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34922. Some remarks on Nagumo's theorem
- Creator:
- Thomas
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- ordinary differential equation and uniqueness
- Language:
- English
- Description:
- We provide a simpler proof for a recent generalization of Nagumo's uniqueness theorem by A. Constantin: On Nagumo's theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation $x'=f(t,x)$, $ x(0)=0$ and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution. The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math. Jap. 35 (1990), 351–367. Some classical existence and uniqueness results for initial-value problems for ordinary differential equations are particular cases of our result.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34923. Some remarks on the Akivis algebras and the Pre-Lie algebras
- Creator:
- Chen, Yuqon and Li, Yu
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- non-associative algebra, Akivis algebra, universal enveloping algebra, Pre-Lie algebra, and Gröbner-Shirshov basis
- Language:
- English
- Description:
- In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov's result that any Akivis algebra is linear and D. Segal's result that the set of all good words in $X^{**}$ forms a linear basis of the free Pre-Lie algebra ${\rm PLie}(X)$ generated by the set $X$. For completeness, we give the details of the proof of Shirshov's Composition-Diamond lemma for non-associative algebras.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34924. Some remarks on the date of the actual solar activity minimum
- Creator:
- Dinulescu, Vasile
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- heliophysics, sunspots, and solar activity minimum
- Language:
- Czech
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34925. Some remarks on the product of two $C_\alpha$-compact subsets
- Creator:
- García-Ferreira, Salvador, Sanchis, Manuel, and Watson, Stephen W.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- bounded subset, $C_\alpha$-compact, $\alpha$-pseudocompact, degree of $C_\alpha$-pseudocompactness, and $\alpha_r$-space
- Language:
- English
- Description:
- For a cardinal $\alpha $, we say that a subset $B$ of a space $X$ is $C_{\alpha }$-compact in $X$ if for every continuous function $f\: X \rightarrow \mathbb R^{\alpha }$, $f[B]$ is a compact subset of $\mathbb R^{\alpha }$. If $B$ is a $C$-compact subset of a space $X$, then $\rho (B,X)$ denotes the degree of $C_{\alpha }$-compactness of $B$ in $X$. A space $X$ is called $\alpha $-pseudocompact if $X$ is $C_{\alpha }$-compact into itself. For each cardinal $\alpha $, we give an example of an $\alpha $-pseudocompact space $X$ such that $X \times X$ is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness” Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg’s Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34926. Some remarks on the Stroke-Ornamented Ware culture in Poland
- Creator:
- Kulczyck-Leciejewiczowa, Anna
- Type:
- article and TEXT
- Subject:
- Neolithic, Stroke-Ornamented Ware culture, Poland, neolit, kultura s vypíchanou keramikou, and Polsko
- Language:
- Czech
- Description:
- The existence of the Stroke–Ornamented Ware culture north of the Sudetes and Carpathian Mts. has been a rather controversial problem. There appeared doubts as regards the accuracy of distinguishing this culture in certain regions; finally its presence in Poland was questionable. The former conception of its development – at least in South–Western Poland – has been now taken up again. The diversity of natural conditions in which its settlements were placed favoured regional differentiation. The people with stroked pottery spread from upper Oder to the Vistula basin. There were formed some specific peripheral culture groups. They had a nearly contact with the Lengyel and Polgar environments. At the present state of research it is possible to differentiate in Poland two basic development phases of the Stroke–Ornamented Ware culture. Finds from the later phase reveal in the Oder and Vistula basins evident features of the Lengyel–Polgar style. Radiocarbon dates of the sites with Stroke–Ornamented Ware obtained in Poland are within 4970–4670 B.C. and Existence kultury s vypíchanou keramikou severně od Sudetského masivu a Karpat byla dosud spíše kontroverzním problémem. Vyskytly se pochybnosti o správnosti identifikace této kultury v některých regionech; její prezence v Polsku byla nakonec sporná. Na původní koncepci jejího vývoje bylo ovšem nyní – alespoň v jihozápadním Polsku – znovu navázáno. Různé přírodní podmínky, v nichž se její sídliště vyskytovala, přispěly k regionální diferenciaci. Lidé kultury s vypíchanou keramikou osídlili kraj od horní Odry až k pánvi Visly. Tam se zformovaly některé specifické periferní kulturní skupiny, jež měly blízké kontakty s lengyelským a polgárským prostředím. Za současného stavu poznání je možné v Polsku odlišit dvě základní vývojové fáze kultury s vypíchanou keramikou. Nálezy z mladší fáze odhalují v pánvích Odry a Visly zřejmé projevy lengyelsko–polgárského stylu. Radiokarbonová data z polských sídlišť kultury s vypíchanou keramikou se pohybují mezi 4970–4670 B.C.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/
34927. Some remarks on the transitional phase between Early Roman and Late Roman Periods in the region north of the Middle Danube =
- Creator:
- Jaroslav Tejral
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- archeologie, Early and Late Roman Period, transitional phase, Marcomanic Wars and their aftemath, ethnical and social backround of the B2/C1 phase, 8, and 902
- Language:
- Czech
- Description:
- This paper deals with the so-called transitional phase B2/C1, the nature of which is still being debated in the archaeological literature. The heart of the discussion is in its archaeological relevance, the dating, and its cultural, ethnic and social background. THe general consensus is that it dates to the time of Marcomannic wars. On the basis of new archaeological evidence and an analysis of some diagnostic forms found on the datable sites north of the Danube, it is suggested that the Late Roman phase C1a overlaps to a large extent with the so-called transitional B2/C1 phase, which began shortly before AD 180. A question arises of how to define the subsequent phase C1a and whether both phases in question can be seen as separate stages with separate chronological sequences. Controversy surround the proposed detailed division of the transitional phase between Early and Late Roman Period into two phases and therewith also a sharp chronological diffrentiation of the archaeological material from the late 2nd century and approximatively the first third of the 3rd century. The emergence of a specific archaeological milieu relatin to the transitional phase probably has an ethnic and socio-cultiral background. It shows strong infuences from the Roman provinces. Its characteristic features may be considered as a reflection of wars and their aftermath., Jaroslav Tejral., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34928. Some remarks on the X-ray solar bursts
- Creator:
- Mergentaler, J.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- solar physics and X-ray solar bursts
- Language:
- Czech
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34929. Some results about dissipativity of Kolmogorov operators
- Creator:
- Da Prato, Giuseppe and Tubaro, Luciano
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Kolmogorov equations, invatiant measures, and $m$-dissipativity
- Language:
- English
- Description:
- Given a Hilbert space $H$ with a Borel probability measure $\nu $, we prove the $m$-dissipativity in $L^1(H, \nu )$ of a Kolmogorov operator $K$ that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
34930. Some results about the Henstock-Kurzweil Fourier transform
- Creator:
- Mendoza Torres, Francisco J., Escamilla Reyna, Juan A., and Sánchez Perales, Salvador
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Fourier transform, Henstock-Kurzweil integral, and bounded variation functions
- Language:
- English
- Description:
- We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public