Non-Decreasing Sequences

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science. A non-decreasing sequence of subsets of a finite set S of size s, {S1, S2,.... St}, length t, and strength d, is a sequence of non-empty subsets where the union of any d previous subsets in the sequence does not contain any subsequent subset. The goal of this research is to find properties of these non-decreasing sequences as the variables d, s, and t change. We also explored methods for creating a maximum length for a non-decreasing sequence given d and s. Through our research, we discovered and proved basic properties of these non-decreasing sequences. In addition to this, we can describe a method we used while trying to find the maximum length of a sequence. In the future, research can be conducted to find an exact formula that will generate a maximum length sequence given a non-decreasing sequence of strength d

Decreasing Caregiver Stress

Stress is both critical and personal experience and has significant effects on caregivers’ physical, mental, and social well-being. The nature of caregiving and the responsibility to work and serve individuals at their illness conditions are very personal encounters that often result in adverse effects on the health and well-being of caregivers (Frederick, 2016). A decrease in stress experience can lead to the satisfaction of caregiver roles and improvement of patient’s quality of life (Choi, Jisun & Boyle, Diane, 2013; Yada, Nagata, & Inagaki, 2014). This scholarly project determined that evidence-based stress management interventions have decreased the perceived stress in caregivers. The scholarly project identified low levels of stress among research participants, and how evidence-based interventions decreased caregiver stress by increasing their knowledge and awareness of evidence-based stress management interventions. The results of this scholarly project agree with the literature that caregiver stress experience can be decreased through the implementation of evidence-based stress management interventions (Blom, Zarit, Groot Zwaaftink, Cuijpers, & Pot, 2013). It is significant to implement evidence-based stress management interventions to decrease perceived stress among caregivers

Labelings for Decreasing Diagrams

This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local diagrams decreasing. This approach has two immediate benefits. First, it allows to use labelings for linear rewrite systems also for left-linear ones, provided some mild conditions are satisfied. Second, it admits an incremental method for proving confluence which subsumes recent developments in automating decreasing diagrams. The techniques proposed in the article have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions

Complex zero strip decreasing operators

In this paper we study the effect of linear differential operators coming from the Laguerre-Polya class that act on functions in the extended Laguerre-Polya class with zeros in a horizontal strip in the complex plane. These operator decrease the size of the strip containing the zeros.Comment: 17 pages, corrected several typos, added a citation. appears in Math. Anal. Appl. (2015

Combinatorial Auctions with Decreasing Marginal Utilities

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.Comment: To appear in GEB. Preliminary version appeared in EC'0