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8 articles for “perturbation theory”
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Phase Behaviour Study of a Mesogen in a Solvent Role of Molecular Rigidity and Configurational Entropy
Abstract: The phase behaviour of a nematogen 4’-n-pentyloxy-4-biphenylcarbonitrile (POBPCB) has been studied with respect to the translational and orientational motions. The charges of atoms and their dipole moments have been estimated by implementing the complete neglect differential overlap (CNDO/2) method. The long-range interactions have been analyzed using modified Rayleigh- Schrodinger Perturbation theory together with the multicentred-multipole expansion scheme. The “6- exp” potential function has been considered to study the short-range interactions. …
Published in Research & Reviews : Journal of Physics Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination
Abstract: A tensor-operator framework is developed for fuzzy conjunction, fuzzy disjunction, and symmetry-preserving state discrimination in multi-qubit quantum systems. In this formulation, fuzzy membership and non-membership degrees are represented through expectations of effect operators acting on density matrices, providing a natural bridge between fuzzy logic and quantum measurement theory. Conjunction and disjunction operations are extended to the quantum domain via tensorised channels, constructed using projective measurements and unitary transformations, enabling logical …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 08–15 Read article
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Study on the Method of Constructing a System of Linear Equations for Calculating Aerodynamic Derivatives
Abstract: The aerodynamic derivatives can be calculated from the unsteady hydrodynamic forces experienced by the harmonic-oscillating vehicle. Until now, unsteady flow field analysis in aerodynamic derivative calculations has been applied mainly to thin bodies based on potential theory MSC. Nastran is a typical application based on potential theory MSC. Natran can calculate the aerodynamic derivatives of the vehicle relatively well in the subsonic region, but in the supersonic region, the fuselage …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 3, 2025 · pp. 14–24 Read article
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Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces
Abstract: This paper extends the Hicks contraction theory to multi-valued mappings within generalized b-Manger spaces, a class of metric-like structures that accommodate more flexible distance functions. By introducing new definitions, such as generalized admissibility conditions and weak compatibility in the multivalued sense, we provide a comprehensive analysis of how these contractions behave in broader topological and metric contexts. Our approach systematically generalizes classical contraction principles by relaxing conventional constraints, thereby broadening …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 1–05 Read article
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From Rural to Urban: Understanding Taobao Villages to Redress Planetary Urbanisation
Abstract: This study examines Taobao Villages as an innovative model of urbanisation under China’s planetary urbanisation framework. These rural communities, driven by the rise of e-commerce and digital infrastructure, have successfully integrated into the broader urban ecosystem by reconfiguring their historical socio-spatial legacies. Through Lefebvre’s spatial triad framework, the research identifies three key historical legacies that underpin this transformation: (1) Collective Production Practices: Rooted in socialist collectivisation, these legacies include organisational …
Published in International Journal of Urban Design and Development · Vol. 3, Issue 1, 2025 · pp. 1–7 Read article
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LQR-Based Optimal Control of Inverted Pendulum System with State Estimation and Stability Analysis
Abstract: The inverted pendulum on a cart is a canonical benchmark problem in control systems engineering, capturing the essential challenges of stabilizing an inherently unstable, underactuated, and nonlinear plant. Classical Proportional-Integral-Derivative (PID) controllers, while widely employed in industrial practice, exhibit fundamental performance limitations when applied to such systems, primarily due to their inability to account for multivariable coupling, process noise, and the absence of a systematic optimization framework. This paper presents …
Published in International Journal of Advanced Control and System Engineering · Vol. 4, Issue 1, 2026 · pp. 31–43 Read article
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Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems
Abstract: This paper presents a representation-theoretic framework for symmetry-aware vibration control in modular structural systems. Exploiting cyclic symmetry, the mass, damping, and stiffness operators are block-diagonalised into irreducible representations, reducing the full structural dynamics to a collection of lower-dimensional modal subsystems. This decomposition provides both computational efficiency and a rigorous mathematical description of symmetry-preserving dynamic behaviour. To account for imperfections arising in practical implementations, near-symmetry defects in stiffness and damping are …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 22–30 Read article