show the following: (1) For any ultraregular space $X$ the space $C_p(X;K)$ is K-analytic if and only if it has a compact resolution (a non-archimedean variant of Tkachuk's theorem); (2) For any ultrametrizable space $X$ the space $C_p(X;K)$ is analytic if and only if $X$ is $\sigma$-compact (a non-archimedean variant of Christensen's theorem).Show more Item On linear isometries on non-archimedean powerseries spaces(2012-05) Śliwa, Wiesław; Ziemkowska, AgnieszkaShow more The non-archimedean power series spaces Ap(a; t) are the most known and important examples of non-archimedean nuclear Frechet spaces. We study when the spaces Ap(a; t) and Aq(b; s) are isometrically isomorphic. Next we determine all linear isometries on the space Ap(a; t) and show that all these maps are surjective.Show more Item Frechet spaces of non-archimedean valued continuous functions(2012) Śliwa, WiesławShow more Let $X$ be an ultraregular space and let $K$ be a complete non-archimedean non-trivially valued field. Assume that the locally convex space $E$ = $C_c(X;K)$ of all continuous functions from $X$ to $K$ with the topology of uniform convergence on compact subsets of $X$ is a Frechet space. We shall prove that $E$ has an orthogonal basis consisting of $K$-valued characteristic functions of clopen (i.e. closed and open) subsets of $X$ and that it is isomorphic to the product of a countable family of Banach spaces with an orthonormal basis.Show more Item The separable quotient problem and the strongly normal sequences(2012) Śliwa, WiesławShow more We study the notion of a strongly normal sequence in the dual $E^*$ of a Banach space $E$. In particular, we prove that the following three conditions are equivalent: (1) $E$ has a strongly normal sequence, (2) $(E^*;\sigma (E ^*;E))$ has a Schauder basic sequence, (3) $E$ has an infinite-dimensional separable quotient.Show more Item On tame operators between non-archimedean power seris spaces(2012) Śliwa, Wiesław; Ziemkowska, AgnieszkaShow more Let p {1∞}. We show that any continuous linear operator T from A1(a) to Ap(b) is tame i.e. there exists a positive integer c such that supx IITxIIk=/IxIck < ∞ for every k N. Next we prove that a similar result holds for operators from A∞(a) to Ap(b) if and only if the set Mba of all finite limit points of the double sequence (bj/ai/I,j N is bounded. Finally we show that the range of every tame operator from A∞(a) to A∞(b) has a Schauder basis.Show more Item On the selection of basic orthogonal sequences in non-archimedean metrizable locally convex spaces(The Belgian Mathematical Society, 2002) Śliwa, WiesławShow more Our main result follows that any infinite-dimensional sub-space F of a non-archimedean metrizable locally convex space E with an or- thogonal basis (e_n) contains a basic orthogonal sequence equivalent to a block basic orthogonal sequence relative to (e_n). Hence any infinite-dimensional non-archimedean metrizable locally convex space F has a basic orthogonal sequence equivalent to a block basic orthogonal sequence relative to an orthogonal basis in c_0^N.Show more Item On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces(The Belgian Mathematical Society, 2002) Śliwa, WiesławShow more We prove that any non-archimedean metrizable locally convex space E with a regular orthogonal basis has the quasi-equivalence property, i.e. any two orthogonal bases in E are quasi-equivalent. In particular, the power series spaces, the most known and important examples of non-archimedean nuclear Frechet spaces, have the quasi-equivalence property. We also show that the Frechet spaces: K^N, c_0xK^N, c_0^N have the quasi-equivalence property.Show more Item On the stability of orthogonal bases in non-archimedean metrizable locally convex spaces(The Belgian Mathematical Society, 2001) Śliwa, WiesławShow more It is proved that an orthogonal basis in a non-archimedean metrizable locally convex space E (in particular, a Schauder basis in a non-archimedean Frechet space E) is stable if and only if there is a continuous norm on E. Many others results are also obtained.Show more Item Closed subspaces without Schauder bases in non-archimedean Frechet spaces(Royal Netherlands Academy of Arts and Sciences, 2001-06) Śliwa, WiesławShow more Let E be an infinite-dimensional non-archimedean Frechet space which is not isomorphic to any of the following spaces: $c_0,c_0 x K^N,K^N$. It is proved that E contains a closed subspace without a Schauder basis (even without a strongly finite-dimensional Schauder decomposition). Conversely, it is shown that any closed subspace of $c_0 x K^N$ has a Schauder basis.Show more Item On closed subspaces with Schauder bases in non-archimedean Frechet spaces(Royal Netherlands Academy of Arts and Sciences, 2001-12) Śliwa, WiesławShow more The main purpose of this paper is to prove that a non-archimedean Frechet space of countable type is normable (respectively nuclear; reflexive; a Monte1 space) if and only if any its closed subspace with a Schauder basis is normable (respectively nuclear; reflexive; a Monte1 space). It is also shown that any Schauder basis in a non-normable non-archimedean Frechet space has a block basic sequence whose closed linear span is nuclear. It follows that any non-normable non-archimedean Frechet space contains an infinite-dimensional nuclear closed subspace with a Schauder basis. Moreover, it is proved that a non-archimedean Frechet space E with a Schauder basis contains an infinite-dimensional complemented nuclear closed subspace with a Schauder basis if and only if any Schauder basis in E has a subsequence whose closed linear span is nuclear.Show more Item Examples of non-archimedean nuclear Frechet spaces without a Schauder basis(Royal Netherlands Academy of Arts and Sciences, 2000-12) Śliwa, WiesławShow more We solve the problem of the existence of a Schauder basis in non-archimedean Frechet spaces of countable type. Using examples of real nuclear Frechet spaces without a Schauder basis we construct examples of non-archimedean nuclear Frechet spaces without a Schauder basis (even without the bounded approximation property).Show more Item Every infinite-dimensional non-archimedean Frechet space has an orthogonal basic sequence(Royal Netherlands Academy of Arts and Sciences, 2000-09) Śliwa, WiesławShow more It is proved that any infinite-dimensional non-archimedean metrizable locally convex space has an orthogonal basic sequence.Show more Item On Universal Schauder Bases in Non-Archimedean Frechet Spaces(Canadian Mathematical Society, 2004) Śliwa, WiesławShow more We prove that there exists a non-archimedean Frechet space U with a basis $(u_n)$ such that any basis $(x_n)$ in a non-archimedean Frechet space X is equivalent to a subbasis $(u_k_n)$ of $(u_n)$. Then any non-archimedean Frechet space with a basis is isomorphic to a complemented subspace of U. Next we prove that there is no nuclear non-archimedean Frechet space H with a basis $(h_n)$ such that any basis $(y_n)$ in a nuclear non-archimedean Frechet space Y is equivalent to a subbasis $(h_k_n)$ of $(h_n)$.Show more Item The Invariant Subspace Problem for Non-Archimedean Banach Spaces(Canadian Mathematical Society, 2008) Śliwa, WiesławShow more It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits a linear continuous operator without a non-trivial closed invariant subspace. This solves a problem stated by A. C. M. van Rooij and W. H. Schikhof in 1992.Show more Item On Quotients of Non-Archimedean Kothe Spaces(Canadian Mathematical Society, 2007) Śliwa, WiesławShow more We show that there exists a non-archimedean Frechet-Montel space W with a basis and with a continuous norm such that any non-archimedean Frechet space of countable type is isomorphic to a quotient of W. We also prove that any non-archimedean nuclear Frechet space is isomorphic to a quotient of some non-archimedean nuclear Frechet space with a basis and with a continuous norm.Show more Item An explicit example concernig the invariant subspace problem for Banach spaces(Rocky Mountain Mathematics Consortium, 2010-04) Śliwa, WiesławShow more We simplify the negative solution to the invariant subspace problem for Banach spaces. Developing the ideas of Read we give an explicit example of a continuous linear operator on the Banach space of all absolute summable scalar sequences without nontrivial closed invariant subspacesShow more Item On non-archimedean Frechet spaces with nuclear Kothe spaces(The American Mathematical Society, 2010-06) Śliwa, WiesławShow more Assume that K is a complete non-archimedean valued field. We prove that every Frechet-Montel space over K which is not of finite type has a nuclear Kothe quotient.Show more