A Hybrid SVD-Based Image Watermarking Scheme Utilizing Both U and V Orthogonal Vectors for Robustness and Imperceptibility by Yuan Ju Teoh, Huo-Chong Ling, Wei Kitt Wong, Thomas Anung Basuki

“…SVD-based watermarking algorithm is one of the most preferable algorithms for copyright protection due to its singular values (SVs) that have outstanding stability and represents intrinsic algebraic image properties. Hence, there is a good trade-off between robustness and imperceptibility. …”
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Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator by Kholmat Shadimetov, Aziz Boltaev, Roman Parovik

“…Using discrete analogs of differential operators, optimal interpolation, quadrature, and difference formulas exact for algebraic polynomials, trigonometric and exponential functions can be constructed. …”
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On the Hodge, Tate and Mumford-Tate Conjectures for Fibre Products of Families of Regular Surfaces with Geometric Genus 1 by Olga V. Oreshkina (Nikol’skaya)

“…Assume that the discriminant loci \(\Delta_i=\{\delta\in C\,\,\vert\,\, Sing(X_{i\delta})\neq\varnothing\} \quad (i = 1, 2)\) are disjoint, \(h^{2,0}(X_{ks})=1,\quad h^{1,0}(X_{ks}) = 0\) for any smooth fibre \(X_{ks}\), and the following conditions hold:\((i)\) for any point \(\delta \in \Delta_i\) and the Picard-Lefschetz transformation \( \gamma \in GL(H^2 (X_{is}, Q)) \), associated with a smooth part \(\pi'_i: X'_i\to C\setminus\Delta_i\) of the morphism \(\pi_i\) and with a loop around the point \(\delta \in C\), we have \((\log(\gamma))^2\neq0\);\((ii)\) the variety \(X_i \, (i = 1, 2)\), the curve \(C\) and the structure morphisms \(\pi_i:X_i\to C\) are defined over a finitely generated subfield \(k \hookrightarrow C\).If for generic geometric fibres \(X_{1s}\) \, and \, \(X_{2s}\) at least one of the following conditions holds: \((a)\) \(b_2(X_{1s})- rank NS(X_{1s})\) is an odd prime number, \(\quad\,\,\) \(b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})\); \((b)\) the ring \(End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp\) is an imaginary quadratic field, \(\quad\,\, b_2(X_{1s})- rank NS(X_{1s})\neq 4,\) \(\quad\,\, End_{ Hg(X_{2s})} NS_ Q(X_{2s})^\perp\) is a totally real field or \(\,\, b_2(X_{1s})- rank NS(X_{1s})\,>\, b_2(X_{2s})- rank NS(X_{2s})\) ; \((c)\) \([b_2(X_{1s})- rank NS(X_{1s})\neq 4, \, End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp= Q\); \(\quad\,\,\) \(b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})\),then for the fibre product \(X_1 \times_C X_2\) the Hodge conjecture is true, for any smooth projective \(k\)-variety \(X_0\) with the condition \(X_1 \times_C X_2\) \(\widetilde{\rightarrow}\) \(X_0 \otimes_k C\) the Tate conjecture on algebraic cycles and the Mumford-Tate conjecture for cohomology of even degree are true.…”
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Graded Rings Associated with Factorizable Finite Groups by Mohammed M. Al-Shomrani, Najla Al-Subaie

“…In this article, we introduce two different ways to put <i>R</i> into a non-trivial <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">G</mi></semantics></math></inline-formula>-weak graded ring that is a ring graded by the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">G</mi></semantics></math></inline-formula> which is defined with a binary operation ∗ and satisfying an algebraic structure with specific properties. The first one is by choosing a subset <i>S</i> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">G</mi></semantics></math></inline-formula> such that <i>S</i> is a group under the ∗ operation and putting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mi>t</mi></msub><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>∈</mo><mi mathvariant="fraktur">G</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>∉</mo><mi>S</mi></mrow></semantics></math></inline-formula>. …”
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A 2D Membrane MEMS Device Model with Fringing Field: Curvature-Dependent Electrostatic Field and Optimal Control by Paolo Di Barba, Luisa Fattorusso, Mario Versaci

“…In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> that weighs the terms <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow><mn>2</mn></msup></semantics></math></inline-formula>. …”
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Analytical and Numerical Methods for Solving Second-Order Two-Dimensional Symmetric Sequential Fractional Integro-Differential Equations by Sondos M. Syam, Z. Siri, Sami H. Altoum, R. Md. Kasmani

“…Then, we propose a numerical approach based on the operational matrix method, which involves deriving operational matrices for the differential and integral terms of the equation and combining them to generate a single algebraic system. This method allows for the efficient and accurate approximation of the solution without the need for projection. …”
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Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space by Erhan Güler, Ömer Kişi, Christos Konaxis

“…We define <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="fraktur">H</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </semantics> </math> </inline-formula> in <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>&#952;</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> coordinates for positive integers <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>&#8800;</mo> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>&#8800;</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mo>-</mo> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo>&#8800;</mo> <mo>-</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, and also in <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> coordinates, and then we obtain implicit algebraic equations of the Henneberg-type minimal surface of values <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mn>4</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>.…”
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Effective Sample Size with the Bivariate Gaussian Common Component Model by Letícia Ellen Dal Canton, Luciana Pagliosa Carvalho Guedes, Miguel Angel Uribe-Opazo, Tamara Cantu Maltauro

“…All properties affecting the univariate methodology were verified for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>S</mi><msub><mi>S</mi><mrow><mi>b</mi><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula> using simulation studies or algebraic methods, including scenarios to verify the impact of the BGCCM common range parameter on the estimated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>S</mi><msub><mi>S</mi><mrow><mi>b</mi><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula> values. …”
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Quantum Fractionary Cosmology: K-Essence Theory by J. Socorro, J. Juan Rosales

“…In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. …”
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Models and Algorithms for the Refinement of Therapeutic Approaches for Retinal Diseases by Elfriede Friedmann, Simon Dörsam, Gerd U. Auffarth

“…Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. …”
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The application of analytical methods to the study of Pareto - optimal control systems by I. K. Romanova

“…Considers the General algorithm of calculation: determine the scope of permissible values of parameters; investigates properties comonotonicity and contraventanas; to build an equal level (indifference curves); determined touch type: single sided (task is not strictly multicriteria) or bilateral (objective relates to the Pareto); for Pareto - tasks in the presence touch formed the system of algebraic equations whose solution yields the equation of the line Pareto in the parameter space. …”
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Implementation of Multidigit Multiplication Basing on Discrete Cosine and Sine Transforms by Andrii Tereshchenko, Valeriy Zadiraka

“…Among such problems are the calculation of systems of linear algebraic equations with the number of unknown 33-35 million, the calculation of nuclear reactor shells, modeling of physical and chemical processes, aerodynamics, hydrodynamics, information security, and so on. …”
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Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm by Oscar Danilo Montoya, Luis Fernando Grisales-Noreña, Lázaro Alvarado-Barrios, Andres Arias-Londoño, Cesar Álvarez-Arroyo

“…Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>26.89</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>27.60</mn><mo>%</mo></mrow></semantics></math></inline-formula> for each test feeder with respect to the benchmark cases.…”
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Inverse heat transport problems for coefficients in two‐layer domains and methods for their solution by S. Guseinov, A. Buikis

“…The proposed method reduces the non‐homogeneous inverse problem for coefficients to a set of two transcendent algebraic equations. Finally, the analytical solution to direct problem is obtained using Green's function. …”
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Introduction to double issue 41.1–2 on Features by Peter Svenonius, Martin Krämer

“…Interacting with these questions about the “geometric” relations among features is the algebraic structure of the features. For example, it is often assumed that privativity, in which opposition is marked by presence versus absence, is conceptually simplest and therefore the zero hypothesis. …”
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Editorial by Christian Gütl

“…Tucker from the United Kingdom introduce the Naive Fracterm Calculus, which is a new perspective on elementary arithmetic and can be described as naive when compared to a variety of algebraic and logical, axiomatic formalisations of elementary arithmetic. …”
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Ontological approach to consolidation of 3D models of objects of historical and cultural heritage and GIS by Андрій Володимирович Гончар, Станіслав Олексійович Довгий, Марина Андріївна Попова

“…To achieve this goal, a set of methods was used: to develop operational ontological models of heritage conservation objects – system analysis, set theory, graph theory, to formalize knowledge representation – algebraic-logical and obvious methods; for software implementation of information technology – design patterns and object-oriented analysis. …”
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Enhanced gauge symmetry in 6D F-theory by Johnson, Samuel Buck

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Monochromatic triangles, intermediate matrix products, and convolutions by Williams, Virginia Vassilevska, Polak, Adam, Lincoln, Andrea

“…The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(nω) time algorithms for ω < 2.373. …”
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Automated Optimization and Control of Modular Chemical Systems by Nikolakopoulou, Anastasia

“…The models are incorporated into a nonlinear MPC algorithm implemented in the JuMP algebraic modeling language, which results in very fast computational times. …”
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