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Recall that an integer is t−free iff it is not divisible by pt for some prime p. We give a method to check Robin inequality (n) < e n log log n, for t−free integers n and apply it for t =...
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant . The bound is expressed in ...
Let d ≥ 2 and T be the convolution operator T f(x) = R Rd−1 f(x′ − t, xd − |t|2) dt, which is is bounded from L(d+1)/d(Rd) to Ld+1(Rd). We show that any critical point f ∈ L(d+1)/d o...
An inequality for sums of binary digits, with application to Takagi functions.
A revised conjugate gradient projection method for nonlinear inequality constrained optimization problems is proposed in the paper, since the search direction is the combination of the conjugate proje...
In this paper, we propose a feasible QP-free method for solving nonlinear inequality constrained optimization problems. A new working set is proposed to estimate the active set. Specially, to deter...

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