Revisiting Rademacher's Formula for the Partition Function p(n

We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.     

A new rearranged chamigrane sesquiterpene from Laurencia okamurai

A new rearranged chamigrane sesquiterpene,named laurenokamurin,was isolated from the marine red alga Laurencia okamurai.Its structure was determined on the basis of spectroscopic methods.     

Simple upper bounds for partition functions

We tweak Siegel’s method to produce a rather simple proof of a new upper bound on the number of partitions of an integer into an exact number of parts. Our approach, which exploits the delightful dilogarithm function, extends easily to numerous other counting functions. This work was supported by PSC/CUNY Research Awards (# 67261-00 36 and # 68327-00 37).     

New nanohybrid materials for biophotonics

Hybrid nanomaterials were prepared by one- and two-step procedures in the absence of water. Femtosecond laser ablation of a ZnO target in absolute ethanol afforded a colloidal ZnO solution. Dye molecules were grafted onto the ZnO nanoparticle surface by mixing the ZnO solution with an ethanol solution of tetramethylrhodamine B isothiocyanate or rhodamine B. Formation of strongly facetted nanohybrid particles with the average size of 21 nm was observed by HRTEM measurements. Ablation of ZnO in the presence of the dyes afforded nanohybrids with the average size of 12 nm. The occurrence of energy transfer from the ZnO nanoparticles towards the attached dye molecules was demonstrated by photoluminescence spectroscopy of the nanohybrids after single and multi-photon excitations. In particular, two-photon absorption of the nanohybrids ZnO core gave rise to emission of the grafted dyes. PACS 81.07.Bc; 81.07.Nb; 78.67.Bf; 78.55.Et; 81.15.Fg     

Element geochemistry of Holocene sediment and paleoenvironmental change in the Changjiang Estuary

Analyses of 41 elements reveal that Holocene sediments In the Changjiang Estuary bear regular elemental compositions in different sedimentary environments, and Holocene sediments came mainly from the Changjiang River based on compositions of REEs and most trace elements. Some heavy metals are more enriched in the surface sediment than in the deltaic sediments, reflecting human impact. Elemental compositions of the river channel sediment are related to the influence of proximal sediments. Sedimentary environments exert some influences on elemental compositions. Some chemical indices can be used to record chemical weathering undergone by the Changjiang sediment and environmental change.     

Ecologically friendly xanthan gum-PVA matrix for solid polymeric electrolytes

Two water-soluble and biodegradable polymers: xanthan gum (XG) and poly(vinyl alcohol) (PVA) were used to synthesize ecologically friendly solid polymer electrolyte (SPE) matrices. While XG is a natural polymer, PVA is a synthetic one, but both are colorless and form transparent membranes. To obtain ionic conductivity properties, the samples were doped with acetic acid and characterized by electrochemical impedance spectroscopy (EIS), X-ray diffraction, UV-Vis spectroscopy, and tensile test. The best results of ionic conductivity of 1.97 × 10^?4 and 7.41 × 10^?4 S/cm at room temperature and 80 °C, respectively, were obtained for the sample containing 55 wt% of acetic acid. Moreover, this electrolyte was found to be predominantly amorphous with transmittance in the visible region of 80% and absorbance values below 0.5 between 240 and 375 nm. Tensile test of this sample, applied up to 18 N of maximum force, resulted in strain of 2322% and Young’s modulus of 0.02 MPa. The obtained results showed that these new eco-friendly materials are promising for use as electrolytes in electrochemical devices.     

Laser-assisted local patterning of ZnO-based spots for mirror-less lasing

ZnO is known as one of the best materials for the implementation of the random lasing effect, associated with mirror-less laser emission in a simultaneously amplifying and highly scattering medium. Normally, the fabrication of this medium requires a rather complicated procedure of deposition and thermal treatment of ZnO-based films on some specific substrates, yielding wurtzite-orientation ZnO nanocrystals. We demonstrate a rapid synthesis of highly efficient ZnO-based random lasing spots on a piece of Zn by employing the phenomenon of laser-induced air breakdown. Being ignited near the surface of a Zn target, plasma of the air breakdown serves as a local reactor to locally transform its properties and thus form a film of well-packed 20–40 nm ZnO nanospheres. Exhibiting extremely high amplification and scattering, this medium is capable of generating the random lasing effect within the exciton-based photoluminescent band.     

Speech identification based on temporal fine structure cues

The contribution of temporal fine structure (TFS) cues to consonant identification was assessed in normal-hearing listeners with two speech-processing schemes designed to remove temporal envelope (E) cues. Stimuli were processed vowel-consonant-vowel speech tokens. Derived from the analytic signal, carrier signals were extracted from the output of a bank of analysis filters. The "PM" and "FM" processing schemes estimated a phase- and frequency-modulation function, respectively, of each carrier signal and applied them to a sinusoidal carrier at the analysis-filter center frequency. In the FM scheme, processed signals were further restricted to the analysis-filter bandwidth. A third scheme retaining only E cues from each band was used for comparison. Stimuli processed with the PM and FM schemes were found to be highly intelligible (50-80% correct identification) over a variety of experimental conditions designed to affect the putative reconstruction of E cues subsequent to peripheral auditory filtering. Analysis of confusions between consonants showed that the contribution of TFS cues was greater for place than manner of articulation, whereas the converse was observed for E cues. Taken together, these results indicate that TFS cues convey important phonetic information that is not solely a consequence of E reconstruction.