scholarly journals Intersection curve of two parametric surfaces in Euclidean n-space

2021 ◽  
Vol 25 (2) ◽  
pp. 259-279
Author(s):  
Mustafa Düldül ◽  
Merih Özçetin
Keyword(s):  
Computer Code ◽  
Higher Order ◽  
Order Derivative ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Intersection Curve ◽  
Transversal Intersection ◽  
Derivative Formula ◽  
Derivatives Of

The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

scholarly journals A new general fractional derivative Goldstein-Kac-type telegraph equation

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3893-3898
Author(s):  
Ping Cui ◽  
Yi-Ying Feng ◽  
Jian-Gen Liu ◽  
Lu-Lu Geng
Keyword(s):  
Fractional Order ◽  
Telegraph Equation ◽  
Order Derivative ◽  
Mathematical Tool ◽  
Fractional Order Derivative ◽  
Derivative Formula ◽  
The Laplace Transform ◽  
The One ◽  
First Time ◽  
Derivatives Of

In this paper, we consider the Riemann-Liouville-type general fractional derivatives of the non-singular kernel of the one-parametric Lorenzo-Hartley function. A new general fractional-order-derivative Goldstein-Kac-type telegraph equation is proposed for the first time. The analytical solution of the considered model with the graphs is obtained with the aid of the Laplace transform. The general fractional-order-derivative formula is as a new mathematical tool proposed to model the anomalous behaviors in complex and power-law phenomena.

scholarly journals Some Identities for a Sequence of Unnamed Polynomials Connected with the Bell Polynomials

2017 ◽  
Author(s):  
Feng Qi ◽  
Da-Wei Niu ◽  
Bai-Ni Guo
Keyword(s):  
Stirling Numbers ◽  
Higher Order ◽  
Recursive Relation ◽  
Order Derivative ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Derivative Formula ◽  
Higher Order Derivative ◽  
Determinantal Expression

In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two dierentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

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