Complex Variables Research Articles

ТАБИҒИ ОРТАНЫҢ ҒАЛАМДЫҚ ӨЗГЕРІСТЕРІ ЖАҒДАЙЫНДАҒЫ ФИЗИКАЛЫҚ-ГЕОГРАФИЯЛЫҚ ЗЕРТТЕУЛЕРДІҢ МАҢЫЗДЫЛЫҒЫ

The article reviews complex field studies, which are fundamental research methods in the physical-geographical direction of «Sciences of the Earth and the Environment». Component-by-component field study and description of natural-territorial complexes using the “Key Areas” method along the route, compiling a landscape profile, spatio-temporal analytics on digital platforms Ventusky and EOS, creating a database – are presented based on the results of a comprehensive long study by the authors of the geosystems of the Sharyn River basin located in Almaty areas. Methodological principles and approaches are analyzed in the field period of research and in the period of cameral processing. These questions are a practical confirmation of general theoretical knowledge about the structural organization, development, functional dynamics and variability of natural-territorial complexes. Physical and geographical studies acquire great scientific and practical relevance in the context of the influence of global changes in the natural environment at the regional level. The modern applied value of field studies of natural-territorial complexes, including hard-to-reach geosystems, is analyzed, the effectiveness of which is to study the structure, dynamics and variability in time and space, using the possibilities of digital technologies, ensuring the reliability of the results.

Synergizing Smart Agriculture with Hybrid Deep Learning: Predicting Crop Yields Using IoT

Agriculture can be defined as the systematic and intentional practice of cultivating and managing plants and animals to produce food, fiber, and other agricultural products. Agricultural practices in India hold the second position globally and encompass approximately 61.1% of the total land area in the country. The Indian economy primarily relies on agriculture and agro-industrial products. Various factors, such as soil composition (including elements like Nitrogen, phosphorus, and Potassium), crop rotation practices, soil moisture content, ambient temperatures, precipitation patterns, and other relevant variables, can significantly influence crop productivity. Smart Agriculture (SA) implementation has recently yielded significant practical benefits, establishing it as a highly significant and valuable system. Using environmental information, including wind velocity, temperature, and moisture, in outdoor plantations facilitates farming operations’ strategic management and regulation, enhancing crop yield and quality. Accurately predicting crop yield trends poses a challenge due to the intricate nature of sensing data, characterized by complexity, nonlinearity, and multiple variables. This study proposes a Hybrid Deep Learning model for Predicting Crop Yields (HDL-PCY) using the Internet of Things (IoT). The HDL-PCY system utilizes the Empirical Mode Decomposition (EMD) technique to break down the crop yield information into distinct element groups with varying frequency attributes. Subsequently, a Long Short-Term Memory (LSTM) network is trained for each group to serve as a sub-predictor. Finally, the predictions generated by the LSTM networks are combined to produce the overall prediction result. The obtained results demonstrate that the proposed HDL-PCY can achieve higher levels of accuracy of 97.32%, 98.03%, 98.74%, and 95.92% for precipitation, temperature, pH, and moisture content, respectively, thereby catering to the requirements of SA.

Physics-informed machine learning enabled virtual experimentation for 3D printed thermoplastic.

The performance of 3D printed thermoplastics largely depends on the ink formulation, which is composed of tremendous chemical space as an increased number of monomers, making it very difficult to identify an optimum one with desired properties. To tackle this challenge, we demonstrate a virtual experimentation platform that is enabled by a physics-informed machine learning algorithm. As a case study, the algorithm was trained based on a multilayer perceptron (MLP) model to predict the experimental stress-strain curves of the 3D printed thermoplastics given the ink compositions made of six monomers. To solve the issue of experimental data scarcity, we first reduced the dimensions of the curves to eight principal components (PCs), which serve as the outputs of the model. In addition, we incorporated the physics-informed descriptors into the input dataset. These two strategies afford the model with a prediction accuracy of R2 of 0.97 and an RMSE value of 1.01 for fracture strength, and an R2 of 0.95 and a RMSE of 0.40 for toughness. To perform virtual experimentation, the well-trained model was then utilized to predict 100 000 sets of the PCs from the randomly given 100 000 ink formulations. The PC sets were then converted back to the corresponding stress-strain curves. To validate the prediction results, some of the virtual experiments were performed. The results showed a good match between the predicted and experimental curves. This methodology offers a general and efficient pathway to virtual experimentation for establishing the correlation between the complex input variables and the output performance metrics of new materials.

Inequalities for meromorphic functions with prescribed poles

The extremal problems for functions of complex variables, as well as approaches for obtaining classical inequalities on the base of various methods of the geometric function theory, are known for various norms and for many classes of functions such as rational functions with various constraints and for various domains in the complex plane. It is important to mention that different types of Bernstein-type inequalities appeared in the literature in more generalized forms in which the underlying polynomial was replaced by a more general class of functions. One such generalization is the passage from polynomials to rational functions. In this paper, we prove some inequalities for meromorphic functions with prescribed poles and restricted zeros. These results not only generalize some Bernstein-type inequalities for rational functions, but also improve and generalize some known polynomial inequalities. These inequalities have their own importance in the approximation theory.

Route to chaos and resonant triads interaction in a truncated rotating nonlinear shallow-water model.

The route to chaos and the phase dynamics of the large scales in a rotating shallow-water model have been rigorously examined through the construction of an autonomous five-mode Galerkin truncated system employing complex variables, useful in investigating how large/meso-scales are destabilized and how their dynamics evolves and transits to chaos. This investigation revealed two distinct transitions into chaotic behaviour as the level of energy introduced into the system was incrementally increased. The initial transition manifests through a succession of bifurcations that adhere to the established Feigenbaum sequence. Conversely, the subsequent transition, which emerges at elevated levels of injected energy, is marked by a pronounced shift from quasi-periodic states to chaotic regimes. The genesis of the first chaotic state is predominantly attributed to the preeminence of inertial forces in governing nonlinear interactions. The second chaotic state, however, arises from the augmented significance of free surface elevation in the dynamical process. A novel reformulation of the system, employing phase and amplitude representations for each truncated variable, elucidated that the phase components present a temporal piece-wise locking behaviour by maintaining a constant value for a protracted interval, preceding an abrupt transition characterised by a simple rotation of ±π, even as the amplitudes display chaotic behaviour. It was observed that the duration of phase stability diminishes with an increase in injected energy, culminating in the onset of chaos within the phase components at high energy levels. This phenomenon is attributed to the nonlinear term of the equations, wherein the phase components are introduced through linear combinations of triads encompassing disparate modes. When the locking durations vary across modes, the resultant dynamics is a stochastic interplay of multiple π phase shifts, generating a stochastic dynamic within the coupled phase triads, observable even at minimal energy injections.

An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables

Weak fuzzy complex numbers are defined as , with as an extension of real numbers with . This paper is dedicated to studying weak fuzzy complex linear Diophantine equations in two weak fuzzy complex variables, by transforming the weak fuzzy complex Diophantine equation to a classical equivalent Diophantine system and going directly from the solutions of classical system into the desired equation. Algorithms for generating solutions of the previous equation will be presented in terms of theorems with many related examples that clarify the validity of our work.

Spatial Dynamics of Theatrical Success: Unveiling the Impact of Performance Venues on Audience Turnout in Lagos Stateof Nigeria

In the realm of performing arts, the theatre transcends mere physicality, evolving into a sacred space where shared experiences unfold between thespians and their discerning audience. The sanctity of this exchange is rooted in the symbiotic relationship between the performance and the spectator. This study explores the revered intersection of performance spaces and audience turnout, focusing on Lagos State's vibrant cultural landscape. Despite numerous factors influencing audience attendance, scant scholarly attention has addressed the profound impact of the performance venue itself. This research remedies this gap by applying Alfred Weber's Location Theory and Jerome McCarthy's Four Ps (Product, Place, Promotion, and Price) to unravel the complex variables dictating venue selection. The National Arts Theatre, the MUSON Centre, and Terra Culture serve as distinct performance spaces for our investigation. Through rigorous literature review and astute venue observations, this research unveils nuanced determinants shaping venue selection. It posits that a venue's geographical location and architectural aesthetics are intrinsic determinants in realizing a production's objectives. Findings illuminate a compelling narrative: the performance venue is not a mere backdrop but a protagonist in the drama of audience patronage. Every spatial configuration becomes choreography, orchestrating the audience's journey toward pleasure and satisfaction. The judicious allocation of time, diligence, and resources in this research reflects a commitment to unravelling the intricate tapestry ofspatial dynamics, ensuring each theatrical presentation is a magnum opus of artistic resonance and audience delight. This study is a clarion call for a paradigm shift in the discourse on theatrical success, heralding an era where the venue itself emerges as a pivotal player in the grand symphony of performance art

Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂ n#

Abstract In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in C n {{\mathbb{C}}}^{n} . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483 (2020), 123641, 1–22, DOI: https://doi.org/10.1016/j.jmaa.2019.123641.] and [H. Y. Xu and Y. Y. Jiang, Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, RACSAM 116 (2022), 8, DOI: https://doi.org/10.1007/s13398-021-01154-9.] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.

Prophet와 GRU을 이용하여 단중기 전력소비량 예측

The building energy management system (BEMS), a system designed to efficiently manage energy production and consumption, aims to address the variable nature of power consumption within buildings due to their physical characteristics, necessitating stable power supply. In this context, accurate prediction of building energy consumption becomes crucial for ensuring reliable power delivery. Recent research has explored various approaches, including time series analysis, statistical analysis, and artificial intelligence, to predict power consumption. This paper analyzes the strengths and weaknesses of the Prophet model, choosing to utilize its advantages such as growth, seasonality, and holiday patterns, while also addressing its limitations related to data complexity and external variables like climatic data. To overcome these challenges, the paper proposes an algorithm that combines the Prophet model's strengths with the gated recurrent unit (GRU) to forecast short-term (2 days) and medium-term (7 days, 15 days, 30 days) building energy consumption. Experimental results demonstrate the superior performance of the proposed approach compared to conventional GRU and Prophet models.

Hamilton energy of a complex chaotic system and offset boosting

The complex differential system can be obtained by introducing complex variable in the real differential system. Complex variables can be decomposed into real component and imaginary component, which makes the complex differential systems have more complex dynamic behaviors. Complex chaotic system is used in secure communications to increase the security of cryptographic systems. In this study, we designed a complex differential system by incorporating a complex variable into a 3D differential system. Dynamics of this complex differential system are investigated by applying typical nonlinear analysis tools. Furthermore, Hamilton energy function for complex differential system is obtained based on Helmholtz’s theorem. The values of Hamilton energy with different oscillations of complex differential system are calculated. In addition, offset boosting control for the complex chaotic signal is realized by adding a constant to variable of complex system. Simulation shows that the position of the chaotic attractor in phase space can be flexibly shifted by applying the offset parameter.

Recognition of motor imagery electroencephalogram based on flicker noise spectroscopy and weighted filter bank common spatial pattern

Due to the high complexity and subject variability of motor imagery electroencephalogram, its decoding is limited by the inadequate accuracy of traditional recognition models. To resolve this problem, a recognition model for motor imagery electroencephalogram based on flicker noise spectrum (FNS) and weighted filter bank common spatial pattern ( wFBCSP) was proposed. First, the FNS method was used to analyze the motor imagery electroencephalogram. Using the second derivative moment as structure function, the ensued precursor time series were generated by using a sliding window strategy, so that hidden dynamic information of transition phase could be captured. Then, based on the characteristic of signal frequency band, the feature of the transition phase precursor time series and reaction phase series were extracted by wFBCSP, generating features representing relevant transition and reaction phase. To make the selected features adapt to subject variability and realize better generalization, algorithm of minimum redundancy maximum relevance was further used to select features. Finally, support vector machine as the classifier was used for the classification. In the motor imagery electroencephalogram recognition, the method proposed in this study yielded an average accuracy of 86.34%, which is higher than the comparison methods. Thus, our proposed method provides a new idea for decoding motor imagery electroencephalogram.

Design and Implementation of K-Band Electromagnetic Wave Rain Gauge System

In order to prevent and manage damage caused by localized torrential downpours, the quantitative observation of rainfall is crucial. Considering the spatial complexity and vertical variability of rainfall, it is important to obtain low-altitude, high-resolution radar observations to reduce uncertainty in radar rainfall estimates. In this paper, we present an electromagnetic wave rainfall gauge system (EWRG) that detects rainfall within the observation area and estimates the areal rainfall using electromagnetic waves. The EWRG system was developed based on a subminiature size antenna, a K-band dual-polarization transceiver, and advanced high-resolution, high-speed signal processing technology. The system design and signal processing techniques are described in detail. The EWRG has the advantage of overcoming the limitations of conventional cylindrical ground rain gauges, such as the contamination and spatial inaccuracy of rain gauges, which cause uncertainty in quantitative precipitation measurement.

A Data-Driven Artificial Neural Network Approach to Software Project Risk Assessment

In the realm of software project management, predicting and mitigating risks are pivotal for successful project execution. Traditional risk assessment methods have limitations in handling complex and dynamic software projects. This study presents a novel approach that leverages artificial neural networks (ANNs) to enhance risk prediction accuracy. We utilize historical project data, encompassing project complexity, financial factors, performance metrics, schedule adherence, and user-related variables, to train the ANN model. Our approach involves optimizing the ANN architecture, with various configurations tested to identify the most effective setup. We compare the performance of mean squared error (MSE) and mean absolute error (MAE) as error functions and find that MAE yields superior results. Furthermore, we demonstrate the effectiveness of our model through comprehensive risk assessment. We predict both the overall project risk and individual risk factors, providing project managers with a valuable tool for risk mitigation. Validation results confirm the robustness of our approach when applied to previously unseen data. The achieved accuracy of 97.12% (or 99.12% with uncertainty consideration) underscores the potential of ANNs in risk management. This research contributes to the software project management field by offering an innovative and highly accurate risk assessment model. It empowers project managers to make informed decisions and proactively address potential risks, ultimately enhancing project success.

Coalescence of Al2O3/Al, MgO/Mg, and MgO/Al two nanoparticles during combustion

Metal and metal oxide aggregates are easily sintered by migration–diffusion in combustion, and the aggregates hold a complex morphological and structural variability that increases with temperature. The underlying thermomechanical response remains a challenging mystery for active nanoparticles. Here, a computational strategy based on ReaxFF molecular dynamics were performed to shed much light on the coalescence behavior of Al2O3/Al, MgO/Mg, and MgO/Al nanoparticles – a doublet of two spheres. The complex sintering phenomenon was further quantitatively described in terms of coordination number, charge distribution, density distribution, atomic displacement, radius ratio, shrinkage, and sintering time, etc. Results showed that the Al2O3/Al and MgO/Mg two nanoparticles undergo collision and coalescence, and the two were connected through the neck. MgO/Al aggregates are unstable at higher temperatures (T > 1200 K) and segregate at junctions, followed by re-coalescence in the simulation box. A stable neck structure can be formed when enough O atoms are dissolved in MgO nanoparticles or at a lower temperature. The diffusion of Mg, Al, and O atoms in aggregates is driven by concentration gradients and self-generated electromotive forces. The Al2O3 passivation layer forms and hinders the diffusion of O atoms, and the oxygen-rich regions are distributed in the neck (Al2O3/Al) or the contact surface on the side of the Al nanoparticles (MgO1.5/Al) during sintering. In MgO/Al aggregates, Mg atoms tend to wrap Al nanoparticles by surface diffusion.

On the problem of a Gurtin–Murdoch cylindrical material surface embedded in an infinite matrix

The problem of an infinite isotropic elastic matrix subjected to uniform far-field load and containing a Gurtin–Murdoch material surface of cylindrical shape is considered in plane strain setting. The governing equations and the boundary conditions for the problem, reduced to that of an infinite plane containing a material curve along a circular arc, are reviewed. The displacements inside the matrix are sought in the complex variables form of a single layer elastic potential whose density represents the jump in complex tractions across the curve. Exact complex integral representations for the elastic fields everywhere in the material are provided and the problem is further reduced to the system of real variables hypersingular boundary integral equations in terms of the strain and rotation components associated with the curve. The components are then approximated by the series of trigonometric functions that are multiplied by the square root weight functions to allow for automatic incorporation of the tip conditions. The unknown coefficients in the series are found from the system of linear algebraic equations that is solved using standard collocation method. The numerical examples are presented to illustrate the influence of dimensionless parameters with the main focus on the study of curvature-induced effects.

Application of Cauchy’s Residue Theorem in Several Improper Integrals

Calculating definite integrals in complex functions requires the Cauchy's residue theorem, which is a key concept in the complex variables. It is based on several ideas, including the isolated singular points theory, the Laurent theorem, and the Cauchy integral theorem. Nevertheless, it is highly challenging to calculate closed curves using the conventional integrals method since numerous formulas must be substituted. The singular points must all be isolated in the case of a holomorphic function that belongs to an enclosing contour and is positively oriented, at which time the contour integral can be used to resolve the issue. Additionally, the problem can be solved by using visual aids to help people understand them. By doing so, the notion of solving the problem will be made clearer and some calculating steps will be cut short. This study exhibits the residue theorem's potent efficiency in computing improper integrals and other difficult problems.

Applications of Cauchy-Riemann Equations on Several Examples

Cauchy-Riemann equations is always a heated topic in mathematics. It is widely used to solve both mathematic problems and daily issues. In this paper, basic knowledge which is needed for the study of Cauchy-Riemann equations has been explained carefully. This includes the understanding of analytic function, derivatives, and partial derivatives, as well as the method to derive the final equations. The method mainly used to obtain the equations in the paper is to calculate the limits of a function with complex variables along two axes. The application that Cauchy-Riemann equations are most frequently applied to is to find derivatives of complex functions, and some relevant examples are included. In addition, there is an extension of the basic use of Cauchy-Riemann equations in functions that are in Cartesian forms. This study can help to inspire the green hands in the field of complex analysis and let them have a good command of knowledge of the most superficial level of this field.

The east of the Neanderthal universe: a comparative analysis of Sukhaya Mechetka and Altai Micoquian complexes

Late European Neanderthals, associated with the Micoquian techno-complex, spread over vast area from Western Europe to the Altai. There were no sites found in the territories to the east of the Volga region. The key site of the Eastern Micoquian, Sukhaya Mechetka, which was discovered in 1951 in the Volgograd region, was for a long time the eastern outpost of Neanderthals in Eurasia. In the last five years, the results of paleogenetic analysis have confirmed the archaeological hypothesis of the migration of late European Neanderthals, the producers of the Micoquian, from Central and Eastern Europe to Altai. Until then, the genesis of Altai industries was associated with a wide range of European and Near Eastern techno-complexes, and anthropological remains were interpreted more in a Near Eastern context. In this regard, the industry of the Sukhaya Mechetka site, located on the route of the supposed migration of the Micoquians, acquires additional relevance in the research of the variability of the easternmost complexes of this cultural tradition. The attributive and technological analysis of tool kit from Sukhaya Mechetka was carried out and, using mathematical statistics methods, their results were compared with the available data on the Altai sites: Chagyrskaya and Okladnikov Caves. The new data were supplemented by the published materials from the Sukhaya Mechetka site. As a result, high level of technical-typological similarity of the compared industries in the context of primary flaking, bifacial tool production, tool typology and morphology was revealed. The structure of the Sukhaya Mechetka tool kit is closest to the Chagirskaya Сave, which is characterized by a large number of simple side-scrapers. At the same time, the site lacks of high-quality raw materials used to make bifacial items and intensively worked unifacial tools. In the Okladnikov Cave complexes this deficit is less. In composition and morphology of unifacial and bifacial tools, Sukhaya Mechetka is closest to the assemblages of the Antonovka I site and Chagyrkaya Cave. They share similarity with Okladnikov Cave in terms of a significant number of leaf-shaped and crescent-shaped tools. Some new characteristics were additionally determined for the assemblage of Sukhaya Mechetka. It was established that the primary decortications of cores was carried out outside the site. We also reconstructed the stages of production, rejuvenating and reshaping of bifaces on the site.

Mineralogical fingerprint and human health risk from potentially toxic elements of Fe mining tailings from the Fundão dam

In 2015, >50 million cubic meters of Fe mining tailings were released into the Doce River basin from the Fundão dam, raising the question of its consequences on the affected ecosystems. This study aimed to establish a mineralogical-(geo)chemical association of potentially toxic elements (PTEs) from Fe mining tailings from the Fundão dam, collected seven days after the failure, through a multidisciplinary approach combining assessment of the risk to human health, environmental geochemistry, and mineralogy. Thus, eleven tailings samples were collected with the support of the Brazilian Military Police Fire Department. Granulometry, magnetic measurements, optical microscopy, X-ray diffraction, Fourier transform infrared spectroscopy, and sequential chemical extraction of PTEs analyses were performed. Contamination indexes, assessment of risk to human health, and Pearson correlation were calculated using the results of sequential chemical extraction of PTEs. The predominance of goethite in Fe oxyhydroxide concentrates from the mud indicates that the major source of hematite may not be from tailings, but from pre-existing soils and sediments, and/or preferential dissolution of hematite in deep flooded zones of the tailings column of the Fundão dam. Moreover, the high correlation of most carcinogenic PTEs with their crystallographic variables indicates that goethite is the primary source of contaminants. Goethites from Fe mining tailings showed high specific surface area and Al-substitution, and due to their greater stability and reactivity, the impacts on PTE sorption phenomena and bioavailability may be maintained for long periods. However, their lower dissolution rate, and the consequent release of heavy metals would promote greater resilience for affected ecosystems, preventing significant PTE inputs under periodic reduction conditions. More specific studies, involving the crystallographic characteristics of Fe oxyhydroxides should be developed since they may provide another critical component of this set of complex and dynamic variables that interfere with the bioavailability of metals in ecosystems.

УМОВИ ВИКОРИСТАННЯ КОНФОРМНИХ ВІДОБРАЖЕНЬ ДЛЯ ВИВЧЕННЯ ФРАКТАЛЬНОГО СТИСНЕННЯ ІНФОРМАЦІЇ

To describe the properties of self-similarity and invariance observed in various physical situations, the theory of fractals and multifractals is actively used in modern science. We consider a conformal mapping of the first kind, which is given by the entire linear function w = az + b, where w, z are complex variables, a, b are complex constants, a ≠ 0 . With its help, affine transformations are performed to construct the Sierpinski triangle and the Koch curve by specifying the functions w3(z) and finding the coefficients Re аі, Im аі, Re bi, Im bi, і = 1,2,3 or і = 1,2,3,4. These coefficients encode the image of the object and it can be unambiguously reconstructed by them. It is determined that the method in which self-similar regions in an object are detected and conformal mapping coefficients are found for them works under the condition that each such mapping is compressive. Only then will Banach’s fixed point theorem ensure image collection during decompression. This method of compressing graphic information is called fractal.