Upper and lower bounds and the generalized variation-perturbation approach of many-electron theory

The theory of upper and lower bounds is used in conjunction with the “varied-portions approach” (VPA ) of the “many-electron theory of atoms and molecules” (MET ). Upper and lower bounds equations are derived. It is recognized that if a very natural portion of the full variational expression is made stationary, according to (VPA ), a for of Löwdin's lower bound wave equation results. By using the bracketing theorem it is also possible to give lower bounds to the quantities arising from the (VPA ) of (MET ). This will be useful to study in the future the (MET ) pair correlations and to supplement the computational methods currently available with lower bound estimates as well.     

The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.     

Synthesis and Study of the Photophysical Properties of a New Eu<Superscript>3+</Superscript> Complex with 3-Hydroxypicolinamide

This work reports on the synthesis and characterization of a new complex of Eu³⁺ with the 3-hydroxypicolinamide ligand (Hhpa). Here we present an approach for obtaining bis[2-carbamoyl(κO)pyridin-3-olato(κO’)] lanthanide complexes, which were characterized through elemental analysis, thermal analysis, infrared and photoluminescence spectroscopies (emission, excitation, luminescence lifetimes, quantum efficiencies, Judd-Ofelt parameters and quantum yields). Although hpa can act as a bidentate ligand in different conformations, the results attest for the occurrence of a unique coordination site of low symmetry for the Eu³⁺ ions, in which two anionic hpa ligands coordinate the cations through an O/O chelating system. The phosphorescence of the synthesized gadolinium complex provides the energy of the triplet state, which is determined to be at 20,830 cm^-1 over the ground state. This makes the Hhpa ligand very adequate for sensitizing the Eu³⁺ luminescence, which leads to a very efficient antenna effect and opens a wide range of applications for the complex in light emitting organic-inorganic devices.     

Fabrication of phytic acid sensor based on mixed phytase-lipid Langmuir-Blodgett films

This paper reports the surface activity of phytase at the air-water interface, its interaction with lipid monolayers, and the construction of a new phytic acid biosensor on the basis of the Langmuir-Blodgett (LB) technique. Phytase was inserted in the subphase solution of dipalmitoylphosphatidylglycerol (DPPG) Langmuir monolayers, and its incorporation to the air-water interface was monitored with surface pressure measurements. Phytase was able to incorporate into DPPG monolayers even at high surface pressures, ca. 30 mN/m, under controlled ionic strength, pH, and temperature. Mixed Langmuir monolayers of phytase and DPPG were characterized by surface pressure-area and surface potential-area isotherms, and the presence of the enzyme provided an expansion in the monolayers (when compared to the pure lipid at the interface). The enzyme incorporation also led to significant changes in the equilibrium surface compressibility (in-plane elasticity), especially in liquid-expanded and liquid-condensed regions. The dynamic surface elasticity for phytase-containing interfaces was investigated using harmonic oscillation and axisymmetric drop shape analysis. The insertion of the enzyme at DPPG monolayers caused an increase in the dynamic surface elasticity at 30 mN m(-)(1), indicating a strong interaction between the enzyme and lipid molecules at a high-surface packing. Langmuir-Blodgett (LB) films containing 35 layers of mixed phytase-DPPG were characterized by ultraviolet-visible and fluorescence spectroscopy and crystal quartz microbalance nanogravimetry. The ability in detecting phytic acid was studied with voltammetric measurements.     

Langmuir-Blodgett films of diazobenzene molecules

Langmuir-Blodgett (LB) films from diazobenzene Sudan III have been investigated using surface potential measurements as a function of number of layers and deposition pressures, with the surface potential data being related to molecular dipole moments obtained from theoretical electronic structure calculations. The surface potential increased with the number of layers for SIII LB films, and then tended to saturate. Results from density functional theory (DFT) and UV-vis spectroscopy indicated that the increase is due to addition of layers with oriented molecular dipoles, with the saturation tendency being attributed to a decrease in the amount of material deposited in each layer. The surface potential increased with the surface pressure used for deposition, probably owing to a higher contribution from the vertical component of the dipole moment as a closer molecular packing, which is associated with decreasing conformational entropy, was reached.     

Bovine lactoferrin purification from whey using Yellow HE‐4R as the chromatographic affinity ligand

The worldwide production of whey increases by around 186 million tons each year and it is generally considered as a waste, even when several whey proteins have important economic relevance. For its valorization, inexpensive ligands and integrated chromatography methods need to be developed for specific and low‐cost protein purification. Here, we describe a novel affinity process with the dye Yellow HE‐4R immobilized on Sepharose for bovine lactoferrin purification. This approach based on a low‐cost ligand showed an efficient performance for the recovery and purification of bovine lactoferrin directly from whey, with a yield of 71% and a purification factor of 61.     

The mechanism of enzymatic and biomimetic oxidations of aromatic sulfides and sulfoxides

Biomimetic and enzymatic oxidations of benzyl sulfides and sulfoxides lead to products (sulfoxides or sulfones) different from those obtained with bona fide electron transfer oxidations (products of C---H and/or C---S bond cleavage), which suggests the operation of an oxygen transfer mechanism.     

Information-Theoretic Generalization Bounds for Meta-Learning and Applications

Meta-learning, or “learning to learn”, refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key performance measure for meta-learning is the meta-generalization gap, that is, the difference between the average loss measured on the meta-training data and on a new, randomly selected task. This paper presents novel information-theoretic upper bounds on the meta-generalization gap. Two broad classes of meta-learning algorithms are considered that use either separate within-task training and test sets, like model agnostic meta-learning (MAML), or joint within-task training and test sets, like reptile. Extending the existing work for conventional learning, an upper bound on the meta-generalization gap is derived for the former class that depends on the mutual information (MI) between the output of the meta-learning algorithm and its input meta-training data. For the latter, the derived bound includes an additional MI between the output of the per-task learning procedure and corresponding data set to capture within-task uncertainty. Tighter bounds are then developed for the two classes via novel individual task MI (ITMI) bounds. Applications of the derived bounds are finally discussed, including a broad class of noisy iterative algorithms for meta-learning.     

Carbon Quantum Dot Optical Properties for potential infiltration into Hollow Core Photonic Crystal Fibers

Carbon quantum dots (CQD) have received significant attention in recent years due to their potential applications in optics and sensing. In this study, the authors report on the first characterization of the optical activity and broad absorption spectrum covering from short-wave ultraviolet, at 200 nm, to mid-infrared, at 1600 nm, of CQD synthesized using the “low-molecular-weight alcohols electrochemical carbonization” method. The CQD are analyzed using spectroscopic techniques, optical activity in the infrared, and high-resolution transmission electron microscopy. Results show a CQD size distribution of 5±3 nm and spherical morphology. The absorption spectra show increased absorption at both, high and low frequency. Additionally, the specific rotation of the CQD solution is significantly higher than that of pure ethanol, by three orders of magnitude. These findings suggest that CQD may have potential applications in polarized infrared filters and/or sensors due to their ability to rotate the polarization state of light at 1550 nm. The results of this study provide valuable insights into the optical properties of CQD and their potential for infiltration into hollow core photonic crystal fibers, making them a promising material for future research and development in the field of optics and sensing.     

Influence of two grinding methods on the uncertainty of determinations of heavy metals in atomic absorption spectrometry/electrothermal atomisation of plant samples

 Chemical analyses of trace elements are affected by relatively high analytical errors due to the different steps of the laboratory procedures: samples grinding, mineralisation and instrumental measurements. In the present communication, the influence of the grinding phase on the global uncertainty of Pb, Cd, Ni and Cr determinations in plant samples by the classical method of atomic absorption spectrometry/electrothermal atomisation (AAS-ETA) after dry ashing is quantified. Two grinding machines, a planetary mill with balls and jars of agate versus a stainless steel grinder were compared by analysing leaf samples of cucumber, strawberry, kiwivines, apple trees and grapevines from agricultural experimental plots under controlled conditions. Variance components due to the difference between grinding methods and experimental plots were estimated. Further, the simultaneous effects of the grinding methods on all considered metals have been evaluated by analysis of variance. With the stainless steel grinder, on average, higher levels of the considered heavy metals were obtained (up to 67% of the mean values). On average, the increments were similar for metals contained in steel (Ni and Cr) and those not contained (Pb and Cd). The true causes of these differences need further investigation to determine whether the higher metal detection is due to possible contamination, to a different grinding quality or to other reasons. Finally, the grinding methods did not seem to affect the combined uncertainty of the analyses. Received: 3 November 1997 · Accepted: 29 November 1997