A contribution to kolmogorov problem of relationships among upper bounds of derivatives of real functions given on entire axis

1975 ◽  
Vol 26 (3) ◽  
pp. 246-259 ◽  
Author(s):  
V. K. Dzyadyk ◽  
V. A. Dubovik
Keyword(s):  
Upper Bounds ◽  
Entire Axis ◽  
Real Functions ◽  
Derivatives Of

On A. N. Kolmogorov's inequalities relating the upper bounds of derivatives of real functions defined on the whole axis

1976 ◽  
Vol 27 (3) ◽  
pp. 233-240
Author(s):  
V. K. Dzyadyk ◽  
V. A. Dubovik
Keyword(s):  
Upper Bounds ◽  
Real Functions ◽  
Derivatives Of

On a dissimilarity of polynomial derivatives of single- and multivariable positive real functions

1982 ◽  
Vol 70 (10) ◽  
pp. 1233-1234 ◽  
Author(s):  
V. Ramachandran ◽  
M.O. Ahmad
Keyword(s):  
Positive Real ◽  
Real Functions ◽  
Positive Real Functions ◽  
Derivatives Of

scholarly journals Upper Bounds of Derivatives of the Heat Kernel on an Arbitrary Complete Manifold

1995 ◽  
Vol 127 (2) ◽  
pp. 363-389 ◽  
Author(s):  
A. Grigoryan
Keyword(s):  
Heat Kernel ◽  
Upper Bounds ◽  
Complete Manifold ◽  
Derivatives Of

scholarly journals An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1382
Author(s):  
Ye Tian ◽  
Tao Ning ◽  
Jixing Li ◽  
Jianmin Zheng ◽  
Zhitong Chen
Keyword(s):  
Upper Bounds ◽  
Basis Functions ◽  
Nurbs Surface ◽  
Degree Reduction ◽  
B Spline ◽  
Partial Derivatives ◽  
Spline Basis ◽  
Rational Bézier Surface ◽  
Nurbs Surfaces ◽  
Derivatives Of

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

Inequalities between the upper bounds of the derivatives of an arbitrary function on the half-line

1967 ◽  
Vol 1 (6) ◽  
pp. 442-447
Author(s):  
S. B. Stechkin
Keyword(s):  
Arbitrary Function ◽  
Upper Bounds ◽  
Half Line ◽  
Derivatives Of

scholarly journals Using Complex Variables to Estimate Derivatives of Real Functions

SIAM Review ◽  
1998 ◽  
Vol 40 (1) ◽  
pp. 110-112 ◽  
Author(s):  
William Squire ◽  
George Trapp
Keyword(s):  
Complex Variables ◽  
Real Functions ◽  
Derivatives Of

UNCERTAINTY AND IMPRECISION IN ANALYTICAL CONTEXT: FUZZY LIMITS AND FUZZY DERIVATIVES

2001 ◽  
Vol 09 (05) ◽  
pp. 563-585
Author(s):  
MARK BURGIN
Keyword(s):  
Incomplete Information ◽  
Differential Calculus ◽  
Classical Case ◽  
Open Problems ◽  
Weak Derivative ◽  
The Third ◽  
Differentiable Functions ◽  
Fourth Part ◽  
Real Functions ◽  
Derivatives Of

The main goal of the present paper is to extend such classical constructions as limits and derivatives making them appropriate for management of imprecise, vague, uncertain, and incomplete information. In the second part of the paper, going after introduction, elements of the theory of fuzzy limits are presented. The third part is devoted to the construction of fuzzy derivatives of real functions. Two kinds of fuzzy derivatives are introduced: weak and strong ones. It is necessary to remark that the strong fuzzy derivatives are similar to ordinary derivatives of real functions being their fuzzy extensions. The weak fuzzy derivatives generate a new concept of a weak derivative even in a classical case of exact limits. In the fourth part fuzzy differentiable functions are studied. Different properties of such functions are obtained. Some of them are the same or at least similar to the properties of the differentiable functions while other properties differ in many aspects from those of the standard differentiable functions. Many classical results are obtained as direct corollaries of propositions for fuzzy derivatives, which are proved in this paper. Some of the classical results are extended and completed. The fifth part of the paper contains several interpretations of fuzzy derivatives aiming at application of fuzzy differential calculus to solving practical problems. At the end, some open problems are formulated.

scholarly journals Upper bounds on derivatives of the logarithm of the heat kernel

1998 ◽  
Vol 6 (4) ◽  
pp. 669-685 ◽  
Author(s):  
Daniel W. Stroock ◽  
James Turetsky
Keyword(s):  
Heat Kernel ◽  
Upper Bounds ◽  
Derivatives Of
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