S-sets and semigroups of quotients

During the last two decades, a good deal of work has been conducted on S-sets and semigroups of quotients, establishing several concepts and results which are more or less analogous to the classicalas well as ring-theoretical ones. Clearly there are different (and sometimes, we feel, too restrictive) assumptions in these papers, in particular on the semigroups S and on the S-sets under consideration, and various notations need to be unified. Generalizing diverging dispositions, we try to give a self-contained survey of the most fundamental parts (and other considerable parts) of these investigations, and add some new results. A forthcoming paper will deal with S-semimodules over semirings S, including some relationships with rings and modules.     

Measurement of charge distributions for 229Th(nth,f) and 232U(nth,f)

A gas ΔE ? E_R telescope has been used to measure charge yields and their correlations with kinetic energies for ²²⁹Th and ²³²U. Even-charge yields are enhanced compared with odd-charge yields for both fissioning systems; this enhancement increases for events with higher kinetic energy. The mean odd-even effect $\text{δ}{}_{\mathrm{<mtext>p</mtext>}}\text{is}\text{= (40±4)\%}\text{for}{}^{229}\text{Th}$; it is $\text{(21 ± 3)\%}\text{for}{}^{232}\text{U-the same as for}{}^{233}\text{U}\text{((22.1±2.1)\%)}\text{and}{}^{235}\text{U}\text{((23.7±0.7)\%)}$. The energy-integrated δ_p and δ_p for different energy windows, vary strongly as a function of charge (Z) due to the underlying shells. The δ_p averaged over Z increases fast with kinetic energy, contrary to the existing results for ²³³U and ²³⁵U, where δ_p flattens off at low energies. For both systems, the most probable kinetic energy ē shows a strong odd-even stagger; the mean odd-even effect on energy, $\text{δE}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>o?e</mtext>}}\text{,}\text{is}\text{1.4 ± 0.3}\text{MeV for}{}^{229}\text{Th, and}\text{1.7±0.4}\text{MeV for}{}^{232}\text{U}\text{—}$ the latter is about twice the value for ${}^{233}\text{U}\text{(0.95 ± 0.09}\text{MeV}\text{)}\text{and}{}^{235}\text{U}\text{(0.7}\text{MeV}\text{)}$. These results are discussed in terms of the existing models.     

Breit interaction determination of muonic hyperfine anomalies: Large but not giant

Muon-nuclear-hyperfine anomalies are determined from Breit interaction calculations based on unrestricted Dirac-Fock solutions which explicitly include all electrons and the negative muon. We obtain anomalies of a few (3) percent, which are much larger than corresponding Bohr-Weisskopf electron-nuclear anomalies, but are much smaller than the giant, ≈(36 ± 5)%, anomaly reported by Yamazaki et al. for μ^-Pd⁺ vs. Rh. We suggest the possibility that interstitial μ^-Pd⁺ was observed and that the small anomaly for substitutional μ^-Pd⁺ may also be seen at higher temperatures.     

Über die Einzigkeit der Ternionenalgebra und linksalternative Algebren kleinen Ranges

Ohne Zusammenfassung     

Atomistic view of the autosurfactant effect during GaN epitaxy

The Ga-N site exchange critical to the autosurfactant effect during GaN epitaxy is studied. On the GaN(0001) pseudo (1x1), the first site exchange results in N incorporation at the subsurface T1 site, forming ghost islands. The second exchange that converts these islands to that of bilayer height can be triggered by continued scanning tunneling microscopy imaging, which involves electrons tunneling to or from localized states associated with the second layer Ga. The resulting electrostatic force sets off a chain reaction which frees these Ga atoms, allowing N to form covalent Ga-N-Ga bonds of a new GaN bilayer.     

Mathematical modelling of the SSD-process

In order to achieve a better agreement between the calculated and experimental results of crystal production by the SSD-process, it was essential to extend the application of the modell presented earlier (Weinert et al.). The thermal and geometrical conditions, which vary strongly during the course of the process and influence the GaP crystallisation, have never been taken into consideration. It has been attempted, in the present work, to consider these changes by dividing the total time of crystallisation into so small durations (Δt), that the evaluation model presented earlier for instant times can be successfully applied. The results of crystallisation for the total period can then be obtained through a mathematical analysis named as sequence correction of process parameters. It has been shown that an exact knowledge of the temperature distribution in the furnace will yield results which are in very good agreement with the experimental values. Moreover, the changes in the process parameters during the whole time of crystallisation have been represented graphically. — Application of this model to other systems, for example to GaAs, is also possible.     

Synthesis of distibiranes and azadistibiranes by cycloaddition reactions of distibenes with diazomethanes and azides

Cycloaddition reactions of distibene [L(Me₂N)GaSb]₂ (L = HC[C(Me)NDipp]₂; Dipp = 2,6-i-Pr₂C₆H₃) with a series of organoazides RN₃ (R = Ph, p-CF₃Ph, 1-adamantyl (ada)) yielded azadistibiranes [L(Me₂N)GaSb]₂NR (R = Ph 1, p-CF₃Ph 2, ada 3), whereas Me₃SiN₃ reacted with insertion into one Ga–Sb bond and formation of L(Me₂N)GaSbSb(NSiMe₃)Ga(NMe₂)L (4). Analogous compounds 5 and 6 formed after heating of 1 and 2 above 60 °C. Prolonged heating of 5 resulted in a [2 + 2] cycloaddition accompanied by elimination of LGa(NMe₂)₂ and formation of tetrastibacyclobutane 7, while the reaction of 5 with a second equivalent of PhN₃ gave heteroleptic azadistibirane 9, which isomerized at elevated temperature to distibene 10. Cycloaddition also occurred in reactions of [L(X)GaSb]₂ (X = NMe₂, OEt, Cl) with Me₃Si(H)CN₂, yielding distibiranes [L(X)GaSb]₂C(H)SiMe₃ (X = NMe₂11, OEt 12, Cl 13). Compounds 1–13 were characterized by IR, UV-Vis and NMR spectroscopy and sc-XRD. The mechanism of the reaction of [L(Me₂N)GaSb]₂ with PhN₃ and Me₃SiN₃ and the electronic nature of the resulting compounds were studied by DFT calculations.

Azadistibiranes and distibiranes formed in cycloaddition reactions of distibene [L(Me₂N)GaSb]₂ with RN₃ and Me₃Si(H)CN₂. The mechanism of the reactions with PhN₃ and Me₃SiN₃ and the electronic nature of the products were studied by DFT calculations.     

Phytosanitary irradiation of fresh tropical commodities in Hawaii: Generic treatments,commercial adoption,and current issues

Hawaii is a pioneer in the use of phytosanitary irradiation. The commercial X-ray irradiation facility, Hawaii Pride LLC, has been shipping papaya and other tropical fruits and vegetables to the United States mainland using irradiation for 11 years. Irradiation is an approved treatment to control quarantine pests in 17 fruits and 7 vegetables for export from Hawaii to the US mainland. Hawaiian purple sweet potato is the highest volume product with annual exports of more than 12 million lbs (5500 t). The advent of generic radiation treatments for tephritid fruit flies (150 Gy) and other insects (400 Gy) will accelerate commodity export approvals and facilitate worldwide adoption. Lowering doses for specific pests and commodities can lower treatment costs and increase capacity owing to shorter treatment times, and will minimize any quality problems. Current impediments to wider adoption include the 1 kGy limit for fresh horticultural products, the labeling requirement, and non-acceptance of phytosanitary irradiation in Japan, the European Union, and elsewhere. Irradiation has potential as a treatment for unregulated imports to prevent new pest incursions.     

Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations

This paper is concerned with the asymptotic behaviour and the stability of a class of linear neutral delay difference equations with variable coefficients and constant delays. Via an appropriate solution of the so-called generalized characteristic equation, an asymptotic criterion and a stability result are established.