Classifying Problems on Linear Congruences and Abelian Permutation Groups Using Logspace Counting Classes

In this paper we classify the complexity of several problems based on Abelian permutation groups and linear congruences using logspace counting classes. The problems we consider were defined by McKenzie & Cook (1987).     

Effect of Nitrogen Content on the Tensile and Stress Corrosion Cracking Behavior of AISI Type 316LN Stainless Steels

This paper deals with the effect of nitrogen on the tensile and stress corrosion cracking (SCC) behavior of type 316LN stainless steel. Yield stress (YS) and ultimate tensile stress (UTS) increased while the ductility [% total elongation (% TE)] decreased with increasing nitrogen content. Evaluation by conventional assessment parameters, such as ratios of UTS, % TE and SCC susceptibility index, derived by SCC testing using the slow strain rate testing (SSRT) technique indicated an improvement in SCC resistance on increasing the nitrogen content. However, crack growth rates, calculated from ratios of fracture stress from the SSRT tests in liquid paraffin and boiling 45 % magnesium chloride in SSRT tests, and the constant load tests at loads corresponding to 20 % YS in boiling 45 % magnesium chloride conclusively established that the SCC resistance of type 316LN stainless steel decreased with increasing nitrogen content.     

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

We briefly survey some results on the orderfield property of 2-player and multi-player stochastic games and their mixtures. Some of these classes of stochastic games can be solved by formulating them as a Linear Complementarity Problem (LCP) or (Generalized) Vertical Linear Complementarity Problem (VLCP). We discuss some of these results and prove that certain new subclasses and mixtures of multi-player (or n-person) stochastic games can be solved via LCP formulations. Mohan, Neogy and Parthasarathy (in Proceedings of the International Conference on Complementarity Problems, 1997) proposed an LCP formulation of ??-discounted (multi-player) polystochastic games where the transitions are controlled by one player, and proved that this LCP is processible by Lemke??s algorithm. Using this formulation repeatedly, we prove that we can solve a subclass of ??-discounted switching control polystochastic games. As our proof is constructive, we have an algorithm for solving this subclass. This algorithm only involves iteratively solving different LCPs and hence, it follows that this subclass has the orderfield property, a?question left open in the paper on orderfield property of mixtures of stochastic games by Krishnamurthy et al., (Indian J. Stat. 72:246?C275, 2010). Furthermore, we use results from Krishnamurthy et al., Indian J. Stat. 72:246?C275, (2010) to solve some mixture classes using LCP (or VLCP) formulations. We also propose two different VLCP formulations for ??-discounted zero-sum perfect information stochastic games, the underlying matrices of both formulations being R ₀. As a result, we also have an alternative proof of the orderfield property of such games.     

UV absorption studies of undoped and fluorine-doped tin oxide films

Tin oxide films undoped and doped with fluorine are prepared by a chemical vapour deposition technique involving the oxidation of SnCl₂. For fluorine doping a mixture of trifluoroacetic acid and deionized water is used. The optical properties of these films are investigated in the UV region (225–350 nm). It is observed that for an undoped tin oxide the absorption edge lies at 3.71 eV. It is also observed that for fluorine-doped tin oxide films the absorption edge shifts towards higher energies, which is related to the Moss-Burstein shift. In the case of fluorine-doped tin oxide films, depending on the fluorine concentration, the absorption edge lies in the range 3.89–4.07 eV. Undoped and fluorine-doped tin oxide films show a direct transition at 4.03 eV and in the range 4.17–4.29 eV respectively, whereas the indirect transition for undoped and fluorine-doped tin oxide films occurs at 3.35 eV and in the range 3.55–3.67 eV respectively.     

NP-hardness of Euclidean sum-of-squares clustering

A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al. (Mach. Learn. 56:9–33, 2004), is not valid. An alternate short proof is provided.     

Effect of increasing the energy gap between the two lowest energy states on the mixing time of the Metropolis algorithm

In order to understand what makes natural proteins fold rapidly, ?ali, Shakhnovich and Karplus (1994) [6], [7] had used the Metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the Metropolis algorithm would find the minimum energy conformation of a chain of beads within an acceptable time scale if and only if there is a large gap between the energies of the minimum energy conformation and that of the second minimum. Clote (1999) [1] attempted to support this conclusion by a proof that the mixing time of the underlying Markov chain would decrease as the gap in energies of the minimum energy conformation and that of the second minimum increased. He was able to show that an upper bound on the mixing time does indeed decrease as the energy gap increases. We show in this paper that the mixing time itself, however, is a non-decreasing function of the value of the energy gap. Therefore, our result contradicts what Clote had attempted to prove.     

Trust-based Intelligent Scheme for Mitigating Black Hole Attacks in IoT

Internet of Things (IoT) networks are characterized by a multitude of wireless, interconnected devices that can dynamically join or exit the network without centralized administration or fixed infrastructure for routing. While multipath routing in IoT networks can improve data transmission reliability and load balancing by establishing multiple paths between source and destination nodes, these networks are susceptible to security threats due to their wireless nature. Traditional security solutions developed for conventional networks are often ill-suited to the unique challenges posed by IoT environments. In response to these challenges, this paper proposes the integration of the Ad hoc On-demand Multipath Distance Vector (AOMDV) routing protocol with a trust model to enhance network performance. Key findings from this research demonstrate the successful fusion of AOMDV with a trust model, resulting in tangible improvements in network performance. The assessment of trustworthiness bolsters both security and routing capabilities in IoT networks. The trust model plays a crucial role in mitigating black hole attacks in IoT networks by evaluating the trustworthiness of nodes and helping in the identification and avoidance of malicious nodes that may act as black holes. Simulation results validate the efficacy of the proposed trust-based routing mechanism in achieving its objectives. Trust plays a pivotal role in decision-making and in the creation of secure distribution systems. By assessing the trustworthiness of nodes, both network security and routing efficiency can be enhanced. The effectiveness of the proposed trust-based routing mechanism is scrutinized through simulations, offering insights into its potential advantages in terms of improved network security and routing performance in the context of the IoT.