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Closed-form steady-state solutions for forced vibration of second-order axially moving systems
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional...
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Closed-Form Solutions for Single-Axis Slew Maneuvers Under a Fixed Final Time Constraint
This paper addresses a single-axis rotation problem in diverse space applications. In the problem, spin-to-spin boundary conditions, a finite jerk...
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A highly effective analytical approach to innovate the novel closed form soliton solutions of the Kadomtsev–Petviashivili equations with applications
Nonlinear partial integro-differential equations (PIDEs) are applied to present the various practical phenomena in a multitude of sectors of modern...
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Closed-form solutions for two-layer Timoshenko beams with interlayer slip, uplift and rotation compliance
An analytical model for a two-layer Timoshenko beam allowing for interlayer slip, uplift, and relative rotations of the layers’ cross-sections...
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Finding the closed-form solutions of dissipative oscillatory systems
This paper shows how to use the approximate Hamiltonian approach for the non-conservative system not capable of possessing Hamiltonian. Using the...
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Recurrence Equations and Their Closed-Form Solutions
In so-called “divide and conquer” algorithms one usually ends up with a recurrence relation (i.e., inductive or recursive definition!) that defines...
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New closed-form solutions for flexural vibration and eigen-buckling of nanoplates based on the nonlocal theory of elasticity
This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The...
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Closed-form solutions of consistency ratio in best worst method minmax optimization model: max of edge error matrix and minmax edge error determinant methods
The Best Worst Method (BWM), a reduced version of the AHP, is a recent multi-criteria decision-making tool based on pairwise comparisons with...
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Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture
This paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local...
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Linear Systems Under Gaussian White Noise Excitation: Exact Closed-Form Solutions
In Chap. 3 , the Wiener path integral formulation developed in Chap. 2 for...
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Closed-form formulae for inflation correlators
We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a...
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Closed-form solutions for regional earthquake–induced landslide prediction: rotational failure mechanism
Seismic slope stability analysis at regional scale (e.g., landslide hazard map**, infrastructure slope management) is essential in areas that are...
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An Approximate Closed-Form Solution for Mass Transfer Flow Due to a Rotating Rough and Porous Disk
It is often difficult to obtain exact solutions of nonlinear differential equations and one looks for their approximate solutions. These approximate...
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Closed-Form Time-Domain Solutions of Arbitrary-DOF Forced Vibrations and of Surface Location Error for General-Helix Cylindrical Milling Tools
BackgroundPeriodic cutting forces are inevitably generated during milling processes and the associated forced vibrations leave behind an imprint...
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Closed-Form Solution of Conic in Point-Line Enumerative Problem of Conic
We use the reciprocal transformation to propose the closed-form solutions to the conics through m points and tangent to n lines satisfying
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Closed-form continuous-time neural networks
Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making...
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Newly constructed closed-form soliton solutions, conservation laws and modulation instability for a (2+1)-dimensional cubic nonlinear Schrödinger’s equation using optimal system of Lie subalgebra
The primary goal of this work is to derive newly constructed invariant solutions, conservation laws, and modulation instability in the context of the...
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Theory and Closed-Form Solutions for Three- and n-Layer Flat Refractive Geometry
We develop in this paper a new formulation for the calibration and pose estimation of three-layer flat-refractive geometry. We then extend it into...
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