We show that Plebanski’s second heavenly equation, when written as a firstorder nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri’s theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions. PACS numbers: 11.10.Ef, 02.30.Ik, 04.20.Fy Mathematics Subject Classification: 35Q75, 35L65

Ian E. H. Yen 1 * [email protected] Xiangru Huang 1 * [email protected] Kai Zhong 2 [email protected] Pradeep Ravikumar 1,2 [email protected] Inderjit S. Dhillon 1,2 [email protected] * Both authors contributed equally. 1 Department of Computer Science, University of Texas at Austin, TX 78712, USA. 2 Institute for Computational Engineering and Sciences, University of Tex...

The KAI,II'SOS prototype we have developed at the IBM Paris Scientific Center is able to analyze texts written in l;reneh and to produce a semantic representalion of these texts expressed as a set of inter-related Conceptual Graphs [6, 1]. It uses a semantic lexicon which contains, for each word to be defined, one or more Conceptual Graphs corresponding to one or more meanings of the word. The ...

Human persons can act with libertarian freedom in heaven according to one prominent view, because they have freely acquired perfect virtue their pre-heavenly lives such that acting rightly is volitionally necessary. But since the character of human not at death, how perfected? On unilateral model, God alone completes perfection character, and, on cooperative continues work them purgatory own ch...

In Ma’aseh Tuviyah, a Hebrew medical treatise published in Venice at the dawn of the eighteenth century, there is a magnificent illustration in which the human body is portrayed as a house. What was the function of such an illustration?What is its significance? In the following article I will postulate that such an illustration would have served primarily as a mnemonic device for (Jewish) stude...

Second heavenly equation hierarchy is considered using the framework of hyper-Kähler hierarchy developed by Takasaki [1, 2]. Generating equations for the hierarchy are introduced, they are used to construct generating equations for reduced hierarchies. General N reductions, logarithmic reduction and rational reduction for one of the Lax-Sato functions are discussed. It is demonstrated that rati...

A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit ultra-hyperbolic selfdual vacuum spaces admiting only one Killing vector which is not selfdual, we also give the corresponding explicit Einstein–Weyl structures.

Since the hapax legomenon * מִשְׁטָר of Job 38:33b is understood as a "scripture heaven," its meaning can be deduced only from environment Old Near East but in particular context, 38:31-33 (including 9:9). Thus, separate consideration verbs, "link, loosen, lead out, guide" and constellations, "Pleiades, Orion, Hyades, Big Bear over cubs, chambers South" (Job 38:31-32; 9:9) - including parallel "ord...