Adjoint and Direct Characteristic Equations for Two-Dimensional Compressible Euler Flows
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D steady-state Euler equations and the first goal of this ...
Kevin Ancourt +2 more
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Stability Behaviour in Functional Differential Equations of the Neutral Type
In this study, we examine the behavior of solutions of the neutral functional differential equations. Using a suitable real root of the corresponding characteristic equation, the asymptotic behavior of the solutions and the stability of the trivial ...
Ali Fuat Yeniçerioğlu +2 more
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Relative Free Energy Function and Structural Theory of Thermoeconomics
This paper explores the advantages of using relative free energy instead of exergy to build a mathematical theory of thermodynamic costs to diagnose malfunctions in thermal systems.
Antonio Valero, César Torres
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Specificity of the Mathematical Modeling of Light Fields in a Sensing Element for the Fiber-Based Evanescent-Wave Mid-IR Spectroscopy [PDF]
Background and Objectives: The fiber-based evanescent-wave mid-IR spectroscopy is a prospective tool for the real-time remote chemical analysis of various substances, which have their vibrational spectra in the mid-IR spectral range.
Korsakova, Svetlana Vladimirovna +1 more
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Characteristic Neural Ordinary Differential Equations
We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an ODE, C-NODE models the evolution of the latent variables as the solution of a family of first-order quasi-linear ...
Xingzi Xu +4 more
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Hopf bifurcation analysis of a delayed five-neuron BAM neural network with two neurons in the X-layer [PDF]
In this paper, a bidirectional associative memory (BAM) neural network, which consists of two neurons in the X-layer and three neurons in the Y-layer, with two time delays will be studied.
E. Javidmanesh, Z. Afsharnezhad
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Characteristics of Conservation Laws for Difference Equations [PDF]
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem.
Timothy J. Grant 0002, Peter E. Hydon
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To the solution of one pseudo-Volterra integral equation
In this paper, we study a homogeneous singular integral Volterra equation of the second kind (pseudoVolterra integral equation). The singularity of the integral equation is shown. Properties of its kernel are proved.
M.T. Jenaliyev +3 more
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On the Characteristic Values of Linear Integral Equations [PDF]
on the basis of the general analytic properties of the kernel K (x, ~) such as im tegrability, continuity, differentiability, analyticity and the like? The l i tera ture where this and analogous questions are t rea ted is v e r y considerable [HELLI~G~n-To~eLITZ, I].
Hille, Einar, Tamarkin, J. D.
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Characteristic polynomials of complex random matrix models [PDF]
We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of
Akemann, G +3 more
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