The role of Fourier modes in extension theorems of Hartogs-Chirka type

We generalize Chirkas theorem on the extension of functions holomorphic in a neighbourhood of (F)(D×D) – where D is the open unit disc and (F) is the graph of a continuous D-valued function F – to the bidisc. We extend holomorphic functions by applying the Kontinuitätssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by Chirkas theorem.Mathematics Subject classification (2000): 32D15Work supported by NSF Grant DMS-0072237.     

On L1 and Chebyshev estimation

The problem considered here is that of fitting a linear function to a set of points. The criterion normally used for this is least squares. We consider two alternatives, viz., least sum of absolute deviations (called the L₁ criterion) and the least maximum absolute deviation (called the Chebyshev criterion). Each of these criteria give rise to a linear program. We develop some theoretical properties of the solutions and in the light of these, examine the suitability of these criteria for linear estimation. Some of the estimates obtained by using them are shown to be counter-intuitive.     

Viscosity studies of polyethylene in a cosolvent mixture composed of two nonsolvents

Polyethylene, normally soluble at an elevated temperature in some single solvents, is found to be soluble in the following binary mixtures of nonsolvents at a much lower temperature, (often in the vicinity of room temperature): xylene–carbon disulfide, cyclohexane–carbon disulfide, cyclohexane–trichloroethylene, and cyclohexane–cyclohexanone. The fractionated polymer samples show a maximum in [η] values at the optimum solvent compositions corresponding to a minimum in cloud temperature T_e. The results are discussed with respect to the current theories on solubility. The optimum solvent composition agrees with the prediction of a newly developed theoretical equation in two of the above four mixtures.     

Sub- and above-barrier fusion of loosely bound 6Li with 28Si

Fusion excitation functions are measured for the system ⁶Li + ²⁸Si using the characteristic $ \gamma$ -ray method, encompassing both the sub-barrier and above-barrier regions, viz, E _lab = 7-24 MeV. Two separate experiments were performed, one for the above-barrier region ( E _lab = 11-24 MeV) and another for the below-barrier region ( E _lab = 7-10 MeV). The results were compared with our previously measured fusion cross-section for the ⁷Li + ²⁸Si system. We observed the enhancement of the fusion cross-section at sub-barrier regions for both ⁶Li and ⁷Li , but the yield was substantially larger for ⁶Li . However, for well-above-barrier regions, a similar type of suppression was identified for both the systems.     

Ultrafast dynamics and excited state deactivation of [Ru(bpy)2Sq]+ and its derivatives

Femtosecond transient absorption spectroscopy has been employed to understand the excited state dynamics of [Ru(bpy)(2)Sq](+) (I; bpy is 2,2'-bipyridyl, and Sq is the deprotonated species of the semiquinone form of 1,2-dihydroxy benzene) and its derivatives, a widely studied near-infrared (NIR) active electrochromic dye. Apart from the well-defined dpi(Ru) --> pi(bpy)-based metal-to-ligand charge transfer (MLCT) transition bands at approximately 480 nm, this class of molecules generally shows another dpi(Ru) --> pi(Sq)(SOMO)-based intense MLCT band at around 900 nm, which is known to be redox active and bleaches reversibly upon a change in the oxidation state of the coordinated dioxolene moiety. To have better insight into the photoinduced electron transfer dynamics associated with this MLCT transition, detailed investigations have been carried out on exciting this MLCT band at 800 nm. Immediately after photoexcitation, bleach at 900 nm has been observed, whose recovery is found to follow a triexponential function with major contribution from the ultrafast component. This ultrafast component of approximately 220 fs has been ascribed to the S(1) to S(0) internal conversion process. In addition to the bleach, we have detected two transient species absorbing at 730 and 1000 nm with a formation time approximately 220 fs for both species. The excited state lifetimes for these two transient species have been measured to be 1.5 and 11 ps and have been attributed to excited singlet ((1)MLCT) and triplet ((3)MLCT) states, respectively. Transient measurements carried out on the different but analogous derivatives (II and III) have also shown similar recovery dynamics except that the rate for the internal conversion process has increased with the decrease in the S(1) to S(0) energy gap. The observed results are consistent with the energy gap law for nonradiative decay from S(1) to S(0).     

Twisting dynamics in the excited singlet state of Michler's ketone

Ultrafast relaxation dynamics of the excited singlet (S(1)) state of Michler's ketone (MK) has been investigated in different kinds of solvents using a time-resolved absorption spectroscopic technique with 120 fs time resolution. This technique reveals that conversion of the locally excited (LE) state to the twisted intramolecular charge transfer (TICT) state because of twisting of the N,N-dimethylanilino groups with respect to the central carbonyl group is the major relaxation process responsible for the multi-exponential and probe-wavelength-dependent transient absorption dynamics of the S1 state of MK, but solvation dynamics does not have a significant role in this process. Theoretical optimization of the ground-state geometry of MK shows that the dimethylanilino groups attached to the central carbonyl group are at a dihedral angle of about 51 degrees with respect to each other because of steric interaction between the phenyl rings. Following photoexcitation of MK to its S1 state, two kinds of twisting motions have been resolved. Immediately after photoexcitation, an ultrafast "anti-twisting" motion of the dimethylanilino groups brings back the pretwisted molecule to a near-planar geometry with high mesomeric interaction and intramolecular charge transfer (ICT) character. This motion is observed in all kinds of solvents. Additionally, in solvents of large polarity, the dimethylamino groups undergo further twisting to about 90 degrees with respect to the phenyl ring, to which it is attached, leading to the conversion of the ICT state to the TICT state. Similar characteristics of the absorption spectra of the TICT state and the anion radical of MK establish the nearly pure electron transfer (ET) character of the TICT state. In aprotic solvents, because of the steep slope of the potential energy surface near the Franck-Condon (FC) or LE state region, the LE state is nearly nonemissive at room temperature and fluorescence emission is observed from only the ICT and TICT states. Alternatively, in protic solvents, because of an intermolecular hydrogen-bonding interaction between MK and the solvent, the LE region is more flat and stimulated emission from this state is also observed. However, a stronger hydrogen-bonding interaction between the TICT state and the solvent as well as the closeness between the two potential energy surfaces due to the TICT and the ground states cause the nonradiative coupling between these states to be very effective and, hence, cause the TICT state to be weakly emissive. The multi-exponentiality and strong wavelength-dependence of the kinetics of the relaxation process taking place in the S1 state of MK have arisen for several reasons, such as strong overlapping of transient absorption and stimulated emission spectra of the LE, ICT, and TICT states, which are formed consecutively following photoexcitation of the molecule, as well as the fact that different probe wavelengths monitor different regions of the potential energy surface representing the twisting motion of the excited molecule.     

Misassigned C-H...Cu agostic interaction in a copper(II) ephedrine derivative is actually a weak, multicentred hydrogen bond

Agostic interactions and weak hydrogen bonds to metal acceptors, M, are chemically and geometrically distinct, and this distinction must be maintained in the classification of new C-H...M interactions.     

On the repetitive operation of a self-switched transversely excited atmosphere CO<Subscript>2</Subscript> laser

The repetition rate capability of self-switched transversely excited atmosphere (TEA) CO₂ laser was studied for different gas flow configurations. For an optimized gas flow configuration, repetitive operation was achieved at a much smaller gas replenishment factor between two successive pulses when compared with repetitive systems energized by conventional pulsers.     

Phase Separation in the Advective Cahn–Hilliard Equation

The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection–hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection–diffusion equation.