Prouhet-Thue-Morse sequence and atomic functions in applications of physics and techniques

In present article a number of results are described in a systematic way concerning both signal and image processing problems with respect to atomic functions theory and Prouhet-Tbue-Morse sequence.

Description of nonstationary non-Gaussian processes using finite atomic functions

The possibility of using finite atomic functions of Kravchenko-Rvachev for description of the laws of distribution of the refractive index of the troposphere,the intensity of the scattering from the sea,seasonal behavior unit radar cross section(RCS)of land areas with vegetation covering,as well as the spectrum of electromagnetic spikes of lithospheric origin is considered.

Theory and Properties of Atomic Spacetime

Following A. Einsteins aspirations for an atomic theory, a novel theory of spacetime quantization/atomization based on finite Atomic AString Functions evolving since the 1970s is offered. Atomization Theorems allow representing polynomials, analytic functions, and solutions of General Relativity via the superposition of solitonic atoms which can be associated with flexible spacetime quanta, metriants, or elementary distortions. With multiple interpretations discussed, discrete-continuous spacetime is conceptualized as a lattice network of flexible solitonic atoms adjusting locations to reproduce different metrics. The theory may offer some variants of unified field theory under research based on Atomic AString Function where, like in string theory, fields become interconnected having a common mathematical ancestor.

The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application

The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions.

Atomic Spacetime Model Based on Atomic AString Functions

A novel model of spacetime and fields atomization based on Atomic Series over finite Atomic AString Functions is offered. Formulated Atomization Theorems allow representing polynomials, analytic functions, and solutions of field equations including General Relativity via superposition of solitonic atoms which can be associated with flexible spacetime quantum, metriants, or elementary distortions. Spacetime is conceptualized as a lattice of flexible Atomic Solitons adjusting locations to reproduce different metrics and other physical fields. It may offer the variants of unified field theory based on Atomic Solitons where, like in string theory, fields become interconnected having a common mathematical ancestor.

Atomic Exponential Basis Function Eup(x,w) - Development and Application

This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.

Atomic pair distribution function method development at the Shanghai Synchrotron Radiation Facility

The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility（SSRF）. The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.

Kravchenko atomic transforms in digital signal processing

The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L~ and L2 on the basis of the theory of atomic functions （AF） are presented. The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.

New WA-system of kravchenko functions in digital signal processing

On the basis of modified atomic transformations the new WA-systems of Kravchenko functions are constructed.As an example the digital processing of time series of the various physical nature processing is considered.The numerical experiments and physical analysis of the results confirm the efficiency of the proposed WA-systems of Kravchenko functions.

Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.

Atomization Theorems in Mathematical Physics and General Relativity

Formulated Atomization Theorems extend the theory of Atomic AString Functions evolving since the 1970s allowing representation of polynomials, complex analytic functions, and solutions of linear and nonlinear differential equations via Atomic Series over smooth finite Atomic Splines. Noting the preservation of analyticity for Ricci and Einstein tensors, special new theorems are formulated for General Relativity representing spacetime field via superpositions of flexible finite “solitonic atoms” resembling quanta. The novel Atomic Spacetime model correlates with A. Einstein’s 1933 paper predicting a new “atomic theory”. The theorems can be applied to many theories of mathematical physics, elasticity, hydrodynamics, soliton, and field theories for unified representation of fields via series over finite Atomic AString Functions which may offer a unified theory under research where fields are connected with a common mathematical ancestor.

Backscattering by sea of centimeter and millimeter waves at small grazing angle

Using experimental data reflected by the sea on specific radar cross-section （SRCS） at millimeter and centimeter waves, the approximations of the wind speed, angle of the sea surface radiation and polarization of the incident field can be calculated. The simulation model of the scattered signal has been proposed on the basis of the semi-Markov nested processes. For the first time it has been proved that for the description of reflections at spikes and pauses, it is possible to use finite atomic functions. The proposed model allows us to estimate the baekscatter intensity of millimeter and centimeter radio waves by the sea at grazing angle of surface radiation, as well as to simulate scattered signal.

Experimental and Theoretical Study of Hydrogen Atom Abstraction from C2H6 and C4H10 by Zirconium Oxide Clusters Anions

The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H- and Zr3O7H- are observed after the reaction. Den-sity functional theory calculations indicate that the hydrogen abstraction is favorable in the reaction of Zr2O5- with C2H6, which supports that the observed Zr2O5H- and Zr3O7H- are due to hydrogen atom abstraction from the alkane molecules. This work shows a newpossible pathway in the reaction of zirconium oxide cluster anions with alkane molecules.

Description and analysis of non-stationary signals by nested semi-Markov processes

The possibility of describing the time-dependent processes of scattering by underlying surfaces and the clear sky, as well as the seasonal behaviour of the refractive index of troposphere by using nested semi-Markov processes has been consid- ered. Local Gaussian models can be used to describe the process inside each phase state. The possibility of describing the sta- tistics of reflections from the sea and the refractive index by using Kravchenko finite functions has been shown for the first time.

Novel polymer acceptors achieving 10.18% efficiency for all-polymer solar cells

Polymer acceptors based on extended fused ring p skeleton has been proven to be promising candidates for all-polymer solar cells(all-PSCs), due to their remarkable improved light absorption than the traditional imide-based polymer acceptors. To expand structural diversity of the polymer acceptors, herein,two polymer acceptors PSF-IDIC and PSi-IDIC with extended fused ring p skeleton are developed by copolymerization of 2,20-((2 Z,20 Z)-((4,4,9,9-tetrahexadecyl-4,9-dihydro-s-indaceno [1,2-b:5,6-b']dithio phene-2,7-diyl)bis(methanylylidene))bis(3-oxo-2,3-dihydro-1 H-indene-2,1-diylidene))dimalononitrile(IDIC-C16) block with sulfur(S) and fluorine(F) functionalized benzodithiophene(BDT) unit and silicon(Si) atom functionalized BDT unit, respectively. Both polymer acceptors exhibit strong light absorption.The PSF-IDIC exhibits similar energy levels and slightly higher absorption coefficient relative to the PSi-IDIC. After blended with the donor polymer PM6, the functional atoms on the polymer acceptors show quite different effect on the device performance. Both of the acceptors deliver a notably high open circuit voltage(V_(OC)) of the devices, but PSi-IDIC achieves higher V OCthan PSF-IDIC. All-PSC based on PM6:PSi-IDIC attains a power conversion efficiency(PCE) of 8.29%, while PM6:PSF-IDIC-based device achieves a much higher PCE of 10.18%, which is one of the highest values for the all-PSCs reported so far. The superior device performance of PM6:PSF-IDIC is attributed to its higher exciton dissociation and charge transport, decreased charge recombination, and optimized morphology than PM6:PSi-IDIC counterpart. These results suggest that optimizing the functional atoms of the side chain provide an effective strategy to develop high performance polymer acceptors for all-PSCs.

Curvature and Size Effects on Reactivities of Mono-to Octa-vacancies in a(5,5) Single-walled Carbon Nanotube

Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vacancies in a（5,5） tube. An ab initio calculation results showed that E_f decreased with increasing the defect curvature K_（V_s）（s = 1~8）. The structures with removed carbon atoms along zigzag chain or the tubular axis were the most stable in each kind of Vs, because their corresponding K_（V_s） was the largest. In addition, local product structures disturbed the variation rule of E_f as K_（V_s）. There was an odd-even oscillation rule in the smallest E_f among each kind of Vs as the s value and vacancies V2, V4 and V6 were more stable. The stabilities of the related vacancy structures were confirmed by two dissociation processes.

Ultra-low lattice thermal conductivity and promising thermoelectric figure of merit in borophene via chlorination

Monolayer boron-based materials are of current interests due to its polymorphism.Herein,motivated by the recent experimental synthesis of semiconducting hydrogenatedαʹ-borophene and the regulation of the physical properties in layered materials by surface functionalization,we study the thermal and electronic properties ofαʹ-borophene with three different types of gas functional groups(H,F,and Cl)based on first-principles and Boltzmann transport theory.It is found thatαʹ-borophene can be well stabilized by fluorination and chlorination and maintain the semiconductor nature.More interestingly,when hydrogen is replaced with fluorine or chlorine,the lattice thermal conductivity changes from 24.3 to 5.2 or 0.73 W/(m·K)along armchair direction at 300 K,exhibiting a huge reduction by two orders of magnitude.The main reason is the decrease of both phonon group velocities and acoustic phonon relaxation time resulting from the strong phonon mode softening due to the weaken B-B bond strength and heavier atomic mass of fluorine and chlorine.Consequently,the chlorinatedαʹ-borophene exhibits a high thermoelectric figure of merit~2 at 300 K along armchair direction.Our study illustrates the importance of the modulation of transport properties by gas functional groups,which may promote the thermoelectric application of boron-based materials.

Anisotropic Hardy-Lorentz spaces and their applications

Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A.

Tight-binding models for ultracold atoms in optical lattices：general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.