Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures, it makes sense to study fault-tolerant versions of the above structures. This turns out to be a surprisingly difficult task. For every small but arbitrary se...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

In the paper, an almost sure convergence result for weighted sums of extended negatively dependent random variables is obtained. By using the almost sure convergence result, we further study the strong consistency of M estimator of the regression parameter in linear models based on extended negatively dependent random errors under some mild conditions. Mathematics subject classification (2010):...

<p><span data-preserver-spaces="true">The demands of 21st Century learning are now in the Industrial Revolution Era 4.0 with 4C characters. Educators must develop their creativity to improve quality so that students can be more creative learning. </span><em>Instrumental Analytical Chemistry</em><span data-preserver-spaces="true"> is a course studies modern in...

This paper models a machine replacement and capacity expansion problem as an infinite-horizon linear program. We establish a strong duality result and show that stationary dual prices are optimal, regardless of initial conditions. These prices measure the economic value of owning vintage machinery and thus define depreciation schedules. We present necessary and sufficient conditions for straigh...

This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be appli...

In 1951, Dantzig showed the equivalence of linear programming problems and two-person zerosum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of the relationship between the Minimax Theorem of game theory and the Strong Duality Theorem of linear p...