Results 41 to 50 of about 341 (205)
Application of the Residue Theorem to Trigonometric Sum Identities
, 2011 By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special ...
Wang Xin
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen +3 more
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
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On Compressible Fluid Flows of Forchheimer‐Type in Rotating Heterogeneous Porous Media
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer‐type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo‐pressure.
Emine Celik, Luan Hoang, Thinh Kieu
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On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
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, 2022 We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the 1+1-dimensional nonlinear Schrödinger equation. Similar to a Gaussian profile, the Fourier transform for the hyperbolic secant
Natanael Karjanto
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Stop Using Limiting Stimuli as a Measure of Sensitivities of Energetic Materials
Propellants, Explosives, Pyrotechnics, EarlyView.ABSTRACT Accurately estimating the sensitivity of explosive materials is a potentially life‐saving task that requires standardised protocols across nations. One of the most widely applied procedures worldwide is the so‐called ‘1‐In‐6’ test from the United Nations (UN) Manual of Tests in Criteria, which estimates a ‘limiting stimulus’ for a material. In
Dennis Christensen, Geir Petter Novik
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On Small Complete Sets of Functions
, 2000 Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα ⊂ C2. The completeness theorem
Alekos Vidras, Lev Aizenberg
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International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This paper is concerned with the platooning control problem of connected automated vehicles (CAVs) under non‐uniform stochastic vehicle‐to‐vehicle (V2V) communication delays. Most existing relevant studies assume uniform or deterministic or slowly varying delays, or design platoon controllers based on worst‐case delay bounds, resulting in ...
Dengfeng Pan +3 more
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IET Smart Energy Systems, EarlyView.A resilient estimation and control framework is developed for smart‐grid cyber‐physical systems to simultaneously detect cyberattacks and estimate physical faults. The proposed method ensures accurate estimation and robust performance under disturbances and sparse sensor attacks.
Jin Li, Youmin Zhang
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