Analytic Functions Research Articles

ANALYSIS AND FORECAST OF THE EMPLOYEES IN THE PUBLIC AND PRIVATE HEALTH SYSTEMS IN ROMANIA

In this paper, a statistical analysis is made of the health personnel in Romania in the public and private systems using data from the period 1990-2022, provided by the National Institute of Statistics. Using the least squares method, analytical functions are found that model the trend and forecasts are made for the years 2023 and 2024. The confidence intervals for the predictions are also found, at a significance threshold of 5%, and the correlations between certain indicators are analysed. It was found that in the public sector there was a downward trend, in general, for all categories of medical personnel in the period 1990-2017, followed by an increasing evolution after 2018, due to salary increases in the system. However, there is still a shortage of physicians in the public sector, even if their number has steadily increased in the last years. There is no correlation between the number of physicians and the number of beds in public hospitals, although this should be positive and high. On the other hand, in the private sector the trend is obviously increasing throughout the studied period, the correlations are very strong between the analysed indicators, a situation explained by the fact that in this system the goal is to minimize expenses and increase profit and less access of all citizens to health services.

An improved model for primary prediction of performance map for turbocharger radial turbine

In the contemporary landscape, possessing an intricate understanding of the performance characteristics of turbocharger radial turbine proves invaluable during engine development phases, to improve predictive capabilities of calculation codes and enhance the critical process of matching engines with turbochargers. This research deals with offering two precise yet straightforward analytical functions intended to generate comprehensive performance maps of turbocharger turbines. This is achieved through a refined adjustment of a preexisting analytical function, after introducing an inventive multiplication factor that aligns numerical calculations with experimental data to predict the turbine’s expansion ratio. Besides, a second analytical function forecasts the turbine’s thermo-mechanical efficiency by establishing a power balance equation between the turbine and supplied compressor map. The outcome of the developed model is compared with existing method on two distinct turbochargers, encompassing various rotational speeds. Additionally, a sensitive analysis aiming to detect the most important factors affecting our developed model while exploring it possible validity range for different thermodynamic parameters. The results indicate that the two functions yield reliable estimations of turbine performance, with maximum; root mean square error, R2, and mean absolute percentage error indices find around 9.47%, 0.993, and 9.03% for the turbine expansion ratio, and about 4.42%, 0.612, and 19.78% for efficiency prediction. This novel model enhances simulation accuracy while preserving user-friendliness and robustness based on the prerequisite of limited geometric and thermodynamic parameters at the turbocharger boundaries. Finally, the main advantages of the proposed model is its adaptability for the implementation in calculation codes, turbomachinery optimization strategies and assessments of the design and performance, addressing scenarios where the original turbine maps are rarely provided by turbocharger manufacturers.

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q̧-Calculus

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.

Third-order Hankel determinants for q-analogue analytic functions defined by a modified q-Bernardi integral operator

In this paper we define a Bernardi type quantum integral operator. It transforms the starlike univalent in the unit disk into a starlike region in it. We show that the upper-bound of the third-order Hankel determinant for classes of q-starlike functions is connected with a q-analogue integral operator, defined by a modified q-Bernardi integral operator. The Fekete-Szegö inequality of these classes is also investigated. Numerous well-known specific instances, examples and graphics are listed in the paper. The computations are done by Mathematica 13.3.

The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained.

Open-Circuit Voltage Variation in LiCoO2 Battery Cycled in Different States of Charge Regions

Open-Circuit Voltage Variation in LiCoO2 Battery Cycled in Different States of Charge Regions

Error bounds for Gauss–Jacobi quadrature of analytic functions on an ellipse

For the Gauss–Jacobi quadrature on [ − 1 , 1 ] [-1,1] , the location is estimated where the kernel of the error functional for functions analytic on an ellipse and its interior in the complex plane attains its maximum modulus. For the Jacobi weight ( 1 − t ) α ( 1 + t ) β (1-t)^\alpha (1+t)^\beta ( α > − 1 \alpha >-1 , β > − 1 \beta >-1 ) except for the Gegenbauer weight ( α = β \alpha =\beta ), the location is the intersection point of the ellipse with the real axis in the complex plane. For the Gegenbauer weight, it is the intersection point(s) with either the real or the imaginary axis or other axes with angle 1 4 π \tfrac {1}{4}\pi and 3 4 π \tfrac {3}{4}\pi . Our results support the empirical results provided by Gautschi and Varga [SIAM J. Numer. Anal, 20 (1983), pp. 1170–1186] for the Jacobi weight, the Gegenbauer weight and the Legendre weight. The results obtained are also illustrated numerically.

Conceptual approaches to the development and establishment of the bankruptcy institute in Ukraine

Conceptual approaches to the development and establishment of the bankruptcy institute in Ukraine

FAST: Filter-Adapted Spatio-Temporal Sampling for Real-Time Rendering

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and spatial denoising is an integral part of the real-time graphics pipeline. The main insight presented in this paper is that we can optimize the samples used in stochastic sampling such that the post-processing error is minimized. The core of our method is an analytical loss function which measures post-filtering error for a class of integrands --- multidimensional Heaviside functions. These integrands are an approximation of the discontinuous functions commonly found in rendering. Our analysis applies to arbitrary spatial and spatiotemporal filters, scalar and vector sample values, and uniform and non-uniform probability distributions. We show that the spectrum of Monte Carlo noise resulting from our sampling method is adapted to the shape of the filter, resulting in less noisy final images. We demonstrate improvements over state-of-the-art sampling methods in three representative rendering tasks: ambient occlusion, volumetric ray-marching, and color image dithering. Common use noise textures, and noise generation code is available at https://github.com/electronicarts/fastnoise.

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

A semi-analytic approximation for a single-particle continuum wavefunction

A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.

New Properties of Analytic Functions

In the present paper, we consider the class A¯ of functions f(z) of the form f(z)=z+∑k=1∞a1+k3z1+k3 that are analytic in the open unit disc U. If a1+k3=0 for k≠3n(n=1,2,3,⋯), then f(z) is given by f(z)=z+∑k=2∞akzk. For such functions f(z)∈A¯, some interesting properties for subordinations and strongly starlike functions are given. Also, some interesting examples for the results are shown.

Growth of hypercyclic functions: a continuous path between -frequent hypercyclicity and hypercyclicity

Abstract We are interested in the optimal growth in terms of Lp-averages of hypercyclic and $\mathcal{U}$ -frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic functions on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between $\mathcal{U}$ -frequent hypercyclicity and hypercyclicity.

A class of analytic functions associated with sine hyperbolic functions

A class of analytic functions associated with sine hyperbolic functions

Practical Approach to Nuclear Shelter Wall Thickness Estimation

Abstract The authors goal was to provide a practical guideline on nuclear shelter wall thickness estimation. The shelter wall thickness is assessed on the basis of published data on radiation dose calculations, corroborated by field data from nuclear tests, and information or calculations of the dose attenuation in the shelter wall. Dose criterion is selected as the acceptable dose behind the shield. Doses from nuclear tests or simulations are summarized in tables in relation to bomb yield and distance from the explosion point. Neutron dose transmission factors, defined as ratio of the dose behind the shielding to the dose without shielding, and their interdependence with shield thickness for different materials were found in the references. Based on the required dose transmission factor, calculated with the selected dose criterion, the corresponding shelter concrete wall thickness is assessed, taken into account the relation with the dose transmission factors from the literature. For gamma rays the shield thickness is calculated on the basis of analytical functions describing the dependence between dose without shield, dose criterion and shield thickness. Data tables are provided with the assessed concrete wall thickness in relation to bomb yield and distance.

Insights into Bitcoin and energy nexus. A Bitcoin price prediction in bull and bear markets using a complex meta model and SQL analytical functions

AbstractCryptocurrencies are in the center of attention of investors, public authorities and researchers, but the interest has shifted from purely financial aspects regarding the way of trading, lack of regulation and supervision of transactions, volatility, correlation with other assets to aspects related to sustainability taking in account the high energy consumption generated by the mining process and the impact on environmental pollution. Bitcoin was chosen for the research considering the dominance that this financial asset has on the cryptocurrency market and its position as alpha currency.The article focuses on the relationship between Bitcoin transactions and energy consumption, for period 1st January 2019—31st of May 2022, this interval having significant price movements. The authors made a prediction of the Bitcoin price using a complex meta-model and SQL analytical functions. The analysis is based on 15 fundamental variables in order to forecast the price: Bitcoin data (prices and volume), electricity price and traded quantity on day-ahead market (DAM), gas price and traded quantity on DAM, inflation in EU, EU-ETS emissions certificates and oil prices. The study reveals the importance of the relationship Bitcoin—energy—carbon emissions, elements that capture the impact of the mining process on the environment from the perspective of energy consumption. Investors on the Bitcoin market must be aware not only of the importance of financial aspects on the price of cryptocurrencies (inflation, demand, offer), but also of other elements related to the evolution of energy prices (electricity, oil, gas, renewable energy) and the evolution of emissions certificates prices. Considering the promotion of the principles of sustainable development on the capital market, portfolio investors have become increasingly attentive to the social and environmental performance of financial assets. This study aims to make financial market players aware of the non-financial implications of their transactions. In addition, the energy transition and the reconfiguration of the energy mix are elements of impact on the cryptocurrency market through the technical levers involved in the mining process.

Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions

Let H∞ be the Banach algebra of bounded analytic functions on the unit open disc D equipped with the supremum norm. As well known, inner functions play an important role in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define Qinn and Qout the maps from H∞ to I the set of inner functions and F the set of outer functions, respectively. In this paper, we study the H2-norm continuity and H∞-norm discontinuity of Qinn and Qout on some subsets of H∞. On the other hand, the Beurling theorem connects inner functions and invariant subspaces of the multiplication operator Mz. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of Qinn and Qout on Hol(D‾), the set of all analytic functions in the closed unit disk, are considered. In addition, we also study the factor maps Q[inn] and Q[out] from H∞ to I/T and F/T, where I/T is the quotient space of I mod T and F/T is the quotient space of F mod T.

Directional reflectance of light from landscapes on a long transect in Australia – forest to desert

The reflectance of land and vegetation observed in satellite imagery depends on sun and viewing geometry. This bidirectional reflectance requires correction for monitoring changes in vegetation cover and condition. We used a digital camera mounted in a light aircraft, and fitted with a fisheye lens, to measure directional reflectance of a diverse range of landscapes along a long transect in Australia — between Brisbane and the Simpson desert. All, except one, of the measured directional reflectances were able to be characterised accurately (adjusted r2 > 0.95) by the product of two analytical functions. The first, G(θ1,θ2), which represents volume scattering, is a function of illumination and viewing zenith angles, θ1andθ2, and has one parameter k:

Shift invariant subspaces in growth spaces and sets of finite entropy

AbstractWe investigate shift invariant subspaces within the realm of analytic functions in the unit disc, whose radial growth is determined by a majorant . Our main result offers a complete characterization of the shift invariant subspaces generated by Nevanlinna class functions within the aforementioned class of growth spaces. Our description is expressed in terms of a certain ‐entropy condition, which naturally arises in connection with boundary zero sets for analytic functions in the unit disc, having modulus of continuity not exceeding on the unit circle. Furthermore, we utilize our findings to establish a structural theorem on approximation in model spaces.

General form of the function [formula omitted] using cylindrically static spacetime

We find an exact static solution in four dimensions to the field equations of the f(Q) gravity by using a cylindrically static spacetime with two different ansatz, ν(r) and μ(r). This solution is derived without imposing any conditions on f(Q). The black hole solution involves four constants: c1, c2, c3, and c4. Among these, c1 is linked to the cosmological constant, c2 to the black hole's mass, while c3 and c4 are responsible for the deviation of the solution from the linear form of f(Q). We demonstrate how the analytical function f(Q) relies on c3. When c3 is zero, f(Q) becomes a constant function, leading to the non-metricity case. We investigate the singularity of this solution and show that the Kretschmann invariant has a much milder singularity compared to the non-metricity case. We produce a black hole that rotates with non-vanishing values of Q and f(Q) by using a coordinate transformation. Then, we analyze the laws of thermodynamics to determine the physical characteristics of this black hole solution and demonstrate that it is locally thermodynamically stable.