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Mahler/Zeta Correspondence

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arXiv 2022年

作者： Komatsu, Takashi Konno, Norio Sato, Iwao Tamura, Shunya Math. Research Institute Calc for Industry Minami Hiroshima732-0816 Japan Department of Applied Mathematics Faculty of Engineering Yokohama National University Hodogaya Yokohama240-8501 Japan Oyama National College of Technology Oyama Tochigi323-0806 Japan Graduate School of Science and Engineering Yokohama National University Hodogaya Yokohama240-8501 Japan

The Mahler measure was introduced by Mahler in the study of number theory. It is known that the Mahler measure appears in different areas of math.matics and physics. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on "Zeta Correspondence". The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Mahler measure and our zeta function for quantum walks. Firstly we consider this relation in the case of one-dimensional quantum walks. Afterwards we deal with higher-dimensional quantum walks. For comparison with the case of the quantum walk, we also treat the case of higher-dimensional random walks. Our results bridge between the Mahler measure and the zeta function via quantum walks for the first time. Copyright © 2022, The Authors. All rights reserved.

关键词： Random processes

A generalized grover/zeta correspondence

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arXiv 2022年

We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function and a generalized zeta function of a graph G with respect to its generalized Grover matrix as an analog of the Ihara zeta function and present explicit formulas for their zeta functions for a vertex-transitive graph. As applications, we express the limit on the generalized zeta functions of a family of finite vertex-transitive regular graphs by an integral. Furthermore, we give the limit on the generalized zeta functions of a family of finite tori as an integral *** Codes 60F05, 05C50, 15A15, 05C25 © 2022, CC0.

关键词： Functions

ABELIAN VON NEUMANN ALGEBRAS, MEASURE ALGEBRAS AND L∞-SPACES

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arXiv 2021年

作者： Blecher, David P. Goldstein, Stanislaw Labuschagne, Louis E. Department of Mathematics University of Houston HoustonTX77204-3008 United States Faculty of Mathematics and Computer Science University of Lódz Banacha 22 Lódz90-238 Poland DSI-NRF CoE in Math. and Stat. Sci Pure and Applied Analytics Internal Box 209 School of Math. & Stat. Sci. NWU PVT. BAG X6001 Potchefstroom2520 South Africa

We give a fresh account of the astonishing interplay between abelian von Neumann algebras, L∞-spaces and measure algebras, including an exposition of Maharam’s theorem from the von Neumann algebra *** Codes Primary:... 详细信息

关键词： Radon

Which Activation Function Works Best for Training Artificial Pancreas: Empirical Fact and Its Theoretical Explanation

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Which Activation Function Works Best for Training Artificial...

IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Lehel Dénes-Fazakas László Szilágyi György Eigner Olga Kosheleva Martine Ceberio Vladik Kreinovich Physiological Controls Research Center Appl. Informatics & Appl. Math. Doctoral School Óbuda University Budapest Hungary Computational Intelligence Res. Group Sapientia University Tg. Mures Romania Physiological Controls Res. Center Óbuda University Budapest Hungary Physiological Controls Res. Center John von Neumann Faculty of Informatics Biomatics and Applied AI Institute Obuda University Budapest Hungary Department of Teacher Education University of Texas at El Paso El Paso Texas USA Department of Computer Science University of Texas at El Paso El Paso Texas USA

One of the most effective ways to help patients at the dangerous levels of diabetes is an artificial pancreas, a device that constantly monitors the patient's blood sugar level and injects insulin based on this level. Patient's reaction to insulin is highly individualized, so the artificial pancreas needs to be trained on each patient. It turns out that the best training results are attained when instead of the usual ReLU neurons, we use their minor modification known as Exponential Linear Units (ELU). In this paper, we provide a theoretical explanation for the empirically observed effectiveness of ELUs.

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EVALUATION OF THE PRONUNCIATION OF TAJWEED RULES BASED ON DNN AS A STEP TOWARDS INTERACTIVE RECITATION LEARNING

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arXiv 2025年

作者： Shaiakhmetov, Dim Gimaletdinova, Gulnaz Cankurt, Selcuk Momunov, Kadyrmamat Department of Computer Science Ala-Too International University Bishkek Kyrgyzstan Department of Applied Math Ala-Too International University Bishkek Kyrgyzstan Department of Computer Engineering Vistula University Warsaw Poland Department of Engineering and Natural Sciences Suleyman Demirel University Almaty Kazakhstan

Proper recitation of the Quran, adhering to the rules of Tajweed, is crucial for preventing mistakes during recitation and requires significant effort to master. Traditional methods of teaching these rules are limited by the availability of qualified instructors and time constraints. Automatic evaluation of recitation can address these challenges by providing prompt feedback and supporting independent practice. This study focuses on developing a deep learning model to classify three Tajweed rules—separate stretching (Al Mad), tight noon (Ghunnah), and hide (Ikhfaa)—using the publicly available QDAT dataset, which contains over 1,500 audio recordings. The input data consisted of audio recordings from this dataset, transformed into normalized mel-spectrograms. For classification, the EfficientNet-B0 architecture was used, enhanced with a Squeeze-and-Excitation attention mechanism. The developed model achieved accuracy rates of 95.35%, 99.34%, and 97.01% for the respective rules. An analysis of the learning curves confirmed the model’s robustness and absence of overfitting. The proposed approach demonstrates high efficiency and paves the way for developing interactive educational systems for Tajweed study. Copyright © 2025, The Authors. All rights reserved.

关键词： Transfer learning

Calcination Temperature-Dependent Structural and Photoluminescence Properties of Hydroxyapatite Derived from Labeo Rohita Fish Scales

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Journal of The Institution of Engineers (India): Series D 2020年第2期101卷 223-232页

作者： Sinha, Arijit Pal, Anindya Santra, A. Murmu, S. Ghorai, U.K. Chowdhury, Amit Roy Banerjee, D. Dr. M.N. Dastur School of Materials Science Engineering Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Ramakrishna Mission Vidyamandira Department of Industrial Chemistry & Applied Chemistry Swami Vivekananada Research Centre Belur Math Howrah711202 India Aerospace Engineering and Applied Mechanics Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Faculty of Engineering and Computer Science Teerthanker Mahaveer University MoradabadUP244001 India

The nanocrystalline hydroxyapatite was synthesized from Labeo Rohita fish scales by calcination of raw scales at temperatures ranges from 400 to 1000 °C. The synthesized powders were characterized using, X-ray diffraction (XRD), thermogravimetric/differential thermal analyzer (TG–DTA), Fourier transform infrared spectroscopy, scanning and high-resolution transmission electron microscope and energy-dispersive X-ray analysis, respectively. Crystallite size, crystallinity and lattice parameters of HAp were evaluated from XRD, and it is shown that the average crystallite sizes were significantly enhanced with the calcination temperature attending its maximum value at ~ 40 nm. TG–DTA analysis predicts the thermal stability of the samples, and it has been observed that the thermal stability increases with the calcination temperature. Moreover, a detailed photoluminescence study of the as-synthesized samples has been carried out for the first time and an appropriate excitation energy gives rise to several distinct peaks in the emission spectra which has not been reported previously. © 2020, The Institution of Engineers (India).

关键词： Optical properties

Electrical Detection of Magnetization Switching in Single-Molecule Magnets

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arXiv 2024年

作者： Alqahtani, Amjad Henry, DaVonne Havlíček, Lubomír Marie, Luke St. Hrubý, Jakub Sojka, Antonín Hale, Morgan Felsenfeld, Samuel El Fatimy, Abdelouahad Myers-Ward, Rachael L. Kurt Gaskill, D. Nemec, Ivan Neugebauer, Petr Liu, Amy Y. Barbara, Paola Department of Physics Georgetown University WashingtonDC20057 United States Central European Institute of Technology CEITECBUT Purkyňova 656/123 Brno61200 Czech Republic Department of Math Computer Science and Physics Roanoke College RoanokeVA24153 United States Department of Physics University of Maryland College ParkMD20742 United States Institute of Applied Physics Mohammed VI Polytechnic University Lot 660 Hay Moulay Rachid Ben Guerir43150 Morocco U.S. Naval Research Laboratory WashingtonDC20375 United States Institute for Research in Electronics and Applied Physics University of Maryland College ParkMD20742 United States Department of Inorganic Chemistry Faculty of Science Palacký University Olomouc Olomouc77146 Czech Republic

Single-molecule magnets (SMMs) with chemically tailorable properties are potential building blocks for quantum computing, high-density magnetic memory, and spintronics.1 2 3,4 These applications require isolated or few molecules on substrates, but studies of SMMs have mainly focused on bulk crystals. Moreover, fabrication of SMM-based devices and electrical detection of the SMM magnetic state are still coveted milestones that have so far been achieved mainly for double-decker rare-earth phthalocyanines at temperatures below 1 K.5-8 Here we demonstrate electrical detection of magnetization switching for a modification of the archetypal SMM Mn12, up to 70 K, based on the supramolecular spin valve effect5 with graphene quantum dots9. Notably, the exchange interaction between the molecules and the graphene, as well as the dot-mediated intermolecular interaction, can be directly extracted from the electrical response, opening the way to an effective characterization of the quantum properties of different types of SMMs in a wide temperature range. Copyright © 2024, The Authors. All rights reserved.

关键词： Nanocrystals

Stem and topological entropy on cayley trees

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arXiv 2021年

作者： Ban, Jung-Chao Chang, Chih-Hung Wu, Yu-Liang Wu, Yu-Ying Department of Mathematical Sciences National Chengchi University Taipei11605 Taiwan Math. Division National Center for Theoretical Science National Taiwan University Taipei10617 Taiwan Department of Applied Mathematics National University of Kaohsiung Kaohsiung81148 Taiwan Department of Applied Mathematics National Chiao Tung University Hsinchu30010 Taiwan Department of Mathematics National Central University Taoyuan32001 Taiwan

We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced. For shift spaces on a strict free semigroup, the stem entropy coincides with the topological entropy. We reveal a sufficient condition for the existence of the stem entropy of shift spaces on a semigroup. Furthermore, we demonstrate that the topological entropy exists in many cases and is identical to the stem entropy. Copyright © 2021, The Authors. All rights reserved.

关键词： Entropy

RBL-STEM learning activity framework: Improving combinatorial thinking skills by solving local (a, d)-edge antimagic coloring problem and its application to vertical farming analysis using GNN

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AIP Conference Proceedings 2024年第1期3148卷

作者： Eric Dwi Putra Slamin Arika Indah Kristiana Abi Suwito Dafik Mathematics Education Departement PGRI University Argopuro Jember Jember Indonesia Department of Computer Science University of Jember Jember Indonesia Department of Math. Education Postgraduate University of Jember Jember Indonesia PUI-PT Combinatorics and Graph CGANT University of Jember Jember Indonesia

Combinatorial thinking skills are needed in the technological era. Combinatorial thinking skills are essential in many fields, including math.matics, computer science, and statistics. Combinatorial thinking consists of five indicators: identifying various problems, understanding problem patterns, applying math.matical patterns, math.matical proof, and considering various combinations of problems. These indicators can be achieved by honing higher-order thinking skills. However, students’ combinatorial thinking skills are still relatively low. One of the reasons for this low ability is that the learning model applied so far has not developed this ability adequately. Therefore, this study will use a research-based learning (RBL) model integrated with a STEM approach to solve local antimagic coloring (a,d) in solving vertical farming problems with artificial neural network techniques. While the local antimagic (a,d)-edge coloring of G if the set of edge colors form an arithmetic sequence with different initial values of a and d. The local antimagic (a,d)-edge chromatic number χ^’ le(G) is the minimum number of colors required to color G such that the graph G satisfies the local antimagic (a,d)-edge coloring. This type of research uses qualitative methodology. This research will formulate syntax to develop learning activities using research-based learning (RBL) and STEM approach, by including assessment indicators for digital marketing literacy skills. The results show six stages of learning activities as a framework for developing RBL-STEM learning materials. Recommendations for further research related to the development of tools and analysis of RBL-STEM implementation

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