The Chowla-Selberg formula

The Chowla-Selberg formula is a monomial relation connecting the values of certain automorphic form at special points to the values of Γ functions at rational points. A generalization of this formula is established in the context of CM-fields: the values of a distinguished Hilbert automorphic form at special points are expressed in terms of multiple Γ functions.     

Carbon-13 nuclear magnetic resonance spectroscopy of naturally-occurring substances- LVII Triterpenes related to lupane and hopane

The ¹³C NMR spectra of lupeol and related triterpenes were recorded and all carbon shifts assigned. Their analysis aided in the shift assignment of the structurally related hopane-like triterpenes.     

A quick proof of Hardy's estimate for Ramanujan function τ(n)

In this note we give a proof of the estimate τ(n) = 0(n⁵σ(n)) for the Ramanujan function τ(n). The proof depends on a double application of the Eichler-Selberg trace formula to the evaluation of the eigenvalues of the Hecke operators.     

Studies on the equilibrium among poly(sodium 4‐styrenesulfonate), Cu2+, and iminodiacetic acid by ultrafiltration at constant ionic strength

The ultrafiltration technique evaluates the interactions of water‐soluble polymers with metal ions. Aqueous solutions containing poly(sodium 4‐styrenesulfonate) (PSS), Cu(NO₃)₂, NaNO₃, and iminodiacetic acid (IDAA) are examined by this technique. Cu²⁺ undergoes complex formation with IDAA and intreracts electrostatically with PSS. On the other hand, Na⁺ ions are in competition with Cu²⁺ for the electrostatic binding to PSS. The solutions are ultrafiltered keeping the ionic strength constant, so their compositions are allowed to change continuously. The concentration of Cu²⁺ bound to the polymer showed an exponential decay during filtration. The concentration of Cu²⁺ bound to the polymer before ultrafiltration is calculated by extrapolation. The concentration of the different species in solution is proposed as a function of the filtration factor. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2587–2593, 2002     

Electrochemical reduction of tricarbonyl compounds: Reduction mechanism of alloxan on a mercury electrode

A study has been carried out on the reduction mechanism of alloxan over a DME corresponding to the first two-electron transfer over the pH range 0–12.Polarographic and voltammetric results show the reduction process to be kinetically controlled. Rate and equilibrium constant data for the prior chemical reaction have been evaluated and several reaction mechanisms for different pH zones have been proposed.     

Interaction of acrylodan with human serum albumin. A fluorescence spectroscopic study

The binding of the fluorescent probe acrylodan (AC) to human serum albumin (HSA) was studied by fluorescence spectroscopy. The binding isotherms could be fitted to two types of sites. Competition experiments using iodoacetamide suggested that AC binds tightly on HSA by the cysteine-34. Attempts were made to find the location of the second site using high concentrations of warfarin, phenylbutazone, diazepam, indomethacin, palmitic acid or bilirubin in order to displace the bound AC to the HSA. Bilirubin was the only ligand able to displace the bound AC. This result suggests that AC, which is a very hydrophobic molecule also capable of labeling lysine residues, should also bind the human albumin in the primary site of bilirubin, but with less affinity than to the cysteine-34.     

Measurement of spatial gain distribution for a neonlike germanium 19.6-nm laser

We measure the transverse spatial distribution of the gain region for the 19.6-nm neonlike germanium laser line by use of a short amplifier, which is backlit by a longer laser, both of which are created by illumination of a germanium slab target with a series of short 100-ps pulses from the Nova laser. The backlighting technique enables us to reduce greatly the refraction effects that dominated previous imaging experiments and made direct gain measurements impossible. Measurements are made with a two-dimensional high-resolution spatial-imaging diagnostic, and simulations of the gain are compared with experiments.     

Sensitized Two‐NIR‐Photon Z→E Isomerization of a Visible‐Light‐Addressable Bistable Azobenzene Derivative

Two‐NIR‐photon‐triggered Z→E isomerization of an azobenzene was accomplished by covalently linking a two‐photon‐harvesting triarylamine antenna to a thermally stable ortho‐fluorinated azobenzene derivative. The obtained photoswitch is fully addressable with visible and NIR light by using one‐photon and two‐photon excitation, respectively, with the latter offering enhanced penetration depth and improved spatial resolution.     

A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

The dynamical mean field theory (DMFT) has emerged as one of the most importantframeworks for theoretical investigations of strongly correlated lattice models and realmaterial systems. Within DMFT, a lattice model can be mapped onto the problem of amagnetic impurity embedded in a self-consistently determined bath. The solution of thisimpurity problem is the most challenging step in this framework. The available numericallyexact methods such as quantum Monte Carlo, numerical renormalization group or exactdiagonalization are naturally unbiased and accurate, but are computationally expensive.Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gainedsubstantial importance. Although such methods are not always reliable in various parameterregimes such as in the proximity of phase transitions or for strong coupling, theadvantages they offer, in terms of being computationally inexpensive, with real frequencyoutput at zero and finite temperatures, compensate for their deficiencies and offer aquick, qualitative analysis of the system behavior. In this work, we have developed such amethod, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) tostudy N-folddegenerate and non degenerate Anderson impurity models. As applications of the solver, wehave embedded the MO-IPT within DMFT and explored lattice models like the single orbitalHubbard model, covalent band insulator and the multi-orbital Hubbard model fordensity-density type interactions in different parameter regimes. The Hund’s couplingeffects in case of multiple orbitals is also studied. The limitations and quality ofresults are gauged through extensive comparison with data from the numerically exactcontinuous time quantum Monte Carlo method (CTQMC). In the case of the single orbitalHubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models,we obtained an excellent agreement between the Matsubara self-energies of MO-IPT andCTQMC. But for the degenerate multi-orbital Hubbard model, we observe that the agreementwith CTQMC results gets better as we move away from particle-hole symmetry. We have alsointegrated MO-IPT+DMFT with density functional theory based electronic structure methodsto study real material systems. As a test case, we have studied the classic, stronglycorrelated electronic material, SrVO₃. A comparison of density of states and photo emissionspectrum (PES) with results obtained from different impurity solvers and experimentsyields good agreement.