The policy change was announced the day after a passenger of a Metro train videotaped the operator texting while operating the train.
The proximity operator (text {prox}_{iota _{B_{epsilon }}(cdot -b)}) is given by the following lemma.
We first give an explicit form for the proximity operator (text {prox}_{frac {1}{beta }iota _{mathcal {C}}}).
Indeed, the proximity operator (text {prox}_{frac {1}{alpha }|cdot |_{1}}) is the soft-thresholding operator defined for (u in mathbb {R}^{n}) by: begin{array}rcl@ left text{prox}_{frac{1}{alpha}|cdot|_{1} u rightt)[!i]=maxleft{|u[!i]|-frac{1}{alpha},0right} text{sign} u[!i]), end{array} (6).
Indeed, the proximity operator (text {prox}_{alpha |cdot |_{1} circ Gamma }) is given at (z in mathbb {R}^{n}) as follows: for j=1,2,…,n left text{prox}_{alpha|cdot|_{1} circ Gamma} z right)_{j}=maxleft{|z_{j}|-alpha gamma_{j},0right} cdot text{sign} z_{j}), (29).
For some operators, text messages now account for more than 10% of revenue.This money is thoroughly welcome.
Both proximity operators (text {prox}_{alpha |cdot |_{1} circ Gamma }) and (text {prox}_{beta varphi ^phantom {dot {i}!}) should be computed easily and efficiently in order to make the iterative scheme in Algorithm 2 numerically efficient.
Since the explicit forms of the proximity operators (text {prox}_{frac {1}{alpha }|cdot |_{1}}) and (text {prox}_{iota _{B_{epsilon }}(cdot -b)}) are given by (6) and Lemma 2.2, respectively, based on Theorem 3.2, a unified approach for solving both (BP and BPBP ε ) is depicted in Algorithm 1.
In some parts of the world, text messaging accounts for 10% of operator revenues.Normal text messages are limited to 160 characters, costing an average of 10 cents each to send, but text messaging can be used to do more than just send quasi-telegrams to other people.
where the operator (max text {eig vec}_{L_{u}}) calculates the L u orthonormal eigenvectors corresponding to the largest eigenvalues.
It resembled a giant typewriter -- the operator entered text on a keyboard, and then cast a single piece, called a "slug," of type metal.
