An asymptotic expansion related to the Dickman function

We prove a conjecture of Broadhurst on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.     

Extreme values of zeta and <Emphasis Type="Italic">L</Emphasis>-functions

We introduce a resonance method to produce large values of the Riemann zeta-function on the critical line, and large and small central values of L-functions. The author is partially supported by the National Science Foundation (DMS 0500711) and the American Institute of Mathematics (AIM).     

Degree 1 elements of the Selberg class

We provide a short and simple proof of a beautiful result of Kaczorowski and Perelli classifying the elements of degree one in the Selberg class.     

An Improved Synthesis Route to Functionalized 2-Alkyn-1-ylboronates: Useful Intermediates for the Preparation of α-Allenic Alcohols

Summary. Functionalized 2-alkyn-1-ylboronates were successfully prepared in good yields by reacting various acyclic and cyclic (iodomethyl)boronates with various alkynyllithium salts. Amongst various (iodomethyl)boronates studied, 2-(iodomethyl)-1,3,2-dioxa-4,4,5,5-tetramethylborolane provided improved chemical yields of 2-alkyn-1-ylboronates with pyran- and triisopropylsilyl-substituted alkynyllithium salts. 2-Alkyn-1-ylboronate bearing an acid sensitive structure (pyran) was successfully synthesized which would be very difficult to achieve under previously reported reaction conditions. The exceptionally rapid rearrangement of the “ate” complex derived from the pinacol (iodomethyl)boronate, suppression of the side product formation, and the stability of the pinacol 2-alkyn-1-ylboronate are some of the notable merits of this protocol. This new procedure offers a simple and convenient alternative route to the existing methodologies, in terms of the milder reaction conditions, functional group compatibility, and the ease of the operation. The synthesis scope of this class of 2-alkyn-1-ylboronates was demonstrated by reacting the pinacol 2-alkyn-1-ylboronate with benzaldehyde, which yielded the α-allenic alcohol in good yield and regioselectivity.     

Acute oral toxicity and brine shrimp lethality of Elaeis guineensis Jacq., (oil palm leaf) methanol extract

Elaeis guineensis (Arecaceae) is widely used in West African traditional medicine for treating various ailments. An evaluation on the toxicity of extracts of this plant is crucial to support the therapeutic claims. The acute oral toxicity and brine shrimp lethality of a methanolic extract of this plant was tested. Oral administration of crude extract at the highest dose of 5,000 mg/kg resulted in no mortalities or evidence of adverse effects, implying that E. guineensis is nontoxic. Normal behavioral pattern, clinical signs and histology of vital organs confirm this evidence. The E. guineensis extracts screened for toxicity against brine shrimp had 50% lethal concentration (LC??) values of more than 1.0 mg/mL (9.00 and 3.87 mg/mL, at 6 and 24 h, respectively), confirming that the extract was not toxic. Maximum mortalities occurred at 100 mg/mL concentration while the least mortalities happened to be at 0.195 mg/mL concentration. The results of both tests confirm that E. guineensis is nontoxic and hence safe for commercial utilization.     

2,6-Lutidine-N-oxide complexes of rare-earth bromides

2,6-Lutidine-N-oxide (LNO) complexes of rare-earth bromides of the composition wheren = l for M = La, Pr, Nd, Sm, Gd, Ho, Er; andn = 0 for M = Y have been prepared and characterised by analyses, conductance and infrared data. Infrared spectra of the complexes indicate that the coordination of ligand to the metal ion takes place through the oxygen of the ligand, and the water molecule in the complexes present is coordinated to the metal. A coordination number of seven has been suggested to all the rare-earth metal ions.