scholarly journals CURVES OF CONSTANT BREADTH ACCORDING TO DARBOUX FRAME IN GALILEAN SPACE G3>

2019 ◽  
pp. 837
Author(s):  
Hülya Gun Bozok
Keyword(s):  
Differential Equation ◽  
3 Dimensional ◽  
Special Cases ◽  
Darboux Frame ◽  
Constant Breadth ◽  
Galilean Space

In this work, the curves of constant breadth according to Darboux frame in the 3-dimensional Galilean Space are investigated. Firstly the curves of constant breadth according to Darboux frame are determined then the differential equation of the constant breadth curve with this frame is found. After that some special cases of this differential equation are researched.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Characterizations of special time-like curves in Lorentzian plane 𝕃2

2017 ◽  
Vol 14 (10) ◽  
pp. 1750140
Author(s):  
Abdullah Mağden ◽  
Süha Yılmaz ◽  
Yasin Ünlütürk
Keyword(s):  
Differential Equation ◽  
Position Vector ◽  
Constant Breadth ◽  
Lorentzian Plane ◽  
Special Time

In this paper, we first obtain the differential equation characterizing position vector of time-like curve in Lorentzian plane [Formula: see text] Then we study the special curves such as Smarandache curves, circular indicatrices, and curves of constant breadth in Lorentzian plane [Formula: see text] We give some characterizations of these special curves in [Formula: see text]

The Out-of-Plane Stability Analysis of Crane Jib with Two Symmetric Drawbars

2013 ◽  
Vol 446-447 ◽  
pp. 469-473
Author(s):  
Nian Li Lu ◽  
Ce Chen ◽  
Shi Ming Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Characteristic Equation ◽  
Critical Condition ◽  
Design Rules ◽  
Special Cases ◽  
Out Of Plane

The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.

scholarly journals New Results on the Motions of Asteroids in Resonances

1992 ◽  
Vol 152 ◽  
pp. 145-152 ◽  
Author(s):  
R. Dvorak
Keyword(s):  
Initial Conditions ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Close Approach ◽  
Integration Time ◽  
Time Interval ◽  
Time Intervals ◽  
3 Dimensional ◽  
Special Cases ◽  
Good Agreement

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

Surface Colour Matching under Conditions of Multiple Illuminants

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 190-190 ◽  
Author(s):  
H Irtel
Keyword(s):  
Light Source ◽  
Green Light ◽  
Light Sources ◽  
Local Contrast ◽  
Colour Constancy ◽  
Lighting Condition ◽  
3 Dimensional ◽  
Special Cases ◽  
Type Pattern ◽  
Light And Shadow

Most theories of colour constancy assume a flat coloured surface and a single homogenous light source. Natural situations, however, are 3-dimensional (3-D), are hardly ever restricted to a single light source, and object illumination is never homogenous. Here, two special cases of secondary light sources with sharp boundaries were simulated on a computer screen: a house-like 3-D object with colour patches in sunlight and shadow, and a Mondrian-type pattern with a coloured transparency covering some of the colour patches. Subjects made ‘paper’-matches between colour patches in light and shadow and between patches under the transparency and without the transparency. Matching did not depend on whether the simulated lighting condition was natural (yellow light, blue shadow) or artificial (green light, magenta shadow). Patches under a coloured transparency produced lightness constancy but subjects could not discount chromaticity shifts induced by the transparency. The number of context patches (2 vs 6) made no difference, and it made no difference whether the transparency covered the Mondrian completely or only partially. These results indicate that subjects were not able to use local contrast cues at sharp illumination boundaries to discount for the illuminant.

The integral of geometric Brownian motion

2001 ◽  
Vol 33 (1) ◽  
pp. 223-241 ◽  
Author(s):  
Daniel Dufresne
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Laplace Transform ◽  
Finite Time ◽  
Geometric Brownian Motion ◽  
Time Interval ◽  
Finite Time Interval ◽  
Special Cases ◽  
The Laplace Transform

This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the reciprocal integral, and is shown to yield an expression for the density of the distribution. This expression has some advantages over the ones obtained previously, at least when the normalized drift of the Brownian motion is a non-negative integer. Bougerol's identity and a relationship between Brownian motions with opposite drifts may also be seen to be special cases of these results.

On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers

1967 ◽  
Vol 63 (4) ◽  
pp. 1327-1330 ◽  
Author(s):  
S. Leibovich
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Stagnation Point ◽  
Boundary Layers ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stagnation Point Flow ◽  
Special Cases ◽  
Rear Stagnation Point

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

scholarly journals Linear global instability of non-orthogonal incompressible swept attachment-line boundary-layer flow

2012 ◽  
Vol 710 ◽  
pp. 131-153 ◽  
Author(s):  
José Miguel Pérez ◽  
Daniel Rodríguez ◽  
Vassilis Theofilis
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Flow Instability ◽  
Angle Of Attack ◽  
Basic Flow ◽  
Critical Conditions ◽  
Simple Extension ◽  
Global Instability ◽  
Special Cases ◽  
Attachment Line

AbstractFlow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via solution of the pertinent global (BiGlobal) partial differential equation (PDE)-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler–Hämmerlin ordinary differential equation (ODE)-based polynomial model proposed by Theofilis et al. (2003) for orthogonal flow, which includes previous models as special cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the analysis results and unravel the limits of validity of the basic flow model analysed. The effect of the angle of attack, $\mathit{AoA}$, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from $\mathit{AoA}= 0$ (orthogonal flow) up to values close to $\lrm{\pi} / 2$ which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at $0\leq \mathit{AoA}\leq \lrm{\pi} / 2$ are shown to be recoverable from those of orthogonal flow, via a simple algebraic transformation involving $\mathit{AoA}$.

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