Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

New approaches to liquid interfaces through changes in the refractive index and nonlinear susceptibility utilizing ultrashort laser pulses.

Molecules in inhomogeneous liquid environments, such as air/liquid, liquid/liquid, solid/liquid interfaces interact with each other specifically, and sometimes form characteristic structures and emerge unique properties. Here, we introduce two newly developed spectroscopic techniques, the total-internal-reflection ultrafast transient lens method (TIR-UTL) and second harmonic generation-coherent vibrational spectroscopy (SHG-CVS), to investigate the characteristic behaviors of molecules in such inhomogeneous environments. TIR-UTL probes the refractive-index change with sub-picosecond resolution and provides information on ultrafast changes in the population, density, and thermal properties, such as temperature increase and energy transfer from the solute molecules to the surrounding solvent molecules. On the other hand, SHG-CVS probes nonlinear susceptibility changes at the interfacial areas, and is expected to provide spectroscopic information on the low-frequency vibrational modes that reflect the corrective motion of the molecules in such an inhomogeneous environment. These new approaches are based on pump-probe techniques utilizing (ultra) short laser pulses. They are expected to provide further information on inhomogeneous environments from the viewpoints of solute-solvent interactions, changes in the molecular orientation, and the corrective motion of molecules at liquid interfaces.     

On singularities arising from the contraction op the minimal section of a ruled surface

We will discuss the Gorenstein property of the singularity which is blown down from the minimal section of a ruled surface in terms of the extension class. In the case that the base field has positive characteristic, we find a new example (3.4) of Gorenstein singularity in connection with Theorem B.     

Symmetry-Breaking Phenomena in an Optimization Problem for some Nonlinear Elliptic Equation

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings.     

New Chiral Kemp's Acid Diamides for Chiral Amine Recognition by 1 H NMR

Two Kemp's acid diamides were synthesized and applied to chiral amine recognition using ¹H NMR analysis. One derivative based on 1-(1-naphthyl)ethylamine had good chiral recognition of six amines and was useful to determine the optical purity for three amines, i.e., methylbenzylamine, 1-(1-naphthyl)ethylamine and 1- henylpropylamine,however, the cyclohexylethylamine derivative showed little discrimination for the amines studied. Together with the results for alkylamines, it was shown that aromatic structure was important for aromatic shielding anisotropy and –– interactions between host and guest. The structure of the 1-(1-naphthyl)ethylamine derivative in solution was also considered based on ¹H NMR data and computer simulation.     

Determination of the aminoglycoside antibiotics sisomicin and netilmicin in dried blood spots on filter discs, by high-performance liquid chromatography with pre-column derivatization and fluorimetric detection

A simple method for the determination of the aminoglycoside antibiotic sisomicin or its 1-N-ethyl derivative, netilmicin in whole blood, using dried blood spots (DBSs) on filter-paper punched discs has been developed. Sisomicin or netilmicin in the DBSs were recovered most effectively in 0.5 M Na2HPO4 using ultrasonication. The eluates from the DBSs were treated by ultrafiltration for deproteinization and subjected to pre-column fluorescent derivatization using o-phthalaldehyde and beta-mercaptopropionic acid in 0.05 M KH2PO4-borate buffer (pH 9.0), followed by determination by reversed-phase high-performance liquid chromatography. The detection limits of sisomicin and netilmicin in the DBSs on punched discs (10.1 microliters of whole blood) were 0.053 and 0.50 micrograms per ml of whole blood, respectively (signal-to-noise ratio greater than or equal to 2). The method permits a simple collection of blood at the microlitre level and should prove particularly useful for monitoring sisomicin and netilmicin in blood at therapeutic levels in geriatric and paediatric patients.