For hexachiral cells the auxetic property of the lattice together with the elastic coupling modulus between the normal and the asymmetric strains is obtained; a property that has been confirmed here for the tetrachiral lattice.
In this paper, we use the theory of fixed point index for the Schrödinger operator equations to obtain a geometrical property of a-rarefied sets at infinity on cones.
We obtain a certain property of F-contractions, which enables us to generalize and extend Wardowski's (Fixed Point Theory and Applications 2012 94, 2012) result and other fixed point theorems to the class of nonexpansive operators in real Banach spaces.
Q.E.D. Corollary 2. In the case of (4.11), we obtain an antisymmetric property of E αβ as - E α β = E β α ( α, β = 1, 2 ).
Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition.
In one such quasi-linear space, we can easily obtain an additional property, namely for a given (ain IR), there exists a unique (din IR) such that (aominus_{g}d=0).
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As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in smooth bounded domains and the half-space, and (b) the optimality of blowup rates of Aronsson's examples of singular solutions in cones.
Based on H, we can obtain a sufficient decrease property of the iterates, the existence of a subgradient lower bound for the iterate gap, and some important analytic features of the objective function.
The hyaluronic acid matrix reinforced by cellulose and elastin-like polypeptide fibers with adding collagen, hyaluronic acid, and chondroitin sulfate can obtain a better collision property [ 34– 34].
