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A scalable and secure federated learning authentication scheme for IoT. [PDF]
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2021
Comparison theorems are the main subjects of this book. They are concerned with quantitative or qualitative properties of a space with a certain condition on its curvature. In this book, we will consider Finsler manifolds whose flag or (weighted) Ricci curvature is bounded from below or above by a constant.
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Comparison theorems are the main subjects of this book. They are concerned with quantitative or qualitative properties of a space with a certain condition on its curvature. In this book, we will consider Finsler manifolds whose flag or (weighted) Ricci curvature is bounded from below or above by a constant.
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Annals of Physics, 1986
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2009
In the previous chapter, we have discussed various versions of the Hardy–Littlewood inequality for a pair of solutions u and v of the conjugate A-harmonic equation. The purpose of this chapter is to present some norm comparison inequalities for differential forms satisfying the conjugate A-harmonic equations, which have been recently established in ...
Ravi P. Agarwal +2 more
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In the previous chapter, we have discussed various versions of the Hardy–Littlewood inequality for a pair of solutions u and v of the conjugate A-harmonic equation. The purpose of this chapter is to present some norm comparison inequalities for differential forms satisfying the conjugate A-harmonic equations, which have been recently established in ...
Ravi P. Agarwal +2 more
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Two comparison theorems of bsdes
Journal of Applied Mathematics and Computing, 2007The present paper studies an extension of Peng's comparison theorem for backward stochastic differential equations [\textit{S. Peng}, Stochastics Stochastics Rep. 38, No. 2, 119--134 (1992; Zbl 0756.49015)] to backward equations of the following form: \[ dY_t=-f(t,Y_t,Z_t)dt+g(t,Y_t,Z_t)dW_t,\quad t\in[0,T],\;Y_T=\xi\in L^2({\mathcal F}_T^W), \] where \
Huang, Xiaoqin +2 more
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Comparison theorems for eigenvalues
Annali di Matematica Pura ed Applicata, 1974Comparison theorems are proved relating the smallest positive eigenvalues λ and λ* of two operator equations of type Au=λBu and A*v=λ*B*v, respectively. Sufficient conditions on the operators are given which guarantee that λ⩽λ*, with special reference to the case that A and A* are elliptic differential operators.
Allegretto, W., Swanson, C. A.
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Mathematical Notes, 1995
The author considers comparison theorems (scalar and multidimensional cases) for Carathéodory type differential inclusions. The conditions are expressed in terms of solution spaces.
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The author considers comparison theorems (scalar and multidimensional cases) for Carathéodory type differential inclusions. The conditions are expressed in terms of solution spaces.
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Comparison Theorems for Constrained Rods
SIAM Review, 1964they prove' that "the fastest oscillation possible for a solution of (1.4) is at least as fast as the fastest oscillation permitted by equation (1.3)". However, when this result is expressed in terms of zeros of solutions we no longer get the simple separation property characteristic of the second order case.
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