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.

On the distribution of zeros of analytic functions in angles in $$\mathbf{C} \backslash \{ {0}\} $$

AbstractIn this article some results on the value distribution theory of analytic functions defined in angles of $$\mathbb{C}$$ C , due mainly to B. Ja. Levin and A. Pfluger, will be extended to the more general situation where the functions are defined in angles of $$\mathbb{C}\backslash\{ 0\}$$ C \ { 0 } . More precisely, angles $$S ( \theta_{1},\theta_{2}) $$ S ( θ 1 , θ 2 ) with vertex at the origin will be considered and where a singularity at zero is allowed. An special class of these functions are those of completely regular growth for which it is proved a basic result which yields an expression of the density of its zeros in terms of the indicator function.

Starlikeness of analytic functions using special functions and subordination

Starlikeness of analytic functions using special functions and subordination

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases.

Energy dependence of GafChromic LD-V1 film dose response to X-ray photons in the 60 to 180 kV range

Abstract Introduction: Radiochromic film (RCF) is suitable for use as a dosimeter owing to its inherently superior spatial resolution and near-water equivalence. A new model of RCF recommended for measuring imaging dose in the kV nominal energy range was recently introduced onto the market. In this study, we investigate the dependence on the beam quality of GafChromic LD-V1 film’s radiation dose response. Material and methods: Pieces of LD-V1 film were irradiated to air kerma ranging from 0 to 570 mGy in X-ray photons with beam qualities of 60 kV (HVL = 1.32 mm Al), 100 kV (HVL = 2.83 mm Al), 120 kV (HVL = 5.11 mm Al), 150 kV (HVL = 6.23 mm Al), and 180 kV (HVL = 0.54 mm Cu). The net reflectance from each film was obtained from a color flatbed scanner. For each beam quality, an analytical power function was fitted to the net reflectance - air kerma relationship and tested for differences. Results: We have found that for the beam qualities investigated, the response of the Gafchromic LD-V1 film was not significantly dependent on energy, and a single calibration curve could be used. The total relative uncertainty and absolute error reached maxima of 18% and 80%, respectively for air kerma values less than 50 mGy, and remained below 10% for air kerma in the range 50 mGy to 570 mGy. Conclusions: The results of our investigation revealed that the response of Gafchromic LD-V1 film is not significantly dependent on beam quality. A minimum air kerma irradiation of 50 mGy is recommended to minimise uncertainty.

A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder

The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.

#541 Secular trends in CKD and ESKD mortality rates in the United States, 2011–2021

Abstract Background and Aims Patients with chronic kidney disease (CKD) and end-stage kidney disease (ESKD) have a considerably higher mortality than the general population. Nevertheless, in the United States, mortality rates in the CKD and ESKD populations have declined steadily over the last decade until the onset of the COVID-19 pandemic [1]. Through a quantitative analysis of the age- and time-dependence of mortality rates in renal patient populations in the US, we aimed at quantifying trends in life expectancy between 2011 and 2021. Method We analysed CKD and ESKD mortality rates as reported in the US Renal Data System's (USRDS) Annual Data Report 2023 for the years 2011–2021 [1]. There, CKD mortality rates were determined from a Medicare 5% random sample (CKD stages 4 and 5) for patients aged 65 and above (“CKD 65+”). ESKD mortality rates were obtained from the USRDS database; we analysed data for patients aged 45 and above (“ESKD 45+”). We used fits of analytical functions to the data to hosphorzed their dependence on age and time. This technique enables us to extract quantitative trends in time by tracking fit parameters. Results We found that for each year between 2011 and 2021, mortality rates in the adult CKD and ESKD populations in the US largely conformed to an exponential dependence on patient age, $m = {{m}_0}( t ){{2}^{a/{{\Delta }}a}}$, that is, mortality rates doubled over constant age increments ${{\Delta }}a$. While overall, mortality rates were declining between 2011 and 2019, the age increments over which mortality rates doubled were nearly identical for each year (CKD 65+: ${{\Delta }}a$ = 10.5 ± 0.4 y, ESKD 45+: ${{\Delta }}a$ = 15.1 ± 0.9 y; mean ± SD). Exploiting this simple relationship, we found that the changes in mortality rates over time could largely be reduced to a steady right-shift of an otherwise unchanged mortality curve over time (shown for the ESKD 45+ group in Fig. 1a). By quantifying this right-shift over time, we estimated the gain in 1-year survival probability for different ages (Fig. 1b,c). This gain in survival does not necessarily imply a prolonged time on renal replacement therapy (RRT), e.g., when patients concomitantly start RRT at a later age. The onset of the COVID-19 pandemic in 2020 coincides with an abrupt cessation of these positive trends, reflected by a setback of mortality curves close to those in the year 2016 for the CKD population and to before 2011 for the ESKD population. Conclusion Public health data on CKD and ESKD show systematic dependencies of mortality rates on age and time, which can be revealed using analytical parameterisations of the data. Using this technique, we can capture trends in mortality rates and 1-year survival probability in adult kidney patient populations in the US during the years 2011–2019 and can quantify the abrupt cessation of these trends during the onset of the COVID-19 pandemic. In the CKD population we observed a setback of mortality rates close to those in the year 2016 with the onset of the pandemic. Changes in mortality rates in the ESKD population were more distinct. Specifically in elderly patients (aged 65 and above) 1-year survival dropped abruptly to levels lower than those observed in the previous decade.

Leveraging the concept of information entropy to improve a multi-fidelity design framework for early-stage design exploration of complex vessels

Early-stage design exploration is crucial since most of the major design decision are locked-in and only small design modifications are possible at later stages. To assess the performance of the various design candidates while performing design exploration, there are available methods and tools of various fidelities. These methods can be combined to form a multi-fidelity (MF) framework that guarantees accuracy through the high-fidelity model and achieves faster computational speeds through low-fidelity models. The present study proposes the adoption of information-theoretic entropy to improve a MF design framework based on Gaussian Processes (GPs). Entropy quantifies the uncertainty associated with the prediction of the design space. We propose using this uncertainty metric both as a criterion to determine whether further designs should be sampled to construct a reliable approximation of the design space and as a criterion to establish in which optimization step the optimization of the covariance matrix for the MF-GPs should be performed. The approach was tested to benchmark analytical functions and to a ship design problem of an AXEfrigate. The approach holds potential in practical applications, as it aids in the determination of whether additional resources should be allocated for high-fidelity analysis to support early-stage exploration.

Fuzzy Subordination Results for Meromorphic Functions Connected with a Linear Operator

The concept of subordination is expanded in this study from the fuzzy sets theory to the geometry theory of analytic functions with a single complex variable. This work aims to clarify fuzzy subordination as a notion and demonstrate its primary attributes. With this work’s assistance, new fuzzy differential subordinations will be presented. The first theorems lead to intriguing corollaries for specific aspects chosen to exhibit fuzzy best dominance. The work introduces a new integral operator for meromorphic functions and uses the newly developed integral operator, which is starlike and convex, respectively, to obtain conclusions on fuzzy differential subordination.

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.

On a Certain Subclass of Analytic Functions Defined by Bessel Functions

In this work, we introduce and investigate a new subclass of analytic functions in the open unit disc with negative coefficients. The object of the present paper is to determine the coefficient estimates, extreme points, integral means inequalities and subordination results for this class.

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

Phase retrieval on circles and lines

Abstract Let f and g be analytic functions on the open unit disk ${\mathbb D}$ such that $|f|=|g|$ on a set A. We give an alternative proof of the result of Perez that there exists c in the unit circle ${\mathbb T}$ such that $f=cg$ when A is the union of two lines in ${\mathbb D}$ intersecting at an angle that is an irrational multiple of $\pi $ , and from this, deduce a sequential generalization of the result. Similarly, the same conclusion is valid when f and g are in the Nevanlinna class and A is the union of the unit circle and an interior circle, tangential or not. We also provide sequential versions of this result and analyze the case $A=r{\mathbb T}$ . Finally, we examine the most general situation when there is equality on two distinct circles in the disk, proving a result or counterexample for each possible configuration.