Deduction of the Differential Equation of the Box-Like Thin Wall Contortion (Distortion) of the Cross-Section and the Approximate Calculation of the Normal Stress
Deduction of the Differential Equation of the Box-Like Thin Wall Contortion (Distortion) of the Cross-Section and the Approximate Calculation of the Normal Stress
As for the variable depth box girders, difference method is applied to solve the differential equations and the boundary conditions of the variable depth box girders, which are derived according to the differential equations of the constant depth box girder.
Based on the Terzaghi consolidation theory and the Carrillo theorem, the differential equations for vertical, radial and total consolidation of gravel pile composite foundation under embankment are derived, as well as their analytic solutions.
In order to find the dynamic response of the free span, combining Matteo Luca Facchinetti's wake oscillator model with the differential equation of the free span to get the coupling equations between pipe and fluid, the finite element method combined with the simple iteration is used to solve the system of equations.
Taking the bending stiffness, static sag, and geometric non-linearity into account, the space nonlinear vibration partial differential equations are derived. The partial differential equations are discretized in space by finite center difference approximation, then the nonlinear ordinary differential equations are obtained.
Using Runge-Kutta method,the time history of model amplitude,the power of exciting force and damping force are simulated by solving the ordinary differential equation respectively,and the changing of system energy during vibration is expatiated.
MATLAB programs are programmed to resolve the dynamic derivative equations, in order to obtainthe acceleration time history of human, which makes preparation for putting into the ISO stardard to evaluate the vertical automobile ride comfort.
Firstly, the backcalculation of modulus is transferred into finding zero points of nonlinear maps according to extreme conditions of optimization problems. A mathematical model for backcalculation of pavement layer modulus based on the homotopy method is established with partial derivatives of the l st and 2nd order for deflections to modulus computed by numerical derivative methods.
In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
We express them in terms of generatorsEij ofU(gl(n)) and as differential operators on the space of matrices These expressions are a direct generalization of the classical Capelli identities.
Quantum integrable systems and differential Galois theory
This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues.
In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues.
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
Of special interest are the Mellin operators of differentiation and integration, more correctly of anti-differentiation, enabling one to establish the fundamental theorem of the differential and integral calculus in the Mellin frame.
It is shown that there is a similar identity when the inner product is replaced by an indefinite quadratic formq and h is a Л-harmonic distribution, where Л is the differential operator canonically associated toq.
The minimum energy solutions of the differential equations are proven to correspond to the tight frames that minimize the error term.
The method converts the frame problem into a set of ordinary differential equations using concepts from classical mechanics and orthogonal group techniques.
On the existence of periodic solutions for the third-order nonlinear ordinary differential equations
In this paper, the existence of periodic solution for the third-order nonlinear ordinary differential equation of the form {} is considered, where f, g, h and p are the continuous functions, and p(t+T)=p(t).
Uniqueness of positive solutions of a class of quasilinear ordinary differential equations
Uniqueness results are obtained for positive solutions of a class of quasilinear ordinary differential equations.
Aliasing error bounds are derived for one- and two-channel sampling series analogous to the Whittaker-Kotel'nikov-Shannon series, and for the multi-band sampling series, and a "derivative" extension of it, due to Dodson, Beaty, et al.
Examples are considered, and the frame bounds in the case of sampling of the signal and its first derivative are calculated explicitly.
This article also gives a single necessary-and-sufficient condition for a holomorphic function to be the transform of a function f such that any derivative of f multiplied by any polynomial is in Lp (d, ρ).
Applying a special derivative reproducing property, we show that when the kernel is real analytic, every function from the RKHS is real analytic.
5-Aza analogs were prepared of several tryptamine derivatives and a skatole derivative known to bind at human 5-HT6 receptors and evaluated to determine if they bind in a manner similar to their indolic analogs.
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