Gennadius II was a Byzantine philosopher and theologian, Ecumenical Patriarch of Constantinople from 1454 to 1464. He was a strong advocate for the use of Aristotelian philosophy in the Eastern Church. Gennadius was, together with his mentor, Mark of Ephesus, involved in the Council of Florence which aimed to end the schism between East and West. Gennadius had written extensively on Western theology. After the failure of the union of Florence and the Fall of Constantinople, Gennadius became the first Ecumenical Patriarch of Ottoman Constantinople. A polemicist, Scholarios left in writing several treatises on the differences between Eastern and Western theology, the Filioque, a defence of Aristotelianism and excerpts from an exposition of the Orthodox faith addressed to Mehmed II. Scholarius is believed to have been born as Georgios in Constantinople in c. 1400. His abecedary was Mark of Ephesus. Following his tutelage under the famous John Chortasmenos, Manuel-Mark might have recommended him to study under his own previous master, Georgios Gemistus Pletho, c.
1428. However, his studies under Pletho are a matter of speculation and, at any rate, would have been more attendance at Pletho's lectures at Mistra. Scholarius had been a teacher of philosophy before entering the service of the emperor John VIII Palaeologus as a theological advisor. In fact, in 1437 – in anticipation of the Council of Ferrara-Florence – the emperor formally studied Nilus Cabasilas' works along with Mark of Ephesus and Gennadius Scholarius. Curiously, the trio formally studied the works of John Duns Scotus because of his rejection of the Filioque in Thomistic metaphysics, as well as Scotus' doctrine of a "formal distinction" between the persons and essence of God, as well as God's attributes, it was for this reason that Scholarius wrote an academic refutation of the first eighteen of Mark of Ephesus' "Syllogistic Chapters against the Latins." From this, we can surmise that Scholarius was writing an academic exercise to inform his former master that Thomas Aquinas' opinions did not constitute a universally Latin approach to questions on the Trinity.
Scholarius becomes important when, as judge in the civil courts under John VIII, he accompanied his Emperor to the Council of Ferrara-Florence, held in 1438–1439 in Ferrara and Florence. The object of this endeavor was bringing a union between the Greek and Latin Churches, which he supported at that time, he made four speeches at the council – all exceedingly conciliatory. At the same council appeared the celebrated Platonist, Gemistus Pletho, the most powerful opponent of the dominant Aristotelianism, an antagonist of Scholarius. In church matters, as in philosophy, the two were opposed – Pletho advocated a partial return to Greek paganism in the form of a syncretic union between Christianity and Zoroastrianism. Scholarius was at a serious disadvantage because, being a layman, he could not directly take part in the discussions of the council. Despite his initial advocacy of the union, Genaddius soured on union during the council, left it early in June of 1400. At the behest of his mentor Mark of Ephesus, who converted him to anti-Latin Orthodoxy, till his death, Scholarius was known as the most uncompromising enemy of the union.
It was at just about this time that Scholarius began to draw attention to the putative heterodoxy of Aquinas' "distinction of reason" between the attributes and essence of God. First, as contained in Jugie's edition of his opera omnia, Scholarius interrupts chapters 94–96 of his discourse "On Being and Essence" of Thomas Aquinas, replaces the Thomistic explanation with that of Scotism in order to agree better with Palamas. However, he mitigates total condemnation of Aquinas, noting that Scholastics interpret Aquinas in a more Orthodox light; this point marks Scholarius' increasing theological distance from Aquinas, where he begins to be more theologically condemnatory of him in works. However, this distance can be overstated. Marcus Plested observes that Scholarios' "love and esteem for Thomas was to continue undimmed throughout his career" "although he would accentuate the note of caution in works." Despite his cautions, Scholarios writes of Thomas "we love this divinely-inspired and wise man."
He wrote many works to defend his new convictions, which differ so much from the earlier conciliatory ones that Allatius thought there must be two people of the same name. After the death of John VIII in 1448, Georgios entered the Pantokrator monastery in Constantinople under Constantine XI and took, according to the invariable custom, a new name: Gennadius. Before the fall of the city he was well known as a bitter opponent of the union, he and Mark of Ephesus were the leaders of the anti-Latin party. In 1444, Mark of Ephesus on his deathbed praised Gennadius's irreconcilable attitude towards the Latins and the union, it was to Gennadius that the angry people went after seeing the Uniate services in the grea
The Reynolds Equation is a partial differential equation governing the pressure distribution of thin viscous fluid films in Lubrication theory. It should not be confused with Osborne Reynolds' other namesakes, Reynolds number and Reynolds-averaged Navier–Stokes equations, it was first derived by Osborne Reynolds in 1886. The classical Reynolds Equation can be used to describe the pressure distribution in nearly any type of fluid film bearing; the general Reynolds equation is: ∂ ∂ x + ∂ ∂ y = ∂ ∂ x + ∂ ∂ y + ρ − ρ u a ∂ h ∂ x − ρ v a ∂ h ∂ y + ρ ∂ h ∂ t Where: p is fluid film pressure. X and y are the bearing length coordinates. Z is fluid. H is fluid film thickness. Μ is fluid viscosity. Ρ is fluid density. U, v, w are the bounding body velocities in y, z respectively. A, b are subscripts denoting the bottom bounding bodies respectively; the equation nondimensionalized. The Reynolds Equation assumes: The fluid is Newtonian. Fluid viscous forces dominate over fluid inertia forces; this is the principal of the Reynolds number.
Fluid body forces are negligible. The variation of pressure across the fluid film is negligibly small The fluid film thickness is much less than the width and length and thus curvature effects are negligible.. For some simple bearing geometries and boundary conditions, the Reynolds equation can be solved analytically. However, the equation must be solved numerically; this involves discretizing the geometric domain, applying a finite technique - FDM, FVM, or FEM. A full derivation of the Reynolds Equation from the Navier-Stokes equation can be found in numerous lubrication text books. In general, Reynolds equation has to be solved using numerical methods such as finite difference, or finite element. In certain simplified cases, analytical or approximate solutions can be obtained. For the case of rigid sphere on flat geometry, steady-state case and half-Sommerfeld cavitation boundary condition, the 2-D Reynolds equation can be solved analytically; this solution was proposed by a Nobel Prize winner Pyotr Kapitsa.
Half-Sommerfeld boundary condition was shown to be inaccurate and this solution has to be used with care. In case of 1-D Reynolds equation several analytical or semi-analytical solutions are available. In 1916 Martin obtained a closed form solution for a minimum film thickness and pressure for a rigid cylinder and plane geometry; this solution is not accurate for the cases when the elastic deformation of the surfaces contributes to the film thickness. In 1949, Grubin obtained an approximate solution for so called elasto-hydrodynamic lubrication line contact problem, where he combined both elastic deformation and lubricant hydrodynamic flow. In this solution it was assumed; the model is therefore accurate at high loads, when the hydrodynamic pressure tends to be close to the Hertz contact pressure. The Reynolds equation is used to model the pressure in many applications. For example
Section 51 of the Australian Constitution, is a subsection of Section 51 of the Australian Constitution that gives the Commonwealth Parliament the power to legislate with respect to "foreign corporations, trading or financial corporations formed within the limits of the Commonwealth". This power has become known as "the corporations power", the extent of, the subject of numerous judicial cases. After the High Court's decision in Huddart, Parker & Co Ltd v Moorehead, the "corporations" power was ignored as a basis for Commonwealth legislation; the majority judges agreed in this case that the power should be construed narrowly, though they were unable to agree on any appropriate interpretation. Their approach reflected the perceived need to protect "the reserved powers of the States", an idea abandoned in 1920 as a result of the Engineer' case. Justice Issacs dissent in Huddart, Parker gave a broad meaning to s 51 but attempted to set limits to the power, in particular pointing out: it is exerciseable wherever these specific objects are found, irrespective of whether they are engaged in foreign or interstate commerce, or commerce confined to a single State the power is to operate only on corporations of a certain kind, foreign and financial corporations it is not a power to create or dissolve corporations it is not restricted to internal company regulation it is concerned with the regulation of the conduct of the corporations in their transactions with, or as affecting, the publicIt was not until Huddart Parker was overruled in Strickland v Rocla Concrete Pipes Ltd that the modern development of the power began.
In that case, the leading judgment was delivered by Chief Justice Barwick, although agreeing that Isaacs' dissent in Huddart Parker conformed to the reasoning in Engineers, refused to define the scope of the corporations power. He stated instead that "the decision as to the validity of particular laws yet to be enacted must remain for the Court when called upon to pass upon them"; the High Court in New South Wales v Commonwealth confirmed that the ambit of the corporations power extends only to corporations that have been formed, therefore, it does not include the power to incorporate them. It extends only to domestic corporations of a trading or financial character, to all corporations formed outside Australia, they are collectively referred to as "constitutional corporations". In most of the early cases, the question of what aspects or activities of a corporation can be regulated under s 51 was not directly addressed; some incidental points were clarified in R v Australian Industrial Court.
That case established that, where the activities of a s 51 corporation were validly regulated, the conduct of individual persons taking part in those activities, such as company directors, could incidentally be regulated as well. In Actors and Announcers Equity Association v Fontana Films Pty Ltd, the Court still did not deal directly with the regulation of a corporation's activities; the whole Court upheld a section. The legislative purpose thus upheld; the case provided an opportunity for extensive discussion of how far the "corporations" power might extend. The WorkChoices case provides the current definition for the extent of the corporations power, as noted in its majority opinion: the regulation of the activities, functions and the business of the specified types of corporation the creation of rights, privileges belonging to such a corporation the imposition of obligations on it the regulation of the conduct of those through whom it acts, its employees and shareholders and the regulation of those whose conduct is or is capable of affecting its activities, relationships or business including laws prescribing the industrial rights and obligations of corporations and their employees and the means by which they are to conduct their industrial relations Whether a corporation falls within the group of "trading or financial corporations" has been the focus of much attention and debate.
The dominant issues revolve around the type of corporation and the nature of the activities that characterise it as falling within s. 51. In that regard: A constitutional corporation can be a "trading corporation" and a "financial corporation" at the same time A "trading corporation" is one where trading is a substantial or significant part of its activities, that determination is irrespective of the purpose for which the corporation formed A trading corporation can be found to exist on the basis of the nature of its established activities, or with respect to the objects for which it was incorporated "Trading activities" are those that involve some form of buying and selling, generate revenue, regardless of whether carried out at a profit The type of ownership is not material—a State corporation established to generate electricity has been held to be subject to regulation Where a corporation has not yet commenced trading, it can still be subject to regulation based on its objects of incorporation however, the High Court, in a controversial ruling, has held that a municipal corporation was to be distinguished from a trading corporation, notwithstanding the fact that it carried out trading activities A "financial corporation" is one that engages in substantial financial activities or intends to do so, but it is