We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain Ω under the general outflow condition. Let T be a 2-dimensional straight channel R × (−1, 1). We suppose that Ω ∩ {x1 < 0} is bounded and that Ω ∩ {x1 > −1} = T ∩ {x1 > −1}. Let V be a Poiseuille flow in T and µ the flux of V . We look for a solution which tends to V as x1 → ∞. Assuming that the domain and the boundary data are symmetric with respect to the x1-axis, and that the axis intersects every component of the boundary, we have shown the existence of solutions if the flux is small (Morimoto-Fujita [8]). Some improvement will be reported in this note. We also show certain regularity and asymptotic properties of the solutions.
Let $L(H)$ denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space $H$ into itself. Given $A\in L(H)$, we define the elementary operator $\Delta _A\colon L(H)\longrightarrow L(H)$ by $\Delta _A(X)=AXA-X$. In this paper we study the class of operators $A\in L(H)$ which have the following property: $ATA=T$ implies $AT^{\ast }A=T^{\ast }$ for all trace class operators $T\in C_1(H)$. Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of $\Delta _A$ is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints operators.
In the paper a new proof of Lemma 11 in the above-mentioned paper is given. Its original proof was based on Theorem 3 which has been shown to be incorrect.
In 2000, Figallo and Sanza introduced n × m-valued Lukasiewicz-Moisil algebras which are both particular cases of matrix Lukasiewicz algebras and a generalization of n-valued Lukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLMn×m of tense n × m-valued Lukasiewicz-Moisil algebras (or tense LMn×m-algebras), namely n×m-valued Lukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Lukasiewicz-Moisil algebras (or tense LMn-algebras). Our most important result is a representation theorem for tense LMn×m-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LMn-algebras.
This paper deals with Japan and Vietnam in the latter half of the 19th century. when China as a large country abundant both in treasure, trade and industrial opportunities, found itself in the centre of Western Powers´ interests which made them more involved in the Far East. The objective of the paper is to analyze the main factors which determined the way Japan and Vietnam faced up to Western encroachment, and to explain why Vietnam became a part of French Indochina and why Japan came into power. Namely, it points out the different situations and conditions of Japan and Vietnam before their openings to the Western World, and thereby clarifies the rwo countries´ positions within international relations in the Far East. Additionally, it brings up some differences in Japan´s and Vietnam´s domestic situations in order to document their readiness to meet external challenges.
For a multivalued map ϕ: Y ⊸ (X, τ ) between topological spaces, the upper semifinite topology A(τ ) on the power set A(X) = {A ⊂ X : A ≠ ∅} is such that ϕ is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map ϕ: Y → (A(X), A(τ )). In this paper, we seek a result like this from a reverse viewpoint, namely, given a set X and a topology Γ on A(X), we consider a natural topology R(Γ) on X, constructed from Γ satisfying R(Γ) = τ if Γ = A(τ ), and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued map ϕ: Y ⊸ (X, R(Γ)) to be equivalent to the continuity of the singlevalued map ϕ: Y → (A(X), Γ).
The present-day mass function (PDMF) of field stars in the solar neighborhood is discussed. Major uncertainties in the derivation exist, in partlcular the luminosity-mass relation and the bolometric corrections. Consequently, It is not clear whether the PDMF turns over at very low masses (M < 0.3 Mq), and the slope at the
high-mass end (M > 10 Mq) is more uncertain than usually assumed. The reality of two features in the PDMF (at M = 1.2 Mq and M = 3 Mq respectively) is an open question. Next, the concept of a bimodal IMF is critically examined. Both Gůsten and Mezger's (1983) and Larson's (1986) bimodal models may run into problems. If the effects of high-mass stars prevent low-mass stars from forming, the term "biassed IMF" is a better
description of the situation than "bimodal IMF". The IMF is probably not universal; reported IMF variations in open clusters and globular clusters are unlikely to be spurious. Finally the physics of the IMF is discussed. The. fact that the mass of a star in the making depends on many random-valued (multlplicative) input parameters
suggests a stochastic rather than a deterministic approach for the origin of the IMF.
Some results about the continuity of special linear maps between $F$-spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia's theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space $X$ is said to have a (relatively countably) compact resolution if $X$ admits a covering $\{A_{\alpha }\:\alpha \in \Bbb N^{\Bbb N}\}$ consisting of (relatively countably) compact sets such that $A_{\alpha }\subseteq A_{\beta }$ for $\alpha \leq \beta $. Some applications and two open questions are provided.
Using ideas from John Searle, Roy Harris, Michael Reddy, and Nelson Goodman, I argue that texts, such as they are commonly conceived, lack brute existence. The common idea of texts is a conceptual construction which is useful in practical everyday contexts but not in serious theorizing, where it creates illusions and contradictions. One of these illusions is the idea of an objective textual meaning, a meaning which is ''in the text'': what we actually have in the way of textual meaning are the ideas of various persons – authors, readers, and commentators – about the meaning of the text. When applied to fictional characters, this way of viewing things explains why it makes sense to regard fictional characters as being created and as lacking brute existence., Použitím nápadů od Johna Searleho, Roy Harris, Michaela Reddyho a Nelsona Goodmana, tvrdím, že texty, tak jak jsou běžně koncipovány, postrádají hrubou existenci. Společná myšlenka textů je koncepční konstrukce, která je užitečná v praktických každodenních kontextech, ale ne ve vážném teoretizování, kde vytváří iluze a protiklady. Jednou z těchto iluzí je myšlenka objektivního textuálního významu, významu, který je "v textu": to, co vlastně máme ve způsobu textuálního významu, jsou myšlenky různých osob - autorů, čtenářů a komentátorů - o významu textu. Při použití na fiktivní postavy vysvětluje tento způsob prohlížení věci, proč má smysl považovat fiktivní postavy za vytvořené a chybějící hrubou existenci., and Anders Pettersson