We study the complex Ginzburg-Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between the nonlinear Schrödinger equation and dissipative parabolic dynamics through a complex time-derivative prefactor, capturing the interplay between dispersion and dissipation. As a continuation of our previous study on the existence and uniqueness of solutions, we prove here some strong stabilization properties. In particular, we show the finite time extinction of solutions induced by the nonlinear saturation mechanism, which, sometimes, can be understood as a bang-bang control. The analysis relies on refined energy methods. Our results provide a rigorous justification of nonlinear dissipation as an effective stabilization mechanism for this class of complex equations where the maximum principle fails.
Guillermo José Barroso García, José Pedro Monteagudo Yanes, Luis Angel Iturralde Carrera
et al.
This study evaluates the energy performance of a BOGE C 22-2 oil-injected rotary screw compressor under real industrial conditions. Using direct measurements with a power quality analyzer and thermodynamic modeling, key performance indicators such as compression work, mass flow rate, compressor efficiency, and motor efficiency were determined. The results revealed actual efficiencies of 27–48%, significantly lower than the expected 60–70% for this type of equipment, mainly due to partial-load operation and low airflow demand. A low power factor of approximately 0.72 was also observed, caused by a high share of reactive power consumption. To address these inefficiencies, the study recommends the installation of an automatic capacitor bank to improve power quality and the integration of a secondary variable speed compressor to enhance performance under low-demand conditions. These findings underscore the importance of assessing compressor behavior in real-world environments and implementing techno-economic strategies to increase energy efficiency and reduce industrial electricity consumption.
Richard Lane, Hannah State-Davey, Claire Taylor
et al.
Behavioural analytics provides insights into individual and crowd behaviour, enabling analysis of what previously happened and predictions for how people may be likely to act in the future. In defence and security, this analysis allows organisations to achieve tactical and strategic advantage through influence campaigns, a key counterpart to physical activities. Before action can be taken, online and real-world behaviour must be analysed to determine the level of threat. Huge data volumes mean that automated processes are required to attain an accurate understanding of risk. We describe the mathematical basis of technologies to analyse quotes in multiple languages. These include a Bayesian network to understand behavioural factors, state estimation algorithms for time series analysis, and machine learning algorithms for classification. We present results from studies of quotes in English, French, and Arabic, from anti-violence campaigners, politicians, extremists, and terrorists. The algorithms correctly identify extreme statements; and analysis at individual, group, and population levels detects both trends over time and sharp changes attributed to major geopolitical events. Group analysis shows that additional population characteristics can be determined, such as polarisation over particular issues and large-scale shifts in attitude. Finally, MP voting behaviour and statements from publicly-available records are analysed to determine the level of correlation between what people say and what they do.
AmirHossein Ghaemi, Abbas Ebrahimi, Majid Hajipour
et al.
This study investigates the effectiveness of Model Predictive Control (MPC) and Reinforcement Learning (RL) for active flow control over a NACA 4412 airfoil near static stall at Reynolds number 4*10^5. By systematically evaluating these strategies, the research addresses a critical gap in optimizing excitation frequency and improving response time in flow control. The work contributes to understanding RL adaptability and performance versus MPC in aerodynamic flow separation control. Numerical simulations of the Reynolds Averaged Navier-Stokes equations with the Scale-Adaptive Simulation turbulence model are used. Dielectric Barrier Discharge plasma actuators in dual-point excitation mode control flow separation. The study evaluates adaptive MPC, temporal difference RL (TDRL), and deep Q-learning (DQL) for optimizing excitation frequency and expediting stabilization. An integrated signal processing DQL approach is also examined. Adaptive MPC achieved Cl = 1.60 at 110 Hz but struggled near physical limits. RL optimized excitation frequencies, reaching Cl = 1.62 in under 2.5 s at 100 or 200 Hz. The study presents a novel RL - MPC comparison for active flow control with DBD actuators, contrasting with prior work focusing on MPC or RL alone. Using an online learning framework, RL methods dynamically adapt to real-time conditions. Evaluating adaptive MPC and RL together in this setup yields new insights into comparative performance in dynamic environments.
Mammalian whole-brain connectomes are a foundational ingredient for holistic understanding of brains. Indeed, imaging connectomes at sufficient resolution to densely reconstruct cellular morphology and synapses represents a longstanding goal in neuroscience. Mouse connectomes could soon come within reach while human connectomes remain a more distant yet still worthy goal. Though the technologies needed to reconstruct whole-brain connectomes have not yet reached full maturity, they are advancing rapidly. Close examination of these technologies may help plan connectomics projects. Here, we quantitatively compare imaging technologies that have potential to enable whole-brain mammalian connectomics. We perform calculations on electron microscopy (EM) techniques and expansion light-sheet fluorescence microscopy (ExLSFM) methods. We consider techniques that have sufficient resolution to identify all synapses and sufficient speed to be relevant for whole mammalian brains. We offer this analysis as a resource for those considering how to organize efforts towards imaging whole-brain mammalian connectomes.
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This nontechnical article discusses the motivating ideas behind the constructive approach to mathematics and the implications of constructive mathematics for the history of mathematics.
Lean and flexible manufacturing is a matter of necessity for the automotive industries today. Rising consumer expectations, higher raw material and processing costs, and dynamic market conditions are driving the auto sector to become smarter and agile. This paper presents a machine learning-based soft sensor approach for identification and prediction of lean manufacturing (LM) levels of auto industries based on their performances over multifarious flexibilities such as volume flexibility, routing flexibility, product flexibility, labour flexibility, machine flexibility, and material handling. This study was based on a database of lean manufacturing and associated flexibilities collected from 46 auto component enterprises located in the Pune region of Maharashtra State, India. As many as 29 different machine learning models belonging to seven architectures were explored to develop lean manufacturing soft sensors. These soft sensors were trained to classify the auto firms into high, medium or low levels of lean manufacturing based on their manufacturing flexibilities. The seven machine learning architectures included Decision Trees, Discriminants, Naive Bayes, Support Vector Machine (SVM), K-nearest neighbour (KNN), Ensembles, and Neural Networks (NN). The performances of all models were compared on the basis of their respective training, validation, testing accuracies, and computation timespans. Primary results indicate that the neural network architectures provided the best lean manufacturing predictions, followed by Trees, SVM, Ensembles, KNN, Naive Bayes, and Discriminants. The trilayered neural network architecture attained the highest testing prediction accuracy of 80%. The fine, medium, and coarse trees attained the testing accuracy of 60%, as did the quadratic and cubic SVMs, the wide and narrow neural networks, and the ensemble RUSBoosted trees. Remaining models obtained inferior testing accuracies. The best performing model was further analysed by scatter plots of predicted LM classes versus flexibilities, validation and testing confusion matrices, receiver operating characteristics (ROC) curves, and the parallel coordinate plot for identifying manufacturing flexibility trends for the predicted LM levels. Thus, machine learning models can be used to create effective soft sensors that can predict the level of lean manufacturing of an enterprise based on the levels of its manufacturing flexibilities.
This paper is concerned with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in $b$-Metric spaces with three-point boundary conditions. The results are based on the ${\omega}-{\varpi}$-Geraghty type contraction, the ${\digamma}$-contraction and the fixed point theory. In addition, two illustrations are provided to highlight the plausibility of our findings.
SARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. Th positivity and boundedness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases.
Abstract In this paper, the existence and uniqueness of the solutions of Caputo fractional delay differential equations under nonlocal and integral boundary value conditions are studied. By using the Banach contraction principle and the Burton and Kirk fixed-point theorem, some new conclusions about the existence and uniqueness of solutions are obtained. An example is given to illustrate the main results.
This essay explores the impact of automated proof construction on three key areas of mathematical cognition: on how we judge the role one piece of mathematics plays in another, on how we make mistakes in reasoning about mathematical objects, and on how we understand what our theorems are truly about. It concludes by speculating on a new form of mathematical experience that these methods could make possible: ``glitching'', a game-like search for uncanny consequences of our definitions.
Francisco Hermes Santos da Silva, Rudinei Alves dos Santos
O processo de ensino e aprendizagem de conceitos abordados na disciplina matemática, não exigem do professor apenas o domínio do conteúdo a ser ensinado, mas, também, sobre como o aluno aprende. Então, estudar, implementar e avaliar estratégias de ensino ancoradas em teorias de aprendizagem e conhecimento precisam ser ações constantes na prática docente. Desse contexto emerge o problema: que contribuições podem advir de práticas docentes que, ancoradas às teorias de aprendizagem e conhecimento, visam o desenvolvimento do conhecimento em termos das conexões dos conteúdos matemáticos ensinados na escola? Assim, este artigo, baseado em pesquisa com abordagem qualitativa de cunho bibliográfico, recorre, principalmente, a Piaget, com o objetivo de mostrar conceitos piagetianos, que encerram a importância da interconexão dos conteúdos matemáticos. Ademais, visa apresentar outras duas teorias que, similarmente, contribuem para o conceito de conexão dos conteúdos – Aprendizagem Significativa e Teoria dos Campos Conceituais. Este trabalho aponta no sentido de que práticas docentes que buscam a tomada de consciência do aluno, sobre a importância da conexão dos conteúdos prévios com os conteúdos matemáticos a serem aprendidos, favorecem a efetivação da abstração reflexiva e da equilibração majorante que implicam em aprendizagem significativa dos conceitos reunidos em um campo conceitual. Outrossim, frente a importância da conexão dos conteúdos para compreensão de conteúdos matemáticos, o presente artigo, abre caminho para pesquisas originais que apresentem práticas docentes construídas e/ou experimentadas, com essas e outras teorias, a fim de indicar caminhos, quiçá melhores dias, para o processo de ensino e aprendizagem de matemática.
Special aspects of education, Applied mathematics. Quantitative methods
هدف: ارزیابی کارایی هزینه در یک سیستم شبکه با استفاده از مدلهای تحلیل پوششی دادهها میتواند از جنبه های مختلفی که در برنامههای واقعی وجود دارد، بهبود یابد. در این مطالعه، هدف آن است که یک مجموعه خاص از وزنها را برای ارزیابی کارایی هزینه در یک سیستم شبکه دو مرحلهای در نظر بگیریم.روششناسی پژوهش: در این پژوهش، با استفاده از روش تحلیل پوششی دادهها، سعی در ارائه مدلی برای ارزیابی هزینه سیستم شبکه است.یافته ها: نتایج نشان داد که در نظر گرفتن روابط بین مراحل مختلف در یک سیستم شبکه میتواند مستقیماً بر نتایج بدست آمده تأثیر بگذارد. این موضوع از ارزیابی بهینهسازی هزینه بررسی شده است. در نظر گرفتن مجموعه وزنهها از جنبههای مختلف میتواند در امتیازات به دست آمده تأثیر بگذارد.اصالت/ارزش افزوده علمی: با توجه به مدلها و روشهای موجود در ادبیات، در این مطالعه مدلی ارائه شده است که کارایی هزینه را در یک مدل دو مرحلهای در نظر میگیرد.
In this paper, we define and study the category of L-algebras, proving that this category has equalizers, coequalizers, kernel pairs and products. We investigate the existence of injective objects in this category and show that an object in the subcategory of cyclic L-algebras is injective if and only if it is a complete and divisible cyclic L-algebra.
The current and future wireless communication systems, WiFi, fourth generation (4G), fifth generation (5G), Beyond5G, and sixth generation (6G), are mixtures of many frequency spectrums. Thus, multi-functional common or shared aperture antenna modules, which operate at multiband frequency spectrums, are very desirable. This paper presents a multiple-input and multiple-output (MIMO) antenna design for the 5G/B5G Internet of Things (IoT). The proposed MIMO antenna is designed to operate at multiple bands, i.e., at 3.5 GHz, 3.6 GHz, and 3.7 GHz microwave Sub-6 GHz and 28 GHz mm-wave bands, by employing a single radiating aperture, which is based on a tapered slot antenna. As a proof of concept, multiple tapered slots are placed on the corner of the proposed prototype. With this configuration, multiple directive beams pointing in different directions have been achieved at both bands, which in turn provide uncorrelated channels in MIMO communication. A 3.5 dBi realized gain at 3.6 GHz and an 8 dBi realized gain at 28 GHz are achieved, showing that the proposed design is a suitable candidate for multiple wireless communication standards at Sub-6 GHz and mm-wave bands. The final MIMO structure is printed using PCB technology with an overall size of 120 × 60 × 10 mm<sup>3</sup>, which matches the dimensions of a modern mobile phone.
A series of ceramic artworks are presented, inspired by the author's research connecting theoretical physics to the beautiful theory of Riemann surfaces. More specifically the research is related to the classification of curves on the surfaces based on a description of them as built from basic building blocks known as "pairs of pants". The relevant background on this mathematics of these two dimensional spaces is outlined, some of the artistic process is explained: Both the conceptual ideas and their implementation. Many photos of the ceramics are included to illustrate this and the connected physics problem is briefly mentioned.
We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.