By John Edward Campbell

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This quantity marks the 20 th anniversary of the Bialowieza sequence of conferences on Differential Geometric tools in Physics; the anniversary assembly used to be held in the course of July 1-7, 2001. The Bialowieza conferences, held each year in the course of the first week of July, have now grown into an annual pilgrimage for a global workforce of physicists and mathematicians.

**Monomialization of Morphisms from 3-folds to Surfaces**

A morphism of algebraic forms (over a box attribute zero) is monomial if it will possibly in the community be represented in e'tale neighborhoods by means of a natural monomial mappings. The publication supplies facts dominant morphism from a nonsingular 3-fold X to a floor S could be monomialized by way of acting sequences of blowups of nonsingular subvarieties of X and S.

This monograph is an annotated translation of what's thought of to be the world’s first calculus textbook, initially released in French in 1696. That anonymously released textbook on differential calculus was once in accordance with lectures given to the Marquis de l’Hôpital in 1691-2 through the good Swiss mathematician, Johann Bernoulli.

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H. : Convolution of convex valuations. Geom. Dedicata 123 (2006), 153–169. [25] Bernig, A. and Fu, J. H. : Hermitian integral geometry. Ann. of Math. 173 (2011), 907–945. : On the curvatura integra in a Riemannian manifold. Ann. of Math. 46 (1945), 674–684. : Curvature measures. Trans. Amer. Math. Soc. 93 (1959), 418– 491. [28] Fu, J. H. : Curvature measures and generalized Morse theory, J. Diﬀerential Geom. 30 (1989), 619–642. [29] Fu, J. H. : Monge–Amp`ere functions, I. Indiana Univ. Math. J.

4. (1) Any smooth measure on X is a smooth valuation. 2. (2) The Euler characteristic χ is also a smooth valuation. This fact is less obvious. In the current approach, it is a reformulation of a version of the Gauss–Bonnet formula due to Chern [26], who has constructed μ and ω to represent the Euler characteristic; his construction depends on the choice of a Riemannian metric on X. (3) The next example is very typical for integral geometry. Let X = CPn be the complex projective space. Let C Gr denote the Grassmannian of all complex projective subspaces of CPn of a ﬁxed complex dimension k.

The ﬁrst general result in this direction is as follows. 31 ([1]). Let G be a compact subgroup of the orthogonal group. The space ValG is ﬁnite-dimensional if and only if G acts transitively on the unit sphere. 18, if G acts transitively on the sphere, then ValG ⊂ Valsm . This equips ValG with the product. Evidently, we have also McMullen’s decomposition n ValG = ValG i . i=0 Thus ValG becomes a ﬁnite-dimensional commutative associative graded algebra with unit. 10. Moreover, it was shown by Bernig [20] that for such G G all G-invariant valuations are even.