There are infinitely many limit points of the fractional parts of powers

Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα ⁿ , n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.     

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

Phase Transfer Catalysis Preparation of Acyl Isothiocyanates

The use of phase transfer catalysis, PTC, for nucleophillic substitution reactions is well documented.^1,2 Included among these reactions is the preparation of both alkyl³ and aryl⁴ thiocyanates. However, PTC reactions at an acyl carbon are much less common. Brándstróm⁵ has reported the preparation of acyl azides and Weber⁶ has used PTC to prepare benzoyl cyanide. Recently Illi⁷ has used PTC to acylate sterically crowded phenols.     

Phase Transfer Catalysis Preparation of Arvl,Thiocyanates

Phase transfer catalvsis, PTC, has become a common preparative method in organic chemistry. Numerous aliphatic substitution reactions have been performed yielding cvanides,¹ azides,² thiocyanates,³ ethers,⁴ and many other types of substitution products.¹     

Biotransformation-mediated synthesis of (1S)-1-(2,6-dichloro-3-fluorophenyl)ethanol in enantiomerically pure form

An efficient four-step biotransformation-mediated synthesis of (1S)-1-(2,6-dichloro-3-fluorophenyl)ethanol in enantiomerically pure form is described. This compound is a key intermediate required for the preparation of PF-2341066, a potent inhibitor of c-Met/ALK that is currently in clinical development. The described synthesis was used to manufacture 6 kg of the title compound and can also be employed to produce the corresponding (1R)-enantiomer.     

Surface-charge-governed ion transport in nanofluidic channels

A study of ion transport in aqueous-filled silica channels as thin as 70 nm reveals a remarkable degree of conduction at low salt concentrations that departs strongly from bulk behavior: In the dilute limit, the electrical conductances of channels saturate at a value that is independent of both the salt concentration and the channel height. Our data are well described by an electrokinetic model parametrized only by the surface-charge density. Using chemical surface modifications, we further demonstrate that at low salt concentrations, ion transport in nanochannels is governed by the surface charge.