The generation of liquid crystal display waste is becoming a serious social problem. Predicting liquid crystal display waste status is the foundation for establishing a recycling network; however, the difficulty in predicting liquid crystal display waste quantity lies in data mining. In order to determine the quantity and the distribution of liquid crystal display waste in China, the four top-selling liquid crystal display products (liquid crystal display TVs, desktop PCs, notebook PCs, and mobile phones) were selected as study objects. Then, the extended logistic model and market supply A method was used to predict the quantity of liquid crystal display waste products. Moreover, the distribution of liquid crystal display waste products in different regions was evaluated by examining the consumption levels of household equipment. The results revealed that the quantity of waste liquid crystal displays would increase rapidly in the next decade. In particular, the predicted quantity of waste liquid crystal displays would rise to approximately 4.262 × 10 9 pieces in 2020, and the total display area (i.e. the surface area of liquid crystal display panels) of waste liquid crystal displays would reach 5.539 × 10 7 m 2 . The prediction on the display area of waste liquid crystal display TVs showed that it would account for 71.5% of the total display area by 2020. Meanwhile, the quantity of waste mobile phones would significantly grow, increasing 5
Abstract. Given a finite set K, a Boolean linear map on K is a map f from the set 2 K of all subsets of K into itself with f (∅) = ∅ such that f (A ∪ B) = f (A) ∪ f (B) holds for all A, B ∈ 2 K . For fixed subsets X, Y of K, to predict if Y is reachable from X in the dynamical system driven by f , one can assume the existence of nonnegative integers h with f h (X) = Y , find an upper bound α for the minimum of all such assumed integers h, and test if Y really appears in f 0 (X), . . . , f α (X). In order to get such an upper bound estimate, this paper establishes an expansion property for the Boolean linear map f . Namely, the authors find a lower bound on the size of f h (X) for any nonnegative integer h. Besides presenting several direct applications of the derived expansion property, this paper collects some related problems on Boolean linear dynamical systems, including problems on primitive multilinear maps and inhomogeneous topological Markov chains.
Generalizing the idea of viewing a digraph as a model of a linear map, we suggest a multi-variable analogue of a digraph, called a hydra, as a model of a multi-linear map. Walks in digraphs correspond to usual matrix multiplication while walks in hydras correspond to the tensor multiplication introduced by Robert Grone in 1987. By viewing matrix multiplication as a special case of this tensor multiplication, many concepts on strongly connected digraphs are generalized to corresponding ones for hydras, including strongly connectedness, periods and primitiveness, etc. We explore the structure of all possible periods of strongly connected hydras, which turns out to be related to the existence of certain kind of combinatorial designs. We also provide estimates of largest primitive exponents and largest diameters of relevant hydras. Much existing research on tensors are based on some other definitions of multiplications of tensors and so our work here supplies new perspectives for understanding irreducible and primitive nonnegative tensors.
Sensitivity is an important complexity measure of Boolean functions. In this paper we present properties of the minimal and maximal sensitivity of the simplified weighted sum function. A simple close formula of the minimal sensitivity of the simplified weighted sum function is obtained. A phenomenon is exhibited that the minimal sensitivity of the weighted sum function is indeed an indicator of large primes, that is, for large prime number p, the minimal sensitivity of the weighted sum function is always equal to one.
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