Asymptotic Primes of Delta Closures of Ideals

Abstract

For an ideal H in a Noetherian ring R let H? = ∪{H ⁱ⁺¹ : _R H ⁱ | i ≥ 0} and for a multiplicatively closed set Δ of nonzero ideals of R let H _Δ = ∪{HK: _R K | K ? Δ}. It is shown that four standard results concerning the associated prime ideals of the integral closure (bR)_a of a regular principal ideal bR do not hold for certain Δ closures (bR)_Δ of bR. To do this it is first shown that if I is an ideal in R such that height (I) ≥ 1, then each radical ideal J of R containing I is of the form J = K? :_R cR for some ideal K closely related to I, and if I _a :_R J ? U = ∪{I?R _P ∩ R | P is a minimal prime divisor of J} (where I _a is the integral closure of I), then J = I _Δ :_R CR and I ? I _Δ ? I _a).     

Permanently oriented antibody immobilization for digoxin determination with a flow-through fluoroimmunosensor

This paper reports a new flow-through fluoroimmunosensor, the function of which is based on antibodies immobilized on an inmunoreactor of controlled-pore glass (CPG), for determination of digoxin, used in the treatment of congestive heart failure and artery disease. The immunosensor has a detection limit of 1.20 microg L(-1) and provides high reproducibility (RSD=4.5% for a concentration of 0.0025 mg L(-1), and RSD=6.7% for 0.01 mg L(-1)). The optimum working concentration range was found to be 1.2 x 10(-3)-4.0 x 10(-2) mg L(-1). The lifetime of the immunosensor was about 50 immunoassays; if stored unused its lifetime can be extended to three months. A sample speed of about 10-12 samples per hour can be attained. Possible interference from substances with structures similar to digoxin (morphine, heroin, tebaine, codeine, pentazocine and narcotine) was investigated. No cross-reactivity was seen at the highest digoxin: interferent ratio studied (1:100). The proposed fluoroimmunosensor was successfully used to determine digoxin concentrations in human serum samples.     

Six notes on chains of prime ideals

Summary The following topics are considered: saturated chains of prime ideals in quadratic (resp., simple, local, and level) integral extension domains of a local domain R; the heights of a prime ideal and its contraction in integral extension domains of R; and, the nonexistence of intermediate rings between R and finite integral extension domains of R that are minimal with spect to having certain properties.Research on this paper was supported in part by the National Science Foundation, Grant MCS 8001597.     

Four notes on GB-rings

The following results are proved: (1) there exist integrally closed Noetherian domains which are not GB-rings, so the GB-conjecture does not hold; (2) Henselian domains of altitude two and integrally closed Henselian domains of altitude three are GB-rings; and there exist Henselian local domains of altitude three and integrally closed Henselian local domains of altitude four which are not GB-rings; (3) the GB-condition does not descend even for Henselian local domains; and, (4) if (R, M) is a local domain, then D=R[X]_(M,X) is a GB-ring if (and only if) adjacent prime ideals in local integral extension domains of D contract in D to adjacent prime ideals.     

Cyclic scheduling via integer programs with circular ones

A fundamental problem of cyclic staffing is to size and schedule a minimum-cost workforce so that sufficient workers are on duty during each time period. This may be modeled as an integer linear program with a cyclically structured 0-1 constraint matrix. We identify a large class of such problems for which special structure permits the ILP to be solved parametrically as a bounded series of network flow problems. Moreover, an alternative solution technique is shown in which the continuous-valued LP is solved and the result rounded in a special way to yield an optimum solution to the ILP.     

Insights into the Ultrafast Photodissociation Dynamics of Isoprene-Derived Criegee Intermediates

Isoprene is the most abundant nonmethane volatile organic compound emitted into the troposphere by terrestrial vegetation. Reaction with ozone represents an important isoprene removal process from the troposphere and is a well-known source of Criegee intermediates (CIs), which are reactive carbonyl oxides. Three CIs, formaldehyde oxide (CH₂OO), methyl vinyl ketone oxide (MVK-oxide) and methacrolein oxide (MACR-oxide) are formed during isoprene ozonolysis. All three CIs contain strongly absorbing ππ* states, electronic excitation, which leads to dissociation to form aldehyde/ketone + oxygen products. Here, we compare the excited state chemistry of CH₂OO, MVK-oxide and MACR-oxide in order to ascertain how increasing molecular complexity affects their photodynamics. In CH₂OO, vertical excitation to the S₂ state leads to prompt O-O bond fission with a unity quantum yield. Branching into both the O (¹D) + H₂CO (S₀) and O (³P) + H₂CO (T₁) product channels is predicted, with 80% of trajectories dissociating to form the former product pair. Analogous vertical excitation of the lowest energy conformers of MVK-oxide and MACR-oxide also undergoes O-O bond fission to form O + MVK/MACR products—albeit with a nonunity quantum yield. In the latter case, ca. 10% and 25% of trajectories remain as the parent MVK-oxide and MACR-oxide molecules, respectively. Additionally, at most only 5% of the dissociating trajectories form O (³P) + MVK/MACR (T₁) products, with a greater fraction forming O (¹D) + MVK/MACR (S₀) products (cf. CH₂OO). This latter observation coupled with the greater fraction of undissociated trajectories aligns with the bathochromic shift in the electronic absorption of the MACR-oxide and MVK-oxide (cf. CH₂OO). We discuss the implications of the results in a broader context, including those that are relevant to the atmosphere.