A finiteness result for Heegaard splittings

In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.     

Universal WCG banach spaces and universal Eberlein Compacts

We prove that for cardinalsτ satisfying τ^ω=τ and forτ=ω ₁, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ. Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist. Thus under GCH universal spaces exist forτ iff cof(τ)=ω. The research of the second author was supported by a grant from the United States-Israel Binational Science Foundation and the Fund for the Promotion of Research at the Technion.     

2 alpha-(3-hydroxypropyl)- and 2 alpha-(3-hydroxypropoxy)-1 alpha,25-dihydroxyvitamin D3 accessible to vitamin D receptor mutant related to hereditary vitamin D-resistant rickets

Hereditary vitamin D-resistant rickets (HVDRR) is a genetic disorder caused by mutations in the vitamin D receptor, which lead to resistance to 1alpha,25-dihydroxyvitamin D(3) [1alpha,25(OH)(2)D(3)]. We found that the A ring-modified analogues, 2alpha-(3-hydroxypropyl)- and 2alpha-(3-hydroxypropoxy)-1alpha,25(OH)(2)D(3), (O1C3 and O2C3) can bind better than the natural hormone to the mutant VDR (R274A), which similar to the HVDRR mutant, R274L, had lost the hydrogen bond to the 1alpha-hydroxyl group of 1alpha,25(OH)(2)D(3).     

Fine Tuning of Chlorophyll Spectra by Protein‐Induced Ring Deformation

The ability to tune the light‐absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light‐harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein–pigment interactions that underlie the spectral‐tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water‐soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.     

Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.

     

Log-normal distribution of pulse amplitudes due to Raman cross talk in wavelength division multiplexing soliton transmission

The effect of delayed Raman response on soliton collisions in wavelength division multiplexing (WDM) transmission systems is investigated. Taking into account the stochastic nature of pulse sequences in different frequency channels and the Raman-induced cross talk, it is shown that the soliton amplitude is a random variable with a log-normal distribution. Moreover, the Raman-induced self-frequency shift and cross-frequency shift are also random variables with log-normal-like distributions. These results imply that fluctuations in soliton amplitude and frequency induced by soliton collisions in the presence of delayed Raman response play an important role in massive WDM transmission.     

Time course of loudness recalibration: implications for loudness enhancement

Loudness recalibration, the effect of a relatively loud 2500-Hz recalibrating tone on the loudness of a relatively soft 2500-Hz target tone, was measured as a function of the interstimulus interval (ISI) between them. The loudness of the target tone, assessed by a 500-Hz comparison tone, declined when the ISI equaled or exceeded about 200 ms and leveled off at an ISI of about 700 ms. Notably, the target tone's loudness did not change significantly at very short ISIs (< 150 ms). The latter result is incompatible with the literature reporting loudness enhancement in this time window, but is compatible with the suggestion made by Scharf, Buus, and Nieder [J. Acoust. Soc. Am. 112, 807-810 (2002)] that early measurements of enhancement were contaminated by the influence of the recalibrating tone on the comparison tone when the two shared the same frequency. In a second experiment the frequency of the comparison tone was changed to 2500 Hz and the results of a loudness enhancement paradigm was successfully predicted from the time course of recalibration obtained in experiment 1.