Abstract. This study gives a comprehensive analysis of the properties and interactions of fibrewise maximal and minimal topological spaces. Fibrewise topology extends classical topological concepts to structured spaces, providing a thorough understanding of spaces that vary across different dimensions. We study the basic theories, crucial properties, and characterizations of maximal and minimal fibrewise topological spaces. We investigate their role in different mathematical contexts and draw connections with related topological concepts. By providing exact mathematical formulations and comprehensive examples, this abstract advances the fields of topology and mathematical analysis by elucidating the unique properties and implications of fibrewise maximal and minimal topological spaces.
The effect of superficial gas velocity within the range 0.01-0.164 m/s on gas holdup (overall, riser and down comer), volumetric oxygen mass transfer coefficient, liquid circulation velocity was studied in an internal loop concentric tubes airlift reactor (working volume 45 liters). It was shown that as the usg increases the gas holdup and also the liquid circulation velocity increase. Also it was found that increasing superficial gas velocity lead to increase the interfacial area that increases the overall oxygen mass transfer coefficient. The hydrodynamic experimental results were modeled with the available equations in the literature. The predicted data gave an acceptable accuracy with the empirical data.
The final
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Typological analysis about the negation marker in different languages is one of the fields of research that has attracted much attention. In Persian language, this constituent has been analysed from different aspects. This study aimed to analyse different aspects of negation marker in the adjectives, the noun phrases and the verb phrases based on typological analysis. Many studies have been revealed that the negation in adjectives has shown lexically and morphologically. In the noun phrases, /hich/ has used as a negative marker necessarily marking the verb phrase as negative too. In the verb phrases, negation occurs morphologically by the addition of the prefix /n
... Show MoreThe main idea that led me to write such research paper within the framework of Germanic linguistics is that I have not found any topic dealing with the term correlate in the German language, except in several articles in linguistic journals as well as one topic in a book describing the use of such a linguistic phenomenon in the language system. The research initially deals with the definition of the correlate at the level of the German language system. Correlate is unity describes specific relation of two sentences and identifies denoted constructs. Correlate is called a placeholder at the syntactic level because it does not occupy its original topological fields in the syntactic structure. The correlate (es) or the prepositiona
... Show MoreDie vorliegende Forschung handelt es um die Satzfelder, besonders das Mittelfeld des Satzes im deutschen und Arabischen. Diese Forschung wurde mit der Satzdefinition, Satzglieder begonnen, damit wir diese klar werden und dann werden die Felder des Satzes gut gekannt. Der erste Abschnitt schlieβt auch den Mittelfeld des Satzes und, wie man das Feld erkennen und bestimmen kann. Die Forschung untersucht auch. Ob es in der arabischen Sprache den selben Struktur wie im Deutschen gibt, z.B Bildung des Satzes sowie Satzfelder bezügllich das Mittelfeld.
Der zweite Abschnitt handelt sich um den arabischen Teil und behandelt die Wortarten im Arabischen sowie den Satz als auch Satzarten (Nominal- Verbal- Halbsatz).
Danach befinden
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