The reactions of O(3P) with ozone and carbonyl sulfide

The competitive reactions between 2-trifluoromethylpropene (TMP) and OCS for O(³P) atoms were studied between 300° and 523°K, using the mercury-senstitized photolysis of N₂O as a source of O(³P). From the known value for the rate constant of the O(³P) + TMP reaction, k₃ was found to be 1.6 × 10^?11 exp (?4500/RT) cm³/particle-sec, where reaction (3) is Mixtures of O₃ and OCS were photolyzed at 197°, 228°, 273°, and 299°K with radiation above 4300 Å to produce O(³P) from the photolysis of O₃, and thus study the competition between reaction (3) and From the above value of k₃, k₁ could be computed. When combined with all the previous data, the best espression for k₁ is k₁ = 1.2 × 10^?11 exp (?4300/RT) cm³/particle-sec.     

Semigroups satisfying variable identities

The purpose of this note is to generalize a theorem of Tamura’s [3] providing a self-contained and, we think, more elementary proof than Tamura’s in that it avoids using the theory of contents. Tamura’s result states that a semigroup S satisfies an identify xy=f(x,y) with f(x,y) a word of length greater than 2 which starts with y and ends in x if and only if S is an inflation of a semilattice of groups satisfying the same identity. We investigate semigroups as in Tamura’s Theorem, except that we permit f(x,y) to vary with x and y.     

Kinetics of particle growth VII. NH4NO3from the NH3-O3 reaction in the presence of air and water vapor

Our earlier work on the formation of particulate NH₄NO₃ in the NH₃? O₃ reaction at 25°C is extended to include air as a diluent and H₂O vapor as an additive. More extensive data at different values of [NH₃]/[O₃]₀ were obtained also, where [O₃]₀ is the initial O₃ concentration. In our earlier work we concluded that NH₄NO₃ vapor was dissociated to NH₃ + HNO₃ and that the HNO₃ was removed by diffusion to the walls with a rate coefficient k_diff = 0.4 min^?1 or by condensation on the suspended particles. Particles were nucleated by 8 NH₃? HNO₃ pairs when their concentration product reached 5.8 × 10²⁷ molec²/cm⁶ with a rate coefficient k_nucl of 6.2 × 10^?224 cm⁴⁵/min and removed by coagulation with a rate coefficient k_coag of 1.3 × 10^?7 cm³/min. A corrected calculation modifies the number of pairs required to 6–7 with a correspondingly changed value of k_nucl. With the more extensive data of the present study the indications are that the vapor-phase NH₄NO₃ monomer is not dissociated and that its diffusion constant for loss to the walls varies between 0.3 and 0.9 min^?1 for different reaction conditions. Nucleation occurs when the NH₄NO₃ vapor concentration reaches 1.0 × 10¹² molec/cm³ via. where r is 9 and the nucleation rate coefficient k_nucl is 3 × 10^?108 cm²⁴/min. With 5.0 or 9.5 torr of H₂O vapor present, there is an excess of particles produced over that expected from this rate coefficient, indicating an additional nucleation step in which H₂O vapor participates directly to produce a hydrated salt. The coagulation coefficient of (1.87 ± 0.14) × 10^?7 cm³/min found here is in good agreement with that found previously.     

New method for estimating survival curves based upon subpopulations

The overall Kaplan-Meier estimate of the survival curve underlying a study population does not individually account for the ages at which patients were first seen and thence followed up in the study. Since the number of patients in these age-specific subgroups varies quite arbitrarily for a given study, the overall Kaplan-Meier curve which assumes that all patients were seen from the beginning of the study usually either overestimates or underestimates the survival probability, depending on the varying sample sizes. In this paper, we therefore propose an estimate of the overall survival curve underlying a study population based on the individual age-specific Kaplan-Meier estimates and the probability distribution of the age at which patients were first seen in the study. In the particular case when there is no censoring, it is shown that the usual overall Kaplan-Meier survival curve which assumes that all patients irrespective of their age at entry into the study were followed from the beginning of the study is identical with the proposed estimate. This result does not seem to necessarily hold good in the presence of arbitrary censoring. Further, the estimate is unbiased and consistent, a property which the Kaplan-Meier estimate also enjoys. The efficiency of the proposed estimate relative to the Kaplan-Meier estimate is being investigated and will be reported along with results of its application in a separate communication.     

Many triangulated 3-spheres

We construct combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves that asymptotically there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d+1)-polytopes for fixed d4.Mathematics Subject Classification (1991): 52B11, 52B70, 57Q15Supported by the Deutsche Forschungsgemeinschaft within the European graduate program Combinatorics, Geometry, and Computation (GRK 588/1) and an MSRI post-doctoral fellowship.Partially supported by Deutsche Forschungs-Gemeinschaft (DFG), via the DFG Research Center Mathematics in the Key Technologies (FZT86), the Research Group Algorithms, Structure, Randomness (Project ZI 475/3), and a Leibniz grant (ZI 475/4).     

Effects of ultraviolet B exposure on the expression of proliferating cell nuclear antigen in murine skin

Proliferating cell nuclear antigen (PCNA) is an active nuclear protein involved in DNA replication, recombination and repair. PCNA is found throughout the basal layer in normal skin and in all layers of the epidermis in malignancy. This study evaluates PCNA's expression after acute and chronic UV-B irradiation. Skh-1 hairless mice exposed to 1.5 and 4.5 kJ/m2 of UV-B were sacrificed at 6, 12, 24, 48, 72 and 168 h. Immunohistochemical analysis revealed PCNA expression throughout the basal layer of untreated skin, with diminished expression at 6 h, indicative of immediate UV damage, and evidenced by the observable upregulation in pyrimidine dimer formation early on. Subsequently, PCNA immunoreactivity progressively increased, demonstrating an aberrant upward epidermal migratory pattern in association with chronic exposure. The 4.5 kJ/m2 group exhibited prolonged recovery in staining and also demonstrated this altered migratory pattern with chronic exposure. Progressive reactivation of PCNA expression occurs with repair. PCNA migration to upper layers of the epidermis indicates proliferation and possibly a subsequent increased malignant potential. We conclude that PCNA can serve as a marker of DNA repair and indirectly as an indicator of UV-B-induced damage, expression being time dependent and dose related. Specific immunoreactivity patterns and the observable atypia in keratinocytes are relevant in elucidating malignant potentiation.     

Generalized frequency selection in multifrequency interferometry

We present a generalized frequency selection method for N-frequency interferometry to form an optimum geometric series at synthetic wavelengths. The absolute range that is measurable is bounded by the number of beat frequency operations, phase noise, and the number of wavelengths used to form the geometric series of synthetic wavelengths. Theoretical predictions are compared with experimental results from a full-field fringe projector. A comparison of this technique with the method of excess fractions shows orders-of-magnitude faster processing with similar measurement reliability.     

Inverse scattering problem for optical coherence tomography

We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature.     

Pseudotwistors

We deal with the Hermitian Hurwitz pairs of signature (, s), + s = 5 + 4, | + 1 – s| = 2 + 4m;, m = 0, 1,.... We introduce the Hurwitz twistors for signature (3, 2) and its dual (1, 4) and we indicate the relationship between Hurwitz and Penrose twistors. The signatures (1, 8) and (7, 6) give rise to pseudotwistors and bitwistors, respectively. For pseudotwistors, we prove a counterpart of the Penrose theorem in the local version, on real analytic solutions of the related spinor equations versus harmonic forms, and in the semiglobal version, on holomorphic solutions of those equations versus Dolbeault cohomology groups. We prove an atomization theorem: There exist complex structures on isometric embeddings for the Hermitian Hurwitz pairs so that the embeddings are real parts of holomorphic mappings.     

Porosity of ill-posed problems

We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.