Equisingular Deformations of Sandwiched Singularities

We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.     

Metabolism of Carotenoids in Salmonids. Part 3. Metabolites of astaxanthin and canthaxanthin in the skin of atlantic salmon (salmo salar,L.)

Diets supplemented with astaxanthin and canthaxanthin, respectively, and a control diet without carotenoid additions, were fed to 1½-year-old Atlantic salmon (Salmo salar, L.) for one year. The integuments were investigated as to their quantitative and qualitative carotenoid composition. Astaxanthin and canthaxanthin deposited in the skin amounted to 20 and 14% of the total carotenoids only. Seventy % must be considered as metabolites of astaxanthin and canthaxanthin and 10% as basic xanthophylls also present in the control groups. Astaxanthin apparently underwent the following metabolic pathway: astaxanthin→idoxanthin→adonixanthin→zeaxanthin→zeaxanthin 5,6-epoxides. Reduction of the 4′-carbonyl group was stereospecific leading to the (4′R)-idoxanthin. Canthaxanthin was obviously converted to β,β-carotene via 4′-hydroxyechinenone, echinenone, and 4-hydroxy-β,β-carotene.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

Synthesis and characterization of new selective Zn fluorescent probes for functionalization: in vitro Cell imaging applications

Herein the synthesis and characterization of new, lipophilic highly Zn²⁺-selective fluorescent probes are reported. High affinity for zinc (K_d 1.1–8.0 nM) over other biologically relevant metals and mixtures of metals was observed. Excitation at 360 nm afforded an emission spectrum with maximum at 530 nm for the zinc bound complex. The linear relationship between fluorescence intensity and zinc concentration indicates that FZnA-probes can be used for quantification. The probes have been synthesized in 28–45% overall yield and the feasibility for further functionalization with biologically relevant side chains has been demonstrated. In vitro studies using PC12 cells and 10 μM of one of the novel probes (FZnA-Ada) visualized endogenous labile Zn²⁺ after 45 min incubation time.     

Total Synthesis of the Anti‐inflammatory and Pro‐resolving Lipid Mediator MaR1n−3 DPA Utilizing an sp3–sp3 Negishi Cross‐Coupling Reaction

The first total synthesis of the lipid mediator MaR1_{n?3 DPA} ( 5 ) has been achieved in 12 % overall yield over 11 steps. The stereoselective preparation of 5 was based on a Pd‐catalyzed sp³–sp³ Negishi cross‐coupling reaction and a stereocontrolled Evans–Nagao acetate aldol reaction. LC‐MS/MS results with synthetic material matched the biologically produced 5 . This novel lipid mediator displayed potent pro‐resolving properties stimulating macrophage efferocytosis of apoptotic neutrophils.     

Notes on Euler’swork on divergent factorial series and their associated continued fractions

Factorial series which diverge everywhere were first considered by Euler from the point of view of summing divergent series. He discovered a way to sum such series and was led to certain integrals and continued fractions. His method of summation was essentialy what we call Borel summation now. In this paper, we discuss these aspects of Euler’s work from the modern perspective.     

Angular-momentum analysis of pionic nucleon capture

The pionic capture reaction A(N, π)(A + 1) is analyzed in terms of the Mandelstam model for pion production by two nucleons. The results are applied to the proton-capture reactions ¹²C(p, π⁺)¹³C and ⁴He(p, π⁺)⁵He, and comparisons are made with experiments.     

A possible explanation of the colinearity effect

There have been indications that in deuteron break-up at low energy, an unexpected enhancement in the cross section is present in kinematic situations for which the residual nucleus is close to being at rest in the overall c.m. system, the three final particles thus being located on the same straight line (the so-called colinearity effect). The extent to which such an enhancement can be explained in terms of off-shell effects within the quasi-free scattering mechanism and in terms of rescattering effects is examined. A formalism is developed for an arbitrary nucleon knock-out reaction A(a, aN)B on a light target, and the reaction d(d, dp)n is then studied as a numerical example.     

Spectral estimation for characterization of acoustic aberration

Spectral estimation based on acoustic backscatter from a motionless stochastic medium is described for characterization of aberration in ultrasonic imaging. The underlying assumptions for the estimation are: The correlation length of the medium is short compared to the length of the transmitted acoustic pulse, an isoplanatic region of sufficient size exists around the focal point, and the backscatter can be modeled as an ergodic stochastic process. The motivation for this work is ultrasonic imaging with aberration correction. Measurements were performed using a two-dimensional array system with 80 x 80 transducer elements and an element pitch of 0.6 mm. The f number for the measurements was 1.2 and the center frequency was 3.0 MHz with a 53% bandwidth. Relative phase of aberration was extracted from estimated cross spectra using a robust least-mean-square-error method based on an orthogonal expansion of the phase differences of neighboring wave forms as a function of frequency. Estimates of cross-spectrum phase from measurements of random scattering through a tissue-mimicking aberrator have confidence bands approximately +/- 5 degrees wide. Both phase and magnitude are in good agreement with a reference characterization obtained from a point scatterer.