We study, as hypersurfaces in toric varieties, elliptic Calabi–Yau fourfolds for F-theory compactifications dual to E8 × E8 heterotic strings compactified to four dimensions on elliptic Calabi–Yau threefolds with some choice of vector bundle. We describe how to read off the vector bundle data for the heterotic compactification from the toric data of the fourfold. This map allows us to construct...

Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish th...

There are by now several attempts to make the theory of the field of one element F1 rigorous. In [10] the authors formalize the transition from rings to schemes on a categorial level and apply this machinery to the category of sets to obtain the category of F1-schemes as in [1]. In [3] and [5] the authors extend the definition of rings in order to capture a structure that deserves to be called ...

In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from ...

We survey known results on spectra of structures and on spectra of relations on computable structures. asking when the set of all highn degrees can be such a spectrum, and likewise for the set of nonlown degrees. We then repeat these questions specifically for linear orders and for relations on the computable dense linear order Q. New results include realizations of the set of nonlown Turing de...

The adverse effects of atrial fibrillation on the circulation are well known. It reduces cardiac output and stroke volume (Kory and Meneely, 1951; Broch and Muller, 1957), may lead to cardiac dilatation and failure (Phillips and Levine, 1949), and is associated with a high risk of systemic embolization (Sokolow, 1951; Fraser and Turner, 1955). Unfortunately, attempts to restore sinus rhythm wit...

A degree is saturated bounding if it can compute a saturated model for any complete, decidable theory whose types are all computable. All high and PA degrees are saturated bounding (following from results of Jockusch and MacIntyre-Marker.) We show that for every n, no lown c.e. degree is saturated bounding, extending the previous known result that 0 is not saturated bounding, by Millar.

PAROXYSMAL atrial tachyeardia with atrioventricular block (PAT with block) has been recognized more often in recent years since Lown and Levine clarified its diagnostic criteria and emphasized its important relation to digitalis excess.1' 2 The present report was prompted by the increasing frequency with which this diagnosis has been made at our hospital and its common association with chronic ...

The significance and treatment of ventricular premature beats (VPBs) in patients without sustained ventricular tachycardia (VT), sudden death, or syncope remains unclear. We undertook a prospective study of programmed electrical stimulation (up to two extrastimuli and burst pacing) in 73 patients (age 60 +/- 10 years) with high-grade VPBs who had no evidence of sustained VT, sudden death, or sy...

This article presents a clinical case of peripartum cardiomyopathy in 21-year-oldpatient with gestational age 32 weeks, accompanied by manifestationsof heart failure and Lown-Ganong-Levine (LGL) syndrome. The patient underwentlaboratory instrumental examinations, including echocardiography Holtermonitoring. Thyrotoxic was ruled out the process differentialdiagnosis. final diagnosis management w...