Results 11 to 20 of about 1,464,296 (288)
Functions of exponential type [PDF]
Transactions of the American Mathematical Society, 1969 (1.5) If'(x)l _ MT12. In this paper we develop a unified method for arriving at these inequalities. In spite of being extremely simple, the method turns out to be very useful and effective. Not only does it give simpler proofs of the above results but yields interesting generalizations as well.
Q. I. Rahman
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The Jacobian of the Exponential Function [PDF]
SSRN Electronic Journal, 2020 We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parameterization of rota- tion matrices governing impulse response functions in structural vector ...
Jan R. Magnus +3 more
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Iteration of exponential functions [PDF]
Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1984 Denote the nth iterate of the entire or rational map f by \(f^ n\), \(n\in {\mathbb{N}}\), and the set of points where \((f^ n)\) is a normal family by N(f). The complement of N(f) is the Julia set J(f). The map f permutes the components of N(f). This study concerns the family of functions \(f(z)=e^{az},\) where a is a complex parameter. This family is
P.J. Rippon, I. N. Baker
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Sensors, 2021 Patch-based medical image registration has been well explored in recent decades. However, the patch fusion process can generate grid-like artifacts along the edge of patches for the following two reasons: firstly, in order to ensure the same size of ...
Liang Wu, Shunbo Hu, Changchun Liu
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On the Exponential Integrability of Conjugate Functions [PDF]
Journal of Fourier Analysis and Applications, 2021 AbstractWe relate the exponential integrability of the conjugate function$${\tilde{f}}$$f~to the size of the gap in the essential range off. Our main result complements a related theorem of Zygmund.
Santeri Miihkinen +3 more
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On Degenerate Truncated Special Polynomials
Mathematics, 2020 The main aim of this paper is to introduce the degenerate truncated forms of multifarious special polynomials and numbers and is to investigate their various properties and relationships by using the series manipulation method and diverse special proof ...
Ugur Duran, Mehmet Acikgoz
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Numerically Stable form of Green’s Function for a Free-Free Uniform Timoshenko Beam
Mathematics, 2022 Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instability ...
Traian Mazilu
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Fractal and Fractional, 2022 Using the Lebedev–Milin inequalities, bounds on the logarithmic coefficients of an analytic function can be transferred to estimates on coefficients of the function itself and related functions.
Lei Shi +4 more
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Expoential bounds on the number of causal triangulations [PDF]
, 2014 We prove that the number of combinatorially distinct causal 3-dimensional triangulations homeomorphic to the 3-dimensional sphere is bounded by an exponential function of the number of tetrahedra.
Durhuus, Bergfinnur, Jonsson, Thordur
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Exponential rings, exponential polynomials and exponential functions [PDF]
Pacific Journal of Mathematics, 1984 An exponential ring is a pair (R,E), where R is a commutative ring with unit 1 and \(E: (R,+)\to U\) (the multiplicative group of units in R) satisfying \(E(x+y)=E(x)E(y)(x,y\in R),E(0)=1.\) In preparation for proving that each subset of \({\mathbb{R}}^ 2\) definable (with parameters) in the language of exponential rings has finitely many connected ...
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