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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]

Using Hartogs' fundamental theorem for analytic functions in several complex variables, we establish a multiple q-exponential differential operational identity for the analytic functions in several variables, which can be regarded as a multiple q-translation formula. This multiple q-translation formula is a fundamental result and play a pivotal role in q-mathematics. Using this q-translation formula, we can easily recover many classical conclusions in q-mathematics and derive some new q-formulas. Our work reveals some profound connections between the theory of complex functions in several variables and q-mathematics. [ABSTRACT FROM AUTHOR]

This study, with the engineering background of the design of a stope involving a sublevel mining method in a certain underground metal mine, explored the application of stress-solving methods based on the complex variable function theory in actual engineering. Three mathematical calculation models based on the functions of a complex variable were established. Through triangle interpolation, mapping functions of a plane with a roadway section and a plane with the stope section were determined. An improved Schwarz alternating method was adopted to study the stability of the roadway and the influence of an adjacent roadway from the perspective of the stress field. In addition, in light of the distribution characteristics of a gangue in the stope, the design parameters of a pillar were optimized, with the pillar's optimal dimensions determined. The results showed that when the magnitudes of two far-field principal stresses in the rock mass are relatively close, the distribution of the surrounding rock stress around the roadway is more uniform, and tensile stress is less likely to occur. The excavation of a neighboring roadway exacerbates to some extent the side stress of the other roadway, especially the compressive stress concentration on the side closer to the neighboring roadway. However, when the distance between the two roadways is significantly larger than the roadway size, this effect is not pronounced. In the engineering case studied in this research, the thickness of the pillar is approximately linearly positively correlated with the safety factor of the pillar approximately linearly negatively correlated with the recovery rate. Overall, this research explored the application of the complex variable function theory in an underground mine design, demonstrating its accuracy and practicality. [ABSTRACT FROM AUTHOR]

Compressed air energy storage (CAES) is attracting attention as one of large‐scale renewable energy storage systems. Its gas storage chamber is one of key components for its success. A successful utilization of an abandoned coalmine roadway depends on the stability of the gas storage chamber. The chamber is a multilayer structure and the redistribution of the stress and displacement in each layer is critical to the chamber stability. So far, this redistribution mechanism under any lateral pressure coefficient and internal air pressure has been unclear and thus a quick and easy evaluation on the CAES chamber stability becomes difficult. In this study, the redistributions of stress and displacement in each layer are analytically solved based on complex variable function theory. First, the stress and displacement in three CAES multilayer structures are obtained under any lateral pressure coefficient and internal air pressure. Then, a comprehensive parameter b1 is obtained to describe the redistribution of stress and displacement in rock mass, lining layer, and grout layer. Its linkage with lateral pressure coefficient, internal air pressure, and material properties is analytically expressed. Thirdly, an analytical expression is obtained for the influence range of internal air pressure on chamber stress. Finally, the role and selection of lining and grouting layers are explored at different lateral pressure coefficient and internal air pressure. It is found that the CAES chamber stability can be effectively and quickly evaluated by these analytical solutions and comprehensive parameters and enhanced by a material with low bulk modulus but high shear modulus. [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]

We have shown the possibility of mathematical analysis of complex biochemical reactions without simplifying assumptions regarding their parameters by investigating the mechanism of adenosine triphosphate (ATP) hydrolysis by the "basal" Mg2+-ATPase in which ATP (substrate), Mg2+ (essential activator) and MgATP (true substrate) compete for binding with the enzyme catalytic site. For this mechanism, we proved, using the quasi-steady state principle by Bodenstein, the existence and uniqueness of a quasi-steady state at any fixed parameters (initial reactant concentrations, positive reaction rate constants). On this basis, the definition of the initial reaction rate v as a function of the initial concentrations of ATP (x1), Mg2+ (x2), ATPase (x3) is given and the dependencies v vs. xi are investigated. We proved that at fixed initial concentrations of any two reactants, the kinetic curve v vs. xi has a unique maximum point. In different regions of the kinetic curve located before and after the maximum point, the initial rate may vary in different ways: in one region it can change more slowly than the reactant concentration, as in the case of hyperbolic dependencies, and in the other it can change much faster than the reactant concentration, as in the case of sigmoid dependencies, which is typical for regulatory enzymes. This initial rate behaviour causes the existence of four different types of bell-shaped kinetic curves. To quantify the degree of sigmoidity of kinetics, we used derivatives ∂ ln v ∂ ln x i which allowed us to estimate the maximal velocity of the initial rate change. [ABSTRACT FROM AUTHOR]

Molecular interactions are key to all cellular processes, and particularly interesting to investigate in the context of gene regulation. Protein–protein interactions are challenging to examine in vivo as they are dynamic, and require spatially and temporally resolved studies to interrogate them. Foerster Resonance Energy Transfer (FRET) is a highly sensitive imaging method, which can interrogate molecular interactions. FRET can be detected by Fluorescence Lifetime Imaging Microscopy (FLIM‐FRET), which is more robust to concentration variations and photobleaching than intensity‐based FRET but typically needs long acquisition times to achieve high photon counts. New variants of non‐fitting lifetime‐based FRET perform well in samples with lower signal and require less intensive instrument calibration and analysis, making these methods ideal for probing protein–protein interactions in more complex live 3D samples. Here we show that a non‐fitting FLIM‐FRET variant, based on the Average Arrival Time of photons per pixel (AAT− FRET), is a sensitive and simple way to detect and measure protein–protein interactions in live early stage zebrafish embryos. LAY DESCRIPTION: All biological systems are made up, in essence, of molecules interacting with another. These can be proteins interacting with proteins, DNA or RNA interacting with each other or with proteins, lipids, sugars or other small molecules. While there are many well described methods for studying intermolecular interactions in test tubes and in cells, it is more challenging to apply these to model organisms such as zebrafish, Xenopus and mice. This is because the samples are thicker, requiring optics with a long depth of field and sensitive detectors since signals from fluorescent proteins can be scattered inside the tissues of these systems. FRET is the non‐radiative energy transfer from an excited donor fluorophore to an acceptor when donor and acceptor are within 1–10 nm of one another – the distance expected between interacting proteins. FRET results in decreased donor fluorescence intensity and lifetime (time spent in exited state). Potential interaction partners are therefore tagged with donor and acceptor fluorophores to measure this interaction by FRET. The extent of interaction (how many donor molecules interact, how strongly) and the distance between interaction partners affect the efficiency of FRET (E = 1 – IDA/ID). We chose FRET as a useful fluorescence microscopy method to study interactions in early zebrafish embryos. This is because it can be assessed using different techniques and does not necessarily require complex mathematical analysis, such as regression and curve fitting. Measuring FRET by Fluorescence Lifetime Imaging Microscopy (FRET‐FLIM) is more robust to photobleaching and changes in relative concentrations than intensity‐based measurements. FLIM‐FRET is a type of FRET where the donor lifetime is measured in presence and absence of the acceptor. Traditional methods of assessing FLIM rely on accurate measurements with a high signal‐to‐noise ratio (SNR), and intensive analysis. Experiments in live 3D samples have been, up until now, difficult as signal is lower and acquisition times are limited because some biological processes happen more quickly than the time needed to obtain FLIM data. Here we applied a newer method of FLIM‐FRET termed Average Arrival Time FRET. It does not require fitting, is comparatively fast, gentle and sensitive so providing accessible, quantitative lifetime‐based information for those interested in using FRET methods to study molecular interactions in real time and 3D in model organisms such as zebrafish. [ABSTRACT FROM AUTHOR]

On the basis of the theory of functions of complex variable and the method of jump functions, we propose a procedure of taking into account the additional influence of surface stresses in the problem of thin interface inclusion in the bimaterial. In this problem, we take into account the possibility of imperfect contact between the inclusion and the matrix and, in particular, the possibility of contact with surface tension. This significantly extends the field of applicability of the results of simulation within the framework of the concept of representative volume element in micro- and macromechanics. We propose a generalized model of thin inclusion with arbitrary mechanical properties. The analysis of test problems reveals high accuracy and efficiency of the proposed approach. We present the results of numerical analyses of the stress fields in the case of interaction of the inclusion with concentrated forces and screw dislocations. [ABSTRACT FROM AUTHOR]

Nanocomposites are heterogeneous media with two or more micro‐structural levels. For instance, a nano‐level is characterized by isolated nano‐inclusions, and a micro‐level is represented by the clusters resulting from aggregation processes. Based on the reiterated homogenization method, we present a procedure to study the influence of this aggregation process and interfacial thermal resistance on the effective thermal conductivity for 2‐D square arrays of circular cylinders. First, an effective intermediate thermal property is obtained by taking into account only the influence of the individual nano‐inclusions in the matrix. Second, the final effective thermal coefficient (k^RH$$ {\hat{k}}_{RH} $$) is calculated considering the clusters immersed in the intermediate effective medium derived in the first step. The conductivity gain (kgain$$ {k}_{gain} $$) is defined as the quotient (k^RH/k^CH$$ {\hat{k}}_{RH}/{\hat{k}}_{CH} $$) where k^CH$$ {\hat{k}}_{CH} $$ is the effective thermal coefficient computed considering only one microstructural level with the same volumetric fraction of inclusions. We apply the theory of complex variable functions deriving in an infinite system of equations solvable by truncation method. The analytical formulas of the effective coefficient used in the calculations generalize other well‐known formulas reported in the literature. We also provide formulas for several truncation orders. The main novel contribution is in the reiterative application of the obtained formulas to illustrate the gain effect in nanocomposites, expressed as a function of the Biot number, thermal conductivities, volumetric fibers fraction, and an aggregation parameter. Furthermore, this result can be used to assess numerical computations and for nano‐reinforced fibers and nanofluids applications. An appendix is included showing similarities and differences with a three‐phase model. [ABSTRACT FROM AUTHOR]

As of 2023, substantiation of the criteria for optimal load balancing of territorial energy islands in the face of uncontrolled power shortages due to unpredictable failure (destruction as a result of military bombardment) of the upper (trunk) level energy infrastructure is relevant. The research aims to substantiate approaches to ensuring the controlled operation of regional power systems under conditions of power shortages. The study applied the theory and methods of mathematical analysis of complex multicomponent systems in the form of mixed Boolean linear programming. A Mathematical Programming Language and modelling methods of the NEOS server based on the Gurobi solver were used to describe the modes of operation of power grids. A proportional power distribution method between load nodes of the post-emergency network configuration was used to determine the direction of electricity transit with the least losses. An algorithm and a program for solving the problem of addressing flows and power losses in multi-node regional power systems are proposed. The optimisation problem is formulated in the form of a mixed Boolean linear programming model with the criterion of minimising the power momentum, considering balance constraints and upper limits on the power between supply and load nodes. The developed transport matrix made it possible to find the optimal power distribution for emergency and post-emergency modes according to the criterion of minimum network losses. Algorithms and scenarios for the response of dispatching services were formed, considering the capacity of power grids and determining temporary power supply schemes, the configuration of which will ensure the "survivability" of energy islands. The levels of efficiency of the Boolean linear programming model associated with the connectivity of the cycles of the transport problem and the order of traversal of its vertices for test examples depending on the constraints imposed on the components of the network structure are established. The process of tracking electricity flows will allow for establishing routes connecting specific electricity supply nodes with load nodes and determining their shares in covering the energy island's demand under conditions of power shortage. [ABSTRACT FROM AUTHOR]

A vector generalization of the main concepts in the theory of functions of a complex variable— the concepts of the modulus and the argument of the complex number—is proposed. The authors introduce a certain generalization of the concept of holomorphic functions and mappings in the case of continuum complex spaces. [ABSTRACT FROM AUTHOR]

Optical Coherence Tomography Angiography (OCTA) is a relatively new imaging technique in ophthalmology for the visualization of the retinal microcirculation and other tissues of the human eye. This review paper aims to describe the basic definitions and principles of OCT and OCTA in the most straightforward possible language without complex mathematical and engineering analysis. This is done to help health professionals of various disciplines improve their understanding of OCTA and design further clinical research more efficiently. First, the basic technical principles of OCT and OCTA and related terminology are described. Then, a list of OCTA advantages and disadvantages, with a special reference to blood flow quantification limitations. Finally, an updated list of the basic hardware and software specifications of some of the commercially available OCTA devices is presented. [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]

Molecular dynamics simulations of reactions in Al/Ni layered systems have been carried out under isothermal conditions for a wide range of temperatures and several system sizes. An embedded atom method potential, known to reasonably reproduce the phase behavior of Al/Ni, was employed. Simulations revealed reaction mechanisms involving an initial fast process and much slower more complex longer-time reactions. The initial reaction process consists of diffusion of Ni from the pure solid Ni phase into the molten Al phase, resulting in the formation of an Al-rich Al/Ni liquid. The initial reaction ends when the Al/Ni liquid becomes saturated in Ni and solid Al/Ni phases begin to form at the interfaces between the pure solid Ni phase and the Al/Ni liquid. The growth of these solid phases is intrinsically slow compared to the formation of the liquid and is further slowed by the need for Ni to diffuse through the growing interfacial Al/Ni solid phases. Analysis of the initial Al/Ni liquid forming process indicates Fickian behavior with the Ni diffusion coefficient exhibiting Arrhenius temperature dependence. The longer-time slow reaction process(es) resulting in the growth of Al/Ni solid phases do not lend themselves to detailed numerical analysis because of the complex dependence of the Ni transport on the detailed nature of the interfacial layers. [ABSTRACT FROM AUTHOR]

One of the urgent tasks in the design of hybrid integrated circuits (HICs) is the construction of adapter-attenuators of film absorbing elements that provide a wide range of attenuations with the given values of input and output resistances. Known versions of adapter-attenuators based on homogeneous and piecewise-homogeneous resistive films provide a resistance transformation ratio of not more than 3 and 10–12, respectively. The paper proposes promising topologies of adapter-attenuators for HICs with an almost optimal profile of the input and output contacts. It is shown that these topologies make it possible not only to obtain a wide range of transformation ratios (more than 100) but also to reduce the maximum values of the potential gradient and power density by a factor of 10 to 30. When calculating the rectangular topology, the apparatus of the theory of functions of a complex variable is used. The optimized topology of adapter-attenuators for HICs is modeled by the finite element method implemented in the Elcut software package. The calculated ratios and graphs that show the relationship between attenuation, the transformation ratio, gain in the potential gradient, and power density depending on the ratio of the dimensions of the film element and the specific resistances of the resistive films used are presented. The features of fitting adapter-attenuators are considered. The results obtained are important for the operation of the film element of adapter-attenuators for well logging in the pulsed mode. [ABSTRACT FROM AUTHOR]

This paper presents an accurate and quick diagnostic scheme for the open switch faults in a cascaded H-bridge multilevel inverter. The fault classification is based on variations in normalised half-cycle means of the bridge voltages under fault. The proposed method can precisely locate the fault within one cycle of the output voltage after the occurrence of fault without any domain transformations or complex mathematical analysis. This generalised diagnostic approach can distinguish the fault positions in the inverter irrespective of the number of levels at the output voltage for various modulation indices. Adaptability of the proposed scheme with different PWM schemes for a three-phase cascaded multilevel inverter under switch fault is substantiated using simulation and experimentation. The proposed technique is validated for different load conditions and under input voltage variations. [ABSTRACT FROM AUTHOR]

Exponential smoothing has been one of the most popular forecasting methods used to support various decisions in organizations, in activities such as inventory management, scheduling, revenue management, and other areas. Although its relative simplicity and transparency have made it very attractive for research and practice, identifying the underlying trend remains challenging with significant impact on the resulting accuracy. This has resulted in the development of various modifications of trend models, introducing a model selection problem. With the aim of addressing this problem, we propose the complex exponential smoothing (CES), based on the theory of functions of complex variables. The basic CES approach involves only two parameters and does not require a model selection procedure. Despite these simplifications, CES proves to be competitive with, or even superior to existing methods. We show that CES has several advantages over conventional exponential smoothing models: it can model and forecast both stationary and non‐stationary processes, and CES can capture both level and trend cases, as defined in the conventional exponential smoothing classification. CES is evaluated on several forecasting competition datasets, demonstrating better performance than established benchmarks. We conclude that CES has desirable features for time series modeling and opens new promising avenues for research. [ABSTRACT FROM AUTHOR]

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A common type problem of optimization is to find simultaneously n$$ n $$ parameters that globally minimize an objective function of n$$ n $$ variables. Such problems are seen in signal and image processing and in various applications of mathematical analysis of several complex variables and Clifford algebras. Objective functions are usually assumed to be Lipschitzian with maybe unknown Lipschitz constants. A number of methods have been established to discard the sets called "bad sets" in a partition that is impossible to contain any optimal point, as well as to treat the unknown Lipschitz bound problem along with the algorithm. In the present paper, a simple criterion of eliminating bad sets is proposed for the first time. The elimination method leads to a concise and rigorous proof of convergence. The algorithm, on the range space side, converges to the global minimum with an exponential rate, while on the domain space side, converges with equal accuracy to the set of all the global minimizers. To treat the unknown Lipschitz constant dilemma, we propose a practical pseudo‐Lipshitz bound process. The methodology is of fundamental nature with straightforward mathematical formulation applicable to multivariate objective functions defined on any compactly connected manifolds in higher dimensions. The method is tested against an extensive number of benchmark functions in the literature. The experimental results exhibit considerable effectiveness and applicability of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the bending problem for an infinite plate weakened by two square-shaped holes. The contours of the holes have the grooves at the vertices of the square along the smooth contours and are the sought part of the plate boundary. Applying the theory of functions of a complex variable and the conformal mapping theory, this problem is reduced to a boundary problem of the analytic function theory. A plate deflection and an unknown part of the boundary are found, assuming that the tangential normal moment on it is a constant value. [ABSTRACT FROM AUTHOR]

In this papers we investigate the Hyers-Ulam stability of the following 2-dimensional Pexider quadratic functional equation f(x + y, z + w) + f(x - y, z - w) = 2g(x, z) + 2g(y, w) in non-Archimedean normed spaces. [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]

We review the main contributions of Professor Gabriela Kohr in her studies in the Geometric function theory in several complex variables and complex Banach spaces with special emphasis on the theory of Loewner chains and the Loewner differential equation. [ABSTRACT FROM AUTHOR]

A common fraud in the sweet almond industry is the presence of bitter almonds in commercial batches. The presence of bitter almonds not only causes unpleasant flavours but also problems in the commercialisation and toxicity for consumers. Hyperspectral Imaging (HSI) has been proved to be suitable for the rapid and non-destructive quality evaluation in foods as it integrates the spectral and spatial dimensions. Thus, we aimed to study the feasibility of using an HSI system to identify single bitter almond kernels in commercial sweet almond batches. For this purpose, sweet and bitter almond batches, as well as different mixtures, were analysed in bulk using an HSI system which works in the spectral range 946.6–1648.0 nm. Qualitative models were developed using Partial Least Squares-Discriminant Analysis (PLS-DA) to differentiate between sweet and bitter almonds, obtaining a classification success of over the 99%. Furthermore, data reduction, as a function of the most relevant wavelengths (VIP scores), was applied to evaluate its performance. Then, the pixel-by-pixel validation of the mixtures was carried out, identifying correctly between 61–85% of the adulterations, depending on the group of mixtures and the cultivar analysed. The results confirm that HSI, without VIP scores data reduction, can be considered a promising approach for classifying the bitterness of almonds analysed in bulk, enabling identifying individual bitter almonds inside sweet almond batches. However, a more complex mathematical analysis is necessary before its implementation in the processing lines. [ABSTRACT FROM AUTHOR]

The stressed environment of the inclined coal seam roadway is complex and changeable, and the damage degree of surrounding rock increases, threatening the safe mining of coal mines. In order to take targeted support measures to control the stability of roadway surrounding rock, it is very important to study the stress and deformation characteristics of roadway surrounding rock in inclined coal seam. Therefore, this paper analyzes the deformation and failure law of inclined coal seam roadway according to the theory of complex variable function. It optimizes the solution process and accuracy of the mapping function coefficient and deduces the analytical solution of surrounding rock stress and deformation inclined coal seam roadway. The deformation and failure mechanism of surrounding rock in inclined coal seam roadway is revealed theoretically, and further use numerical simulation and physical simulation tests for supplementary analysis and verification. The results show that the stress and deformation of roadway surrounding rock in inclined coal seam show obvious asymmetric distribution characteristics. The stress and deformation of roadway surrounding rock on the right side are greater than on the left side. The two sides of the roadway, the right side of the roof and the roof angle of the right side, are the key positions of roadway stress concentration and deformation. According to the variation law of stress and deformation distribution of roadway surrounding rock, roadway cyclic deformation and failure theory is put forward. The numerical simulation and physical simulation tests show that the deformation and failure law of roadway is consistent with the theoretical analysis results, and there are differences in numerical values. The cyclic deformation and failure mechanism of roadway in inclined coal seam is verified, which can provide theoretical guidance for roadway support design. [ABSTRACT FROM AUTHOR]

The mathematical method which will achieve the most accurate and precise age-at-death estimate from the adult skeleton is often debated. Some research promotes Bayesian analysis, which is widely considered better suited to the data construct of adult age-at-death distributions. Other research indicates that methods with less mathematical complexity produce equally accurate and precise age-at-death estimates. One of the advantages of Bayesian analysis is the ability to systematically combine multiple indicators, which is reported to improve the age-at-death estimate. Few comparisons exist between Bayesian analysis and less complex mathematical models when considering multiple skeletal indicators. This study aims to evaluate the performance of a Bayesian approach compared to a phase-based averaging method and linear regression analysis using multiple skeletal indicators. The three combination methods were constructed from age-at-death data collected from 330 adult skeletons contained in the Raymond A Dart and Pretoria Bone Collections in South Africa. These methods were tested and compared using a hold-out sample of 30 skeletons. As is frequently reported in literature, a balance between accuracy and precision was difficult to obtain from the three selected methods. However, the averaging and regression analysis methods outperformed the Bayesian approach in both accuracy and precision. Nevertheless, each method may be suited to its own unique situation—averaging to inform first impressions, multiple linear regression to achieve statistically defensible accuracies and precisions and Bayesian analysis to allow for cases where category adjustments or missing indicators are necessary. [ABSTRACT FROM AUTHOR]

To better understand the penetration mechanism of the elliptical cross-section projectile (ECSP) into semiinfinite concrete target, penetration experiments using three types of ECSPs with different shape ratios (1, 1.25 and 1.61) and with striking velocities ranged from 550 m/s to 1050 m/s were conducted. Penetration depths, penetration trajectory and mass erosion rates of the projectile were obtained after the experiments. The experiment results show that the penetration performance and ballistic stability of the ECSP are equivalent to those of the circular cross-section projectile (CCSP). Based on the theory of complex variable function and conformal transformation, a semi-analytical model which can calculate the cavity boundary stress distribution of elliptical section cavity controlled by the displacement boundary condition was established and the model was validated by comparing the model degenerate solution with Kirsch problem results. Theoretical calculation results show that the radial stress of elliptical section cavity increases progressively from the minor axis to the major axis. In addition, a formula combining with the semi-analytical theoretical model and the local interaction theory was developed. The predicted penetration depths were compared with 30 groups of experiment data with different projectile parameters and striking velocities and coincide quite well with the corresponding experimental data. Finally, the influence of shape ratio and caliberradius- head (CRH) on the penetration performance of projectile and the application prospect of ECSPs on hypersonic weapon platform were studied. [ABSTRACT FROM AUTHOR]

For all Graph $Re>10^3$, Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ and Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ are approximately equal to Graph $1/2$, whereas, for Graph $Re=10^3$, they have higher values, close to Graph $0.9$, see table 1. At Graph $t\approx 5.9$, that is when the third winding forms in Graph $\mathcal {C}$, Graph $\theta ^{\omega \mathcal {C}} 1$ collapses to Graph $s(0)=0$ with the symmetric singularity Graph $2{\rm \pi} -\theta ^{\omega \mathcal {C}} 1$. In figure 15 we show the paths in the complex plane of Graph $\theta 1^{X \mathcal {C}}$ and Graph $\theta 2^{X \mathcal {C}}$ (Graph $\theta 1^{Y \mathcal {C}},\theta 2^{Y \mathcal {C}}$ have the same positions) for various Graph $Re$. However, after time Graph $t\geqslant 1.3$, the characters Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ and Graph $\mu {\theta ^{\omega \mathcal {C}} 2}$ of Graph $\theta ^{\omega \mathcal {C}} 1$ and Graph $\theta ^{\omega \mathcal {C}} 2$ have been reliably determined. In figure 14( I a i ), we represent the singularities in the complex plane Graph $(\theta,\theta {im})$, for different Graph $Re$, at Graph $t s=1.507$ and at Graph $t {1w}$ the time when the first winding forms in Graph $\mathcal {C}$. [Extracted from the article]

The central topic of the workshop was the notion of logarithmic vector fields along a divisor in a smooth complex analytic or algebraic variety, i.e., the vector fields on the ambient variety tangent to the divisor. Following their introduction by K. Saito for the purpose of studying the universal unfolding of an isolated singularity, this fundamental object has been the focus of studies in a wide range of mathematical fields such as algebra, algebraic geometry, singularity theory, root systems, (geometric) representation theory, combinatorics, (toric) topology, or symplectic geometry. In the last few years the logarithmic vector field approach has seen some unexpected and striking advances and deep applications. The aim of the workshop was to provide reports and to share these various new developments in the field. [ABSTRACT FROM AUTHOR]

The autoregressive model is a tool used in time series analysis to describe and model time series data. Its main structure is a linear equation using the previous values to compute the next time step; i.e., the short time relationship is the core component of the autoregressive model. Therefore, short-term effects can be modeled in an easy way, but the global structure of the model is not obvious. However, this global structure is a crucial aid in the model selection process in data analysis. If the global properties are not reflected in the data, a corresponding model is not compatible. This helpful knowledge avoids unsuccessful modeling attempts. This article analyzes the global structure of the autoregressive model through the derivation of a closed form. In detail, the closed form of an autoregressive model consists of the basis functions of a fundamental system of an ordinary differential equation with constant coefficients; i.e., it consists of a combination of polynomial factors with sinusoidal, cosinusoidal, and exponential functions. This new insight supports the model selection process. [ABSTRACT FROM AUTHOR]

Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to Daftardar-Gejji and Jaffri [1]. The new family gives several iterative schemes as special cases. The convergence analysis of proposed methods is also presented. In order to determine the performance of newly developed methods, numerical as well as graphical analysis of four complex mathematical models from diverse fields of science and engineering are considered. We also consider some complex polynomials to visualize the roots through polynomiography in the context of proposed methods. [ABSTRACT FROM AUTHOR]