On translation lengths of Anosov maps on the curve graph of the torus

Geometriae Dedicata - We show that an Anosov map has a geodesic axis on the curve graph of the torus. The direct corollary of our result is the stable translation length of an Anosov map on the...     

Manuals in orthogonal categories

The notion of a manual, introduced and investigated in detail by Foulis, Randall, and their followers, has turned out to be further reaching than its originators had envisaged. Its omnipresence is comparable with the notion of a sheaf, whose significance is well recognized by every pure and applied mathematician. The principal concern of this paper is to give an appropriate vehicle, as general as possible, by which the theory of manuals can be developed. The vehicle is called an orthogonal category, which is akin to the notion of a category with coproducts. Orthogonal categories provide also a new perspective on the notion of a sheaf over a complete Boolean algebra, deepening our comprehension of Boolean mathematics and paving the way to quantum mathematics.     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.