We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation x(t)=L(t)x(t)+f(t,x(t)), t R where {L(t) in R}$ is a family of linear operators from a Banach space E into itself and f R E to E. By L(E) we denote the space of linear operators from E into itself. Furthermore, for a<b and d>0, we let C([-d,0],E) be the Banach space of continuous functions from [-d,0] into E and f^d [a,b] C([-d,0],E) E. Let L: [a,b] to L(E) be a strongly measurable and Bochner integrable operator on [a,b] and for t in [a,b] define tau_tx(s)=x(t+s) for each s in[-d,0]. We prove that, under certain conditions, the differential equation with delay x(t)=L(t)x(t)+f^d(t,tau_tx) if t in [a,b], Q has at least one weak solution and, under suitable assumptions, the differential equation (Q) has a solution. Next, under a generalization of the compactness assumptions, we show that the problem (Q) has a solution too., Adel Mahmoud Gomaa., and Seznam literatury
This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium point for complex-valued neutral-type neural networks are obtained. Finally, numerical examples are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.
For a bounded domain $\Omega \subset \Bbb R ^n$, $n\geq 3,$ we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system $-\Delta u + u \cdot \nabla u + \nabla p=f$, $\div u = k$, $u_{|_{\partial \Omega }}=g$ with $u \in L^q$, $q \geq n$, and very general data classes for $f$, $k$, $g$ such that $u$ may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžička, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669--717, where the existence of a weak solution which is locally regular is proved.
Karl Jaspers proslul v meziválečné době jako zakladatel nové filosofie existence, která však byla v kombinaci s jeho psychologickým školením, zaostřením na ,,mezní situace“ lidského prožívání a kritikou filosofických systémů často dezinterpretována jako forma subjektivismu či iracionalismu. Předložená studie se pokouší vystihnout jádro Jaspersova využití filosofie existence pro novou rekonstrukci lidské racionality, univerzálních charakteristik lidství. Jejich pochopení mělo podle Jasperse vzdorovat pokořování lidské důstojnosti v moderních totalitách a v globálním ekonomicko-technologickém provozu, pro něž hodnoty lidství, jak je definuje Jaspersova filosofie, přestaly být určujícími měřítky. Studie ukazuje Jaspersovo ukotvení existence ve vztahu k transcendenci a individuality v komunikaci s druhým a jeho kritiku monistického myšlení, které pluralitu ve smyslu jeho filosofické koncepce neumožňuje., Karl Jaspers received much attention in the interwar period as the founder of a new philosophy of existence that, however, was – in tandem with his psychological training, focus on “borderline situations” of human experience, and critique of philosophical systems – often misinterpreted as a form of subjectivism or irrationalism. The study presented here strives to depict the substance of Jaspers’ use of the philosophy of existence for a new reconstruction of human rationality, of the universal characteristics of humanity. Understanding these characteristics shall, in his estimation, help us to resist the degradation of human dignity in modern totalitarianism and in the global economic-technological system, in which the values of humanity, as defined by Jaspers’ philosophy, have ceased being decisive criteria. The study presents Jaspers’ anchoring of existence in the relationship to transcendence and of individuality in the communication with others, as well as his critique of monistic thinking, which in his philosophical conception does not allow for plurality., and Karl Jaspers wurde in der Zwischenkriegszeit als Begründer der Existenzphilosophie bekannt, die jedoch im Zusammenhang mit der psychologischen Ausbildung Jaspers’, der Konzentration auf „Grenzsituationen“ des menschlichen Erlebens und der Kritik philosophischer Systeme oft als eine Form von Subjektivismus bzw. Irrationalismus fehlinterpretiert wurde. In der vorliegenden Studie wird der Versuch unternommen, den Kern von Jaspers’ Nutzung der Existenzphilosophie für eine Rekonstruktion der menschlichen Rationalität und der universalen Merkmale des Menschseins zu erfassen. Deren Erkenntnis sollte laut Jaspers der Demütigung der Menschenwürde in modernen totalitären Regimen und im globalen ökonomisch-technologischen Betrieb widerstehen, in denen die in Jaspers’ Philosophie definierten Werte des Menschseins kein Maßstab mehr sind. In der Studie wird Jaspers’ Verankerung der Existenz in der Beziehung zur Transzendenz und zur Individualität in der Kommunikation mit anderen und seine Kritik am monistischen Denken aufgezeigt, das keine Pluralität im Sinne seines philosophischen Konzepts ermöglicht.
In his book Physics of the Impossible, Michio Kaku thinks that psycho-kinesis-i.e., a direct causal influence on physical processes by mental powers-will become a real possibility in a near future. From the point of view of metaphysical realism, this means that mental entities and mental causality are real phenomena. Contemporary scientific methodology regards the use of scientific instruments that amplify our sensibilities as a cognitive technology that deepens our knowledge of, and power over, real processes. It appears that the strongest and most productive methods are connected with scientific theories-they are theories ''in action''. Thus, scientific theories can regarded as mental cognitive technology by means of which humans get to know, and at the same time shape, reality. and Břetislav Fajkus
The text is divided into two parts. In the first part, the author describes the eternalists’ and presentists’ positions as the two basic possible statements of the ontology of time (there exists only what is present - presentism - and there also actually exists both what is past and what is future). The eternalist position and the emphasis it puts on the actual existence of past and future events (expressed usually by the use of present tense or of some tenseless form of the verb) are thoroughlly analysed in order to show that in fact, they end up making strings of symbols that are not correct statements. It is therefore necessary to step beyond these clumsy statements and try to understand more exactly the eternalist intuitions on a deeper, metaphysical level. That is the main concern of the second part of the text, in which the metaphysical implications of both positions are compared. At the end of the linguistical analysis in the first part, we got to a point where it may seem that presentism and eternalism are only different attempts at expressing what is in fact the same understanding of the nature of time, but in the metaphysical analysis that follows, it will turn out that they are not. Presentism and eternalism are shown to be two different ontological approaches of time in relation to space (time as a basically homogenous fourth dimension and time as something essentially different from space). The author then focuses on the consequences these two positions have especially on the concept of the present and of its flow through time. In the end, presentism and eternalism turn out to be completely different positions that - in parallel with the famous McTaggart’s argument - claim a very strong reality of time on the one hand (presentism) or, on the other hand, its utter unreality (eternalism)., Text je rozdělen do dvou částí. V první části autor popisuje postoje eternalistů a presentistů jako dvě základní možná prohlášení ontologie času (existuje pouze to, co je přítomno - presentismus - a tam také skutečně existuje to, co je minulost a co je budoucnost) . Postavení eternalistů a důraz, který kladou na skutečnou existenci minulých a budoucích událostí (vyjádřených obvykle pomocí přítomného času nebo nějaké napjaté podoby slovesa), jsou důkladně analyzovány, aby se ukázalo, že ve skutečnosti končí řetězců symbolů, které nejsou správné. Je proto nutné překonat tyto neohrabané výroky a snažit se přesněji pochopit eternalistické intuice na hlubší, metafyzické úrovni. To je hlavním zájmem druhé části textu, ve kterých jsou porovnány metafyzické důsledky obou pozic. Na konci lingvistické analýzy v první části jsme se dostali do bodu, kdy se může zdát, že presentismus a eternalismus jsou pouze různými pokusy o vyjádření toho, co je vlastně stejné chápání podstaty času, ale v metafyzické analýze, že následuje, ukáže se, že nejsou. Současnost a věčnost jsou ukázány jako dva rozdílné ontologické přístupy času ve vztahu k prostoru (čas jako v podstatě homogenní čtvrtá dimenze a čas jako něco, co je v podstatě odlišné od prostoru). Autor se pak zaměřuje na důsledky, které tyto dvě pozice mají zejména na koncepci přítomnosti a jejího toku v čase.Současnost a eternismus se nakonec ukázaly jako zcela odlišné pozice, které - paralelně s proslulým argumentem McTaggarta - tvrdí na jedné straně velmi silnou realitu času (presentismus) nebo na druhé straně její naprostou neskutečnost (eternalismus)., and Jacques Joseph
In this essay the author argues that an ontological problem of a work of art, one of the long-standing problems of the philosophy of art, is merely an apparent one. The author argues that it in fact comprises two particular, different problems. The first is the question of how the thing being described in aesthetic terms exists, whether the aesthetic and physical description of a thing are so different, indeed disparate, that they cannot – as some philosophers of art assume – relate to the same thing. The second problem is the question of how a work of a multiple art (for example, of music or literature) can exist, whether we can identify it with the individual act of performing or using this work (for example, the performance of music or a reading of a book). The first problem, argues the author, stems from the erroneous assumption that the disparateness of the aesthetic and physical description of a thing leads to the conclusion that the object of aesthetic description must exist differently from the way a physical description exists. The second problem emerges from a lack of understanding of how we use the term “work of art,” when we use it for a work of multiple art. The author also criticizes simultaneous attempts by Arthur Danto and Joseph Margolis, two leading philosophers of art, to solve the ontological problem of the work of art.
Ca2+ has been considered as a necessary ion for alleviation of stress-induced damages in plants. We investigated effects of exogenous Ca2+ on waterlogging-induced damage to pepper and its underlying mechanisms. Pepper seedlings under stress were treated by spraying of 10 mM CaCl2. Applying exogenous Ca2+ increased the biomass of pepper leaves and roots, improved photosynthetic characteristics, membrane permeability, root activity, osmotic substance contents, antioxidant enzyme and alcohol dehydrogenase activities, while it reduced lactate dehydrogenase activity. It maintained hydroxide radical contents and activities of malate dehydrogenase and succinate dehydrogenase relatively high. Our results suggested that applying exogenous Ca2+ could regulate osmotic substance contents, antioxidant system activity, root respiration, and metabolism, and subsequently alleviate waterlogging-induced damages to pepper plants., B. Z. Yang, Z. B. Liu, S. D. Zhou, L. J. Ou, X. Z. Dai, Y. Q. Ma, Z. Q. Zhang, W. C. Chen, X. F. Li, C. L. Liang, S. Yang, X. X. Zou., and Obsahuje bibliografii
The hypothesis that application of exogenous glycine betaine (GBEX) may attenuate the effects of mild water deficit in leaf gas exchange and lipid peroxidation in Carapa guianensis was examined. For this reason, 110-d old plants were sprayed with 0, 25, and 50 mM GBEX and then subjected to two watering regimes. In the first, irrigation was continuously performed to maintain the soil near to field capacity (watered plants). In the second, irrigation was withheld and water deficit resulted from progressive evapotranspiration (water-stressed plants). Treatment comparisons were assessed when predawn leaflet water potential (Ψpd) of stressed plants reached -1.28 ± 0.34 MPa. Regardless of the watering regime, significant (P<0.05) increases in foliar glycine betaine (GBLeaf) concentration were observed in response to increasing GBEX; however, such increases were more expressive in stressed plants. The net photosynthetic rate, stomatal conductance to water vapor, and intercellular to ambient CO2 concentration ratio were significantly lower in water-stressed plants independently of GBEX concentration sprayed on leaves. The application of 25 and 50 mM GBEX caused significant (P<0.05) increases in ascorbate peroxidase (APX) activity in stressed plants, while significant (P<0.05) increases in catalase activity was observed just in the stressed plants treated with 50 mM GBEX. Malondialdehyde concentrations did not differ between watered and stressed plants regardless of GBEX concentration. In conclusion, C. guianensis was able to incorporate GBEX through their leaves and the resulting increases in GBLeaf attenuated lipid peroxidation in stressed plants through positive modulation of APX and CAT activities., F. J. R. Cruz ...[et al.]., and Obsahuje bibliografii