Hasil untuk "Mathematics"

Michael W. Davis

H. Rasiowa, R. Sikorski

V. Smirnov

G. Price

W. Thurston

Author(s): Thurston, William P. | Abstract: In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.

Tehseen Hussain, Fraz Ahmad, Dr. Zia Ur Rehman

The rapid integration of the Internet of Things (IoT) into healthcare ecosystems has revolutionized patient monitoring and data accessibility; however, it has simultaneously expanded the cyber-attack surface, leaving sensitive medical data vulnerable to sophisticated breaches. This systematic literature review (SLR) addresses the critical challenge of balancing high-level security with the severe resource constraints of medical sensors and edge devices. By synthesizing evidence from 80 high-impact studies including 18 primary research articles published between 2022 and 2025 this paper evaluates the quality and efficacy of emerging cryptographic frameworks. The methodology utilizes a rigorous quality assessment framework to categorize research into "Strong," "Moderate," and "Weak" tiers. Key findings reveal a significant paradigm shift toward lightweight symmetric ciphers, such as GIFT and PRESENT, and certificateless authentication protocols like ELWSCAS, which reduce communication overhead in narrow-band environments. The analysis further explores the role of blockchain-assisted decentralization and DNA-based encryption in mitigating Single Point of Failure risks and providing high entropy. While decentralized models significantly enhance data integrity, they frequently encounter a scalability wall regarding transaction latency. Furthermore, the review assesses quantum readiness, noting that while lattice-based standards are being ported to microcontrollers, memory footprints remain a barrier for simpler sensors. Ultimately, this SLR maps the current technical frontiers and provides a strategic roadmap for future research, emphasizing the transition toward lightweight, quantum-resistant architectures as the next essential step in securing the global healthcare IoT infrastructure. Conflict of Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Funding The research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Data Fabrication/Falsification Statement The author(s) declare that no data has been fabricated, falsified, or manipulated in this study. Participant Consent The authors confirm that Informed consent was obtained from all participants, and confidentiality was duly maintained. Copyright and Licensing For all articles published in the NIJEC journal, Copyright (c) of this study is with author(s).

J. Boaler

J. Kilpatrick, W. Martin, D. Schifter

O. Skovsmose

Sezer Erdem, Serkan Demiriz

The primary objective of this study is to construct a novel double sequence space by utilizing the domain of a 4-dimensional (4D) matrix in the space $\mathcal{L}_u$ of the absolutely summable double sequences defined via the well-known Catalan numbers. Within this framework, various algebraic and topological properties of the newly introduced space are investigated. The study further aims to compute the $\alpha$-, $\beta(bp)$-, and $\gamma$-duals of the space. Another essential part of the research involves characterizing certain classes of matrix transformations from the newly defined space to some classical double sequence spaces and vice versa. These contributions are expected to enrich the theory of sequence spaces and matrix transformations by introducing new insights based on special integer sequences.

Khlyupin Ivan, Meshkov Vadim, Sokolova Daria et al.

The aim of this work was to develop a model to describe some microscopic phenomena in the epitaxial thin films based on lead zirconate PbZrO3. The model takes into account the epitaxial contact of the film with the substrate and conditions for mechanical compatibility of the domains. It includes contributions from pseudopolarization, elastic and domain-domain interactions as well as a contribution analogous to electrostriction in ferroelectric materials. The parameter optimization has been performed through free energy minimization with varying the magnitudes of elastic displacements and the pseudopolarization vectors. The results obtained qualitatively reproduced a part of the experimental observations on the domain matching in the thin films, to be exact, the change in microscopic twisting in the domain wall regions when removing the epitaxial structure away from the substrate.

Min Pei, Jianke Yu, Chen Chen et al.

S. Shapiro

P. Starkey, Alice E. Klein, A. Wakeley

Md Mijanur Rahman, Ashik Uzzaman, Sadia Islam Sami et al.

Abstract This study introduces a novel encoder–decoder framework based on deep neural networks and provides a thorough investigation into the field of automatic picture captioning systems. The suggested model uses a “long short‐term memory” decoder for word prediction and sentence construction, and a “convolutional neural network” as an encoder that is skilled at object recognition and spatial information retention. The long short‐term memory network functions as a sequence processor, generating a fixed‐length output vector for final predictions, while the VGG‐19 model is utilized as an image feature extractor. For both training and testing, the study uses a variety of photos from open‐access datasets, such as Flickr8k, Flickr30k, and MS COCO. The Python platform is used for implementation, with Keras and TensorFlow as backends. The experimental findings, which were assessed using the “bilingual evaluation understudy” metric, demonstrate the effectiveness of the suggested methodology in automatically captioning images. By addressing spatial relationships in images and producing logical, contextually relevant captions, the paper advances image captioning technology. Insightful ideas for future study directions are generated by the discussion of the difficulties faced during the experimentation phase. By establishing a strong neural network architecture for automatic picture captioning, this study creates opportunities for future advancement and improvement in the area.

E. Kroesbergen, Johannes E H Van Luit

J. Middleton, P. Spanias

S. Krauss, Martin Brunner, Mareike Kunter et al.

Mareike Kunter, Y. Tsai, U. Klusmann et al.

T. Poggio, S. Smale