Parameterized Complexity of Upper Edge Domination

In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer $k$, the question is to check whether $G$ has a minimal edge dominating set of size at least $k$. We obtain the following results for Upper EDS. We prove that Upper EDS admits a kernel with at most $4k^2-2$ vertices. We also design a fixed-parameter tractable (FPT) algorithm for Upper EDS running in time $2^{\mathcal{O}(k)} \cdot n^{\mathcal{O}(1)}$

Static and impact fatigue behaviour of borosilicate glass

Failure of a borosilicate glass as a result of repeated impact has been studied. Impact fatigue study was Conducted in an improved pendulum type repeated impact apparatus specially designed and fabricated for determining single and repeated impact strength. For elimination of the effect of humidity, repeated impact tests were carried out under liquid nitrogen. Quasi-static measurements were determined under four-point bending. Using a square waveform as applicable to the present impact tests and fracture mechanics interpretation, the number of cycles to failure during impact fatigue tests were predicted from quasi-static fatigue measurements. It has been shown that repeated impact loading has a deleterious effect on the failure cycles compared to slow stressing. The role of an added mechanical effect during repeated impacts has been suggested in controlling the cyclic fatigue behaviour

Permutation Polynomials modulo pnp^n}

A polynomial $f$ over a finite ring $R$ is called a \textit{permutation polynomial} if the mapping $R\rightarrow R$ defined by $f$ is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also present a new class of permutation binomials over finite field of prime order

Maximum Minimal Feedback Vertex Set: A Parameterized Perspective

In this paper we study a maximization version of the classical Feedback Vertex Set (FVS) problem, namely, the Max Min FVS problem, in the realm of parameterized complexity. In this problem, given an undirected graph $G$, a positive integer $k$, the question is to check whether $G$ has a minimal feedback vertex set of size at least $k$. We obtain following results for Max Min FVS. 1) We first design a fixed parameter tractable (FPT) algorithm for Max Min FVS running in time $10^kn^{\mathcal{O}(1)}$. 2) Next, we consider the problem parameterized by the vertex cover number of the input graph (denoted by $\mathsf{vc}(G)$), and design an algorithm with running time $2^{\mathcal{O}(\mathsf{vc}(G)\log \mathsf{vc}(G))}n^{\mathcal{O}(1)}$. We complement this result by showing that the problem parameterized by $\mathsf{vc}(G)$ does not admit a polynomial compression unless coNP $\subseteq$ NP/poly. 3) Finally, we give an FPT-approximation scheme (fpt-AS) parameterized by $\mathsf{vc}(G)$. That is, we design an algorithm that for every $\epsilon >0$, runs in time $2^{\mathcal{O}\left(\frac{\mathsf{vc}(G)}{\epsilon}\right)} n^{\mathcal{O}(1)}$ and returns a minimal feedback vertex set of size at least $(1-\epsilon){\sf opt}$

Pre-emptive Dynamic Source Routing: A Repaired Backup Approach and Stability Based DSR with Multiple Routes

DSR algorithm finds out the best path for communicating between two nodes in a highly dynamic environment. Since, the environment changes frequently, the probability of established path breakage is also high. Again, as the breakage possibility increases, a new route has to be discovered every time .In order to avoid path discovery every time, we propose the modification of the existing DSR algorithm. In this paper we propose an enhancement of the DSR protocol based on a backup route(second best route) which will be provided by the destination node to the source node along with the best route during the process of path discovery. During the path maintenance process, in case any intermediate node identifies that the signal strength falls below a threshold i.e. the established route is about to break, the intermediate node sends a caution message to the source node. The source node switches the communication through the backup path , apprehending that the established route is about to break. As the communication through the backup route takes place, the previous route is repaired, if possible and acts as the new backup route. This process of toggling between backup route and established route reduces the call for path discovery to some extent. The stability in consideration of failure of common link and nodes in the back up repaired algorithm has been investigated with new algorithm for stable route selection

Growth of literature in Higgs Boson: A Scientometric analysis of SCOPUS database (2005-2014)

The paper analyses the growth pattern of Higgs Boson literature during 2005-2014 (10 years). The socups database has been used to retrieve relevant data. Total number of publication has been identified as 4359 records contributed worldwide over a period of 2005-2014.The distribution of publications based on the year of production, country wise productivity, document type of the publications, Major subject categories , authors whose contribution is in the maximum level were studied. The organizations contribute Higgs Boson research have also been studied