Fundamental Operation Research Articles

Multiple Criteria Group Decision-Making Using Fermatean Fuzzy Soft Matrices and Their Medical Applications

This paper introduces a brand new algebraic methodology, Fermatean fuzzy soft matrices. A new hybrid tool called the Fermatean fuzzy soft set combines the strengths of the Fermatean fuzzy set and the parametric tool soft set to handle vague and ambiguous situations in various mathematical problems. Fundamental set operations of Fermatean fuzzy soft matrices are defined, and their properties are examined. Two algorithms using the score matrix and utility matrix have been proposed for medical diagnosis problems. Each of the applications has been successfully demonstrated using numerical examples. Finally, a brief comparison between the proposed model and several previous models is presented to ensure the feasibility of the proposed strategy.

Fundamental Monopole Operators and Embeddings of Kac-Moody Affine Grassmannian Slices

Abstract Braverman, Finkelberg, and Nakajima define Kac-Moody affine Grassmannian slices as Coulomb branches of $3d$ ${\mathcal{N}}=4$ quiver gauge theories and prove that their Coulomb branch construction agrees with the usual loop group definition in finite ADE types. The Coulomb branch construction has good algebraic properties, but its geometry is hard to understand in general. In finite types, an essential geometric feature is that slices embed into one another. We show that these embeddings are compatible with the fundamental monopole operators (FMOs), remarkable regular functions arising from the Coulomb branch construction. Beyond finite type these embeddings were not known, and our second result is to construct them for all symmetric Kac-Moody types. We show that these embeddings respect Poisson structures under a mild “goodness” hypothesis. These results give an affirmative answer to a question posed by Finkelberg in his 2018 ICM address and demonstrate the utility of FMOs in studying the geometry of Kac-Moody affine Grassmannian slices, even in finite types.

Efficient Maximal Biplex Enumerations with Improved Worst-Case Time Guarantee

A k-biplex is an induced subgraph of a bipartite graph which requires every vertex on the one side disconnecting at most k vertices on the other side. Enumerating all maximal k-biplexes in a bipartite graph is a fundamental operator in bipartite graph analysis and finds applications in various domains, including community detection, online recommendation, and fraud detection in finance networks. The state-of-the-art solutions for maximal k-biplex enumeration suffer from efficiency issues as k increases (k ≥ 2), with the time complexity of O(m 2 n ), where n (m) denotes the number of vertices (edges) in the bipartite graph. To address this issue, we propose two theoretically and practically efficient enumeration algorithms based on novel branching techniques. Specifically, we first devise a new branching rule as a fundamental component. Building upon this, we then develop a novel branch-and-bound enumeration algorithm to efficiently enumerate maximal k-biplexes. We prove that our algorithm achieves a worst-case time complexity of O(mα k n ), where α k < 2, thus significantly improving the time complexity compared to previous algorithms. To enhance the performance, we further propose an improved enumeration algorithm based on a novel pivot-based branching rule. Theoretical analysis reveals that our improved algorithm has a time complexity of O(mβ k n ), where β k is strictly less than α k . In addition, we also present several non-trivial optimization techniques, including graph reduction, upper-bounds based pruning, and ordering-based optimization, to further improve the efficiency of our algorithms. Finally, we conduct extensive experiments on 6 large real-world bipartite graphs to evaluate the efficiency and scalability of the proposed solutions. The results demonstrate that our improved algorithm achieves up to 5 orders of magnitude faster than the state-of-the-art solutions.

Low-Latency Adaptive Distributed Stream Join System Based on a Flexible Join Model

Stream join is a fundamental operation in stream processing and has attracted extensive research due to its large resource consumption and serious impact on system performance. As the theoretical basis of stream join systems, the stream join model greatly affects system performance. State-of-the-art stream join models either consume too much computing resources or too much storage resources, thus resulting in lower throughput or higher latency. In this paper, we propose a new stream join model for processing arbitrary join predicates, called CoModel, which offers a flexible trade-off between memory and computing resource consumption. More importantly, CoModel can achieve the minimum sum of the number of store operations and join operations among all existing join models, and thus can achieve the lowest latency and highest throughput when the overheads associated with the local stream join for each input tuple are approximately constant. We give a trade-off strategy for CoModel and theoretically prove its performance advantages based on queuing theory. Furthermore, we design and implement an adaptive distributed stream join system, CoStream, based on CoModel. CoStream can adaptively adjust its structure according to resource constraints and statistics of input data. We conduct extensive experiments for CoStream to evaluate its performance and adaptivity, and the results show that CoStream has the lowest latency and highest throughput in various scenarios.

On Efficient Large Sparse Matrix Chain Multiplication

Sparse matrices are often used to model the interactions among different objects and they are prevalent in many areas including e-commerce, social network, and biology. As one of the fundamental matrix operations, the sparse matrix chain multiplication (SMCM) aims to efficiently multiply a chain of sparse matrices, which has found various real-world applications in areas like network analysis, data mining, and machine learning. The efficiency of SMCM largely hinges on the order of multiplying the matrices, which further relies on the accurate estimation of the sparsity values of intermediate matrices. Existing matrix sparsity estimators often struggle with large sparse matrices, because they suffer from the accuracy issue in both theory and practice. To enable efficient SMCM, in this paper we introduce a novel row-wise sparsity estimator (RS-estimator), a straightforward yet effective estimator that leverages matrix structural properties to achieve efficient, accurate, and theoretically guaranteed sparsity estimation. Based on the RS-estimator, we propose a novel ordering algorithm for determining a good order of efficient SMCM. We further develop an efficient parallel SMCM algorithm by effectively utilizing multiple CPU threads. We have conducted experiments by multiplying various chains of large sparse matrices extracted from five real-world large graph datasets, and the results demonstrate the effectiveness and efficiency of our proposed methods. In particular, our SMCM algorithm is up to three orders of magnitude faster than the state-of-the-art algorithms.

Cerium oxide/polydimethylsiloxane polymer deposited onto tapered fiber for 1.97 µm mode-locked thulium-doped fiber laser

This work presents the use of cerium oxide (CeO2) as saturable absorber (SA) in the mode-locked pulse fiber laser generation. The CeO2 materials were prepared through sonication which then incorporated into a polydimethylsiloxane (PDMS) polymer to be coated on a tapered fiber. The CeO2/PDMS-SA exhibited saturation intensity of 44 MW/cm2 and modulation depth of 3.4%, confirming its nonlinear intensity-dependent transmission characteristics. Integrated into a thulium-doped fiber laser cavity, the CeO2/PDMS-SA enabled mode-locking at a pump power of 420 mW, leading to a fundamental mode-locking operation up to 1484 mW within the net anomalous dispersion regime. The laser emitted pulses at wavelength of 1973 nm with signal-to-noise ratio of 54 dB, repetition rate of 9.04 MHz and pulse width of 1.49 ps. The CeO2/PDMS-SA mode-locked fiber laser demonstrated stability of an average 3 dB bandwidth of 2.89 ± 0.08 nm, average central wavelength of 1973.05 ± 0.14 nm and average pulse width of 1.5 ± 0.01 ps for the duration of 120 min. Notably, the CeO2/PDMS-SA demonstrated a high pulse energy of 10.62 nJ and average output power of 96 mW. This investigation suggests their viability for use in future studies. The results also demonstrated the potential of CeO2 for use in various photonics applications in the “eye-safe” region.

Dual hesitant fuzzy set in multi-objective transportation problems in time sequence frame work

Decision makers may have different information in different situations when making decisions about the same attributes, depending on the circumstances. A time-sequential framework is necessary for navigating these kinds of circumstances. We established the notion of a Time-sequential dual hesitant fuzzy set (TS-DHFS) to illustrate the significance of time sequence in decision-making with the aid of a dual hesitant fuzzy set (DHFS), one of the important tools to handle the uncertainty embedded in the real world. The proposed set describes the hesitant situations more accurately by inducing a time sequence framework. We defined the fundamental operations, two score function for ranking and a series distance measures for the proposed set. For the pragmatic application of our proposed set, we devised the mathematical model in three different types of Time-sequential dual hesitant fuzzy multi-objective transportation problems (TS-DHF-MOTPs). The proposed three models are classified based on the nature of the parameters such as transportation cost (TC), transportation time (TT), availability, and demand. The goal of the proposed transportation systems is TC and TT simultaneously in a single framework. We established an approach utilizing one of the ranking functions that have been proposed, followed by the fuzzy programming (FP) and weighted sum technique (WST), to optimize the constructed models. Additionally, numerical computations are also carried out to emphasize the efficiency and benefits of MOTP under the TS-DHF environment.

Interval-valued bipolar complex fuzzy soft sets and their applications in decision making

In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas.

A complex fuzzy decision model for analysing the post-pandemic immuno-sustainability

The post-effects of the COronaVIrus Disease (COVID-19) vary depending on socioeconomic and biological factors. Similarly, the effects of vaccination on people’s immunity vary across several factors. After the pandemic, real-life post-vaccination anomalies significantly impact women’s health, access to medical treatments and medications, mental well-being, and daily physical activities. However, there has been scant investigation into the physical, psychological, social, and economic ramifications of vaccine effects on women in the post-pandemic era. Therefore, conducting a comprehensive risk assessment is crucial to safeguard women from the post-vaccination effects.To address this issue, the research encompasses complex bipolar spherical fuzzy ℵ-soft set, which has two-sided periodic ambiguous data due to its parametric properties as an adaptable ℵ-soft set and distinguishing criteria as a complex bipolar spherical fuzzy set. In addition, some fundamental operations and properties are presented in a complex bipolar spherical fuzzy ℵ-soft environment. Furthermore, the robust assessment of a real-world application demonstrate the efficacy of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach to optimise the decision result. Finally, the provided decision-making approach is compared with existing techniques to illustrate their remarkable credibility and integrity.

Fuzzy Soft Paranormal Operator in Fuzzy Soft Hilbert Space

This paper defines the fuzzy soft paranormal operator and discusses several fundamental fuzzy soft paranormal operator properties in fuzzy soft hilbert space. Some concepts relevant to the fuzzy soft paranormal operator have been defined in fuzzy soft Hilbert space.

Structure-dependent degradation of phthalate esters with persulfate oxidation activated by thermal in soil

Phthalate esters (PAEs) have become one of the most concerned emerging organic pollutants in the world, due to the toxicity to human health, and hard to remove it efficiently. In this study, the degradation performance of DBP and DEHP in the soil by water bath heating activated sodium persulfate (PS) method under different factors were studied, in which the degradation rate of DBP and DEHP were improved with the increasing of temperature, PS concentration and water/soil ratio, and higher diffusion efficiency treatments methods, due to the improved mass transfer from organic phase to aqueous media. However, the degradation rate of DEHP was much lower than that of DBP, because DEHP in the soil was more difficult to contact with SO4•− for reaction on soil surface, and the degradation rate of PAEs in soil was significantly lower than that in water. Redundancy analysis of degradation rate of DBP and DEHP in water demonstrated that the key factors that determine the degradation rate is time for DBP, and cosolvent dosage for DEHP, indicating that the solubility and diffusion rate of PAEs from soil to aqueous are predominance function. This study provides comprehensive scenes in PAEs degradation with persulfate oxidation activated by thermal in soil, reveal the difference of degradation between DBP and DEHP is structure-dependent. So that we provide fundamental understanding and theoretical operation for subsequent filed treatment of various structural emerging pollutants PAEs contaminated soil with thermal activated persulfate.

Intent and Extent: Computer Science Concepts and Practices in Integrated Computing

Intent and Extent: Computer Science Concepts and Practices in Integrated Computing

Decoding Complexity: A Mathematical Framework for Enhanced Translation Comprehension

Machine translation tools have demonstrated substantial progress in enhancing translation accuracy since the emergence of artificial intelligence. However, challenges persist in reasoning (or the lack thereof), considering contexts, addressing specific word games, and interpreting very long or very short sentences—those exceeding 50 and falling below 7 words (Bowker, 2023 : 893). Additionally, accurately translating technical or specialized terms and their variations remains a hurdle. This research introduces a categorical mathematical formalization of the comprehension stages in translation, along with a model for calculating acceptances (specific meanings of words) during the verification of meaning hypotheses. The goal is to elucidate the comprehension process and integrate contextual considerations. The formalism delineates a series of fundamental cognitive operations involved in comprehension. Furthermore, it advocates for evaluating meaning hypotheses using logical modalities, particularly hypostases, described as phrases (groups of words)—a unit of discourse rather than language—signifying the structure of arguments conveying the speaker's knowledge. The strength of our proposed mathematical model lies in its independence from both source and target languages, as well as the subjectivity of text authors or translators. Additionally, the assessment of meaning hypotheses relies on verifiable logical modalities, ensuring a reliable, explicable, and controllable outcome.

Design and experimental study of a 300 We class combustion-driven high frequency free-piston Stirling electric generator

Portable electric power generator with a power level of several hundred Watts plays an important role in outdoor activities, emergency relief and tactical power supply. As an external-combustion heat engine with outstanding heat source adaptability, free-piston Stirling generator (FPSG) owns attractive advantages of quietness, high thermal efficiency, and high reliability. This paper proposes a novel ultra-high frequency (UHF) FPSG-based portable power supply system driven by a diesel porous media evaporative combustor (PMEC). An experimental setup was designed and built based on the quasi-one-dimension thermoacoustic impedance matching of the FPSG and three-dimension thermal coupling of steady combustion and alternating flow between FPSG and combustor. The fundamental operating characteristics of the system were investigated in terms of combustion powers and electric loads. Preliminary experimental results show that a maximum output electric power of 350 We at a heating temperature of 875 K and a maximum fuel-to-electric efficiency of 11.98 % were obtained. Computational fluid dynamics (CFD) simulations were employed to delve into the intricate combustion and heat transfer processes, unveiling the formation of carbon deposits and confirming the efficacy of cyclone holes in reducing carbon deposition. This pioneering exploration of 130 Hz UHF and evaporative-combustion coupled heat transfer successfully showcases the feasibility of constructing a high-specific-power FPSG-based portable power system.

An Effective Method for Slicing Triangle Meshes Using a Freeform Curve

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing.

On local geometric properties of a tokamak equilibrium

To separate the complexities in plasma physics and geometric effects, compact formulas for local geometric properties of a tokamak equilibrium are presented in this paper. They are written in a form similar to the Frenet formulas. All of the geometric quantities are expressed in terms of curvature and torsion of the three spatial curves for the moving local frame of reference, i.e., local orthogonal vector basis. In this representation, the local magnetic shear and the normalized parallel current are just the differences between two torsions of the vector basis. All of the geometric properties are coordinate invariants and form a prime set of quantities for describing tokamak plasma equilibrium. This prime set can be evaluated in both flux coordinates with closed flux surfaces and cylindrical coordinates including areas with open field lines, which may allow the extension of some analysis on the open field lines outside the last closed surface. Fundamental differential operators for stability and transport studies can be expressed explicitly in terms of these geometric properties. It can also be used to simplify analytic studies.

Stratified Noncommutative Geometry

We introduce a theory of stratifications of noncommutative stacks (i.e., presentable stable ∞ \infty -categories), and we prove a reconstruction theorem that expresses them in terms of their strata and gluing data. This reconstruction theorem is compatible with symmetric monoidal structures, and with more general operadic structures such as E n \mathbb {E}_n -monoidal structures. We also provide a suite of fundamental operations for constructing new stratifications from old ones: restriction, pullback, quotient, pushforward, and refinement. Moreover, we establish a dual form of reconstruction; this is closely related to Verdier duality and reflection functors, and gives a categorification of Möbius inversion. Our main application is to equivariant stable homotopy theory: for any compact Lie group G G , we give a symmetric monoidal stratification of genuine G G -spectra. In the case that G G is finite, this expresses genuine G G -spectra in terms of their geometric fixedpoints (as homotopy-equivariant spectra) and gluing data therebetween (which are given by proper Tate constructions). We also prove an adelic reconstruction theorem; this applies not just to ordinary schemes but in the more general context of tensor-triangular geometry, where we obtain a symmetric monoidal stratification over the Balmer spectrum. We discuss the particular example of chromatic homotopy theory.

Recent advances of ECG monitoring and webserver health monitoring applications: A review

In response to recent improvements in mobile technology and cloud computing-based real-time monitoring systems, numerous cloud-based healthcare services and devices have been developed. In the cloud system, it is feasible to collect and distribute medical data immediately from anywhere to medical specialists, and patients can receive network-based feedback. This paper reviews the most recent developments and trends in wearable technology and biomedical equipment (mostly ECG), as well as the development of a cloud-based solution for mobile device and web browser users. The system contains ECG enhancement, ECG quality grading, and ECG parameter extraction methods. A use case was utilized to showcase the system, in which a web server processed ECG data from a mobile phone in real-time. The system has been proved to be functional, accurate, and efficient. We review the primary principles underlying the operation of the ECG and its fundamental operation, as well as the recording and transmission paradigm for ECG signals. Detailed processes were also provided for the system components, their configuration, and the employed technologies. In conclusion, we examine the complete study and the project's future scope.

Del Emprendimiento a la Enseñanza de Matemáticas. Una Práctica (En La Economía Informal) De Vendedores del Mercado del 5 de Abril En Namibe-Angola

This article aims to identify notable Ethno/mathematical practices in commercial activities among entrepreneurs/sellers in the reference market. We are concerned with knowing how these practices, notable in the informal economy, can influence the teaching of Mathematics in the classroom, based on theories of Ethno/mathematics. To meet the proposed objective and considering the nature of the topic, the research was developed using qualitative methodology, where information was obtained through direct observations and the application of semi-structured interviews to six informal sellers, with greater consistency and details of three sellers. After obtaining information, a reinforced analysis of reports was carried out, investigating knowledge of informal and implicit Mathematics, whose practices lead us to Ethno/mathematical knowledge. Bibliographical research was also used using authors of scientific recognition such as D`Ambrosio (2013), Lúcio (2019), Saraiva (2011), Gerdes (2007) among others. In short, informal sellers use an (Ethno)mathematics that they developed from the transmission of values coming from generation to generation, by the elderly, but which allows them to develop the four fundamental operations of Mathematics (Addition, Subtraction, Multiplication and Division), measures of weight and length. Identifying commercial know-how and considering the mathematics practiced by salespeople and school Mathematics, we developed pedagogical proposals for teaching Mathematics in the classroom, for students in Primary Education and the first cycle of Secondary Education. The suggestions presented will serve as support/reinforcement for researchers and teachers, since the topic under study is open.

Islamic banks' contribution to Indonesia districts' economic growth and poverty alleviation

PurposeThis research investigates the Islamic banks’ intermediation role (e.g. branches and deposits) in financing. It also examines how financing contributes to the regions' economic growth and poverty alleviation as a predictor and mediator variable.Design/methodology/approachA total of 297 observations were extracted from 33 Indonesian districts and 14 Islamic banks during the period 2012–2020. Fixed-effect regression analysis was used to examine variable’s interactions.FindingsThe empirical results indicate that Islamic banks have adopted a channelling role towards redistributing capital from lender to borrower. Besides, there are crucial roles in developing economies and reducing poverty at the district level. This study also reinforces the critical role of financing in mediating the relationship between branches and deposits as predictor variables and GDP and poverty as outcome variables.Research limitations/implicationsThe current study was limited to Indonesian Islamic banks and the district’s perspective. Future research needs to cover sub-districts and other poverty measurements (e.g. human education and development perspectives), including conventional and Islamic banks. It can help practitioners, regulators and researchers observe the dynamic behaviour of the banking sector to understand its role in the economic and social fields.Practical implicationsBank managers and regulators should promote branches, deposits and financing. It also enlightens people about the essential role of Islamic banks and their fundamental operations in business and economics.Originality/valueThis study contributes to economic literature, bank managers and local governments' decision-making processes by developing and testing an economic growth and poverty model.