Analytic Functions Research Articles

Certain Class of <i>P</i>-Valent Analytic Function Associated with Derivative Operator and Their Properties

This study aims to define a new subclass of multivalent analytic functions in the open unit disk. Jackson's derivative operator has been used to generate this subclass. Before getting coefficient characterization, we look at certain needs for the functions related to this subclass. We can see several fascinating features, including coefficient estimates, growth and distortion theorem, extreme points, and the radius of starlikeness and convexity of functions belonging to the subclass are shown using this technique.

Data analytics for research on complex brain disorders

There exist many research tools for complex brain disorders both proprietary and open source. Those tools are mostly focused on specific use cases and don’t offer a holistic view of the research and diagnostic processes. The MES-CoBraD platform offers a holistic tool that participates in all the phases of the process from planning to execution. In it researchers can create workflows of the diagnostic and research procedures. The Data Analytics module provides the functionality described in these workflows, mainly the analytical functions. The tools are integrated with the rest of the platform in a seamless manner. They are capable of analyzing different categories of data including imaging data, electroencephalogram (EEG)/polysomnography (PSG), medical device data, and consumer technology data. In this paper we present a summary of how the MES-CoBraD platform operates, the role of the data analytics in it, the actual functions implemented and integrated in the Data Analytics module and a number of use cases which show how each specific function can be used during the research and clinical procedures.

Recovery of a coefficient in a diffusion equation from large time data

Abstract This paper considers the determination of a spatially varying coefficient in a parabolic equation from time trace data. There are many uniqueness theorems known for such problems but the reconstruction step is severally ill-posed: essentially the problem comes down to trying to reconstruct an analytic function from values on a strip. However, we look at an even more restricted data where the measurements are not made on the whole time axis but only for large values adding further to the ill-conditioning situation. In addition, we do not assume the initial state is known. Uniqueness is restored by making changes to the boundary condition, in particular, to the impedance parameter, for each of a series of measurements. We show that an implementation of the above paradigm leads to both uniqueness and an effective reconstruction algorithm. Extension is also made to the case of fractional model and to replacing the parabolic equation with a damped wave equation.

Spectroscopic Ellipsometry Study of the Temperature Dependences of the Optical and Exciton Properties of MoS2 and WS2 Monolayers

The optical properties of MoS2 and WS2 monolayers are significantly influenced by fabrication methods, especially with respect to the behavior of excitons at the K−point of the Brillouin zone. Using spectroscopic ellipsometry, we obtain the complex dielectric functions of monolayers of these materials from cryogenic to room temperatures over the energy range 1.5 to 6.0 eV. The excitonic structure of each sample is analyzed meticulously by fitting the data to a standard analytical function to extract the energy positions of the excitons at each temperature. At low temperatures, excitonic structures are blue-shifted and sharpened due to the reduction in phonon noise and lattice distance. The excitons of monolayers fabricated by MOCVD separate into sub-structures at low temperatures, while monolayers grown by LPCVD and APCVD remain a single peak. The origin of these peaks as charged or neutral excitons follows from their temperature dependences.

Efficacy of modal curvature damage detection in various pre-damage data assumptions and modal identification techniques

The efficacy of modal curvature approach for damage localization is discussed in the paper in the context of input data. Three modal identification methods, i.e., Eigensystem Realization Algorithm (ERA), Natural Excitation Technique with ERA (NExT-ERA) and Covariance Driven Stochastic Subspace Identification (SSI-Cov), and four methods of determining baseline data, i.e., real measurement of the undamaged state, analytical function, Finite Element (FE) model and approximation of current experimental mode shape, are considered. Practical conclusions are formulated based on analysis of two cases. The first is a laboratory beam with a notch and the second is a stonemasonry historic lighthouse with modern restoration in its upper part. The analysis shows that NExT-ERA and SSI-Cov in combination with approximation of current mode shape provide high efficacy in damage localization alongside relatively straightforward determination of baseline data. It proves that the construction of advanced FE models of a structure can be replaced with a much simpler method of baseline data acquisition. Furthermore, the research shows the structural mode shapes identified with ERA may not always indicate the presence of damage.

Trending in the right direction: critical access hospitals increased adoption of advanced electronic health record functions from 2018 to 2023.

We analyzed trends in adoption of advanced patient engagement and clinical data analytics functionalities among critical access hospitals (CAHs) and non-CAHs to assess how historical gaps have changed. We used 2014, 2018, and 2023 data from the American Hospital Association Annual Survey IT Supplement to measure differences in adoption rates (ie, the "adoption gap") of patient engagement and clinical data analytics functionalities across CAHs and non-CAHs. We measured changes over time in CAH and non-CAH adoption of 6 "core" clinical data analytics functionalities, 5 "core" patient engagement functionalities, 5 new patient engagement functionalities, and 3 bulk data export use cases. We constructed 2 composite measures for core functionalities and analyzed adoption for other functionalities individually. Core functionality adoption increased from 21% of CAHs in 2014 to 56% in 2023 for clinical data analytics and 18% to 49% for patient engagement. The CAH adoption gap in both domains narrowed from 2018 to 2023 (both P < .01). More than 90% of all hospitals had adopted viewing and downloading electronic data and clinical notes by 2023. The largest CAH adoption gaps in 2023 were for Fast Healthcare Interoperability Resources (FHIR) bulk export use cases (eg, analytics and reporting: 63% of CAHs, 81% of non-CAHs, P < .001). Adoption of advanced electronic health record functionalities has increased for CAHs and non-CAHs, and some adoption gaps have been closed since 2018. However, CAHs may continue to struggle with clinical data analytics and FHIR-based functionalities. Some crucial patient engagement functionalities have reached near-universal adoption; however, policymakers should consider programs to support CAHs in closing remaining adoption gaps.

Stability of Schur’s iterates and fast solution of the discrete integrable NLS

We prove a sharp stability estimate for Schur iterates of contractive analytic functions in the open unit disk. We then apply this result in the setting of the inverse scattering approach and obtain a fast algorithm for solving the discrete integrable nonlinear Schrödinger equation (Ablowitz–Ladik equation) on the integer lattice, \mathbb{Z} . We also give a self-contained introduction to the theory of the nonlinear Fourier transform from the perspective of Schur functions and orthogonal polynomials on the unit circle.

OEFFICIENT ESTIMATES OF NEW SPECIAL SUBCATEGORY OF BI-UNIVALENT FUNCTIONS

In the present paper, we introduce and investigate a new subcategory H_Σ (q,β;ς) of analytic and bi-univalent functions in the open unit disk D based on the ideas of q-derivative operator and subordination. For the functions belong to the subcategory H_Σ (q,β;ς) , upper bounds for the second and third coefficients are found and some special outcomes of the main result are also presented.

Application of the Neutrosophic Poisson Distribution Series on the Harmonic Subclass of Analytic Functions using the Salagean Derivative Operator

The authors explore the innovative application of the Neutrosophic series, particularly the Neutrosophic Poisson Distribution Series (NPDS), to investigate various indeterminacy or uncertainties inherent in the classical univalent harmonic function class. The Neutrosophic Poisson Distribution Series is equipped with a Salangean derivative operator and convoluted with analytic univalent harmonic function class to derive new properties, such as inclusion relation, and coefficient inequalities for star-likeness. The results obtained demonstrate the effectiveness of this approach in capturing the inherent uncertainties and complexities associated with harmonic functions. There are several other areas of importance of our results that can be unlocked by computer engineers, scientists, and other experts. In this investigation, some of these indeterminacy and complexities are revealed using graphs by employing Python software tools. This novel integration enhances the analytical techniques available and opens a new stairway for future research in neutrosophic series and geometric function theory.

Reconstruction of Nearshore Surface Gravity Wave Heights From Distributed Acoustic Sensing Data

AbstractDistributed Acoustic Sensing (DAS) is a photonics technology converting seafloor telecommunications and optical fiber cables into dense arrays of strain sensors, allowing to monitor various oceanic physical processes. Yet, several applications are hindered by the limited knowledge of the transfer function between geophysical variables and DAS measurements. This study investigates the quantitative relationship between surface gravity DAS‐recorded wave‐generated strain signals along the seafloor and the pressure at a colocated sensor. A remarkable linear correlation is found over various sea conditions allowing us to reliably determine significant wave heights from DAS data. Utilizing linear wave potential theory, we derive an analytical transfer function linking cable deformation and wave kinematic parameters. This transfer function provides a first quantification of the effects related to surface gravity waves and fiber responses. Our results validate DAS's potential for real‐time reconstruction of the surface gravity wave spectrum over extended coastal areas. It also enables the estimation of waves hydraulic parameters at depth without the need from offshore deployments.

Results on Third-Order Differential Subordination for Analytic Functions Related to a New Integral Operator

In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U=z:z∈C and z&lt;1 involving the new integral operator μα,nm(f∗g). The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems.

Coefficient Estimates for New Subclasses of Bi-Univalent Functions Associated with Jacobi Polynomials

Our research introduces new subclasses of analytical functions that are defined by Jacobi polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a2| and |a3|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings.

Monte Carlo source verification of Elekta Synergy for pMLC collimated electron beams

IntroductionIn previous works, an electron beam source was developed that models its energy spectrum with a Lévy distribution. This source is used in BEAMnrc Monte Carlo simulation. It was benchmarked against water tank measurements for electrons delivered through an applicator collimation system, and it was found to agree with 2%/2 mm. This study uses this electron source further by investigating its ability to simulate electrons collimated by the photon multi-leaf collimators for MERT applications. Simulated and Gafchromic EBT3 depth dose and profile data were compared. MethodMeasured data were obtained from film exposures in a mini phantom with water-equivalent slabs at SSDs of 60 and 70 cm, respectively. Output factors and R90 values were calculated from film strip data taken in the depth direction. Corresponding dose data were simulated in BEAMnrc to obtain phase-space files for each beam and used in DOSXYZnrc to obtain dose data in a 3D water tank with 2 mm side length subvoxels. ResultsSimulation data corresponded with film data within 3 %/2 mm in most cases. Uncertainties in film measurements prevent a more accurate agreement. The output factors showed good agreement and could be fitted satisfactorily with an analytic function. A clinical example of a scalp treatment showed good agreement between simulated and film data. ConclusionIt is concluded that the electron source with the Lévy-based energy distribution can model electron dose for photon multi-leaf collimated electron beams within 3 %/2 mm.

A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials

This paper introduces a novel subclass of bi-univalent analytic functions by utilizing a symmetric q-derivative operator in conjunction with Gegenbauer polynomials. Within this newly defined subclass, we derive bounds for the first two Maclaurin coefficients and address the Fekete-Szeg o problem. By varying the parameters in our results between 0 and 1, we obtain a range of new insights and rediscover some previously established results. This approach not only broadens the scope of bi-univalent function theory but also deepens the understanding of coefficient bounds and extremal problems within this context.

Applications of a q-Integral Operator to a Certain Class of Analytic Functions Associated with a Symmetric Domain

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass.

Some Inclusion Properties for Hohlov Operator to be in Comprehensive Subfamilies of Analytic functions

Some Inclusion Properties for Hohlov Operator to be in Comprehensive Subfamilies of Analytic functions

Some Properties for Certain Subclasses of Spiral-Like and Robertson Analytic Functions

Making use of the definition of subordination, we introduce certain subclasses of spiral-like and Robertson functions in the open unit disk and study some important results such as convolution results, coefficients estimate, subordination properties and Fekete-Szego problems for these subclasses. Further, some known and new outcomes which follow as special cases of our outcomes are also mentioned.

Sharp starlike and convex radius for the differential operator of analytic functions

UDC 517.5 Under given coefficient conditions for analytic functions f in the unit disk D , we first obtain the starlike and convex radius for the linear combination of the differential operator z f ' of analytic functions f in D . Then we obtain the starlike and convex radius for the differential operator z f ' . Furthermore, we present the starlike and convex radius for the linear combination of the differential operator z f ' and analytic functions f in D . Our results imply the related result obtained by Gavrilov [Mat. Zametki, &lt;strong&gt;7&lt;/strong&gt;, 295–298 (1970)].

Inclusive Subclasses of Bi-univalent Functions Specified by Euler Polynomials

Our research delineates novel subclasses of analytical functions using Euler polynomials. Afterwards, we estimate the Fekete -Szeg¨o functional problem and the Maclaurin coefficients for this subfamily, namely |a2| and |a3|. Additionally, several new results are shown to follow after specializing the parameters employed in our main results.

The Enhancement of Machine Learning-Based Engine Models Through the Integration of Analytical Functions

The integration of analytical functions into machine learning-based engine models represents a significant advancement in predictive performance and operational efficiency. This paper focuses on the development of hybrid approaches to model engine combustion and temperature indices and on the synergistic effects of combining traditional analytical methods with modern machine learning techniques (such as artificial neural networks) to enhance the accuracy and robustness of such models. The main innovative contribution of this paper is the integration of analytical functions to improve the extrapolation capabilities of the data-driven models. In this work, it is demonstrated that the integrated models achieve superior predictive accuracy and generalization performance across dynamic engine operating conditions, with respect to purely neural network-based models. Furthermore, the analytical corrective functions force the output of the complete model to follow a physical trend and to assume consistent values also outside the domain of values assumed by the input features during the training procedure of the neural networks. This study highlights the potential of this integrative approach based on the implementation of the effects superposition principle. Such an approach also allows us to solve one of the intrinsic issues of data-driven modeling, without increasing the complexity of the training data’s collection and pre-processing.