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The fractal-fractional derivative is a powerful tool that is generally used for the mathematical analysis of complex and unpredictable structures. In this paper, we study a population dynamical model of (3+1)-dimensional form using the fractal derivative involving fractional order with power law kernel. The proposed scheme is known as the Sumudu Homotopy Transform Method (핊HTM), which depends on the association between the Sumudu Transform (핊T) and the Homotopy Perturbation Method (HPM). The convergence of the derived results is verified by comparing the errors in consecutive iterations with the 핊HTM results. We display the behavior of the obtained results in three-dimensional shape across the various orders of fractal and fractional derivatives. We present three numerical tests to validate the accuracy of 핊HTM and compare the acquired findings to the exact outcomes of the suggested model. This analysis confirms that the 핊HTM results align perfectly with the accurate results. As a result, the 핊HTM is widely recognized as a leading computational method for obtaining approximate solutions to various nonlinear complex fractal-fractional problems. [ABSTRACT FROM AUTHOR]

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise non-overlapping domains. This direction is called extreme problems in classes of pairwise non-overlapping domains. One of the problems of this type is considered in the present work. [ABSTRACT FROM AUTHOR]

The work presents a solution to the bending problem of an infinite piecewise homogeneous isotropic plate with an elastic circular washer and a radial through straight crack. It was assumed that under the action of an external loads at infinity, the edges of the crack are smoothly contacted on area of constant width (strip contact) on the upper base of the plate. The solution of the problem is built using the methods of the theory of functions of a complex variable and complex potentials and is reduced to a system of singular integral equations, which is numerically solved using the method of mechanical quadrature A numerical analysis of the problem is conducted and graphic dependencies of contact force, coefficients of intensity of moments and forces at various parameters of the problem were constructed. [ABSTRACT FROM AUTHOR]

In unbounded media, the acoustic attenuation as function of frequency is related to the frequency-dependent sound velocity (dispersion) via Kramers–Kronig dispersion relations. These relations are fundamentally important for better understanding of the nature of attenuation and dispersion and as a tool in physical acoustics measurements, where they can be used for control purposes. However, physical acoustic measurements are frequently carried out not in unbounded media but in acoustic waveguides, e.g., inside liquid-filled pipes. Surface acoustic waves are also often used for physical acoustics measurements. In the present work, the applicability of Kramers–Kronig relations to guided and surface waves is investigated using the approach based on the theory of functions of complex variables. It is demonstrated that Kramers–Kronig relations have limited applicability to guided and surface waves. In particular, they are not applicable to waves propagating in waveguides characterised by the possibility of wave energy leakage from the waveguides into the surrounding medium. For waveguides without leakages, e.g., those formed by rigid walls, Kramers–Kronig relations remain valid for both ideal and viscous liquids. Examples of numerical calculations of wave dispersion and attenuation using Kramers–Kronig relations, where applicable, are presented for unbounded media and for waveguides formed by two rigid walls. [ABSTRACT FROM AUTHOR]

In this study, the impact of principal stress states on the stress characteristics and initial failure of the rock mass surrounding a three-center arch opening was investigated using complex variable function methods and Discrete Element Method (DEM) numerical modeling. First, the mapping function of the opening was determined using the trigonometric interpolation method, and the influence of the number of terms in the mapping function on its accuracy was revealed. Based on this, the far-field stress state of the underground rock mass was characterized by the ratio of the minimum to maximum principal stress (λ) and the angle (β) between the principal stress and the vertical direction. This stress state was then converted into normal and shear stresses. Using complex variable function theory, the stress characteristics at the boundary of the opening under different stress states were analyzed. Finally, DEM numerical modeling was employed to study the initial failure characteristics at the boundary of the opening and its relationship with the stress distribution. The results indicate that the lateral pressure coefficient significantly affects the stability of the opening by influencing stress concentration around the surrounding rock. Low lateral pressure coefficients lead to tensile stress concentration at the boundary perpendicular to the maximum principal stress. As the coefficient increases, tensile stress decreases, and compressive stress areas expand. While the principal stress direction has a minor effect on stress concentration, it notably impacts stress distribution at the boundary. When λ < 1.0 and β = 45°, stress distribution asymmetry is most pronounced, with the highest compressive stress. The early failure distribution aligns with stress concentration areas, validating the use of stress analysis in predicting opening stability and failure characteristics. [ABSTRACT FROM AUTHOR]

To address the issue of severe mine pressure manifestations and difficult-to-control deformation in deep coal seam roadways,an orthogonal numerical simulation experiment was conducted based on the Kastner formula. This experiment examined five factors affecting the stability of roadway surrounding rock:height-to-width ratio,lateral pressure coefficient,depth,cross-sectional shape,and surrounding rock strength. Sensitivity of each factor to roadway deformation and damage was studied using variance analysis and intuitive analysis charts. The stress distribution patterns of elliptical and rectangular roadways under different lateral pressure coefficients and height-to-width ratios were analyzed using the plane elasticity complex variable function theory. Optimal designs for the height-to-width ratio and shape of elliptical and rectangular roadways were developed. The results showed that the main factors affecting the stability of surrounding rock are the strength of the surrounding rock and the lateral pressure coefficient,while depth,cross-sectional shape,and height-to-width ratio are secondary factors. Elliptical roadways exhibit the smallest difference in surrounding rock stress under isotropic stress ratios. Rectangular roadways have lower stress concentration when the width is 5 m and the height-to-width ratio is approximately 0. 6. For areas with rapid stress increase in rectangular roadways,an optimized rounded rectangular roadway was designed considering bearing characteristics and cross-sectional utilization, and a calculation formula for the corner radius was established. The optimization performance of this design was verified through numerical simulation. [ABSTRACT FROM AUTHOR]

In this article, we delve into the classic Bohr inequality for complex numbers, a fundamental result in complex analysis with broad mathematical applications. We offer refinements and generalizations of Bohr's inequality, expanding on the established inequalities of N. G. de Bruijn and Radon, as well as leveraging the class of functions defined by the Daykin–Eliezer–Carlitz inequality. Our novel contribution lies in demonstrating that Bohr's and Bergström's inequalities can be derived from one another, revealing a deeper interconnectedness between these results. Furthermore, we present several new generalizations of Bohr's inequality, along with other notable inequalities from the literature, and discuss their various implications. By providing more comprehensive and verifiable conditions, our work extends previous research and enhances the understanding and applicability of Bohr's inequality in mathematical studies. [ABSTRACT FROM AUTHOR]

Vito Volterra, an influential Italian mathematician, played a significant role in the rise of Italian mathematics after the country's unification in 1861. However, his career took a downturn under the Fascist regime. Volterra refused to pledge allegiance to the regime and was subsequently removed from his position as a university professor. Despite his contributions to mathematics, Volterra was largely forgotten in Italy until the availability of his letters in the 1970s shed new light on his research and public influence. Volterra's life serves as a lens to examine the trajectory of Italian science during this period. [Extracted from the article]

The object of this research is the decision-making process in the context of selecting recipients of social services using a semi-automated expert system. The main focus is on improving the mechanisms of assessment and selection of candidates eligible for assistance, in order to ensure a more efficient and objective allocation of resources. The problem addressed in this study is the need to improve the accuracy and efficiency of decision-making processes in social services through the implementation of semi-automated systems. In particular, reducing subjective influence in selection processes, as well as reducing the time and resources required to process applications. The study shows that the introduction of a semi-automated system can significantly reduce the response time to applications, increase the accuracy of candidate selection and ensure greater transparency in the decisionmaking process. The system, based on data analysis algorithms and production rules, is able to adapt to changing conditions and requirements, providing solutions based on up-to-date information. The effectiveness of the semi-automated system is due to the use of modern technologies for processing large volumes of data and the use of complex mathematical models for the analysis of this data. The implementation of a modular system with individually adjustable parameters allows the system to accurately evaluate each case based on the expected criteria, ensuring a high level of adaptability and accuracy. The results of the research can be applied in practice in various social security institutions, where there is a need to automate the processes of selection and decision-making. Important conditions for the effective implementation of the system are the availability of sufficient technical support, a high level of qualification of the personnel engaged in putting the system into operation, as well as a clear understanding of the rules and procedures that regulate social protection. In addition, to guarantee the successful application of the system, it is necessary to ensure compliance with all regulatory and legislative requirements, especially regarding the protection of personal data. [ABSTRACT FROM AUTHOR]

The pre-research data of mathematics prospective teachers in one of the universities in Bandung showed that the deductive reasoning ability in complex analysis was still not at good level. Beside the cognitive aspect, the affective aspect could be considered too in doing learning process, such as mathematical resilience. This study aims to analyze and identify the correlation between deductive reasoning and mathematical resilience in complex analysis. The research was conducted in one of the mathematics education departments of a university in Bandung. Correlation was the method used in this study. Mathematics prospective teachers were the sample of this research. This study concluded that mathematical deductive reasoning of prospective teachers was on a moderate level, the mathematical resilience of prospective teachers was on the positive category, and there was a significant correlation between deductive reasoning and the mathematical resilience of prospective teachers on a moderate level. [ABSTRACT FROM AUTHOR]

This document is an editorial that presents an authentic translation of Sergey N. Mergelyan's dissertation titled "Best Approximations in the Complex Domain." Mergelyan was a renowned Soviet and Armenian mathematician known for his work in approximation theory and the theory of functions of complex variables. The dissertation discusses Mergelyan's research on various topics, including polynomial approximation, uniform approximation by harmonic functions, and the approximation of continuous functions. Mergelyan's theorem on approximation by polynomials is highlighted as a significant contribution to the field. The document also acknowledges the individuals involved in the publication of Mergelyan's dissertation. [Extracted from the article]

We give a survey on recent progress on converses of existence theorem and extension theorem which are two main parts in -theory, and their applications in getting criteria of Griffiths positivity and characterizations of Nakano positivity of (singular) Hermitian metrics of holomorphic vector bundles, as well as the strong openness property and stability property of multiplier submodule sheaves associated to singular Nakano semipositive Hermitian metrics on holomorphic vector bundles. [ABSTRACT FROM AUTHOR]

This paper studies the leader–follower synchronization problem of complex‐valued networked multi‐agent systems with time‐delay. A new hybrid protocol including a continuous‐time protocol which is based on the interaction topology of follower agents and a pinning delayed impulsive control protocol is proposed. By employing the Lyapunov functional method in complex domains and the mathematical analysis technique, several delay‐dependent leader–follower synchronization criteria are established that take into account various sizes of delays. Particularly, our result shows that leader–follower synchronization of delayed complex‐valued networked multi‐agent systems can be achieved even if the proposed hybrid protocol is being subject to relatively large impulse delays. A numerical example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This document is an editorial introducing a special issue of the journal Axioms titled "Theory of Functions and Applications." The special issue contains 15 articles that explore various topics in the theory of functions, real and complex variables, and their applications. The articles cover fields such as function approximation, functional analysis, complex analysis, differential equations, numerical methods, and mathematical modeling. The aim of the special issue is to share scholars' theories, methods, and findings in function theory and provide solutions for applied problems in related scientific fields. [Extracted from the article]

This document is a preface to a special issue of the journal "Mathematics in Engineering, Science & Aerospace" focused on mathematical problems in science, engineering, and aerospace. The preface explains that mathematical analysis encompasses various disciplines and is applicable to fields such as engineering, economics, and biology. The special issue includes research articles on mathematical analysis with applications in engineering and applied sciences. The preface also acknowledges the contributors and reviewers who helped develop the issue. [Extracted from the article]

The ratios 8 / 9 = 2 2 / 3 ≈ 0.9428 and 3 / 2 ≈ 0.866 appear in various contexts of black hole physics, as values of the charge-to-mass ratio Q / M or the rotation parameter a / M for Reissner-Nordström and Kerr black holes, respectively. In this work, in the Reissner-Nordström case, I relate these ratios with the quantization of the horizon area, or equivalently of the entropy. Furthermore, these ratios are related to a century-old work of Kasner, in which he conjectured that certain sequences arising from complex analysis may have a quantum interpretation. These numbers also appear in the case of Kerr black holes, but the explanation is not as straightforward. The Kasner ratio may also be relevant for understanding the random matrix and random graph approaches to black hole physics, such as fast scrambling of quantum information, via a bound related to Ramanujan graph. Intriguingly, some other pure mathematical problems in complex analysis, notably complex interpolation in the unit disk, appear to share some mathematical expressions with the black hole problem and thus also involve the Kasner ratio. [ABSTRACT FROM AUTHOR]

This document is an editorial letter from Ashot S. Saghyan, the President of the National Academy of Sciences of Armenia. Saghyan welcomes participants and authors of research articles from a special issue in the Journal of Mathematical Sciences, which resulted from a workshop held in April 2023. He emphasizes the Academy's commitment to cooperation with scientists from around the world and the importance of integrating Armenian researchers into the global scientific community. Saghyan also highlights the historical significance of Armenian mathematics and the need to educate and support young Armenian scientists. He expresses support for initiatives aimed at promoting Armenian mathematics and establishing research partnerships. [Extracted from the article]

• Analytical solution for seismic response of deep tunnels under SV waves is derived. • Lining cross-sectional shape, thickness and interface conditions are considered. • Surrounding rock-lining interaction is key to tunnel seismic design and analysis. • The effect of cross-sectional shape on the internal forces in lining is complex. • Rock and lining stiffness matching achieves lining deformation and force balance. In order to study the seismic response of deep non-circular tunnels under far-field seismic SV waves, a pseudo-static analytical solution for the seismic response of the tunnel was first derived by using complex variable function theory and conformal mapping method. The proposed analytical solution can take into account variations in the lining thickness and the different interactions between the surrounding rock and lining. Then, the validity and correctness of the analytical solution were verified by numerical methods based on engineering examples of circular, elliptical and horseshoe tunnels. Finally, the significant effects of key parameters, such as the surrounding rock–lining interface conditions, the lining cross-sectional geometry, and the relative stiffness of the surrounding rock and the lining, on the seismic response of the tunnel were discussed. The results showed that with the increase in the interface flexibility coefficient, the normalized thrust of elliptical and horseshoe linings decreased, the deformation increased, and the moment first increased and then decreased. The influence of cross-sectional shape on the internal force of the lining is complex. The large-span and flat lining of the tunnel had large deformation and surrounding rock stress. The increase in the elastic modulus of the surrounding rock or the decrease in the lining thickness resulted in a decrease in the lining thrust and moment and an increase in the deformation. The reasonable combination of rock stiffness and lining thickness can be used to achieve the optimal balance between the internal forces and deformation of the flexible lining in the seismic design of the tunnel. The proposed solution can be easily and quickly applied to the preliminary analysis and prediction of the seismic internal force and deformation of deep tunnels, providing a theoretical basis and scientific reference for engineering seismic design and evaluation. [ABSTRACT FROM AUTHOR]