Regular Approximation Research Articles

A fractional Tikhonov method for solving a Cauchy problem of Helmholtz equation

In this paper, we study a fractional Tikhonov regularization method (FTRM) for solving a Cauchy problem of Helmholtz equation in the frequency domain. On the one hand, the FTRM retains the advantage of classical Tikhonov method. On the other hand, our method can prevent the effect of oversmoothing of classical Tikhonov method and conveniently control the amount of damping. The convergence error estimates between the exact solution and its regularization approximation are constructed. Several interesting numerical examples are provided, which validate the effectiveness of the proposed method.

Scaling Up Class-Specific Kernel Discriminant Analysis for Large-Scale Face Verification

In this paper, a novel approximate solution of the criterion used in non-linear class-specific discriminant subspace learning is proposed. We build on the class-specific kernel spectral regression method, which is a two-step process formed by an eigenanalysis step and a kernel regression step. Based on the structure of the intra-class and out-of-class scatter matrices, we provide a fast solution for the first step. For the second step, we propose the use of approximate kernel space definitions. We analytically show that the adoption of randomized and class-specific kernels has the effect of regularization and Nystrom-based approximation, respectively. We evaluate the proposed approach in face verification problems and compare it with the existing approaches. Experimental results show the effectiveness and efficiency of the proposed approximate class-specific kernel spectral regression method, since it can provide satisfactory performance and scale well with the size of the data.

Preferred nanocrystalline configurations in ternary and multicomponent alloys

In nanocrystalline alloys, a range of configurations can have low energies when solute atoms have favorable interactions with interfaces. Whereas binary nanostructured alloys have been well studied, here we lay groundwork for the computational thermodynamic exploration of alloy configurations in multicomponent nanocrystalline alloys. Multicomponent nanostructured systems are shown to occupy a vast space, with many topological possibilities not accessible in binary systems, and where the large majority of interesting configurations will be missed by a regular solution approximation. We explore one interesting ternary case in which the first alloying element stabilizes grain boundaries, and the second forms nano-sized precipitates.

ChemInform Abstract: The Valence States of Copernicium and Flerovium.

AbstractTwo‐component ZORA (Zeroth Order Regular Approximation to the Dirac equation) DFT calculations are used to analyze the valence states of Cn and Fl.

Navier\u2013Stokes Equation and its Fractional Approximations

We consider the Navier–Stokes equation (N-S) in dimensions two and three as limits of the fractional approximations. In 2-D the N-S problem is critical with respect to the standard L^2 a priori estimates and we consider its regular approximations with the fractional power operator (-PDelta )^{1+alpha }, alpha >0 small, where P is the projector on the space of divergence-free functions. In 3-D different properties of the N-S problem with respect to the standard L^2 a priori estimate are obtained and the 3-D regular approximating problem involves fractional power operator (-PDelta )^s with s>frac{5}{4}. Using Dan Henry’s semigroup approach and the Giga-Miyakawa estimates we construct regular solutions to such approximations. The solutions are global in time, unique, smooth and regularized through the equation in time. Solution to 2-D and 3-D N-S equations are obtained next as a limit of such regular solutions of the approximations. Moreover, since the nonlinearity of the N-S equation is of quadratic type, the solutions corresponding to small initial data and small f are shown to be global in time and regular.

The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom.

The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.

Regular approximations of isolated eigenvalues of singular second-order symmetric linear difference equations

This paper is concerned with regular approximations of isolated eigenvalues of singular second-order symmetric linear difference equations. It is shown that the kth eigenvalue of any given self-adjoint subspace extension is exactly the limit of the kth eigenvalues of the induced regular self-adjoint subspace extensions in the case that each endpoint is either regular or in the limit circle case. Furthermore, error estimates for the approximations of eigenvalues are given in this case. In addition, it is shown that isolated eigenvalues in every gap of the essential spectrum of any self-adjoint subspace extension are exactly the limits of eigenvalues of suitably chosen induced regular self-adjoint subspace extensions in the case that at least one endpoint is in the limit point case.

Adsorption Effect on Wetting in a Copper/Lead System

Complex analysis of interfacial thermodynamics was performed for a lead–copper binary system. Contact angle on polycrystalline copper and surface tension was measured for saturated Pb–Cu alloys at 390–1000 and 390–800 °C temperature ranges correspondingly. Liquid–gas and interfacial solid–liquid energies were calculated for Pb–Cu binary system by statistical thermodynamics on the basis of regular solution approximation at 390–950 °C. Calculated values coincide well with measured ones and with literature data, except for the temperature region lower than 700 °C, where the reported values of interfacial energy seem to be overestimated. Analysis of literature data leads us to the conclusion that an adsorbed monolayer film of lead exists in equilibrium with Pb–Cu drop on copper/gas interface between 250 and 900 °C. The decrease of the solid/gas surface energy due to Pb adsorption was calculated on the basis of the Young equation and fitted with the Szyszkowski equation. An adsorption energy of 276 kJ/mol and ...

Prediction of 195Pt NMR chemical shifts of dissolution products of H2[Pt(OH)6] in nitric acid solutions by DFT methods: how important are the counter‐ion effects?

(195) Pt NMR chemical shifts of octahedral Pt(IV) complexes with general formula [Pt(NO3 )n (OH)6 - n ](2-) , [Pt(NO3 )n (OH2 )6 - n ](4 - n) (n = 1-6), and [Pt(NO3 )6 - n - m (OH)m (OH2 )n ](-2 + n - m) formed by dissolution of platinic acid, H2 [Pt(OH)6 ], in aqueous nitric acid solutions are calculated employing density functional theory methods. Particularly, the gauge-including atomic orbitals (GIAO)-PBE0/segmented all-electron relativistically contracted-zeroth-order regular approximation (SARC-ZORA)(Pt) ∪ 6-31G(d,p)(E)/Polarizable Continuum Model computational protocol performs the best. Excellent second-order polynomial plots of δcalcd ((195) Pt) versus δexptl ((195) Pt) chemical shifts and δcalcd ((195) Pt) versus the natural atomic charge QPt are obtained. Despite of neglecting relativistic and spin orbit effects the good agreement of the calculated δ (195) Pt chemical shifts with experimental values is probably because of the fact that the contribution of relativistic and spin orbit effects to computed σ(iso) (195) Pt magnetic shielding of Pt(IV) coordination compounds is effectively cancelled in the computed δ (195) Pt chemical shifts, because the relativistic corrections are expected to be similar in the complexes and the proper reference standard used. To probe the counter-ion effects on the (195) Pt NMR chemical shifts of the anionic [Pt(NO3 )n (OH)6 - n ](2-) and cationic [Pt(NO3 )n (OH2 )6 - n ](4 - n) (n = 0-3) complexes we calculated the (195) Pt NMR chemical shifts of the neutral (PyH)2 [Pt(NO3 )n (OH)6 - n ] (n = 1-6; PyH = pyridinium cation, C5 H5 NH(+) ) and [Pt(NO3 )n (H2 O)6 - n ](NO3 )4 - n (n = 0-3) complexes. Counter-anion effects are very important for the accurate prediction of the (195) Pt NMR chemical shifts of the cationic [Pt(NO3 )n (OH2 )6 - n ](4 - n) complexes, while counter-cation effects are less important for the anionic [Pt(NO3 )n (OH)6 - n ](2-) complexes. The simple computational protocol is easily implemented even by synthetic chemists in platinum coordination chemistry that dispose limited software availability, or locally existing routines and knowhow. Copyright © 2016 John Wiley & Sons, Ltd.

Structure learning in Bayesian Networks using regular vines

Learning the structure of a Bayesian Network from multidimensional data is an important task in many situations, as it allows understanding conditional (in)dependence relations which in turn can be used for prediction. Current methods mostly assume a multivariate normal or a discrete multinomial model. A new greedy learning algorithm for continuous non-Gaussian variables, where marginal distributions can be arbitrary, as well as the dependency structure, is proposed. It exploits the regular vine approximation of the model, which is a tree-based hierarchical construction with pair-copulae as building blocks. It is shown that the networks obtainable with our algorithm belong to a certain subclass of chordal graphs. Chordal graphs representations are often preferred, as they allow very efficient message passing and information propagation in intervention studies. It is illustrated through several examples and real data applications that the possibility of using non-Gaussian margins and a non-linear dependency structure outweighs the restriction to chordal graphs.

Truncated spectral regularization for an ill-posed nonhomogeneous parabolic problem

The non homogeneous backward Cauchy problem ut+Au=f(t), u(τ)=ϕ for 0≤t<τ is considered, where A is a densely defined positive self-adjoint unbounded operator on a Hilbert space H with f∈L1([0,τ],H) and ϕ∈H is known to be an ill-posed problem. A truncated spectral representation of the mild solution of the above problem is shown to be a regularized approximation, and error analysis is considered when both ϕ and f are noisy. Error estimates are derived under appropriate choice of the regularization parameter. The results obtained unify and generalize many of the results available in the literature.

Strong Pseudo Jahn—Teller Effect on the Single Hexagonal Unit of Germanene

ABSTRACTGermanene, the 2D graphene-like Ge nanosheet, has been recently the subject of many theoretical studies and experimental attempts to synthesize it on Ag(111), Au(111) and Pt(111) surfaces. The experimental and theoretical evidences of germanene show a 2D continuous honeycomb layer with a buckled conformation. Density functional theory (DFT) calculations have predicted a larger buckling for germanene than silicene whose origin is also associated with a pseudo Jahn–Teller (PJT) effect. In this work we show that despite the fact that both, silicene and germanene possess a buckled conformation with a PJT origin, their vibronic coupling have different origins. The analysis is based on the PJT puckering instability of the hexagermabenzene molecule, the single hexagonal unit of germanene. This is done through the linear vibronic coupling model between the ground and the lowest excited states, which leads to a puckering distortion of the more symmetric cluster. We study both, the multilevel superposition vibronic model and possible mixing of excited states of different irreducible representations, which have been used to show the origin of similar structural transitions in hexagonal silicon and gold ring systems respectively. We show that contrary to other cases with one six-member rings, for the hexagermabenzene molecule a mixture of both the multilevel PJT and a ground state coupling with two quasi-degenerate excited states is necessary for a satisfactory explanation of puckering. Our model allows a determination of the coupling constants and predicts simultaneously the Adiabatic Potential Energy Surface (APES) behavior for the ground and excited states around the maximum symmetry point. The analysis is based on a scalar relativistic DFT and time-dependent DFT (TD-DFT) calculations in the Zero Order Regular Approximation (ZORA) using the B3LYP hybrid functional.

Predictive Distributed Visual Analysis for Video in Wireless Sensor Networks

We consider the problem of performing distributed visual analysis for a video sequence in a visual sensor network that contains sensor nodes dedicated to processing. Visual analysis requires the detection and extraction of visual features from the images, and thus the time to complete the analysis depends on the number and on the spatial distribution of the features, both of which are unknown before performing the detection. In this paper, we formulate the minimization of the time needed to complete the distributed visual analysis for a video sequence subject to a mean average precision requirement as a stochastic optimization problem. We propose a solution based on two composite predictors that reconstruct randomly missing data, on quantile-based linear approximation of feature distribution and on time series analysis methods. The composite predictors allow us to compute an approximate optimal solution through linear programming. We use two surveillance video traces to evaluate the proposed algorithms, and show that prediction is essential for minimizing the completion time, even if the wireless channel conditions vary and introduce significant randomness. The results show that the last value predictor together with regular quantile-based distribution approximation provide a low complexity solution with very good performance.

DFT and experimental studies on structure and spectroscopic parameters of 3,6-diiodo-9-ethyl-9H-carbazole

The first report on crystal and molecular structure of 3,6-diiodo-9-ethyl-9H-carbazole is presented. Experimental room-temperature X-ray and 13C chemical shift studies were supported by advanced theoretical calculations using density functional theory. The 13C nuclear magnetic shieldings were predicted at the non-relativistic and relativistic level of theory using the zeroth-order regular approximation. Theoretical relativistic calculations of chemical shifts of carbons C3 and C6, directly bonded to iodine atoms, produced a reasonable agreement with experiment (initial deviation from experiment of 44.3 dropped to 4.25 ppm). The changes in ring aromatic character were estimated via a simple harmonic oscillator model of aromaticity and nucleus-independent chemical shift index calculations. A good linear correlation between experimental and theoretically predicted structural and NMR parameters was observed.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed.

DFT as a Powerful Predictive Tool in Photoredox Catalysis: Redox Potentials and Mechanistic Analysis

Visible-light photoredox catalysis has come forth as a powerful activation mode in chemical synthesis, affording the development of a multitude of new strategies for molecular construction. However, detailed mechanistic knowledge of the various subprocesses involved is lacking, and new tools for addressing this are needed to drive innovation forward in the area. Herein, we describe predictions of ground- and excited-state redox potentials of ruthenium and iridium photocatalysts using nonrelativistic and scalar relativistic zero-order regular approximation density functional theory (DFT) methods. The computed redox potentials were correlated with experimental values and found to reproduce them well. Relativistic corrections were found to be important to reproduce experimental data. Moreover, the computational protocol allows us to estimate redox potentials that are not currently available in the literature or are difficult to determine experimentally. The mechanistic details of the photocatalyzed C–H funct...

Investigation of the Electronic Excited States of Small Gold Clusters in Rare Gas Matrices: Spin-Orbit Time-Dependent Density Functional Theory Calculation.

The effects of the weak interactions of rare gas atoms on the UV-visible absorption spectra of gold dimer and tetramer clusters are investigated. The time-dependent density functional theory based on the two-component relativistic zeroth-order regular approximation that considered spin-orbit coupling is performed to estimate the absorption spectra of Au2,4-Rgn (Rg = Ne-Xe, and n = 1-6) complexes. Using spin-orbit, including the appropriate functional, shows a close correlation between experiment and our calculations. It is also demonstrated that the weak interactions between rare gas atoms and gold clusters affect the UV-vis spectra of Au2,4 clusters by shifting the electronic transition toward the blue. Moreover, we find that the order of change in peak position, Δν̃, is proportional to the strength of interactions: Δν̃Au2,4-Xe > Δν̃Au2,4-Kr > Δν̃Au2,4-Ar > Δν̃Au2,4-Ne. In addition, comparing the UV-visible spectra of Au2,4-Rgn complexes with those of isolated Au2 and Au4 clusters shows that for Au2,4-Rg2,4,6 complexes in which Rg atoms interacted symmetrically with gold clusters no additional peaks are observed compared to isolated clusters; however, for Au2,4-Rg1,3,5 complexes, extra peaks appear because of the decrease in symmetry.

The Role of Interfaces in Nanomaterials Behavior at Extremes

The main statements of nanomaterials concept are shortly considered. Current developments in the metallic nanomaterials stability under thermal, irradiation, deformation and corrosion actions are generalized and discussed in detail. Special attention is paid to possible prediction of thermal grain growth characteristics using the regular solution approximation. The key role of nanotwinned interfaces in the stability increase at extremes is described and pointed out. The attention is paid to unresolved and insufficiently studied problems.

Robin coefficient identification for a time-fractional diffusion equation

This paper is devoted to a Robin coefficient identification problem for one-dimensional time-fractional diffusion equation. Based on the separation of variables, we transform the identification problem into a nonlinear Volterra integral equation of the first kind with the Robin coefficient and the Dirichlet data on a part of boundary as unknown functions. Then, we use a boundary element method to discrete the first kind integral equation and obtain a nonlinear system of algebraic equations. The conjugate gradient method is applied to solve a regularized optimization problem and finally, we obtain a suitable regularized approximation to the Robin coefficient. Three numerical examples are provided to show the effectiveness and robustness of the proposed method.

A Theoretical Study of the Binding of [Re₆Se₈(OH)₂(H₂O)₄] Rhenium Clusters to DNA Purine Base Guanine.

Hexanuclear rhenium complexes are promising candidates for use as antitumor drugs. However, to date, there has been no investigation into the nature of their binding to DNA. In this study, density functional theory (DFT) was used to examine the binding of [Re6Se8(OH)2(H2O)4] to the DNA purine base guanine. The geometrical structures of cluster-guanine adducts in water were modeled at the zero order regular approximation (ZORA)-PW91 level. Calculating the bond energies allowed us to compare the cis and trans forms of the cluster, and a possible manners of interaction between [Re6Se8(OH)2(H2O)3] clusters and DNA was obtained and explained.