Prove that p implies q is logically equivalent to not q is to not p. I.e., prove that an implication is logically equivalent to its contrapositive. Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetri...
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When p>N, the embedding W01,p(Ω)↪L∞(Ω) implies the existence of a suitable a>0 such that ‖u‖∞≤a‖u‖,∀u∈W01,p(Ω), (2.1) see [3, Ch. IX]. Given p∈(1,∞), the symbol p′ denotes the conjugate exponent of p while W−1,p′(Ω) stands for the dual ...
We also assume that the Hessian matrix has maximal rank, that is, if and if (since the homogeneity of degree 1 implies that ). In (2) we also assume that for any . We define with , such that for , and that verifies a suitable control with its derivatives, at low and high ...
-q | -quiet means that results are not reported. Exit status of 0 implies all successful -p <driverConfigFile> Java properties file specifying custom capabilities that will be passed as configuration to the driver constructor. Webdriver-specific ...
We prove that the number of composition factors of G that have prime order p is at most (εqd−1)/(p−1), where εq is a function of q satisfying 1⩽εq⩽3/2. For every q, we give examples showing this bound is sharp infinitely often....
This implies that a regulatory event (such as dephosphorylation of the tail peptide) would release the SH3 domain and make it available for interaction with other proteins; on the other hand, high concentrations of a high-affinity SH3 ligand in trans might destabilize the inactive conformation, ...
We now give examples for types of rules to be used further in this paper. 3.1.1 Evolution rules In general, an evolution rule is of the form u ! v with u; v 2 VÃ. An evolution rule u ! v is called ''non-coop- erative'' (abbreviated ''ncoo'') if u 2 V, otherwise it...
For each i, \(\min (1,\mid \alpha _{\mathrm {K_1}}^{p}(\textrm{u}_{i})-\alpha _{\mathrm {K_2}}^{p}(\textrm{u}_{i})\mid +\mid \beta _{\mathrm {K_1}}^{q}(\textrm{u}_{i})-\beta _{\mathrm {K_2}}^{q}(\textrm{u}_{i})\mid )\le 1 \implies \mathrm...