Real Functions Research Articles

Impact and consequences of the error of estimated GFR in patients with heart failure

Heart failure is a highly prevalent disease, which courses with frequent readmissions, mainly by Acute Heart Failure (AHF). Reduced renal function is associated with increased mortality in patients with HF. Therefore, an accurate and precise evaluation of renal function in patients with HF is crucial. The error of estimated GFR (eGFR) is wide and common, showing a ± 30% variability compared to measured GFR (mGFR). However, there is no evidence on the error of formulas in reflecting real renal function and particularly the consequences of this error in patients with AHF. This is a prospective study comparing the impact of mGFR versus eGFR in the onset of cardiovascular (CV) outcomes in patients with AHF. This was tested with cox survival analysis. Measured GFR was determined by the plasma clearance of iohexol-dbs and eGFR by Cockroft-Gould, MDRD, CKD-EPI creatinine, CKD-EPI cystatin-C and CKD-EPI creatinine + cystatin-C equations formulas. Also the agreement between mGFR and eGFR was analyzed. A total of 90 patients were included. Average age was 66 (± 12 years) and 52 (58%) were male. Of them 53 patients (59%) had a cardiovascular event during follow-up, 22 fatal (41%). The agreement between mGFR and eGFR indicated moderate precision and accuracy (concordance correlation coefficient of 0.77; CI = 0.73–0.82). In multiple cox survival analysis, mGFR was significantly associated with cardiovascular events together with NTproBNP, BMI, LVEF and previous coronary artery disease (p = 0.037; HR = 0.98, 95% CI = 0.95–0.99). Estimated GFR by formulas was not significant. In patients with AHF the error of formulas is large, frequent and random, also, mGFR and not eGFR predicted future CV events. The error of eGFR may have clinical consequences in specific subpopulations.

UAV Geo-Localization Dataset and Method Based on Cross-View Matching

The stable flight of drones relies on Global Navigation Satellite Systems (GNSS). However, in complex environments, GNSS signals are prone to interference, leading to flight instability. Inspired by cross-view machine learning, this paper introduces the VDUAV dataset and designs the VRLM network architecture, opening new avenues for cross-view geolocation. First, to address the limitations of traditional datasets with limited scenarios, we propose the VDUAV dataset. By leveraging the virtual–real mapping of latitude and longitude coordinates, we establish a digital twin platform that incorporates 3D models of real-world environments. This platform facilitates the creation of the VDUAV dataset for cross-view drone localization, significantly reducing the cost of dataset production. Second, we introduce a new baseline model for cross-view matching, the Virtual Reality Localization Method (VRLM). The model uses FocalNet as its backbone and extracts multi-scale features from both drone and satellite images through two separate branches. These features are then fused using a Similarity Computation and Feature Fusion (SCFF) module. By applying a weighted fusion of multi-scale features, the model preserves critical distinguishing features in the images, leading to substantial improvements in both processing speed and localization accuracy. Experimental results demonstrate that the VRLM model outperforms FPI on the VDUAV dataset, achieving an accuracy increase to 83.35% on the MA@20 metric and a precision of 74.13% on the RDS metric.

Variations of the zero degrees isotherm and environmental lapse rate recorded with ADSB and Mode S EHS messages

This study focuses on analyzing the altitude of the zero degrees isotherm and variations in the environmental lapse rate (ELR) using the publicly available data collected from Automatic Dependent Surveillance–Broadcast (ADS-B) and Mode S Enhanced Surveillance (EHS) messages emitted by airplanes over a five-month period in 2021. The data was gathered using a professional receiver stationed in Bucharest (Romania). The aviation messages were decoded and the air temperature and pressure were determined, at the location of the airplane. The method has the advantage of the continuous messages that are emitted by the aircrafts during flight that allow instantaneous determination of the meteorological parameters at no additional costs. It can also be extended to permit almost real time maps of the ELR. When data was analyzed and a standard ELR value of 6.5 K/km is employed it was observed that the mean altitude of the 0 degrees isotherm exhibits a seasonal increase during the summer months, with an average altitude of 2874.2 m. The highest recorded altitude of the 0 degrees isotherm was found to be 5346.8 m, near Alexandria city (Romania), on 22.07.2021. Using a standard Least Mean Square algorithm alongside the International Standard Atmosphere pressure formula, the ELR values were calculated from pressure measurements data. The resulting mean ELR for the five-month period was determined to be 5.1331 K/km, slightly lower than the standard value.

Orthogonal Laurent Polynomials of Two Real Variables

ABSTRACTIn this paper, we consider an appropriate ordering of the Laurent monomials , that allows us to study sequences of orthogonal Laurent polynomials of the real variables and with respect to a positive Borel measure defined on such that . This ordering is suitable for considering the multiplication plus inverse multiplication operator on each variable and , and as a result we obtain five‐term recurrence relations, Christoffel–Darboux and confluent formulas for the reproducing kernel and a related Favard's theorem. A connection with the one‐variable case is also presented, along with some applications for future research.

GRID-FAST: A Grid-based Intersection Detection for Fast Semantic Topometric Mapping

This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The topometric map segments areas of the input map into different structural-semantic classes: intersections, pathways, dead ends, and pathways leading to unexplored areas. This method is grounded in a new technique for intersection detection that identifies the area and the openings of intersections in a semantically meaningful way. The framework introduces two levels of pre-filtering with minimal computational cost to eliminate small openings and objects from the map which are unimportant in the context of high-level map segmentation and decision making. The topological map generated by GRID-FAST enables fast navigation in large-scale environments, and the structural semantics can aid in mission planning, autonomous exploration, and human-to-robot cooperation. The efficacy of the proposed method is demonstrated through validation on real maps gathered from robotic experiments: 1) a structured indoor environment, 2) an unstructured cave-like subterranean environment, and 3) a large-scale outdoor environment, which comprises pathways, buildings, and scattered objects. Additionally, the proposed framework has been compared with state-of-the-art topological mapping solutions and is able to produce a topometric and topological map with up to 92% fewer nodes than the next best solution. The method proposed in this article has been implemented in the robotics framework ROS and is open-sourced. The code is available at: https://github.com/LTU-RAI/GRID-FAST.

Scenario Generation Based on Ant Colony Optimization for Modelling Stochastic Variables in Power Systems

Uncertainty is an important subject in optimization problems due to the unpredictable nature of real variables in the power system area, which can condition the solution’s accuracy. The effective modelling of stochastic variables can contribute to the reduction in losses in the system under evaluation and facilitate the implementation of an effective response in advance. To model uncertainty variables, the most extended technique is the scenario generation (SG) method. This method evaluates possible combinations of complete curves. Classical scenario generation methods are founded on probability distributions or robust stochastic optimization. This paper proposes a novel approach for constructing scenarios using the Ant Colony Optimization (ACO) algorithm, referred to as ACO-SG. This methodology does not require a previous statistical study of uncertainty data to generate new scenarios. A historical dataset and the desired number of scenarios are the inputs inserted into the algorithm. In the case study, the algorithm used historical data from the Savona Campus Smart Polygeneration Microgrid of the University of Genoa. The approach was applied to generate scenarios of photovoltaic generation and building consumption. The low values of the Euclidean distance were used in order to check the validity of the scenarios. Moreover, the error deviation of the scenarios generated with the goal of daily power were 1.77% and 0.144% for the cases of PV generation and building consumption, respectively. The different results for both cases are explained by the characteristics of the specific cases. Despite these different results, both were significantly low, which indicates the capability of the algorithm to generate any kind of feature within curves and its adaptability to any case of SG.

Elastic Fields Around Multiple Stiff Prestressed Arcs Located on a Circle

Abstract The plane strain problem of an isotropic elastic matrix subjected to uniform far-field load and containing multiple stiff prestressed arcs located on the same circle is considered. The boundary conditions for the arcs are described by those of either Gurtin–Murdoch or Steigmann–Ogden theories in which the arcs are endowed with their own elastic energies. The material parameters for each arc can in general be different. The problem is reduced to the system of real variables hypersingular boundary integral equations in terms of two scalar unknowns expressed via the components of the stress tensors of the arcs. The unknowns are 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 coefficients in series are found from the system of linear algebraic equations that are solved using the collocation method. The expressions for the stress intensity factors are derived and numerical examples are presented to illustrate the influence of governing dimensionless parameters.

Special homogeneous surfaces

Abstract We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian metric obtained by restricting the negative Hessian of their defining polynomial. Independent of the degree of the polynomials, there exist a finite number of special homogeneous surfaces. They are either flat, or have constant negative curvature.

Path Planning of an Unmanned Aerial Vehicle Based on a Multi-Strategy Improved Pelican Optimization Algorithm.

The UAV path planning algorithm has many applications in urban environments, where an effective algorithm can enhance the efficiency of UAV tasks. The main concept of UAV path planning is to find the optimal flight path while avoiding collisions. This paper transforms the path planning problem into a multi-constraint optimization problem by considering three costs: path length, turning angle, and collision avoidance. A multi-strategy improved POA algorithm (IPOA) is proposed to address this. Specifically, by incorporating the iterative chaotic mapping method with refracted reverse learning strategy, nonlinear inertia weight factors, the Levy flight mechanism, and adaptive t-distribution variation, the convergence accuracy and speed of the POA algorithm are enhanced. In the CEC2022 test functions, IPOA outperformed other algorithms in 69.4% of cases. In the real map simulation experiment, compared to POA, the path length, turning angle, distance to obstacles, and flight time improved by 8.44%, 5.82%, 4.07%, and 9.36%, respectively. Similarly, compared to MPOA, the improvements were 4.09%, 0.76%, 1.85%, and 4.21%, respectively.

On Productiveness and Complexity in Computable Analysis Through Rice-Style Theorems for Real Functions

On Productiveness and Complexity in Computable Analysis Through Rice-Style Theorems for Real Functions

Vitali Theorems in Non-Newtonian Sense and Non-Newtonian Measurable Functions

In this paper, we first state the ν−Vitali theorems in the non-Newtonian sense. In the second part, we give the definition of the non-Newtonian measurable function and the relation between ν−measurable and real measurable functions. We also study some basic properties of ν−-measurable functions.

Pole dynamics and an integral of motion for multiple SLE(0)

We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system that governs the driving functions. Our formulas give a simple method for mapping the class of rational functions into solutions to a non-trivial system of quadratic equations, and for directly showing that the curves in the real locus satisfy geometric commutation. These results are entirely self-contained and have no reliance on probabilistic objects, but make use of an integral of motion for the Loewner chain that is motivated by ideas from conformal field theory. We also show that the dynamics of the driving functions are a special case of the Calogero–Moser integrable system, restricted to a particular submanifold of phase space carved out by the Lax matrix. Our approach complements a recent result of Peltola and Wang, who showed that the real locus is the deterministic κ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa \\rightarrow 0$$\\end{document} limit of the multiple SLE(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\kappa )$$\\end{document} curves.

Comprehensive study on the optoelectronic properties of ZnSnP2 compound by DFT and simulation for the application in a photodetector

Abstract This article presents the density function theory (DFT) calculation of ZnSnP2 (ZTP) and its application as a photodetector. A DFT calculation has been performed to determine ZTP's optical and electronic characteristics. The direct bandgap of ZnSnP2 is found to be 1.0 eV which agrees well with the previously reported bandgap (0.95 eV). The total density of states (TDOS) of ZTP is determined to be 1.40 states/eV which is attributed to the 3p orbital of P, with minor impacts from the 3d orbital of Zn and the 5p orbital of Sn to TDOS. The real and imaginary dielectric functions and refractive indices ZTP have been determined to be 16.44 and 17.60, 4.07 and 2.92, respectively. The absorption coefficient and reflectivity of ZTP obtained from this investigation are 2.6×105 cm-1 and 57.5%, respectively. After calculating the electrionic and optical properties, ZTP-based n-CdS/p-ZnSnP2/p+-AlSb photodetector (PD) with CdS and AlSb as the window and back surface field (BSF) layers, respectively, has been computationally analyzed and optimized using solar cell capacitance simulator (SCAPS-1D). In a single heterojunction, the photocurrent, voltage, responsivity, and detectivity values have been obtained at 44.52 mA/cm2, 0.66 V, 0.73 A/W, and 6.81×1013 Jones, respectively. Insertion of a thin AlSb BSF layer improves the photocurrent, voltage, responsivity, and detectivity to 48.75 mA/cm2, 0.78 V, 0.86 A/W, and 8.22×1014 Jones, respectively. The outcomes are highly promising for the fabrication of a high performance ZTP-based PD in the future.

Reconstructing a Fine Resolution Landscape of Annual Gross Primary Product (1895–2013) with Tree-Ring Indices

Low carbon management and policies should refer to local long-term inter-annual carbon uptake. However, most previous research has only focused on the quantity and spatial distribution of gross primary product (GPP) for the past 50 years because most satellite launches, the main GPP data source, were no earlier than 1980. We identified a close relationship between the tree-ring index (TRI) and vegetation carbon dioxide uptake (as measured by GPP) and then developed a nested TRI-GPP model to reconstruct spatially explicit GPP values since 1895 from seven tree-ring chronologies. The model performance in both phases was acceptable: We chose general regression neural network regression and random forest regression in Phase 1 (1895–1937) and Phase 2 (1938–1985). With the simulated and real GPP maps, we observed that the GPP for grassland and overall GPP were increasing. The GPP landscape patterns were stable, but in recent years, the GPP’s increasing rate surpassed any other period in the past 130 years. The main local climate driver was the Palmer Drought Severity Index (PDSI), and GPP had a significant positive correlation with PDSI in the growing season (June, July, and August). With the GPP maps derived from the nested TRI-GPP model, we can create fine-scale GPP maps to understand vegetation change and carbon uptake over the past century.

Geometrical criterions of generalized subadditivity

The motivation of our studies is a theorem of J. Matkowski and T. Świątkowski from 1993, which provides convenient and sufficient conditions for the subadditivity of real functions. In the work was constructed a family of sets P⊂R×R with the property that each function whose graph is contained in P is subadditive. The purpose of this article is to generalize this result in several directions. We will discuss a more general inequality:f(∑i=1Nαixi)⩽∑i=1Nβif(xi). Moreover, our family of sets is constructed in such a way that an essentially larger class of solutions are covered. Geometric method used in presented paper may be applied to other functional inequalities like Hlawka's, submultiplicative and subquadratic inequalities as well as to obtaining irregular functions satisfying certain inequalities.

Spillover Effects Between the Stock Market and the Real Economy in a Mixed-Frequency Agent-Based Macrofinancial Model

Abstract This paper illustrates a behavioral mixed frequency macro-finance model where both real and financial variables are generated on a daily basis. Further, while financial sector data is collected at the same frequency as it is generated (i.e. daily), real data can only be collected on a quarterly basis. Under these circumstances, output and inflation, upon which data is available with a significant delay, become unsuitable as the sole information guide for monetary policy. We suggest that policy makers can deal with this information problem by reacting to the variable on which data is collected on high frequency basis: the stock price.

Strain effect on the electronic and optical characteristics of FAGeX3 (X=Cl, Br, and I) perovskite materials: DFT analysis

This study investigates the electronic and optical properties of a perovskite material known as Formamidinium Germanium Halide (FAGeX3), where X represents the elements Chlorine (Cl), Bromine (Br), and Iodine (I). We explore the bandgap, density of state (DOS), and partial density of state (PDOS) to understand their electronic properties. We use two methods, PBE and HSE-06, to determine the bandgap. Further, we investigate the optical properties by investigating the real and imaginary functions of the dielectric constant, refractive index, electron energy loss function, and absorption coefficient. Our research extends to the impact of biaxial strain, both tensile and compressive, in the −6% to +6 % range. Without strain, the materials exhibit direct bandgaps at the R point, with FAGeCl3 showing the highest bandgap (2.1359 eV), followed by FAGeBr3 (1.7325 eV), and FAGeI3 with the lowest (1.2581 eV). Our results reveal that applying tensile strain increases the bandgap and induces a blueshift, shifting the optical responses to shorter wavelengths, while compressive strain reduces the bandgap and causes a redshift, enhancing longer wavelength responses. Our findings demonstrate that FAGeX3 perovskites exhibit highly tunable electronic and optical properties under strain, making them exceptional candidates for advanced optoelectronic applications.

ON THE GENERALIZATION OF SOME CLASSES OF CONVEX IN DIRECTION AND TYPICALLY REAL FUNCTIONS

In the article by M.O. Reade (Duke Math. Journal, 1956) using the condition |arg (f'(z)/ g'(z)) | ≤ γπ/2, where g(z) is a convex function,0≤γ≤1 , a class of functions close-to-convex (almost convex) of order γ is introduced. In our paper, we introduce a subclass of the class of close-to-convex (almost convex) order γ functions satisfying the condition |arg [(1-λzn ) f'(z)]| ≤ γπ/2, which, for different parameter values, gives a number of well-known subclasses of univalent (schlicht) functions. Based on this subclass, a class of close-to-starlike (almost star-shaped) functions is constructed, containing a number of subclasses that have been actively studied by many authors in recent years, as well as a classical class of typically real functions. For this classes exact theorems of distortion (growth) and radii of convexity (starlikeness) are obtained, generalizing previously known results. The case is also considered when the functions of the introduced classes have missing members in the power series expansion. The results obtained are accurate and not only generalize previously known results, but also reveal the properties of a number of new subclasses of univalent (schlicht) functions.

On [formula omitted]-lineability

In the paper we study c-lineability and c-spaceability of some families F of real functions defined on an interval I. The main goal is to formulate general conditions under which any non-empty family F⊂RI of functions is c-spaceable or c-lineable. Generally, we consider the families of function of the form F=F1∖F2. In most cases, families of functions for which lineability and spaceability are studied have such a form. Most often, family F2 is seemingly “very close” to F1 or consists of “almost all” functions. The results obtained in this paper are a generalization of previous ideas. The main idea of our constructions is to “reproduce” one function to obtain c-dimensional (closed) linear space. For this “reproduction” we use the Fichtenholz-Kantorovich Theorem, applied to a countable family of pairwise disjoint intervals contained in the domain of functions from the considered class. The initial function is “squashed” and “pasted” into disjoint intervals included in the domain of constructed function.

Semiconductor-metal transition in TlPbF3 under isotropic pressure and its impact on optical, elastic and mechanical properties: a DFT computation with HSE06

This research aims to comprehensively evaluate the structure, elasticity, mechanics, anisotropy, electrical properties, and optical attributes of TlPbF3 at pressures from 0 to 60 GPa. A cubic structure of the material remains same without any phase changes, but there is a reduction in the lattice parameters. The material is determined to be mechanically secure by doing calculations on a variety of mechanical and elastic characteristics, including bulk, shear, and Young’s modulus, stiff, and not particularly flexible. It also shows a significant resistance to shear force. The material’s ability to withstand high pressures, its metallic bond nature, and ductility have been shown by the Kleinman’s parameter, Poisson’s ratio, Cauchy pressure, and Pugh ratio. Anisotropy can be confirmed by activating specific anisotropy factors. When we consider the electronic band structure, we observe a transition from a broad gap in the band (3.719 eV) comparable with a small band distance (0.65 eV), and converts to a metal (0 eV). To explore this, we have estimated the total, partial and elemental partial density of states. Additionally, we have computed the real and imaginary functions of dielectric, absorption factor, refractive index, extinction coefficient, loss function, reflectivity and real/imaginary conductivity to assess the material’s applicability. As pressure is applied, the static values of ε1(ω) and n(ω) increase. This material is also well-suited for optoelectronic devices due to its high conductivity, reflectivity, absorption, and refractive index.