Current Issue : October-December Volume : 2026 Issue Number : 4 Articles : 5 Articles
The objective of this paper is to introduce the application of quantum annealing (QA) to electromagnetic (EM) engineering. We demonstrate that numerous EM design and inverse problems naturally admit a mathematical formulation in terms of binary quadratic interactions. By utilizing didactic, simplified examples, we illustrate how this underlying physical structure allows for a direct mapping of EM problems onto Quadratic Unconstrained Binary Optimization (QUBO) models and equivalent Ising Hamiltonians. All numerical experiments are conducted using Simulated Annealing as a classical proxy, since the primary contribution of this work is the QUBO formulation itself rather than its execution on quantum hardware. Our results suggest that a broad class of EM problems—including array thinning, reconfigurable intelligent surface optimization, subarray partitioning, and electromagnetic inverse scattering—are suitable candidates for optimization using nearfuture quantum annealing architectures, once hardware connectivity and noise floors reach the required specifications....
This paper investigates the dynamics and flutter characteristics of a two-degree- of-freedom airfoil with cubic (third-order) structural stiffness nonlinearity, which captures the hardening behavior essential for predicting limit cycle oscillations and Hopf bifurcation in aeroelastic systems. Herein, the “binary wing” (or “binary airfoil”) specifically refers to the classic two-degree-of-freedom typical-section airfoil model, which idealizes the wing as a rigid profile undergoing plunge (heave) and pitch motions, capturing the fundamental aeroelastic coupling. The equations of motion are derived using Lagrange’s principle, and a state-space representation is formulated by incorporating an aerodynamic model. The variation of system eigenvalues with flow velocity is analyzed to determine the linear flutter critical speed. Numerical simulations are employed to verify the existence of subcritical flutter. The research demonstrates that the binary airfoil with nonlinear stiffness can exhibit stable limit cycle oscillations at subcritical speeds, with distinct patterns in modal coupling and flutter frequency evolution with velocity....
This study examines graphs that demonstrate Gallai’s property, particularly those in which for every prescribed set S of vertices with |S| = j there exists a longest path or cycle that avoids that set. Such graphs are naturally fault-tolerant in the structural sense: if some vertices fail, there can still exist longest routes that bypass the failed vertices. Our main purpose is to construct explicit Gallai-type graphs that admit embeddings into a rigorously defined three-dimensional geometric adjacency structure derived from an icosahedral–tetrahedral polyhedral cell complex. We show that similar graphs may be found in three-dimensional structures obtained from a periodic polyhedral packing (cell complex) built from tetrahedral and icosahedral cells. Importantly, we do not claim a face-to-face tessellation of R3 by congruent regular icosahedra and tetrahedra; instead, we define a specific periodic cell complex IT 3 and work in its associated adjacency graph Γ(IT 3). These geometric constructions expand lattice-based findings to a three-dimensional adjacency setting and provide new embeddings for Gallai-type graphs. Connections to AI systems are mentioned at the conceptual level....
Against the backdrop of accelerated glacier melting caused by global warming, dynamic monitoring of glacial lake water quality has become an important topic in environmental science. There is a significant correlation between lake water color and turbidity, but this relationship is often nonlinear. This paper introduces the logistic regression equation, applies a Logit transformation to turbidity data to convert the nonlinear relationship into a linear one, and then establishes a regression model using the least squares method. Taking a set of simulated RGB image data from a glacial lake as an example, this paper demonstrates the scientific research paradigm of “problem definition to data transformation to linear modeling to inverse transformation prediction to statistical testing”. The results show that the logistic regression-based modeling method can effectively fit the S-shaped relationship between water color and turbidity, with a coefficient of determination R2 reaching 0.996 and a mean absolute error of 0.292 NTU. This paper reveals the extended application of basic mathematics in real scientific research and provides a case study for helping secondary school students understand nonlinear modeling ideas....
We introduce a mathematical model describing a dynamical system made up of interdependent compartments subject to intrinsic fragility and cross-support. The dynamics are driven by the competition between hierarchical sublinear dissipation and cyclic coupling, enabling a natural interpretation of transitions between distinct regimes (e.g., resilience versus degradation, vulnerability and crisis/extinction in finance or biology). We establish the existence, uniqueness, positivity, and global continuation of solutions. We also investigate the qualitative behavior of the system by studying the stability of equilibrium points and deriving threshold conditions characterizing increasing, decreasing, and stationary regimes. Numerical simulations are provided to illustrate the theoretical results and the transition phenomena between extinction and self-sustained dynamics....
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