An interior second derivative bound for solutions of Hessian equations

2001 ◽  
Vol 12 (4) ◽  
pp. 417-431 ◽  
Author(s):  
John Urbas
Keyword(s):  
Second Derivative ◽  
Hessian Equations ◽  
Derivative Bound

scholarly journals Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains

2021 ◽  
Vol 60 (5) ◽  
Author(s):  
Jonah A. J. Duncan ◽  
Luc Nguyen
Keyword(s):  
Strong Solutions ◽  
Second Derivative ◽  
Yamabe Equation ◽  
Hessian Equations ◽  
Euclidean Domains

AbstractWe prove local pointwise second derivative estimates for positive $$W^{2,p}$$ W 2 , p solutions to the $$\sigma _k$$ σ k -Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations are also considered.

Second‐Derivative Spectra for Estimating Crop Residue Cover

1994 ◽  
Vol 86 (2) ◽  
pp. 349-354 ◽  
Author(s):  
Haiping Su ◽  
Michel D. Ransom ◽  
Edward T. Kanemasu ◽  
Tanvir H. Demetriades‐Shah
Keyword(s):  
Crop Residue ◽  
Second Derivative ◽  
Derivative Spectra ◽  
Second Derivative Spectra

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

scholarly journals Second derivative synchronous fluorescence determination of avanafil in the presence of its acid-induced degradation product aided by powerful Lean Six Sigma tools augmented with D-optimal design

RSC Advances ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 3834-3842
Author(s):  
Khalid A. M. Attia ◽  
Ahmad A. Mohamad ◽  
Mohamed S. Emara ◽  
Ahmed M. Abdel-Raoof ◽  
Mohamed A. Hasan ◽  
...  
Keyword(s):  
Optimal Design ◽  
Quantitative Determination ◽  
Degradation Product ◽  
Six Sigma ◽  
Lean Six Sigma ◽  
Synchronous Fluorescence ◽  
Second Derivative ◽  
Fluorescence Determination ◽  
Spectrofluorimetric Method

In this work, the quantitative determination of an erectile dysfunctional drug avanafil in the presence of its acid-induced degradation product was achieved via the application of a pre-optimized novel spectrofluorimetric method.

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