The Invariant Measure of Random Walks in the Quarter-plane: Representation in Geometric Terms

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative

The invariant measure of homogeneous Markov processes in the quarter-plane: Representation in geometric terms

We consider the invariant measure of a homogeneous continuous-time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable linear combination of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric distributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane

One-step hydrothermal synthesis of fluorescence carbon quantum dots with high product yield and quantum yield

A one-step hydrothermal synthesis of nitrogen and silicon co-doped fluorescence carbon quantum dots (N,Si-CQDs), from citric acid monohydrate and silane coupling agent KH-792 with a high product yield (PY) of 52.56% and high quantum yield (QY) of 97.32%, was developed. This greatly improves both the PY and QY of CQDs and provides a new approach for a large-scale production of high-quality CQDs. Furthermore, N,Si-CQDs were employed as phosphors without dispersants to fabricate white light-emitting diodes (WLEDs) with the color coordinates at (0.29, 0.32). It is suggested that N,Si-CQDs have great potential as promising fluorescent materials to be applied in WLEDs.Peer reviewe

The Role of Web-Sphere for Managing Supply Chain Business Objects in Heterogeneous Systems

Abstract— The study discusses the problem of managing supply chain business objects in heterogeneous systems through the use of Business Process Management Systems (BPMS). The purpose of the research is to summarize the experience of domestic enterprises (operating in logistics and other businesses) when using cloud-based logistics systems; to identify general development trends in the domestic market and to develop recommendations for improving the efficiency of supply chain management based on cloud technologies. The research hypothesis is that the competitiveness of the logistics system grows along with its synergy. To test the hypothesis, a survey of 94 respondents working with such systems has been conducted. It has been found that IBM WebSphere is the most preferable system as it provides the maximum synergistic effect that is achieved by the targeted, coordinated, and mutual operation of two or more digital technologies to achieve a certain common goal. In particular, this stems from the fact that it is not enough to produce quality and essential goods or to provide a service; it is important to be able to convey the message to the consumer. The concept of competition has expanded beyond the boundaries of products (goods or services) and has moved into the sphere of competition among management structures

An Efficient Synthesis and Photoelectric Properties of Green Carbon Quantum Dots with High Fluorescent Quantum Yield

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)To greatly improve the production quality and efficiency of carbon quantum dots (CQDs), and provide a new approach for the large-scale production of high-quality CQDs, green carbon quantum dots (g-CQDs) with high product yield (PY) and high fluorescent quantum yield (QY) were synthesized by an efficient one-step solvothermal method with 2,7-dihydroxynaphthalene as the carbon source and ethylenediamine as the nitrogen dopant in this study. The PY and QY of g-CQDs were optimised by adjusting reaction parameters such as an amount of added ethylenediamine, reaction temperature, and reaction duration. The results showed that the maximum PY and QY values of g-CQDs were achieved, which were 70.90% and 62.98%, respectively when the amount of added ethylenediamine, reaction temperature, and reaction duration were 4 mL, 180 °C, and 12 h, respectively. With the optimised QY value of g-CQDs, white light emitting diodes (white LEDs) were prepared by combining g-CQDs and blue chip. The colour rendering index of white LEDs reached 87, and the correlated colour temperature was 2520 K, which belongs to the warm white light area and is suitable for indoor lighting. These results indicate that g-CQDs have potential and wide application prospects in the field of white LEDs.Peer reviewedFinal Published versio

Necessary conditions for the invariant measure of a random walk to be a sum of geometric terms

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure to be a sum of geometric terms. We demonstrate that, under a mild regularity condition, each geometric term must individually satisfy the balance equations in the interior of the state space. We show that the geometric terms in an invariant measure must be the union of finitely many pairwise-coupled sets of infinite cardinality. We further show that for the invariant measure to be a sum of geometric terms, the random walk cannot have transitions to the north, northeast or east. Finally, we show that for an infinite weighted sum of geometric terms to be an invariant measure at least one of the weights must be negative