Theory Of Generalized Functions Research Articles

Extended N-centered ensemble density functional theory of double electronic excitations.

A recent work (arXiv:2401.04685) has merged N-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended N-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.

Effects of intrinsic point defects (Tii-Vo) on the photocatalytic performance of bilayer rutile/anatase TiO2

Despite the progress on the photocatalytic performance of TiO2 as a typical photocatalytic material, previous research has overlooked the systematic study of the coexistence of Tii and Vo on the photocatalytic property of rutile or anatase TiO2 with bilayers. Studies on the comparative photocatalytic property of these materials have been rarely reported. Thus, the influences of point defects (Tii-Vo) on the photocatalytic performance of bilayer rutile or anatase TiO2 were investigated by GGA + U calculations under density general function theory framework. Results showed that the bilayer rutile Ti24TiiO47 (1 1 0) system exhibited the highest relative stability, strong carrier activity, reduced carrier recombination, and the longest lifetime. Furthermore, the absorption spectrum is clearly red shifted. This system is beneficial for the dissociation of water to produce H2 and O2. This research provides certain theoretical reference value on the design and fabrication of novel bilayer rutile TiO2(1 1 0) surface photocatalysts.

First principles study of the electronic structure of antimony (Sb) and samarium (Sm) doped tin dioxide (SnO2) based on big data analysis

Abstract To study the electronic structure of Sb and Sm co-doped SnO2 materials, a lattice model of Sb and Sm co-doped SnO2 is designed in this paper based on a big data analysis algorithm. The physical properties of the SnO2 ground state are described by the particle density function using the density generalized function theory. The interactions between the particles are all subsumed into the exchange-correlation generalized function by the Kohn-Sham equation. A big data analysis algorithm is used to construct the electron wave function to reflect the luminescence mechanism of the spectrum produced by the electron leap between energy levels, which makes the computational effort significantly reduced. The results show that the enthalpy change of Sb and Sm co-doped SnO2 in the design model of this paper is −5.59918, and the energy interval of the density of states of s orbitals is [2.36, 31.45]. It can be seen that the co-doping of Sm and Sb can increase the electron polarization ability and electron leap probability of SnO2 in the infrared band and enhance the infrared reflectivity, and the co-doped system has the highest electron-binding ability reflectivity.

Shear deformation modulates the electronic and optical properties of Al-doped arsenene

The influence of shear deformation on the electronic and optical properties of the Al-doped arsenene has been investigated using the first-nature principle based on density general function theory. Within this study, the 5.882% doping concentration in the Al-doped arsenene makes it reasonably stable and the doping of Al atoms causes the arsenene to exhibit quasi-metallic properties. The combined energy calculations show that the structural stability of the Al-doped arsenene is not significantly affected by shear deformation. With increased shear deformation, the band gap of intrinsic arsenene reduces, and the band gap of the Al-doped arsenene similarly does. Optical properties analysis indicates that shear deformation redshifts both the absorption and reflection peaks of the doped system.

Enhancement of optical properties of two-dimensional Bi2Te2Se by biaxial strain based on first-principles

The study of two-dimensional flexible materials in mechanic and optics has gained significant attention. By applying strain to modify the internal structure of materials, researchers can investigate the resulting mechanical and optical changes, offering exciting opportunities for further exploration in this field. The electronic structure, mechanical properties, and optical properties of the two-dimensional trigonal system Bi2Te2Se under biaxial strain regulation were investigated by using the first-principles plane pseudopotential plane wave method based on density generalized function theory. The analysis reveals that the energy bandwidth of Bi2Te2Se decreases with increasing strain until the band gap reaches 0 at 9% strain, causing the system to shift from a semiconductor to a conductor. The electronic density of states is primarily determined by the 6p orbitals of Bi and 5p orbitals of Te. With regards to its mechanical properties, Bi2Te2Se satisfies the mechanical stability criterion under different strains. As the strain increases from 0% to 6%, the material becomes increasingly brittle, with its interior transitioning from metallic to covalent bonds. However, the material toughness begins to improve from 6% to 9%, with the interior transitioning from covalent to metallic bonding. The performance improvement of Bi2Te2Se varies depending on the two electric field polarization vectors along [1 0 0] and [0 0 1] directions under strain. The material shows distinct application prospects in terms of absorption coefficient, reflectivity, refractive index, and lossiness under two directions. This paper provides a theoretical reference for the future mechanical and optical applications of Bi2Te2Se.

DFT computation of rare earth element doped TiO2 anatase: Tunable absorption spectra for water splitting application

The electronic band structure, density of states and optical properties of pure TiO2 and TiO2 doped with different elements (La, Ce, Hf and Pr) have been calculated using the first-principles density general function theory. The calculated results show that the La and Ce doped materials show a negative shift in the conduction band and an insignificant valence band shift. the band energy band gap values of La (Eg = 1.904 eV), Ce (Eg = 1.756 eV), Hf (Eg = 2.005 eV) and Pr (Eg = 1.970 eV) doped TiO2 are smaller than those of undoped TiO2 (Eg = 2.035 eV), among which, Ce doped anatase TiO2 has a narrower band width, smaller band gap value, high redshift and higher photocatalytic activity in the visible region.

First-principles calculations of phase transition, elasticity, phonon spectra, and thermodynamic properties for ThO2 polymorphs

First-principles calculations based on density generalized function theory (DFT) were used to determine the structural transformation, phonon spectra, thermodynamic properties, and elastic behavior of ThO2 under compressive and tensile loading in this work. In compressive conditions, the transition pressures and calculation of structural parameters agree with the experiment results. Phase transitions of ThO2 from the Fm3‾m phase to the Pnma, P42/mnm and Pnnm phases under tensile conditions were anticipated to happen at 23.2 GPa, −7.69 GPa, and −7.75 GPa, respectively. Within the range of pressures analyzed, both the Fm3‾m and Pnma phases of ThO2 exhibit mechanical stability, but the P42/mnm phase and Pnnm phase are unstable at high pressures, according to the mechanical stability criteria, which is validated concerning elastic constants. Under ambient pressure, the calculated phonon spectra of the ThO2 polymorphs in this study demonstrate that all of the phases taken into consideration are dynamical stability. Also, the predicted heat capacities, isothermal bulk modulus, Gibbs free energies, and thermal expansion coefficients of ThO2 polymorphs as functions of temperature are analyzed and are in comparison with relevant experiments.

Oxygen Vacancies‐Induced Dendritic SrTiO3/CdS p–n Heterostructures Photocatalyst for Ultrahigh Hydrogen Evolution

Owing to great efficient routes for charge carrier separation and transfer, heterostructure photocatalysts play significant roles in many photocatalytic reactions. Based on the bionic structure, an interesting composite photocatalyst of cadmium sulfide dewdrops on ultrathin strontium titanate branches with oxygen vacancies is successfully constructed by a simple chemical bath deposition method. The oxygen vacancies act as electron traps in the dendritic perovskite SrTiO3 nanostructure. Meanwhile, the CdS can provide abundant active sites for the hydrogen evolution reaction. The results demonstrate that SrTiO3/CdS‐5% nanocomposite with oxygen vacancies achieves the highest hydrogen production rate of 4537.9 μmol g−1 h−1 under visible light, which is over 50 times more than that of the single SrTiO3 with oxygen vacancies (79.36 μmol g−1 h−1), pure CdS (81.79 μmol g−1 h−1), and more than 750 times that of pure SrTiO3 (6.132 μmol g−1 h−1). Density generalized function theory calculations show that the bandgap values of SrTiO3/CdS nanocomposite with oxygen vacancies are narrower than that of the original SrTiO3 and CdS, in which the electrons flow from CdS to SrTiO3, and form an internal electric field at the interface, prolonging the carrier lifetime. Importantly, this work provides a reasonable reference for the preparation of efficient structure‐based biomimetic composite photocatalysts.

Two-dimensional Mg2Si-111: A direct bandgap semiconductor with excellent optical response properties predicted by first-principles calculations

A new two-dimensional(2D) direct bandgap semiconductor material, 2D Mg2Si-111, with a reticulated hexagonal structure and excellent photoresponse properties is predicted by using the first-principles calculation method based on density generalized function theory (DFT). 2D Mg2Si-111 has excellent properties that can be tuned with the number of layers and Mg defects. The calculation shows that the semiconductor of 2D Mg2Si-111 is stable at absolute temperature, and the bandgap value increases to a range suitable for light absorption, which is 1.17 eV. The electronic transition in 2D Mg2Si-111 is changed from the indirect transition of three-dimensional(3D) Mg2Si to direct transition, and its high-efficiency application potential in optoelectronic devices is more prominent. The electron effective mass in single-layer Mg2Si-111 ranges from 0.277 mo to 0.357 m0, which is lower than typical 2D materials, and exhibits an unconventional optical response that is not lower than the bulk parent body and has excellent absorption characteristics in the near-infrared region. Meanwhile, consider the effects of layer number modulation and defect regulation on 2D Mg2Si-111. The band gap value of 2D Mg2Si-111 can be modulated with the number of layers, from single layer to four layers, with an adjustable band gap of 0 eV - 1.17 eV that changes with the number of layers. The band gap change caused by Mg vacancy defects is only 0.89 eV - 1.1 eV, lower than the band gap of multilayer modulation, however, defect control can maintain a higher value of the band gap in 2D Mg2Si-111. Therefore, vacancy defects are a more refined means of regulation, and the influence of layer-number modulation on the characteristics of 2D Mg2Si-111 is significant. The light absorption characteristics of three-layer Mg2Si-111 have considerable light absorption responses from short-wave infrared to near-ultraviolet. Therefore, the layer number modulation has obvious changes to 2D Mg2Si-111. Compared with Mg2Si, 2D Mg2Si-111 is predicted to be a more efficient and promising optoelectronic material, and this work paves the way for the preparation, design and application of novel 2D Mg2Si-111 in 2D optoelectronic devices.

Synthesis of polydopamine modified MgAl-LDH for high efficient Cr(VI) removal from wastewater

A highly efficient absorbent was developed in this study by modifying polydopamine film on Mg–Al layered double hydroxide (PDA/MgAl-LDH) to remove Cr(VI) from wastewater. The characterization results showed that the polydopamine film was successfully coated on the MgAl-LDH surface. The preparation ratio, pH, and adsorbent dosage influencing absorption by PDA/MgAl-LDH were systematically investigated. The absorption capacity of Cr(VI) by PDA/MgAl-LDH was 87 mg/g. The equilibrium adsorption isotherm of PDA/MgAl-LDH was in good agreement with that of the Langmuir model. Therefore, the pseudo-second-order kinetic model is suitable for describing adsorption kinetics. The interaction between PDA and Cr(VI) and Cr(III) was investigated using density generalized function theory (DFT), which demonstrated that the PDA amino group could provide electrons for Cr(VI) reduction. Hydrogen and covalent bonding were dominant during the chemisorption process of PDA absorbing Cr(VI), the nitrogen of 5,6-dihydroxyindole was the primary active site for absorbing Cr(III), and electrostatic attraction was mainly responsible for Cr(III) absorption. Therefore, PDA/MgAl-LDH has the potential to adsorb and remove Cr(VI) from wastewater.

MANAJEMEN PELAYANAN MUSIK GEREJA STUDI DESKRIPTIF GEREJA SIDANG JEMAAT ALLAH (GSJA) SUNSET KUPANG DALAM MASA PANDEMI CORONA

This study aims to describe and examine church music services during the Covid-19 pandemic and to find out how the church music service management was used by the worship team of GSJA Sunset Church Kupang during the Covid- 19 pandemic. The research method used is descriptive qualitative research. Data collection techniques were carried out using interview methods, direct observation and document recording in the research area. Qualitative data analysis techniques, namely data reduction, data presentation and verification using general management function theory and church music ministry management theory to analyze the data in the study. Given that because there was during the Covid-19 pandemic, the church music ministry carried out its ministry role only on Sunday services which were conducted online. Team Worship at GSJA Sunset Church Kupang has managed to carry out its management function well, but there are still some obstacles that make the church music service less than optimal, including: it takes longer to get good music and vocals, mistakes occur when taking music and vocals, lack of adequate facilities to carry out the recording process and the occurrence of differences of opinion between fellow serving teams. After explaining the management functions that occurred in the worship team during the pandemic, namely the function of planning, organizing, directing, coordinating and monitoring, according to the writer of the worship team at GSJA Sunset Church Kupang, it has been successfully implemented even though GSJA Sunset Church Kupang did not learn about management science in theory. In line with the results of the above research, the writer can suggest that it would be better if every worship team should be able to train their ability in music and be able to build cooperation between fellow service teams and can learn from other churches in terms of music management or human resource management. exist in the church with the aim of improving the quality of the church.

First-principles study on the electronic structures and optical properties of Cs2XInCl6 (X= Ag, Na)

The excellent properties and diversity of structural composition of environmentally benign and stable double perovskite materials have piqued the curiosity of a wide range of researchers. In the field of optoelectronic materials, all-inorganic halide double perovskite has emerged as a viable alternative to lead-based perovskite in recent years. The energy band structure, density of states, and optical properties of the all-inorganic halide double perovskite Cs2XInCl6 (X = Ag, Na) were calculated and compared in this paper using the Castep code of Materials Studio software based on the density generalized function theory first principle plane wave pseudopotential method (DFT). The analysis of the results shows that Cs2XInCl6 (X = Ag, Na) is a material with a wide direct band gap and exhibits good light absorption in the visible and ultraviolet regions. Cs2AgInCl6 has better optical properties than Cs2NaInCl6 due to differences in reflection spectra, absorption spectra, and energy loss, although the differences are not considerable, and the compound Cs2XInCl6 (X = Ag, Na) has prospective applications in the field of optoelectronics. The computational results of this work contribute to a better understanding of the electronic and optical properties of Cs2XInCl6 (X = Ag, Na), as well as their similarities and differences, and provide some ideas for the design of corresponding innovative experiments to seek more valuable discoveries in the field of optoelectronic and optical applications.

Effect of intrinsic defects on the electronic structure and thermoelectricity of two-dimensional boron arsenide

Systematic study of the two-dimensional (2D) BAs in the inherent defects on the material electronic structure (by using effective band structure), magnetic properties and thermoelectric properties of the impact by means of density general function theory (DFT) calculations. The inversion defect of the As atom replacing the B atom retains the semiconductor properties, other defects all cause the material to exhibit metallic properties. The vacancy defects and interstitial defects makes the system introduce magnetism, the magnetic originate mainly from the s and p orbitals of the atoms near the defects, and the contribution of the d orbital is almost negligible. Novelty is that the defect of a B atom replacing an As atom significantly improves the thermoelectric performance of the system. The results provide the basis for the application of 2D BAs in magnetic materials, microelectronic devices and thermoelectric materials.

First-principles calculations of phase transition, elasticity, phonon spectra, and thermodynamic properties for CeO2 polymorphs

In this work, the structural transformation, elastic behavior, phonon spectra and thermodynamic properties of CeO2 under compressive and tensile loading were investigated by first-principles calculations based on density generalized function theory (DFT). Our calculated structural parameters and transition pressure under compressive condition are in good agreement with the experimental values. Under tensile condition, the phase transitions of CeO2 from fluorite-type (space group Fm3¯m) phase to cotunnite-type (space group Pnma), rutile-type (space group P 42/mnm) and marcasite-type (space group Pnnm) phases were predicted to occur at 23.2 ​GPa, −7.69 ​GPa, and −7.75 ​GPa respectively. The mechanical stability criteria are verified in terms of elastic constants and shows that the cotunnite and fluorite structures of CeO2 are mechanically stable in the studied pressure range, while the rutile and marcasite structures turn out to be mechanical unstable under high pressure. The calculated phonon spectra of CeO2 polymorphs demonstrate that all phases considered in present work are dynamically stable under ambient pressure. Furthermore, the calculated heat capacity, isothermal bulk modulus, Gibbs free energy, thermally expanding coefficient of CeO2 polymorphs as a function of temperature are discussed and compared with available experimental data.

A new aspect of generalized integral operator and an estimation in a generalized function theory

In this paper we investigate certain integral operator involving Jacobi–Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces of generalized functions. The existing theory of the Jacobi–Dunkl integral operator (Ben Salem and Ahmed Salem in Ramanujan J. 12(3):359–378, 2006) is extended and applied to a new addressed set of Boehmians. Various embeddings and characteristics of the extended Jacobi–Dunkl operator are discussed. An inversion formula and certain convergence with respect to δ and Δ convergences are also introduced.

Exact penalty functions with multidimensional penalty parameter and adaptive penalty updates

We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters provides much more flexibility, allows one to adaptively and independently take into account the violation of each constraint during an optimization process, and often leads to a better overall performance of an optimization method using an exact penalty function. We obtain sufficient conditions for the local and global exactness of penalty functions with vectorial penalty parameters and study convergence of global exact penalty methods with several different penalty updating strategies. In particular, we present a new algorithmic approach to an analysis of the global exactness of penalty functions, which contains a novel characterisation of the global exactness property in terms of behaviour of sequences generated by certain optimization methods.

Generalized functions in non-linear thermal conductivity problem for two-layer structure with heat source

Based on the generalized functions theory an exact analytical solution to the stationary non-linear problem of thermal conductivity for two-layer plate with heat sources for the asymmetrical Newton’s limiting conditions. Dependence of thermal conductivity factors of each layer on the temperature was assumed to be linear. The problem for a two-layer structure, using the Heaviside asymmetric unit function, is normalized to a single-layer one with piecewise homogeneous (discontinuous) properties of the medium. The advantage of this method for obtaining analytical solutions is that there is no need to directly fulfill the conjugation conditions at the layers’ contact points, since, thanks to the use of the Heaviside function, they are included in the generalized differential equation of the boundary value problem and are fulfilled in the process of obtaining its solution. A specific example of calculating the temperature state of a two-layer plate is provided.

Dynamics of thermoelastic half-plane by action of periodic loads and heat flows at its boundary

The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.

SYMOIN STOILOV (1887-1961): DETAILS OF SCIENTIfiC CAREER

The present article covers topics of life, scientific, pedagogical and social activities of the famous Romanian mathematician Simoin Stoilov (1887-1961), professor of Chernivtsi and Bucharest universities. Stoilov was working at Chernivtsi University during 1923-1939 (at this interwar period Chernivtsi region was a part of royal Romania. The article is aimed on the occasion of honoring professors’ memory and his managerial abilities in the selection of scientific and pedagogical staff to ensure the educational process and research in Chernivtsi University in the interwar period. In addition, it is noted that Simoin Stoilov has made a significant contribution to the development of mathematical science, in particular he is the founder of the Romanian school of complex analysis and the theory of topological analysis of analytic functions; the main directions of his research are: partial differential equation; set theory; general theory of real functions and topology; topological theory of analytic functions; issues of philosophy and foundation of mathematics, scientific research methods, Lenin’s theory of cognition. The article focuses on the active socio-political and state activities of Simoin Stoilov in terms of restoring scientific and cultural ties after the Second World War.

A nonlinear theory of distributional geometry.

This paper builds on the theory of nonlinear generalized functions begun in Nigsch & Vickers (Nigsch, Vickers 2021 Proc. R. Soc. A 20200640 (doi:10.1098/rspa.2020.0640)) and extends this to a diffeomorphism-invariant nonlinear theory of generalized tensor fields with the sheaf property. The generalized Lie derivative is introduced and shown to commute with the embedding of distributional tensor fields and the generalized covariant derivative commutes with the embedding at the level of association. The concept of a generalized metric is introduced and used to develop a non-smooth theory of differential geometry. It is shown that the embedding of a continuous metric results in a generalized metric with well-defined connection and curvature and that for C 2 metrics the embedding preserves the curvature at the level of association. Finally, we consider an example of a conical metric outside the Geroch-Traschen class and show that the curvature is associated to a delta function.