Stochastic stability and moment Lyapunov exponent for co-dimension two bifurcation system with a bounded noise

In this paper, the pth moment Lyapunov exponent of a co-dimension two bifurcation system that is parametrically excited by a real noise is investigated. By a linear stochastic transformation, the eigenvalue problem of moment Lyapunov exponent is obtained. Then through perturbation method, we deduce the joint probability density function of the phase processes and its eigenvalue problem, which is solved by a Fourier cosine series expansion. Thus, an infinite matrix yields and whose leading eigenvalue is the second order of the asymptotic expansion of the moment Lyapunov exponent. Because of the complexity of elements in matrix A, the eigenvalues of the low order sub-matrices of A are obtained by the truncation of n and the convergence of the eigenvalue sequence is numerically illustrated. Finally, the effects of the system and noise parameters on the moment Lyapunov exponent are discussed

Two sufficient conditions for graphs to admit path factors

Let $\mathcal{A}$ be a set of connected graphs. Then a spanning subgraph $A$ of $G$ is called an $\mathcal{A}$-factor if each component of $A$ is isomorphic to some member of $\mathcal{A}$. Especially, when every graph in $\mathcal{A}$ is a path, $A$ is a path factor. For a positive integer $d\geq2$, we write $\mathcal{P}_{\geq d}=\{P_i|i\geq d\}$. Then a $\mathcal{P}_{\geq d}$-factor means a path factor in which every component admits at least $d$ vertices. A graph $G$ is called a $(\mathcal{P}_{\geq d},m)$-factor deleted graph if $G-E'$ admits a $\mathcal{P}_{\geq d}$-factor for any $E'\subseteq E(G)$ with $|E'|=m$. A graph $G$ is called a $(\mathcal{P}_{\geq d},k)$-factor critical graph if $G-Q$ has a $\mathcal{P}_{\geq d}$-factor for any $Q\subseteq V(G)$ with $|Q|=k$. In this paper, we present two degree conditions for graphs to be $(\mathcal{P}_{\geq3},m)$-factor deleted graphs and $(\mathcal{P}_{\geq3},k)$-factor critical graphs. Furthermore, we show that the two results are best possible in some sense

Spanning k-trees and distance spectral radius in graphs

Let $k\geq2$ be an integer. A tree $T$ is called a $k$-tree if $d_T(v)\leq k$ for each $v\in V(T)$, that is, the maximum degree of a $k$-tree is at most $k$. Let $\lambda_1(D(G))$ denote the distance spectral radius in $G$, where $D(G)$ denotes the distance matrix of $G$. In this paper, we verify a upper bound for $\lambda_1(D(G))$ in a connected graph $G$ to guarantee the existence of a spanning $k$-tree in $G$.Comment: 11 page

SYNTHESIS OF PROPYLENE CARBONATE FROM UREA AND 1,2-PROPYLENE GLYCOL OVER METAL CARBONATES

A series of single-metal carbonates and Pb-Zn mixed-metal carbonates were prepared as catalysts for alcoholysis of urea with 1,2-propylene glycol (PG) for the synthesis of propylene carbonate (PC). The mixed carbonates all show much better catalytic activities than the single carbonates, arising from a strong synergistic effect between the two crystalline phases, hydrozincite and lead carbonate. The mixed carbonate with Pb/Zn = 1:2 gives the highest yield of PC, followed by the mixed carbonate with Pb/Zn = 1:3. Furthermore, Taguchi method was used to optimize the synthetic process for improving the yield of PC. It is shown that the reaction temperature is the most significant factor affecting the yield of PC, followed by the reaction time, and that the optimal reaction conditions are the reaction time 5 h, the reaction temperature 180 °C and the catalyst amount 1.8 mass%, resulting in the highest PC yield of 96.3%

Steep Balmer decrement in weak AGNs may be not caused by dust extinction: clues from low-luminosity AGNs and changing-look AGNs

The hydrogen Balmer decrement (e.g., $\rm H\alpha/H\beta$) is widely adopted as an indicator of the internal reddening of active galactic nuclei (AGNs). This is challenged by some low-luminosity AGNs (LLAGNs) and changing-look AGNs (CLAGNs), which have steep Balmer decrement but without strong evidence for absorption. We compile a sample of normal AGNs and CLAGNs with a wider distribution of bolometric Eddington ratio ($\lambda_{\rm Edd}=L_{\rm bol}/L_{\rm Edd}$) and find a strong negative correlation between $\rm H\alpha/H\beta$ and $\lambda_{\rm Edd}$, which suggests that the Balmer decrement is also accretion-rate dependent. We further explore the Balmer decrement based on the photoionization model using the Cloudy code by considering spectral energy distribution (SED) from the accretion disk with different accretion rates (e.g., disk/corona and truncated disk at high and low Eddington ratios, respectively). Both the standard disk and truncated disk predict a negative correlation of $\rm H\alpha/H\beta-\lambda_{\rm Edd}$, where the relation is steeper in the case of the truncated disk. The negative correlations are also explored in two single CLAGNs. The measured negative correlation of $\rm H\alpha/H\beta$ -- $\lambda_{\rm Edd}$ is mainly caused by the lower responsivity $({\rm dlog}L_{\rm line}/{\rm dlog}L_{\rm cont})$ in $\rm H\alpha$ relative to that in $\rm H\beta$, due to the larger optical depth in the former. We propose that the steep Balmer decrements in low-Eddington-ratio AGNs (e.g., some Seyferts 1.5-1.9 and CLAGNs) are not simply caused by absorption but mainly caused by the relatively low flux of ionizing photons.Comment: 13 pages, 3 figures, Accepted for publication in The Astrophysical Journa

News and Social Media Emotions in the Commodity Market

Purpose--Emotion plays a significant role in both institutional and individual investors\u27 decision-making process. Emotions affect the perception of risk and the assessment of monetary value. However, there is a lack of empirical evidence available that addresses how investors\u27 emotions affect commodity market returns. The purpose of this paper is to investigate whether media-based emotions can be used to predict future commodity returns. Design/methodology/approach--The authors examine the short-term predictive power of media-based emotion indices on the following five days\u27 commodity returns. The research adopts a proprietary data set of commodity-specific market emotions, which is computed based on a comprehensive textual analysis of sources from newswires, internet news sources and social media. Time series econometrics models (threshold generalized autoregressive conditional heteroskedasticity and vector autoregressive) are employed to analyze 14 years (January 1998-December 2011) of daily observations of the CRB commodity market index, crude oil and gold returns, and the market-level sentiments and emotions (optimism, fear and joy). Findings--The empirical results suggest that the commodity-specific emotions (optimism, fear and joy) have significant influence on individual commodity returns, but not on commodity market index returns. Additionally, the research findings support the short-term predictability of the commodity-specific emotions on the following five days\u27 individual commodity returns. Compared to the previous studies of news sentiment on commodity returns (Borovkova, 2011; Borovkova and Mahakena, 2015; Smales, 2014), this research provides further evidence of the effects of news and social media-based emotions (optimism, fear and joy) in the commodity market. Additionally, this work proposes that market emotion incorporates both a sentimental effect and appraisal effect on commodity returns. Empirical results are shown to support both the sentimental effect and appraisal effect when market sentiment is controlled in crude oil and gold spot markets. Originality/value - This paper adopts the valence-arousal approach and cognitive appraisal approach to explain financial anomalies caused by investors\u27 emotions. Additionally, this is the first paper to explore the predictive power of investors\u27 emotions (optimism, fear and joy) on commodity returns

Understanding Mobile Banking Applications’ Security risks through Blog Mining and the Workflow Technology

This paper provides a review of the security aspect of mobile banking applications. We employed blog mining as a research method to analyze blog discussion on security of mobile banking applications. Furthermore, we used the workflow technology to simulate real-life scenarios related to attacks on mobile banking applications. Insights are summarized to help banks and consumers mitigate the security risks of mobile banking applications