Analytic Functions Research Articles

Bi-Univalency of m-Fold Symmetric Functions Associated with a Generalized Distribution

The m-fold symmetric in terms of a generalized distribution series has not been considered in the literature. In this study, however, the authors investigated the bi-univalency of m-fold symmetric functions for the generalized distribution of two subclasses of analytic functions. The initial few coefficient bounds amS and a2mS are obtained for the two subclasses of functions defined and the results serve as a new generalization in this direction.

Tip position control of flexible single‐link manipulators in the frequency domain without model reduction

AbstractThis article develops the fundamentals of the tip position control of flexible single‐link robotic manipulators in the frequency domain without approximating the model. Analytic transfer functions of the hub angle and tip position are derived without any model order reduction. Conditions for the stability of the transfer functions are presented by considering the payload mass change as an uncertain parameter. Using the D‐decomposition method, a simple procedure is introduced to design an output feedback controller which guarantees the stability and a desired tracking performance. The introduced design method leads to less conservatism comparing with design methods established upon model reduction. The controller structure includes two proportional‐derivative and integral loops and needs only two measurements of joint angle and tip position which are easily implementable. A numerical example is provided to demonstrate the merit of the achieved results.

Large-Signal Stability Analysis of AC Micro-Grid Under Quadratic Droop Control

Quadratic droop control is an innovative control strategy for power network, aiming to respect the inherently quadratic nature of reactive power flow. However, the system stability under quadratic droop control has not been addressed completely so far. This paper mainly focuses on the large-signal stability analysis of the AC network under quadratic droop control. We firstly analyze the stability of each equilibrium, it is concluded that the high-voltage equilibrium is stable as long as it exists while all low-voltage equilibria are unstable. Secondly, an analytical energy function for the system under quadratic droop control is established. It is proved that the high-voltage equilibrium is the local minimum of the proposed energy function while all the low-voltage equilibria are saddle points. Thirdly, to estimate the region of attraction (ROA) of the high-voltage equilibrium, an innovative method based on the analytical energy function is proposed. Comparing with the closest UEP method, the proposed ROA method significantly reduce the amount of computations. Simulation results verify the proposed theorems.

Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

<abstract><p>In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.</p></abstract>

Applications of $ q- $Ultraspherical polynomials to bi-univalent functions defined by $ q- $Saigo's fractional integral operators

<abstract><p>This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing $ q- $Ultraspherical polynomials under $ q- $Saigo's fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated.</p></abstract>

Analytical hierarchy process-based maintenance quality function deployment integrating total quality management with total productive maintenance and its application in dairy industry

Analytical hierarchy process-based maintenance quality function deployment integrating total quality management with total productive maintenance and its application in dairy industry

Fast Prediction and Staged Optimization of Electromagnetic Vibration in Permanent Magnet Synchronous Motor

The most common method to suppress electromagnetic vibration is to weaken the electromagnetic force harmonics (EMFHs), which are the vibration sources. Clearly, vibration is related to some other factors, too. Therefore, in this paper, modal analytical model and transmission function of a permanent magnet synchronous motor (PMSM) are studied, based on which a fast analytical method of predicting the electromagnetic vibration is proposed, so that the vibration can be preliminarily evaluated during the machine electromagnetic design. The time-consuming 3-dimensional finite element method (FEM) is not needed when predicting the vibration. Moreover, using the fast prediction method, a 15-dimensional multi-objective optimization problem for vibration, torque and efficiency performances is solved in stages. After optimization, the vibration is greatly reduced, and the torque performance is improved. The proposed methods are also proved to be applicable for different operating conditions and types of motors with various slot-pole combinations.

On the recovery of analytic functions that is exact on subspaces of entire functions

Построены семейства оптимальных методов восстановления аналитических в полосе функций и их производных по неточно заданному следу преобразования Фурье этих функций на вещественной оси. При этом от методов дополнительно требуется, чтобы они были точны на подпространствах целых функций. Библиография: 12 названий.

Mixed quantum/classical calculations of rotationally inelastic scattering in the CO + CO system: a comparison with fully quantum results.

An updated version of the CO + CO potential energy surface from [R. Dawes, X. G. Wang and T. Carrington, J. Phys. Chem. A 2013, 117, 7612] is presented, that incorporates an improved treatment of the asymptotic behavior. It is found that this new surface is only slightly different from the other popular PES available for this system in the literature [G. W. M. Vissers, P. E. S. Wormer and A. Van Der Avoird, Phys. Chem. Chem. Phys. 2003, 5, 4767]. The differences are quantified by expanding both surfaces over a set of analytic functions and comparing the behavior of expansion coefficients along the molecule-molecule distance R. It is shown that all expansion coefficients behave similarly, except in the very high energy range at small R where the PES is repulsive. That difference has no effect on low collision-energy dynamics, which is explored via inelastic scattering calculations carried out using the MQCT program which implements the mixed quantum/classical theory for molecular energy exchange processes. The validity of MQCT predictions of state-to-state transition cross sections for CO + CO is also tested by comparison against full-quantum coupled-states calculations. In all cases MQCT gives reliable results, except at very low collision energy where the full-quantum calculations predict strong oscillations of state-to-state transition cross sections due to resonances. For strong transitions with large cross sections, the results of MQCT are reliable, especially at higher collision energy. For weaker transitions, and lower collision energies, the cross sections predicted by MQCT may be up to a factor of 2-3 different from those obtained by full-quantum calculations.

Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator

<abstract><p>The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $ \mathfrak{q} $-calculus operators. We defined the $ \mathfrak{q} $-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) \mathfrak{f}(\varsigma) \; (s\in \mathbb{N}_{0} = \mathbb{N}\cup \{0\}, \mathbb{ N} = \left\{ 1, 2, 3, ..\right\}; \ell, \lambda, \mu \geq 0, 0 < \mathfrak{q} < 1) $. Our major goal was to build some analytic function subclasses using $ I_{ \mathfrak{q}, \mu }^{s}(\lambda, \ell)\mathfrak{f}(\varsigma) $ and to look into various inclusion relationships that have integral preservation features.</p></abstract>

Structural reliability analysis based on probability density evolution method and stepwise truncated variance reduction

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

DIGITIZATION FUNCTIONS OF MARKETING RESOURCES AT THE ENTERPRISE IN CONDITIONS OF ECONOMIC UNCERTAINTY

The article examines the complex of digitization functions of marketing resources in conditions of economic uncertainty, their interrelationship, and the proven direct impact of the digitization process on the efficiency of enterprise management. It is concluded that modern business structures use digital technologies as a competitive advantage in all areas of their activity: operational processes, business processes, finance, marketing and interaction with market stakeholders. On the basis of the positive correlations summarized by the authors, it can be assumed that the efforts aimed at the digitization of processes can be considered as a managerial innovation that ensures the growth of innovations and increases the efficiency of the functioning of the business structure. On the basis of a systemic approach, the authors substantiated and built a complex functionality of the process of digitization of the company’s marketing resources. In the architecture of complex functionality, the digitization process is determined by the digitization functions of marketing resources, in particular: analytical (data collection and analysis), communication (Internet advertising), sales (sales via the Internet), and the function of regulation and control (regulates and controls the digitization processes of the marketing department). The synthesis of the theory of random processes together with the systemic approach enabled the authors to define marketing resources for enterprise activities as a complete functional dynamic system with a discrete state, in which for each moment of time the economic security of the enterprise in the future depends on the current state of digitization and does not depend on how this state was reached. The prognostic and transformational probabilistic method for determining the effectiveness of digitization of marketing resources of an enterprise’s activities is proposed, which combines the potential of the enterprise’s marketing resources and the functions performed by marketing and allows for taking into account factors of the internal and external environment, the influence of which causes the emergence of risky situations that lead to unjustified losses of the enterprise. The authors have proven the effectiveness of using digital marketing tools within the scope of each marketing function to prevent the occurrence of risky situations in the company’s activities. Within the framework of the analytical function of marketing, a study of the competitive environment has been carried out, the market share of the enterprise has been recognized, an estimate of costs for marketing research has been prepared. Indicators of the communication functionality of marketing activities in the total amount of marketing expenses complement and justify its decisive influence on the general state of not only marketing, but also the entire economic activity of the enterprise. Indicators of the sales function of marketing determine the elasticity of demand for manufactured products, as well as other sales costs. The marketing functionality of regulation and control allows to analyze the relationship between the costs of ensuring the movement of goods and the received income. The markers defined by the authors of each element of the architecture of the process of digitization of the marketing business structure contribute to increasing the efficiency of evaluating the company’s activity in accordance with the main goal and purpose of the company operating in a structured market space and supporting the marketing concept of development, obtaining profit (income) and satisfying the most demanding needs of consumers.

Sufficient Conditions of Subclasses of Spiral-Like Functions Associated with Mittag-Leffler Functions

The purpose of the present paper is to find the sufficient conditions for some subclasses of analytic functions associated with Mittag-Leffler functions to be in subclasses of spiral-like univalent functions. Further, we discuss geometric properties of an integral operator related to Mittag-Leffler functions.

A Distributed Collaborative Learning Approach in 5G+ Core Networks

The 5G+ networks are going through extensive overhauling at both the radio access network (RAN) and core network (CN) to truly support the envisioned 5G+ use cases with ever so increasingly stringent quality of service requirements. Although many academic and industrial advancements have been realized, there are still needs for innovative changes vital for 5G+ connectivity, applications, and services. Consequently, the 3GPP is ushering in the next paradigm shift for CNs. CNs, which consist of several network functions (NFs) working cooperatively to service a RAN, are expected to exploit artificial intelligence (AI) in the form of an all-seeing-eye AI engine known as the Network Data Analytics Function (NWDAF). Its purpose is to optimize and automate network operation and management. However, accurate analytics require extensive machine learning (ML) training and as such, in this article, we present a distributed collaborative ML approach to facilitate said training. Accordingly, we present two variations of a distributed NWDAF architecture to enhance NF data localization, improve security, reduce control overhead during model training, shorten the training time, and finally, enhance the accuracy of the trained models by virtue of local testing on real-time network data. The first architecture distributes the global model training by exploiting the unique learning domain of each local model for each network function instance in a federated learning-based scheme while the second partitions the actual training network between multiple entities for each network function in a split learning-based scheme.

Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions

In this investigation, we study a class of analytic functions of type Carathéodory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory.

Subordinations and superordinations studies using $ q $-difference operator

<abstract><p>The results of this work belong to the field of geometric function theory, being based on differential subordination methods. Using the idea of the $ \mathfrak{q} $-calculus operators, we define the $ \mathfrak{q} $-analogue of the multiplier- Ruscheweyh operator of a specific family of linear operators, $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell). $ Our major goal is to build and investigate some analytic function subclasses using $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) $. Also, some differential subordination and superordination results are obtained. Moreover, based on the new theoretical results, several examples are constructed. For every differential superordination under investigation, the best subordinant is provided.</p></abstract>

Наилучшее приближение аналитических в единичном круге функций в весовом пространстве Бергмана B_(2,μ)

The paper studies the issues of the best approximation of analytical functions in the Bergman weight space B_(2,μ). In this space, for best approximations of functions analytic in the circle by algebraic complex polynomials we obtain the exact inequalities by means of generalized modules of continuity of higher order derivatives Ω_m (z^r f^((r) ),t),m∈N,r∈Z. For classes of functions analytic in the unit circle defined by the characteristic Ω_m (z^r f^((r) ),t), and the majorant Φ, the exact values of some n-widths are calculated. When proving the main results of this work, we use methods for solving extremal problems in normalized spaces of functions analytic in the circle, N.P. Korneichuk’s method for estimating upper bounds for the best approximations of classes of functions by a subspace of fixed dimension, and a method for estimating from below the n-widths of function classes in various Banach spaces.

On the approximation of analytic functions by infinite series of fractional Ruscheweyh derivatives bases

<abstract><p>This paper presented a new Ruscheweyh fractional derivative of fractional order in the complex conformable calculus sense. We applied the constructed complex conformable Ruscheweyh derivative (CCRD) on a certain base of polynomials (BPs) in different regions of convergence in Fréchet spaces (F-spaces). Accordingly, we investigated the relation between the approximation properties of the resulting base and the original one. Moreover, we deduced the mode of increase (the order and type) and the $ \mathbb{T}_{\rho} $-property of the polynomial bases defined by the CCRD. Some bases of special polynomials, such as Bessel, Chebyshev, Bernoulli, and Euler polynomials, have been discussed to ensure the validity of the obtained results.</p></abstract>

Optimal HVAC Energy and Regulation Reserve Scheduling in Power Markets

This paper considers the optimal scheduling of the hourly energy consumed and regulation reserve capacity offered by a Heating, Ventilation and Air-Conditioning (HVAC) system participating in a day-ahead electricity market. We formulate an Integrated hourly energy and regulation reserve Scheduling and Deployment (ISD) problem using high fidelity models of the HVAC and the building structure's thermal storage property. The ISD problem optimizes the hourly costs and benefits resulting from the power consumed, the regulation reserve capacity offered, the occupant thermal comfort utility, and the expected Intra-Hour Costs (IHCs) due to the HVAC's imperfect tracking of the regulation signal broadcasted by the Independent System Operator every few seconds. Addition of the IHCs to the objective function is the major innovation of this paper. It enables optimal HVAC scheduling to internalize expected regulation signal tracking error cost traded-off against incremental occupant thermal discomfort that may result from perfect tracking. The cost causation circle closes by noting that a high hourly regulation reserve offer may result in higher expected IHCs by increasing the associated tracking error and the incremental occupant discomfort. The paper's innovation is achieved by (i) estimating an analytic function of the hourly HVAC scheduling decisions and state variables that approximates the expected IHCs, and (ii) including this exogenously estimated analytic IHCs function in the objective of the hourly ISD optimization problem. Non-convexities and non-linearities introduced to the HVAC optimization problem resulting from high modeling fidelity and the inclusion of the expected IHCs, are addressed efficiently through piecewise convex relaxations that provide tight optimality bounds. Extensive numerical results are finally provided to demonstrate the applicability and performance of our ISD problem formulation on a realistic office building.

MORE POWERFUL HSIC-BASED INDEPENDENCE TESTS, EXTENSION TO SPACE-FILLING DESIGNS AND FUNCTIONAL DATA

The Hilbert-Schmidt independence criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces. This measure can be used for the global sensitivity analysis of numerical simulators whose objective is to identify the most influential inputs on the output(s) of the code. For this purpose, HSIC-based sensitivity measures and independence tests can be used for the ranking and screening of inputs, respectively. In this framework, this work proposes several improvements in the use of HSIC to increase their application spectrum and make the associated independence tests more powerful. First, we introduce a new method to perform the tests in a non-asymptotic framework. This method is much less central-processing-time expensive than the one based on permutation, while remaining as efficient. Then, the use of HSIC-based independence tests is extended to the case of some space-filling designs, where the independent and identically distributed condition of the observations is lifted. For this, a new procedure based on conditional randomization test is used. In addition, we also propose a more powerful test that relies on a well-chosen parameterization of the HSIC statistics: the kernel bandwidth parameter is optimized instead of the standard choices. Numerical studies are performed to assess the efficiency of these procedures and compare it to existing tests in the literature. Finally, HSIC-based indices for functional outputs are defined: they rely on appropriate and relevant kernels for this type of data. Illustrations are provided on temporal outputs of an analytical function and a compartmental epidemiological model.