We give a short review of Frobenius manifolds and algebraic integrability and study their intersection. The simplest case is the relation between the Frobenius manifold of simple singularities, which is almost dual to the integrable open Toda chain. New types of manifolds called extra special Kähler and special F -manifolds are introduced which capture the intersection.

1948 under the Act of March 3, 1879. Acceptance for mailIng at the special rate postage provided for in the Act of February 28, 1925, embodied in paragraph 4, Sec. 538, P. L. and R., authorized January 13, 1948. Articles offered for publication should be sent to the Editor. The AAAS assumes no responsibility for the opinions expressed by contributors. Membership correspondence for the AAAS shou...

We study the Eisenstein ideal for modular forms of even weight $k>2$ and prime level $N$. pay special attention to phenomenon extra reducibility: is strictly larger than cutting out reducible Galois representations. prove a modularity theorem these As consequences, we relate derivative Mazur–Tate $L$-function rank Hecke algebra, generalizing Merel, give new proof case an equivariant main conjec...

INTRODUCTION Ulcerative colitis (UC) and Crohn’s disease (CD) are idiopathic conditions that primarily affect the gastrointestinal tract, but also are associated with a variety of systemic or extra-intestinal manifestations. These extra-intestinal manifestations may implicate multiple organ systems. For some of these disorders there is evidence that the severity and duration of the inflammatory...

Intracranial cavernous angiomas are benign vascular malformations and can be divided into intra-axial and extra-axial lesions. Extra-axial cavernous angiomas are relatively rare and usually arise in relation to the dura mater and mimick meningiomas. We report a case of cavernous angioma that occurred in the falx cerebri of a 22-yr-old female patient with the special focus on neuroradiologic fin...

In the usual aim of discrete tomography, reconstruction an unknown set is considered, by means projection data collected along a U directions. Possible ambiguous reconstructions can arise if and only switching components occur, namely, non-empty images exist having null projections all directions in U. order to lower number allowed reconstructions, one tries incorporate possible extra geometric...