TUḤFAT al-NAṢĀ’IḤ de Yūsuf Gadā

Dans cette copie le bāb 45 est numéroté 46 par erreur, de même que la date de composition (f. 66v) est donnée comme étant 700H.[sic] au lieu de 795H. De la main de Muḥ. Zamān, on trouve des gloses lexicographiques entre les lignes ou dans le marges. La signature d’Aussant figure au f. 1. Ce ms. (Aussant n° 38) a été acquis par la B.N. en 1798. [Anc. cote, Suppl. persan 51].

AḤVĀL-i MAWT-i ḤUSAYN-‛ALĪ HĀN VA AḤVĀL-i MAWT-i PISAR

Poème masnavī compose de deux parties, l’histoire (qiṣṣa) de la chute, puis de la mort, du vizir Sayyid ‛Alī Hān (f. 7v- 59), assassiné le 9 octobre 1720 et remplacé par Muḥ. Amīn Hān I‛timād al-Dawla. Cette partie compte 919 bayt. La seconde (f. 61- 102v) en compte 763 et raconte les circonstances de la mort de Lāla Laliyān Mal, fils de l’auteur (f. 62), survenue dix mois après, alors qu’il avait 30 ans, et les campagnes militaires de cette période. Cette qiṣṣ̣a aurait été rédigée vers 1723 (f. 102).Une préface en prose (dībāča), rédigée (f. 5v) par Zōrāvar Singh [comparer à Supplément persan 247] occupe les f. 1v à 6v. Celui-ci indique qu’il édita, après sa mort l’œuvre du poète Rāy Kirpārām (f. 3v), et dédie cette édition (f. 2v) au moghol Abū l-Fatḥ Nāṣir al-Dīn Muḥ. Šāh (m. en 1161H./1748). Ce serait Rāy Kirpārām l’auteur des deux qiṣṣa.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

André spectral sequences for Baues-Wirsching cohomology of categories

We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild-Mitchell cohomology and those studied before by Watts, Roos, Quillen and others

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

The groups of Poincaré and Galilei in arbitrary dimensional spaces

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincar algebra. The usual contraction of the Poincar to the Galilei group is seen to be equivalent to a certain coordinate transformation.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.