Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks

We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on 1/ε can ε-approximate functions that are analytic on certain regions of Cd.     

Exploration of the Crystal Structure and Thermal and Spectroscopic Properties of Monoclinic Praseodymium Sulfate Pr2(SO4)3

Praseodymium sulfate was obtained by the precipitation method and the crystal structure was determined by Rietveld analysis. Pr₂(SO₄)₃ is crystallized in the monoclinic structure, space group C2/c, with cell parameters a = 21.6052 (4), b = 6.7237 (1) and c = 6.9777 (1) Å, β = 107.9148 (7)°, Z = 4, V = 964.48 (3) ų (T = 150 °C). The thermal expansion of Pr₂(SO₄)₃ is strongly anisotropic. As was obtained by XRD measurements, all cell parameters are increased on heating. However, due to a strong increase of the monoclinic angle β, there is a direction of negative thermal expansion. In the argon atmosphere, Pr₂(SO₄)₃ is stable in the temperature range of T = 30–870 °C. The kinetics of the thermal decomposition process of praseodymium sulfate octahydrate Pr₂(SO₄)₃·8H₂O was studied as well. The vibrational properties of Pr₂(SO₄)₃ were examined by Raman and Fourier-transform infrared absorption spectroscopy methods. The band gap structure of Pr₂(SO₄)₃ was evaluated by ab initio calculations, and it was found that the valence band top is dominated by the p electrons of oxygen ions, while the conduction band bottom is formed by the d electrons of Pr³⁺ ions. The exact position of ZPL is determined via PL and PLE spectra at 77 K to be at 481 nm, and that enabled a correct assignment of luminescent bands. The maximum luminescent band in Pr₂(SO₄)₃ belongs to the ³P₀ → ³F₂ transition at 640 nm.     

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.     

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

Journal of Russian Laser Research - We examine the coherent dynamics of cold atoms in a three-dimensional (3D) optical lattice (OL) without interference between counter-propagating laser beams. The...     

Humic-based bionanocomposites containing stable paramagnetic gold nanoparticles for prospective use in pharmaceuticals

Structural peculiarities and supramolecular organization of medicinally promising nanocomposites, synthesized from humic substances, which essentially differ depending on decomposition degree, have been studied using electron spin resonance, transmission electron, and confocal laser scanning microscopy techniques and some other modern physical–chemical methods. It is shown that stable zero-valent gold nanoparticle of about 10–17?nm in size are formed in a natural macromolecular matrix. The nanocomposites obtained turn out to be stable in aggregative state for a long time and preserve their properties that are extremely important for prospective medicinal substances.     

Performance of a silicon monochromator under high heat load

The performance of a cryogenically cooled double‐crystal silicon monochromator was studied under high‐heat‐load conditions with total absorbed powers and power densities ranging from 8 to 780 W and from 8 to 240 W mm^?2, respectively. When the temperature of the first crystal is maintained close to the temperature of zero thermal expansion of silicon, the monochromator shows nearly ideal performance with a thermal slope error of 0.6 µrad. By tuning the size of the first slit, the regime of the ideal performance can be maintained over a wide range of heat loads, i.e. from power densities of 110 W mm^?2 (at total absorbed power of 510 W) to 240 W mm^?2 (at total absorbed power of 240 W).     

Solvent-free silica gel mediated decarboxylation of C–O coupling products of β-diketones and β-oxo esters with malonyl peroxides

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