AN UPPER BOUND ON ALGEBRAIC CONNECTIVITY OF GRAPHS WITH MANY CUTPOINTS

Let G be a graph on n vertices which has k cutpoints. A tight upper bound on the algebraic connectivity of G in terms of n and k for the case that k>n/2 is provided; the graphs which yield equality in the bound are also characterized. This completes an investigation initiated by the author in a previous paper, which dealt with the corresponding problem for the case that k ≤ n/2

By abandoning ideology for short term pragmatism both left and right are trivialising important constitutional questions

Although Tax Credit changes were accepted in the House of Commons, the failure of the Lords to approve this motion has created some interesting paradoxes. Sagar S Deva and Christopher Kirkland write that rather than suggesting politically-motivated and short-termist changes to affect the passage of legislation, a longer term appreciation of proposed changes is required to reach a modern workable constitutional settlement

Study on Intermittent Faults and Electrical Continuity

connector, or incorrect installation during initial manufacture and assembly. Unless such issues are narrowed down to a specific root cause, any corrective actions or troubleshooting will be difficult to carry out, and hence its resolution may not make its way into future designs of the system. This leads to further susceptibility to NFF. Intermittent behaviour is often a clear sign of a partially damaged connector, or a connector undergoing a particular degradation mechanism, with the level of intermittency being further aggravated through process variation of harsh environments and parametric faults. In order to further our understanding of the relationship between degradation, operating conditions, intermittent behaviour within the subject, an experimental investigations have been carried out. This paper is a work in progress paper that illustrates a test regime that has been used to stimulate intermittence in electronic connectors whilst subjected to vibration, using both a traditional oscilloscope and bespoke intermittent fault detection equipment, in order to capture an intermittent signature. The results of these experiments provide an insight into the limitations of test equipment and requirements for future intermittent fault detection techniques

Cryo-Electron Ptychography: Applications and Potential in Biological Characterisation

There is a clear need for developments in characterisation techniques that provide detailed information about structure-function relationships in biology. Using electron microscopy to achieve high resolution while maintaining a broad field of view remains a challenge, particularly for radiation sensitive specimens where the signal-to-noise ratio required to maintain structural integrity is limited by low electron fluence. In this review, we explore the potential of cryogenic electron ptychography as an alternative method for characterisation of biological systems under low fluence conditions. Using this method with increased information content from multiple sampled regions of interest, potentially allows 3D reconstruction with far fewer particles than required in conventional cryo-electron microscopy. This is important for achieving higher resolution for systems where distributions of homogeneous single particles are difficult to obtain. We discuss the progress, limitations and potential areas for future development of this approach for both single particle analysis and in applications to heterogeneous large objects

Kennesaw State University Wind Ensemble

KSU School of Music presents Wind Ensemble featuring Sam Skelton, soprano saxophone, David Kirkland, guest composer and Daniel S. Papp, special guest conductor.https://digitalcommons.kennesaw.edu/musicprograms/1217/thumbnail.jp

The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain

Essentially Negative News About Positive Systems

In this paper the discretisation of switched and non-switched linear positive systems using Padé approximations is considered. Padé approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability

The Complexity of Power Graphs Associated With Finite Groups

The power graph $\mathcal{P}(G)$ of a finite group $G$ is the graph whose vertex set is $G$, and two elements in $G$ are adjacent if one of them is a power of the other. The purpose of this paper is twofold. First, we find the complexity of a clique--replaced graph and study some applications. Second, we derive some explicit formulas concerning the complexity $\kappa(\mathcal{P}(G))$ for various groups $G$ such as the cyclic group of order $n$, the simple groups $L_2(q)$, the extra--special $p$--groups of order $p^3$, the Frobenius groups, etc.Comment: 14 page