In this paper, we develop computational procedures to approximate the spectral abscissa of the switched linear system via square coordinate transformations. First, we design iterative algorithms to obtain a sequence of the least μ1 measure. Second, it is shown that this sequence is convergent and its limit can be used to estimate the spectral abscissa. Moreover, the stopping condition of Algorithm 1 is also presented. Finally, an example is carried out to illustrate the effectiveness of the proposed method.
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
For a graph property $\mathcal {P}$ and a graph $G$, we define the domination subdivision number with respect to the property $\mathcal {P}$ to be the minimum number of edges that must be subdivided (where each edge in $G$ can be subdivided at most once) in order to change the domination number with respect to the property $\mathcal {P}$. In this paper we obtain upper bounds in terms of maximum degree and orientable/non-orientable genus for the domination subdivision number with respect to an induced-hereditary property, total domination subdivision number, bondage number with respect to an induced-hereditary property, and Roman bondage number of a graph on topological surfaces.
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form $(G\setminus I)\cup J$, where $G$ is open and $I$, $J$ are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form $(G\setminus I)\cup J$.
Let $R$ be an integral domain with quotient field $K$ and $f(x)$ a polynomial of positive degree in $K[x]$. In this paper we develop a method for studying almost principal uppers to zero ideals. More precisely, we prove that uppers to zero divisorial ideals of the form $I = f(x)K[x] \cap R[x]$ are almost principal in the following two cases: – $J$, the ideal generated by the leading coefficients of $I$, satisfies $J^{-1} = R$. – $I^{-1}$ as the $R[x]$-submodule of $K(x)$ is of finite type. Furthermore we prove that for $I = f(x)K[x] \cap R[x]$ we have: – $I^{-1}\cap K[x]=(I:_{K(x)}I)$. – If there exists $p/q \in I^{-1}-K[x]$, then $(q,f)\neq 1$ in $K[x]$. If in addition $q$ is irreducible and $I$ is almost principal, then $I' = q(x)K[x] \cap R[x]$ is an almost principal upper to zero. Finally we show that a Schreier domain $R$ is a greatest common divisor domain if and only if every upper to zero in $R[x]$ contains a primitive polynomial.
The paper’s primary objective is to discuss the arrangements of grave pits at the Early Medieval agglomeration Mikulčice-Valy. They include steps, wooden structures, stone structures and special arrangements. The established facts about the form, frequency, etc., are then compared with the situation at other central fortified settlements in Great Moravia (Pohansko near Břeclav and Staré Město – Uherské Hradiště). The second objective of the book is to critically evaluate the phenomenon of so-called “tombs” at the burial site near the 3rd church on the acropolis of the Mikulčice fortified settlement. Since the introduction of this term in archaeological literature by J. Poulík in 1967, these find units have never been comprehensively presented and their interpretation as tombs with stone structures has not been adequately documented or backed by arguments. The paper is based on the original documentation of the research in 1956–1957; these find units are reinterpreted using analysis and comparison of the burial rite attributes of the graves. Based on the analysis of the find situation, the authors do not consider the term “tomb” as relevant at the Mikulčice agglomeration.
Disordered motility is one of the most important pathogenic characteristics of functional dyspepsia (FD), although the underlying mechanisms remain unclear. Since the sympathetic system is important to the regulation of gastrointestinal motility, the present study aimed to investigate the role of norepinephrine (NE) and adrenoceptors in disordered gastric motility in a rat model with FD. The effect of exogenous NE on gastric motility in control and FD rats was measured through an organ bath study. The expression and distribution of β-adrenoceptors were examined by real-time PCR, Western blotting and immunofluorescence. The results showed that endogenous gastric NE was elevated in FD rats, and hyperreactivity of gastric smooth muscle to NE and delayed gastric emptying were observed in the rat model of FD. The mRNA levels of β1-adrenoceptor and norepinephrine transporter (NET) and the protein levels of β2-adrenoceptor and NET were increased significantly in the gastric corpus of FD rats. All three subtypes of β-adrenoceptors were abundantly distributed in the gastric corpus of rats. In conclusion, the enhanced NE and β-adrenoceptors and NETs may be contributed to the disordered gastric motility in FD rats.