Pure product polynomials and the Prouhet-Tarry-Escott problem

An -factor pure product is a polynomial which can be expressed in the form for some natural numbers . We define the norm of a polynomial to be the sum of the absolute values of the coefficients. It is known that every -factor pure product has norm at least . We describe three algorithms for determining the least norm an -factor pure product can have. We report results of our computations using one of these algorithms which include the result that every -factor pure product has norm strictly greater than if is , , , or .

     

ℤ n 3 -graded colored supersymmetry

We build generalizations of the Grassmann algebras from a few following simple assumptions: the algebras are graded, maximally symmetric and contain an ordinary Grassmann algebra as a subalgebra. These algebras are graded by and display surprising properties that indicate their possible application to the modeling of quark fields. We build the generalized supersymmetry generators based on these algebras and their derivation operators. These generators are cubic roots of the usual supersymmetry generators.     

Spectroscopy and lifetime measurement of high spin states in 73Se

The nucleus ⁷³ Se was studied by the reaction ⁵¹ V(²⁸ Si,αpn)⁷³ Se. The level scheme extended upto $\frac{{41}} {2}\bar h $ in both +ve and ?ve parity bands with 10 new transitions placed in the level scheme. Lifetimes of 17 high spin states measured by DSAM. The transitional quadrupole moment is found to drop down after the band crossing suggesting a less deformed configuration. At the band crossing region, Q _t increases suddenly in both +ve and ?ve parity bands. It is argued that the +ve parity band is a decoupled band.     

Comparisons of sonoluminescence from single-bubbles and cavitation fields: bridging the gap

Sonoluminescence (SL) refers to the generation of light through the energetic pulsations of acoustic cavitation bubbles in a liquid. For years, SL was observed primarily in cavitation fields. These bubbles are believed by many to undergo near-adiabatic compression, resulting in the heating of the bubble contents and the subsequent emission of light. Recently, researchers have discovered a 'new' form of sonoluminescence in which light is observed to emanate from a single bubble undergoing very large volume excursions. The mechanism for light production is unknown, but many believe it is due to a rapid heating of the central core by an imploding shock wave. Based in part on the emission time scales, there is a common belief that the two forms of SL are quite distinct. We address this issue by comparing the two phenomena with regards to their light-flash durations and emission spectra--leading to some surprising differences and similarities.     

Arthrichitin. A New Cell Wall Active Metabolite from Arthrinium phaeospermum

Arthrichitin (1), C(33)H(46)N(4)O(9), is a new cell wall active depsipeptide isolated from the fermentation broth of Arthrinium phaeospermum (HIL Y-903022). Its structure was elucidated on the basis of spectroscopic and chemical degradation studies. Arthrichitin consists of serine, beta-keto tryptophan, glutamic acid, and 2,4-dimethyl-3-hydroxydodecanoic acid units.     

A search for high energy neutrinos from SN 1987A,the Carb,Hercules X-1, and Cygnus X-3 with the Fréjus detector

With the Fréjus detector we studied four astrophysical point-like sources by using \(v_e (\bar v_e )\) and \(v_\mu (\bar v_\mu )\) interactions in the detector and \(v_\mu (\bar v_\mu )\) interactions in the surrounding rock. No excess of events was found. Therefore upper limits of neutrino fluxes and source luminositics are quoted. These limits confirm results from other experiments. In addition new limits are presented for spectral indices above 3.     

Gas phase 1,3-deoxystannylation reactions of γ-substituted organotin alcohols utilizing chemical ionization mass spectrometry

The gas phase 1,3-deoxystannylation reactions of γ-substituted organotin alcohols have been studied by methane and isobutane chemical ionization mass spectrometry. It was found that γ-hydroxybutyltributyltin and γ-hydroxybutyldibutyltin chloride undergo the 1,3-deoxystannylation reaction to a greater extent than the corresponding 1,4-deoxystannylation using the δ-substituted analogues of the above named compounds. This result substantiates the unusual reactivity of γ-substituted organotin alcohols under gas phase protonolysis conditions.The electronic factors affecting the stabilization of the transition state were ascertained with γ-phenyl-γ-hydroxypropyltrimethyltin derivatives, in which the γ-phenyl group was substituted with groups such as H, p-OMe, p-Me, p-Cl, p-F, m-OMe, m-Me, m-Cl and m-CF₃. We observed a reasonably linear Hammett relationship when plotting the log [P ? 17]_x⁺/[P ? 17]_H⁺ vs. σ⁺ with rho (ρ) equal to ?1.0.Thus electron-donating groups stabilize the [P ? 17]⁺ ion and carbon—tin sigma (σ) electrons can either, by a neighbouring group effect, attack the nucleofugic center, or the carbonium ion can attack the carbon—tin σ electrons to form the trimethyltin cation and a cyclopropane derivative. Consequently, we propose that a two-step mechanism for the 1,3-deoxystannylation reaction is operating in the gas-phase with this type of compound. The factors contributing to this gas phase reaction will be discussed.