Ill-Conditioned Plants and Integral Relations

2020 ◽  
pp. 233-247
Author(s):  
J. S. Freudenberg ◽  
K. Saglik
Keyword(s):  
Integral Relations

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals Fullerite C60 optical constants in the C 1s NEXAFS region

2021 ◽  
Vol 2103 (1) ◽  
pp. 012168
Author(s):  
D V Sivkov ◽  
S V Nekipelov ◽  
O V Petrova ◽  
D V Bogachuk ◽  
R N Skandakov ◽  
...  
Keyword(s):  
Cross Sections ◽  
Optical Constants ◽  
Absorption Cross ◽  
X Ray ◽  
Carbon Absorption ◽  
Cross Section Spectrum ◽  
Integral Relations ◽  
Atomic Form Factor ◽  
Using Data ◽  
X Ray Absorption

Abstract Using data on the absorption cross sections the refraction coefficient spectral dependence n(E) and the spectra of the remaining optical coefficients (reflection coefficient, phase shift, and atomic form factor) in the fullerite C60 C 1s near edge X-ray absorption fine structure (NEXAFS) region (280–350 eV) were determined. For the n(E) calculations the Kramers-Kronig integral relations (KKRs) were used. The KKR computations were performed using data on atomic carbon absorption cross sections in the 10–30000 eV range and on solid and gaseous C60 – in the 0–120 eV. Absorption cross section spectrum in the fullerite C60 C 1s NEXAFS region were measured.

Properties of inviscid, recirculating flows

1965 ◽  
Vol 22 (2) ◽  
pp. 337-346 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Velocity Gradient ◽  
Inviscid Flow ◽  
Rotating Cylinder ◽  
Fluid Particle ◽  
Inviscid Fluid ◽  
Viscous Forces ◽  
Rotation Axes ◽  
Total Head ◽  
Recirculating Flows ◽  
Integral Relations

Integral relations are derived for steady, incompressible recirculating motions with small viscous forces. The circuit time of a fluid particle on a closed streamline in steady, inviscid flow is shown to be the same for all the closed streamlines on a surface of constant total head.The discontinuities of velocity and velocity gradient that occur in the motion of inviscid fluid filling a closed, rotating cylinder set in a rotating support with the two rotation axes slightly misaligned are then investigated.

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