Infinite families of surface symmetries

Consider a sequenceN _a,b :g ↦ag+b, g=2,3,… wherea, b are rational numbers anda≥0. We say thatN _a,b is admissible if for infinitely manyg’s there exists a finite groupG of orientation-preserving homeomorphisms of a compact orientable surface of genusg such that |G|=N _a,b (g). In this case we shall also say thatG belongs toN _a,b . The main result of the paper is that ifa+b≠0, then any group belonging toN _a,b contains a cyclic subgroup of bounded index, where the bound depends only ona,b. Moreovera+b is positive, and 2b/a is an integer. This implies, for instance, that there are only finitely many possibilities for perfect subgroups or quotient groups of groups belonging toN _a,b . Partially supported by an NFS grant, and a PSC-CUNY award. Dedicated to A. M. Macbeath with much respect     

On discrete boundary value problems arising in transport phenomena

For the discrete boundary value problems arising in transport processes we provide comparison results. These results are used to develop monotone iterative methods for the construction of the maximal and minimal solutions in a sector. The advantage of this technique is that the successive approximations are the solutions of the initial and terminal value problems. Numerical illustration showing the sharpness as well the importance of the obtained results is also included.     

A facile route for the synthesis of novel γ‐lactams

A selective reduction and its subsequent cyclisation of novel isoxazolidines into γ‐lactams have been examined in presence of Raney ‐ nickel catalyst.     

Infinite Interval Problems Modeling the Flow of a Gas Through a Semi-Infinite Porous Medium

Various existence results are presented for boundary-value problems on the infinite interval. In particular, our theory includes a discussion of a problem arising in the unsteady flow of a gas through a semi–infinite porous medium.     

Scalar field quantization in stationary,non-static spacetimes

A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces. The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in” and “out” Boulware vacua.     

Existence Criteria for Singular Boundary Value Problems with Sign Changing Nonlinearities

A general existence theory is presented for boundary value problems where our nonlinearity may be singular in its dependent variable and may also change sign. In addition from our theory, we give easily verifiable conditions to check existence in practice.     

The Baylis-Hillman reaction: one-pot facile synthesis of 2,4-functionalized 1,4-pentadienes

The Baylis-Hillman coupling between activated alkenes and alkyl 2-(bromomethyl)prop-2-enoates in the presence of DABCO (or DBU) leading to the formation of 2,4-functionalized 1,4-pentadienes, has been described.     

Robustness of the bistable behavior of a biological signaling feedback loop

Biological signaling networks comprised of cellular components including signaling proteins and small molecule messengers control the many cell function in responses to various extracellular and intracellular signals including hormone and neurotransmitter inputs, and genetic events. Many signaling pathways have motifs familiar to electronics and control theory design. Feedback loops are among the most common of these. Using experimentally derived parameters, we modeled a positive feedback loop in signaling pathways used by growth factors to trigger cell proliferation. This feedback loop is bistable under physiological conditions, although the system can move to a monostable state as well. We find that bistability persists under a wide range of regulatory conditions, even when core enzymes in the feedback loop deviate from physiological values. We did not observe any other phenomena in the core feedback loop, but the addition of a delayed inhibitory feedback was able to generate oscillations under rather extreme parameter conditions. Such oscillations may not be of physiological relevance. We propose that the kinetic properties of this feedback loop have evolved to support bistability and flexibility in going between bistable and monostable modes, while simultaneously being very refractory to oscillatory states. (c) 2001 American Institute of Physics.