Real Functions Research Articles

Efficient and Parallel Implementation of Real and Complex Response Functions Employing the Second-Order Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator.

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

On the problem of a Gurtin–Murdoch cylindrical material surface embedded in an infinite matrix

The problem of an infinite isotropic elastic matrix subjected to uniform far-field load and containing a Gurtin–Murdoch material surface of cylindrical shape is considered in plane strain setting. The governing equations and the boundary conditions for the problem, reduced to that of an infinite plane containing a material curve along a circular arc, are reviewed. The displacements inside the matrix are sought in the complex variables form of a single layer elastic potential whose density represents the jump in complex tractions across the curve. Exact complex integral representations for the elastic fields everywhere in the material are provided and the problem is further reduced to the system of real variables hypersingular boundary integral equations in terms of the strain and rotation components associated with the curve. The components are then approximated by the series of trigonometric functions that are multiplied by the square root weight functions to allow for automatic incorporation of the tip conditions. The unknown coefficients in the series are found from the system of linear algebraic equations that is solved using standard collocation method. The numerical examples are presented to illustrate the influence of dimensionless parameters with the main focus on the study of curvature-induced effects.

Zadacha Koshi dlya nagruzhennogo uravneniya Kortevega–de Friza v klasse periodicheskikh funktsiy

The inverse spectral problem method is applied to finding a solution of the Cauchyproblem for the loaded Korteweg–de Vries equation in the class of periodic infinite-gap functions.A simple algorithm for constructing a high-order Korteweg–de Vries equation with loaded termsand a derivation of an analog of Dubrovin’s system of differential equations are proposed. Itis shown that the sum of a uniformly convergent function series constructed by solving theDubrovin system of equations and the first trace formula actually satisfies the loaded nonlinearKorteweg–de Vries equation. In addition, we prove that if the initial function is a real π-periodicanalytic function, then the solution of the Cauchy problem is a real analytic function in thevariable x as well, and also that if the number π/n, n ∈ N, n ≥ 2, is the period of the initialfunction, then the number π/n is the period for solving the Cauchy problem with respect to thevariable x.

Artificial Neural Network-Based Computational Algorithm of Inverse Sumudu Transform Applied to Surface Transient Electromagnetic Sounding Method

Abstract ––The paper discusses the results of the development of a deep learning-based algorithm of the inverse Sumudu transform applied to the problem of on-ground non-stationary electromagnetic sounding. The Sumudu transform has potential for solving forward geoelectric problems in three-dimensional earth models because, unlike using the Laplace or Fourier transform, the Sumudu image of a real function is also a real function. Thus, there is no need to use complex numbers in subsequent calculations, which reduces computational costs and memory requirements in case of successful determination of the Sumudu image of the function. The disadvantages of the approach include the absence of an explicit method for calculating the inverse transform. The inversion can be done by solving the corresponding Fredholm integral equation of the first kind, but this is a poorly conditioned task leading to high requirements for the accuracy of the Sumudu image. The use of modern machine learning techniques can provide a method that is more robust to noise in the input data. This paper describes the process of creating a training dataset and developing a neural network algorithm; we evaluate the accuracy and performance of the obtained solution. The proposed method can contribute to the development of new approaches to physical processes modeling as well as to analysis, processing and interpretation of measured geophysical data.

Identifying oil price shocks with global, developed, and emerging latent real economy activity factors

SummaryThis paper proposes an identification strategy for international oil price shocks while accounting for the heterogeneous sources of oil demand from global, developed, and emerging economies. Unlike existing works, we isolate global oil demand shocks, associated with a global real economic activity factor, from oil demand shocks originating specifically from developed and emerging economies, associated with real economic activity factors within these two groups of economies. The paper uses a structural factor‐augmented vector autoregression (FAVAR) model with latent global and specific factors to model crude oil demand and supply. To identify the shocks, we extract real economic activity factors from a large panel of emerging and developed economies' real activity variables using a two‐level factor model. The paper shows how structural shocks can be identified by solving equations that arise from economically meaningful zero restrictions on the impact matrix of the reduced‐form FAVAR model innovations. The empirical application shows that identifying the international oil demand shocks based on the global and specific latent factors is essential to appropriately quantify their heterogeneous impacts on these factors, the crude oil production, and the real oil price.

Theory of Functions of Several Real Variables and Its Applications

Известно, что результаты об универсальной дискретизации квадратичной нормы по значениям в точках полезны в разреженном восстановлении функций по значениям в точках с ошибкой, измеряемой в квадратичной норме. В работе продемонстрировано, как результаты об универсальной дискретизации равномерной нормы по значениям в точках и недавние результаты об универсальном представлении по значениям в точках позволяют предъявить хорошие универсальные методы восстановления по значениям в точках периодических функций нескольких переменных из анизотропных классов Соболева и Никольского. Наиболее точные результаты получены в случае функций двух переменных, где для восстановления используются множества точек Фибоначчи.

Ab-initio calculation of halogen elements effect on the behavior of new double perovskite Cs2InSbX6 (X = F, Cl, Br, I): 1st part structural and optoelectronic properties

In recent years, there has been a growing fascination with lead-free perovskite materials, particularly in the realms of solar energy and photonics. It is imperative to conduct comprehensive theoretical investigations of these materials to effectively guide experimental pursuits. In this research, we harnessed the power of density functional theory (DFT) calculations, employing the Wien2k code, to delve into the distinctive characteristics of double-perovskite halides Cs2InSbX6 (X = F, Cl, Br, I). The viability and stability of their cubic structures were meticulously assessed, taking into consideration essential metrics such as the tolerance factor, octahedral factor and formation energy. Notably, the pronounced influence of spin–orbit coupling necessitated gap energy adjustments, achieved through a dual-pronged approach utilizing the generalized Perdew–Burke–Ernzerhof gradient approximation (PBE-GGA) and the modified Becke-Johnson (mBJ) exchange potential. The intricacies of band structure and state density were scrutinized using the GGA + mBJ method. The comprehensive findings elucidate that these compounds manifest fundamental electronic bandgaps spanning a range from 0.26 to 2.67 eV. Furthermore, they exhibit remarkably low carrier effective masses and a substantial degree of band dispersion. Of significance is the profound influence of halogen atom substitutions on their optical properties. Notably, a high absorption coefficient in the ultraviolet spectrum and the presence of a negative real dielectric function provide strong evidence for the adoption of metallic properties within a specific energy range. These compelling outcomes underscore the potential of these materials as highly promising candidates for a diverse array of photonic applications.

A Data Stream Ensemble Assisted Multifactorial Evolutionary Algorithm for Offline Data-Driven Dynamic Optimization.

Existing work on offline data-driven optimization mainly focuses on problems in static environments, and little attention has been paid to problems in dynamic environments. Offline data-driven optimization in dynamic environments is a challenging problem because the distribution of collected data varies over time, requiring surrogate models and optimal solutions tracking with time. This paper proposes a knowledge-transfer-based data-driven optimization algorithm to address these issues. First, an ensemble learning method is adopted to train surrogate models to leverage the knowledge of data in historical environments as well as adapt to new environments. Specifically, given data in a new environment, a model is constructed with the new data, and the preserved models of historical environments are further trained with the new data. Then, these models are considered to be base learners and combined as an ensemble surrogate model. After that, all base learners and the ensemble surrogate model are simultaneously optimized in a multitask environment for finding optimal solutions for real fitness functions. In this way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the ensemble model is the most accurate surrogate, we assign more individuals to the ensemble surrogate than its base learners. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art offline data-driven optimization algorithms. Code is available at https://github.com/Peacefulyang/DSE_MFS.git.

Note on: “The Complex Version of a Result for Real Iterative Functions”

Abstract Finta [2], recently proposed a complex version of iteration procedures for holomorphic functions. The general theorem of the complex iteration function has developed by using the complex mean value theorem and discussed several iterative procedures for holomorphic functions. In this paper, we redevelop the general theorem of the complex iteration function by applying the fundamental theorem of the complex line integral. It is shown that all the results derived in the paper of Finta have been improved by the results of this paper.

Surveying and mapping of large-scale 3D digital topographic map based on oblique photography technology

In the fields of geographic information systems and cartography, accurate topographic maps are crucial. Although traditional topographic mapping methods have certain accuracy, they have limitations in capturing features and building details. Therefore, this article proposes a large-scale 3D digital terrain mapping method based on oblique photography technology. Firstly, the UAV route is planned and image control points are arranged, to collect large-scale geographical object data by using UAV oblique photography technology. Then Smart 3D software is used to complete the 3D modeling of real large-scale topographic map through data preprocessing, air-to-air survey, control point import, 3D modeling, texture mapping and other steps based on the obtained geographical object data. The 2D and 3D linkage integrated mapping mode is adopted to obtain geomorphic information and elevation information, complete the data collection of indoor features, confirm the features that cannot be read on both sides of the indoor industry, complete the field supplementary mapping and adjustment, and realize the mapping of large-scale 3D digital topographic map. The experimental results show that this method can use oblique photography technology to collect data and establish a three-dimensional model of large-scale 3D digital terrain maps. The mean square error of accuracy detection is 0.202m, the mean square error of elevation is 0.257m, the mean square error of plane is 0.201m, and the mean square error of elevation is 0.197m. It has high drawing accuracy and excellent aerial triangulation performance.

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Budapester Topografien in den Romanen von Richard Wagner, Cătălin Dorian Florescu und Peter Rosenthal

Abstract This article traces patterns of engaging with Budapest‘s topographies in the auto-fictional works by Richard Wagner, Cătălin Dorian Florescu und Peter Rosenthal. Through a dialogical reading of their novels, the article highlights the links and overlaps between the genre of autofiction and space. The article argues that through mapping fictional settings and routes on a real map of Budapest, one may explore the intersection of literature and geography and the ways in which space influences the movement and behavior of the characters.

Novel Definitions of α-Fractional Integral and Derivative of the Functions

An α-fractional integral and derivative of real function have been introduced in new definitions and then, they compared with the existing definitions. According to the properties of these definitions, the formulas demonstrate that they are most significant and suitable in fractional integrals and derivatives. The definitions of α-fractional derivative and integral coincide with the existing definitions for the polynomials for 0 ≤ α < 1. Furthermore, if α = 1, the proposed definitions and the usual definition of integer derivative and integral are identical. Some of the properties of the new definitions are discussed and proved, as well, we have introduced some applications in the α- fractional derivatives and integrals. Moreover, α-power series and α–rule of integration by parts have been proposed and implemented in this study.

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

Asymptotic normality for the wavelet partially linear additive model components estimation

The focus of this article is on studying a partially linear additive model, which is defined using a measurable function . The model is given as follows: where and are vectors of explanatory variables, is a vector of unknown parameters, are unknown univariate real functions, and are independent random errors with mean zero, finite variances σ ε . Additionally, it is assumed that almost surely. The main contributions of this article are as follows. First, under certain mild conditions, we establish the asymptotic normality of the non linear additive components of the model. These components are estimated using the marginal integration device with the linear wavelet method. Second, we leverage our main result to construct confidence intervals for the estimated model.

Continuity of limit surfaces of locally uniform random permutations

A locally uniform random permutation is generated by sampling n points independently from some absolutely continuous distribution ρ on the plane and interpreting them as a permutation by the rule that i maps to j if the ith point from the left is the jth point from below. As n tends to infinity, decreasing subsequences in the permutation will appear as curves in the plane, and by interpreting these as level curves, a union of decreasing subsequences gives rise to a surface. In a recent paper by the author it was shown that, for any r≥0, under the correct scaling as n tends to infinity, the surface of the largest union of ⌊rn⌋ decreasing subsequences approaches a limit in the sense that it will come close to a maximizer of a specific variational integral (and, under reasonable assumptions, that the maximizer is essentially unique). In the present paper we show that there exists a continuous maximizer, provided that ρ has bounded density and support.The key ingredient in the proof is a new theorem about real functions of two variables that are increasing in both variables: We show that, for any constant C, any such function can be made continuous without increasing the diameter of its image or decreasing anywhere the product of its partial derivatives clipped by C, that is the minimum of the product and C.

An operational approach to near real time global high resolution mapping of the terrestrial Human Footprint

An operational approach to near real time global high resolution mapping of the terrestrial Human Footprint

A general algorithm to build mixed real and virtual antenna functions for higher-order calculations

The antenna-subtraction technique has demonstrated remarkable effectiveness in providing next-to-next-to-leading order in αs (NNLO) predictions for a wide range of processes relevant for the Large Hadron Collider. In a previous paper [1], we demonstrated how to build real-radiation antenna functions for any number of real emissions directly from a specified list of unresolved limits. Here, we extend this procedure to the mixed case of real and virtual radiation, for any number of real and virtual emissions. A novel feature of the algorithm is the requirement to match the antenna constructed with the correct unresolved limits to the other elements of the subtraction scheme. We discuss how this can be achieved and provide a full set of real-virtual NNLO antenna functions (together with their integration over the final-final unresolved phase space). We demonstrate that these antennae can be combined with the real-radiation antennae of ref. [1] to form a consistent NNLO subtraction scheme that cancels all explicit and implicit singularities at NNLO. We anticipate that the improved antenna functions should be more amenable to automation, thereby making the construction of subtraction terms for more complicated processes simpler at NNLO.

The Full Renormalization Horseshoe for Real Box Maps With Minimal Post-Critical Sets

Abstract In this paper, we consider the renormalization operator $\mathcal R$ for real box maps with minimal post-critical sets. We show the existence of the full renormalization horseshoe for real box maps with minimal post-critical sets. Moreover, the renormalization operator is exponentially contracting along the hybrid leaves.

An efficient mixed-variable generation operator for integrated energy system configuration optimization

Energy consumption has skyrocketed as society has progressed, resulting in energy crises and environmental issues. New energy technologies are being developed to address these challenges, and technologies such as the cogeneration of electricity, heating, and cooling are being used to improve energy utilization. The configuration of an energy system has a critical impact on the economics of the system, its ability to supply energy, etc. This study establishes a multiobjective mixed-variable configuration optimization model for a comprehensive combined cooling, heating, and power energy system. The model considers equipment types (categorical variables), equipment quantities (integer variables), and critical parameters (real variables) as optimization variables, where economic performance, the proportion of renewable energy, supply shortage, and dependence on the external power grid are considered unoptimized objectives. This is a multiobjective and mixed-variable problem, and the combination of the two properties poses an excellent challenge for evolutionary algorithms in optimizing the model. Therefore, we propose an efficient generating operator based on a fully connected weighted neural network, called the FCWN operator. This operator overcomes the challenge of the discrete variable space and broken neighborhood relationships in mixed-variable problems. During the algorithm search process, search history information is used to update the fully connected weight network for distribution estimation of the variable space. Offspring are generated based on the fully connected network to improve the algorithm’s search efficiency. In the experimental section, we construct a model with 20 variables and conduct simulation-based configuration optimization for scenarios with 3, 5, and 8 available equipment types. The final obtained Pareto frontier solution set is evaluated using the hypervolume metric, a widely used multiobjective evaluation metric. The Wilcoxon rank sum test on the experimental results shows that the proposed algorithm has better results than other state-of-the-art algorithms at a 95% confidence level.