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Generalization of Advanced Encryption Standard Based on Field of Any Characteristic

Computers, Materials & Continua 2022年第12期73卷 6121-6138页

作者： Nabilah Abughazalah Majid Khan Noor Munir Ammar SAlanazi Iqtadar Hussain Department of Mathematical Sciences College of SciencePrincess Nourah Bint Abdulrahman UniversityP.O.Box 84428Riyadh 11671Saudi Arabia Department of Applied Mathematics&Statistics Institute of Space TechnologyIslamabadPakistan King Abdulaziz City for Science and Technology RiyadhSaudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar Statistical Consulting Unit College of Arts and ScienceQatar UniversityDohaQatar

Nowadays most communications are done by utilizing digital transmission *** security of this digital information transmitted through different communication systems is quite *** secrecy of digital data is one of the burning topics of the digitally developed *** exist many traditional algorithms in the literature to provide methods for robust *** most important and recent modern block cipher named the advanced encryption standard(AES)is one of the extensively utilized encryption schemes with binary *** is a succession of four fundamental steps:round key,sub-byte,shift row,and mix *** this work,we will provide an innovative methodology for extending the AES in a Galois fieldwith any characteristic *** four steps in the fundamental process with binary characteristics will be adjusted because of the new *** applying double affine transformations,we have enhanced the number of options in our suggested substitution *** reconstruction of the nonlinear confusion component and encryption structure provides robustness in the generalized *** increase in the keyspace due to the Galois field generalization implies that we have improved additional confusion abilities and broadened the current *** implementation of the proposed structure of AES for image,audio,and video encryption will provide high security for secure communication.

关键词： AES generalized AES binary field ternary function

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Synergetic effects of multiple junction and surface hydroxyl in Cu/CuO/Cu2O/TiO2 heterostructures towards highly efficient photocatalysts for hydrogen generation

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Materials Science for Energy Technologies 2025年 8卷 131-142页

作者： Subagyo, Riki Anindika, Garcelina Rizky Aufkani, Afif Akmal Zhang, Lei Ardhyananta, Hosta Burhan, R.Y. Perry Nugraheni, Zjahra Vianita Akhlus, Syafsir Bahruji, Hasliza Prasetyoko, Didik Wellia, Diana Vanda Ivansyah, Atthar Luqman Arramel Kusumawati, Yuly Department of Chemistry Faculty of Science and Analytic Data Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Center of Excellence Applied Physics and Chemistry Nano Center Indonesia Jl PUSPIPTEK South Tangerang Banten15314 Indonesia Department of Physics National University of Singapore Singapore117551 Singapore Department of Materials and Metallurgical Engineering Faculty of Industrial Technology and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Centre of Advanced Material and Energy Science Universiti Brunei Darussalam Jalan Tungku Link BE 1410 Brunei Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Andalas Padang25163 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Science Institut Teknologi Bandung Jalan Ganesha No. 10 Bandung40132 Indonesia Instrumentation and Computational Physics Research Group Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesha No.10 West Java Bandung40132 Indonesia

The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide band gap of a photo-sensitive material of TiO2 are detrimental toward the targeted catalytical reaction. In this study, we present the rational design, fabrication, photocatalytic performance of TiO2-Cu/CuO/Cu2O heterostructures (CuTi) using viable chemical reduction method. The Z-scheme and S-scheme are succesfully generated across the TiO2/CuO/Cu2O interfaces, while the Schottky junction arises on the Cu perimeters. This is evidenced from the blue shifted about 0.3 eV of Cu 2p core level determined by using X-ray photoemission spectroscopy (XPS), in combination with the formation of inverse V-shape of the Mott-Schottky plots. In addition, we find that Cu/CuO/Cu2O facilitates photon absorption range up to the visible region. The multiple heterojunction and the large number of OHsurface enhanced charge carrier transfer are associated to the suppression of photoluminescence (PL) intensity, high surface hydroxyl (OHsurface) density in CuTi probed by XPS, and fast electron transfer based on the electrochemical measurements. The presence of OHsurface inhibits the recombination of electron. A significant H2 photogeneration rate enhancement is achieved when an optimized 5 wt% Cu/CuO/Cu2O concentration is used on TiO2 to achieve 7,157.19 μmol·g−1 (1,789.30 μmol·g−1·h−1). Based on this finding, zero emission energy innitiative could be materialized under multiple heterojunctions in photocatalytic process is beneficial for enhancing the H2 production. © 2025 The Authors

关键词： Titanium dioxide

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Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes

arXiv

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arXiv 2023年

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of O(∈2) (∈ > 0 and arbitrary) with a cost of O(∈-2.5) versus using a particle filter which has a cost of O(∈-3) to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation. Key words: Unbiased Methods, Multilevel Monte Carlo, Non-Linear Filtering, Point Processes, Parameter *** Codes 60G55, 60G35, 62M20, 62F30 © 2023, CC BY.

关键词： Diffusion

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Bayesian Parameter Inference for Partially Observed Stochastic Volterra Equations

arXiv

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arXiv 2023年

作者： Jasra, Ajay Ruzayqat, Hamza Wu, Amin Applied Mathematics & Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many areas such as physics and mathematical finance. In the latter field they can be used to represent long memory in unobserved volatility processes. In many cases of practical interest, SVEs must be time-discretized and then parameter inference is based upon the posterior associated to this time-discretized process. Based upon recent studies on time-discretization of SVEs (e.g. [24]) we use Euler-Maruyama methods for the afore-mentioned discretization. We then show how multilevel Markov chain Monte Carlo (MCMC) methods [19] can be applied in this context. In the examples we study, we give a proof that shows that the cost to achieve a 4 mean square error (MSE) of O(ϵ2), ϵ > 0, is O(ϵ− 4/2H+1 ), where H is the Hurst parameter. If one uses a single level MCMC method then the cost is O(ϵ−2(2H+3)/ 2H+1 ) to achieve the same MSE. We illustrate these results in the context of state-space and stochastic volatility models, with the latter applied to real *** Codes 62F15, 62M20, 60J10, 60J22, 65C40 © 2023, CC BY.

关键词： Mean square error

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Semiclassical Wkb Problem for the Non-Self-Adjoint Dirac Operator Withan Analytic Rapidly Oscillating Potential

SSRN

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SSRN 2022年

作者： Fujiie, Setsuro Hatzizisis, Nicholas Kamvissis, Spyridon Department of Mathematical Sciences Ritsumeikan University Japan Department of Mathematics & Applied Mathematics University of Crete Institute of Applied and Computational Mathematics FORTH Greece

In this paper we examine the semiclassical behaviorof the scattering data of anon-self-adjoint Dirac operator with a rapidly oscillatingpotential that is complex analytic in some neighborhood of the real *** of our results are rigorous and quite *** the other hand, complete and concrete understanding requires the investigation ofthe WKB geometry of specific *** such detailed computations we use a particular example that has been investigated numericallymore than 20 years ago by Bronski and Miller and rely heavily on their numerical *** employing the exact WKB method, we provide the complete rigorous uniformsemiclassical analysis of the Bohr-Sommerfeld condition for the location of theeigenvalues across unions of analytic arcs as well as the associated norming *** the reflection coefficient as well as the eigenvalues near 0 in the spectral plane, weemploy instead an older theory that hasbeen developed in great detail by Olver. Our analysis is motivatedby the need to understand the semiclassical behaviour of the focusing cubic NLS equationwith initial data $A\exp\{iS/\epsilon\}$, in view of the well-known fact discoveredby Zakharov and Shabat that the spectral analysis of the Dirac operator enablesthe solution of the NLS equation via inverse scattering theory. © 2022, The Authors. All rights reserved.

关键词： Spectrum analysis

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Semiclassical WKB Problem for the non-self-adjoint Dirac operator with an analytic rapidly oscillating potential

arXiv

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arXiv 2022年

作者： Fujiié, Setsuro Hatzizisis, Nicholas Kamvissis, Spyridon Department of Mathematical Sciences Ritsumeikan University Japan Department of Mathematics & Applied Mathematics University of Crete Institute of Applied and Computational Mathematics FORTH Greece

In this paper we examine the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a rapidly oscillating potential that is complex analytic in some neighborhood of the real line. Some of our results are rigorous and quite general. On the other hand, complete and concrete understanding requires the investigation of the WKB geometry of specific examples. For such detailed computations we use a particular example that has been investigated numerically more than 20 years ago by Bronski and Miller and rely heavily on their numerical computations. Mostly employing the exact WKB method, we provide the complete rigorous uniform semiclassical analysis of the Bohr-Sommerfeld condition for the location of the eigenvalues across unions of analytic arcs as well as the associated norming constants. For the reflection coefficient as well as the eigenvalues near 0 in the spectral plane, we employ instead an older theory that has been developed in great detail by Olver. Our analysis is motivated by the need to understand the semiclassical behaviour of the focusing cubic NLS equation with initial data Aexp{iS/Ε}, in view of the well-known fact discovered by Zakharov and Shabat that the spectral analysis of the Dirac operator enables the solution of the NLS equation via inverse scattering theory. © 2022, CC BY.

关键词： Eigenvalues and eigenfunctions

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Unbiased Parameter Estimation for Partially Observed Diffusions

arXiv

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arXiv 2023年

作者： Awadelkarim, Elsiddig Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically out-perform existing unbiased *** Codes 60J22, 62M05, 65C40, 62M20 © 2023, CC BY.

关键词： Parameter estimation

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CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR QUASICONVEX AND RELAXED VARIATIONAL PROBLEMS

arXiv

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arXiv 2025年

作者： Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambo Vikelis, Andreas Computer Electrical Mathematical Sciences and Engineering Division KAUST Saudi Arabia Department of Mathematics University of Sussex United Kingdom Institute of Applied & Computational Mathematics Foundation for Research & Technology-Hellas Greece Department of Mathematics and Applied Mathematics University of Crete Greece Faculty of Civil Engineering Czech Technical University of Prague Czech Republic

In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential flexibility by removing inter-element continuity while also guaranteeing convergent approximations in the quasiconvex case. Notably, quasiconvexity is the weakest form of convexity pertinent to elasticity. Furthermore, we show that in the non-convex case discrete minimisers converge to minimisers of the relaxed problem. In this case, the minimisation problem corresponds to the energy defined by the quasiconvex envelope of the original energy. Our approach covers all discontinuous Galerkin formulations known to converge for convex energies. This work addresses an open challenge in the vectorial calculus of variations: developing and rigorously justifying numerical schemes capable of reliably approximating nonlinear energy minimization problems with potentially singular solutions, which are frequently encountered in materials science. © 2025, CC BY.

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Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

arXiv

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arXiv 2025年

作者： Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou School of Mathematical Sciences Fudan University China Electrical and Computer Engineering North Carolina State University United States Department of Mathematics Department of Physics Department of Chemistry Duke University United States School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Key Laboratory of Computational Physical Sciences Ministry of Education China

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of O(n) with about n ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry. © 2025, CC BY.

关键词： Wave functions

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Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

arXiv

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arXiv 2024年

作者： Koutsimpela, Angeliki Loulakis, Michail Department of Mathematics University of Augsburg Augsburg86159 Germany School of Applied Mathematical and Physical Sciences National Technical University of Athens Athens15780 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas Crete Heraklion70013 Greece

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake *** Codes 93E20, 60H30, 49L25 Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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