This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\infty$ and spaces of two-sided absolutely summing series of vectors in $\mathbb{C}^s$ for some positive integer $s>1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications.
Imma Lory Aprea, Gianni Bosi, Gabriele Sbaiz
et al.
In this paper, we tackle a bi-objective optimization problem in which we aim to maximize the portfolio diversification and, at the same time, minimize the portfolio volatility, where the ESG (Environmental, Social, and Governance) information is incorporated. More specifically, we extend the standard portfolio volatility framework based on the financial aspects to a new paradigm where the sustainable credits are taken into account. In the portfolio’s construction, we consider the classical constraints concerning budget and box requirements. To deal with these new asset allocation models, in this paper, we develop an improved Multi-Objective Particle Swarm Optimizer (MOPSO) embedded with ad hoc repair and projection operators to satisfy the constraints. Moreover, we implement a deep learning architecture to improve the quality of estimating the portfolio diversification objective. Finally, we conduct empirical tests on datasets from three different countries’ markets to illustrate the effectiveness of the proposed strategies, accounting for various levels of ESG volatility.
This report is the first of two publications of a joint Working Group of the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathematics (ICIAM). In it, we shall analyze the current state of publishing in the mathematical sciences and explain the resulting problems. Our second publication will offer concrete recommendations, guidelines, and best practices for researchers, policymakers, and evaluators of mathematical research. It will explain how to detect and counteract attempts to game bibliometric measures, empowering the community to reclaim control over research evaluation and drive necessary change.
This article is the first in an occasional series for the Australian Mathematical Society Gazette on diverse aspects and topics of Indigenous mathematical knowledge. This is an important, but neglected, part of the mathematical heritage of humankind, and as such is the concern of the mathematics community as a whole. It is hoped that this and future articles may help to inspire mathematics researchers, students, and educators at tertiary and school levels who are seeking to widen their mathematical horizons and develop course and research materials of broad cultural relevance. I would like to honour the Mithaka peoples of the Kurrawoolben and Kirrenderri (Diamantina) and Nooroondinna (Georgina) river channel country of south-western Qld, Australia. The material in this article does not involve culturally restricted knowledge or images, and is shared with respect for the Mithaka ancestors and their descendants.
Ravinder Jangra, Etender Singh, Sunil Manglaw
et al.
پیشینه: ارزیابی ظرفیت ، جزء مهمی در حفظ پایداری در بخش گردشگری است. تمام نگرانیها در گردشگری به تعداد گردشگرانی که از یک مکان خاص بازدید میکنند، مرتبط است. منطقه مورد مطالعه دارای مناظر زیبا در اکوسیستم بیابان سرد و همچنین ویژگیهای متمایز بودایی است که گردشگری انبوه را جذب میکند. امروزه، توسعه گردشگری نگرانیهایی را در مورد پایداری و ایجاد استانداردهایی برای قابلیتهای مقصد گردشگری ایجاد کرده است.
اهداف: مطالعه حاضر با هدف تجزیه و تحلیل اهداف زیر انجام میشود: 1) ارزیابی ظرفیت برد فیزیکی (PCC)، ظرفیت برد واقعی (RCC) و ظرفیت برد مؤثر (ECC) نقاط گردشگری منتخب در روستای ناکو و 2) محاسبه ظرفیت پارکینگ صومعه.
روش شناسی: روشهای مشخصشده در اتحادیه بینالمللی حفاظت از طبیعت و منابع طبیعی (IUCN) برای اندازهگیری ظرفیت برد مقاصد گردشگری خاص در ناکو استفاده شد. تکنیکهای سه سطحی برای ارزیابی ظرفیت برد فیزیکی (۲۸۱۶۱ نفر)، ظرفیت برد واقعی (۴۱۶۲ نفر) و ظرفیت برد مؤثر (۲۹۶۸ نفر) به کار گرفته شد.
نتایج: نتایج نشان میدهد که ظرفیت برد مؤثر (ECC) مناسبترین روش برای تخمین است و وضعیت فعلی گردشگری در منطقه مورد مطالعه کمتر از ظرفیت خود بهرهبرداری شده است.
نتیجهگیری: سیستمهای بسیار کوچک تا بزرگ در ناکو یافت میشوند و این سیستمها از انواع مختلف فعالیتها نیز پشتیبانی میکنند. گردشگری یک فعالیت بسیار رایج است و تأثیرات زیستمحیطی، اجتماعی، فرهنگی و اقتصادی دارد. این تأثیرات به پارامترهای مختلفی وابسته بوده و با تغییر ماهیت تعامل نیز تغییر میکنند. مشخص شده است که وضعیت فعلی فعالیت گردشگری در منطقه مورد مطالعه در مقایسه با ظرفیت برد آن، بسیار کمتر از حد بهرهبرداری قرار گرفته است.
General. Including nature conservation, geographical distribution
Educational robots offer a platform for training aspiring engineers and building trust in technology that is envisioned to shape how we work and live. In education, accessibility and modularity are significant in the choice of such a technological platform. In order to foster continuous development of the robots as well as to improve student engagement in the design and fabrication process, safe production methods with low accessibility barriers should be chosen. In this paper, we present Robotont 3, an open-source mobile robot that leverages Fused Deposition Modeling (FDM) 3D-printing for manufacturing the chassis and a single dedicated system board that can be ordered from online printed circuit board (PCB) assembly services. To promote accessibility, the project follows open hardware practices, such as design transparency, permissive licensing, accessibility in manufacturing methods, and comprehensive documentation. Semantic Versioning was incorporated to improve maintainability in development. Compared to the earlier versions, Robotont 3 maintains all the technical capabilities, while featuring an improved hardware setup to enhance the ease of fabrication and assembly, and modularity. The improvements increase the accessibility, scalability and flexibility of the platform in an educational setting.
Mechanical engineering and machinery, Electronic computers. Computer science
Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation, this paper explores another class of tools for advancing mathematics research: databases of mathematical objects that enable semantic search. In addition to defining and exploring examples of these tools, we illustrate a particular line of research that was inspired and enabled by one such database.
Jacob Collard, Valeria de Paiva, Eswaran Subrahmanian
Mathematics is a highly specialized domain with its own unique set of challenges. Despite this, there has been relatively little research on natural language processing for mathematical texts, and there are few mathematical language resources aimed at NLP. In this paper, we aim to provide annotated corpora that can be used to study the language of mathematics in different contexts, ranging from fundamental concepts found in textbooks to advanced research mathematics. We preprocess the corpora with a neural parsing model and some manual intervention to provide part-of-speech tags, lemmas, and dependency trees. In total, we provide 182397 sentences across three corpora. We then aim to test and evaluate several noteworthy natural language processing models using these corpora, to show how well they can adapt to the domain of mathematics and provide useful tools for exploring mathematical language. We evaluate several neural and symbolic models against benchmarks that we extract from the corpus metadata to show that terminology extraction and definition extraction do not easily generalize to mathematics, and that additional work is needed to achieve good performance on these metrics. Finally, we provide a learning assistant that grants access to the content of these corpora in a context-sensitive manner, utilizing text search and entity linking. Though our corpora and benchmarks provide useful metrics for evaluating mathematical language processing, further work is necessary to adapt models to mathematics in order to provide more effective learning assistants and apply NLP methods to different mathematical domains.
Lev Raskin , Larysa Sukhomlyn, Dmytro Sokolov
et al.
Object of research is technical state of deteriorating systems whose operating conditions depend on a large number of interacting factors. The caused inhomogeneity of the sample of initial data on the technical state leads to impossibility of correct use of traditional methods of assessing the state of a system (meaning methods using mathematical tools of regression analysis). Subject of research is developing a method for constructing a regression polynomial based on the results of processing a set of controlled system parameters. Non-linearity of the polynomial describing the evolution of the technical state of real systems leads to an increase in the number of regression polynomial coefficients subject to estimation. The problem is further complicated by the growing number of factors affecting the technical state of the system. In these circumstances, the so-called <small sample effect> occurs. Goal the research consists in developing a method for constructing an approximation polynomial that describes evolution of the system state in a situation where the volume of the initial data sample is insufficient for correct estimating coefficients of this polynomial. The results obtained. The paper proposes a method for solving the given problem, based on implementation of a two-stage procedure. At the first stage a functional description of the approximation polynomial coefficients is performed; and this radically reduces the number of regression polynomial parameters to be estimated. This polynomial is used for preliminary estimation of its coefficients with the aim of filtering out insignificant factors and their interactions. At the second stage, parameters of the truncated polynomial are estimated by means of using standard technologies of mathematical statistics. Two approaches to constructing a modified polynomial have been studied: the additive one and the multiplicative one. It has been shown that the additive approach is, on average, an order of magnitude more effective than the multiplicative one.
The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface. This communication may manipulate for the aim such as the delivery of the drug, cooling of electronic chips, nanoscience and the fields of nanotechnology. The impact of heat source/sink is employed. Brownian motion and thermophoresis aspects are discussed. The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized. Furthermore, the influence of activation energy is analyzed in the current article. The numerical analysis is simplified with the help of befitted resemblance transformations. The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations. The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented. According to outcomes, it can be analyzed that the flow profile declined with the rotational parameter. It is observed that angular velocity diminishes via a larger porosity parameter. Furthermore, the temperature gradient is declined via a larger magnitude of the Prandtl number. The heat transfer is enhanced in the occurrence of Brownian motion. The activations energy parameter causes an increment in the volumetric concentration field. Moreover, the local Nusselt number is reduced via a greater estimation of the porosity parameter.
The Partitioned Global Address Space (PGAS) library DASH provides C++ container classes for distributed N-dimensional structured grids. This article presents enhancements on top of the DASH library to support stencil operations and halo areas to conveniently and efficiently parallelize structured grids. The improvements include definitions of multiple stencil operators, automatic derivation of halo sizes, efficient halo data exchanges, as well as communication hiding optimizations. The main contributions of this article are two-fold. First, the halo abstraction concept and the halo wrapper software components are explained. Second, the code complexity and the runtime of an example code implemented in DASH and pure Message Passing Interface (MPI) are compared.
Navaneethakrishna Makaram, Sarvagya Gupta, Matthew Pesce
et al.
In drug-resistant epilepsy, a visual inspection of intracranial electroencephalography (iEEG) signals is often needed to localize the epileptogenic zone (EZ) and guide neurosurgery. The visual assessment of iEEG time-frequency (TF) images is an alternative to signal inspection, but subtle variations may escape the human eye. Here, we propose a deep learning-based metric of visual complexity to interpret TF images extracted from iEEG data and aim to assess its ability to identify the EZ in the brain. We analyzed interictal iEEG data from 1928 contacts recorded from 20 children with drug-resistant epilepsy who became seizure-free after neurosurgery. We localized each iEEG contact in the MRI, created TF images (1–70 Hz) for each contact, and used a pre-trained VGG16 network to measure their visual complexity by extracting unsupervised activation energy (UAE) from 13 convolutional layers. We identified points of interest in the brain using the UAE values via patient- and layer-specific thresholds (based on extreme value distribution) and using a support vector machine classifier. Results show that contacts inside the seizure onset zone exhibit lower UAE than outside, with larger differences in deep layers (L10, L12, and L13: <i>p</i> < 0.001). Furthermore, the points of interest identified using the support vector machine, localized the EZ with 7 mm accuracy. In conclusion, we presented a pre-surgical computerized tool that facilitates the EZ localization in the patient’s MRI without requiring long-term iEEG inspection.
The articles published in the Special Issue “Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges” of the MDPI Mathematics journal are here collected [...]
In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∇</mo><mo>·</mo><mi mathvariant="italic">u</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>”, which allows us to transform the saddle point problem into two smaller problems to solve. The Euler semi-implicit scheme is based on a first order backward difference formula for time discretization and semi-implicit treatments for nonlinear terms. It is worth mentioning that the error estimates of the fully discrete PFEM are rigorously derived, which depend on the penalty parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>, the time-step size <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, and the mesh size <i>h</i>. Finally, two numerical tests show that our scheme is effective.
Human-computer interaction and computer-mediated behavioral psychology research studies often rely on capturing user interaction data to characterize online behaviors. IRB considerations, site policies, and/or security and privacy concerns may force researchers to use screenshots or offline copies of pages of interest, instead of live websites, in their study designs. These interaction modalities reduce the fidelity and contextual realism of web content and often affect interface aesthetic quality – due to broken links, missing images, and/or malfunctioning scripts. StudySandboxx is a tool that allows websites to be saved exactly as they appear online. The tool sandboxes websites in a way that removes dangerous scripts that threaten privacy and security. Saved websites are encapsulated into a single portable file that contains all related website resources. Finally, the tool also supports certain types of permutations commonly used in research – such as changing links in a page. The project is housed within a GitHub repository at https://github.com/gewethor/study-sandbox.
Faltings; Gabber and Ramero introduced almost mathematics. In another way, almost mathematics can be characterized bilocalization abelian category of modules mentioned in Quillen's unpublished note. Applying the concept of Quillen's bilocalization to Gabber and Ramero's work, this paper establishes the almost version of algebraic $K$-theory and cobordism. As a result of almost $K$-theory, we prove that in the case an almost algebra containing a field, the almost $K$-theory of the almost algebra is a direct factor of the $K$-theory of the field, implying that almost $K$-theory holds the Gersten property. We clarify that an almost $K$-theory is a $K$-theory spectrum of non-unital firm algebras in the sense of Quillen. Furthermore, we obtain that almost algebraic cobordism holds tilting equivalence on the category of zero-section stable integral perfectoid algebras with finite syntomic topology.