On the ideal convergence of sequences of fuzzy numbers

In this paper we introduce and study the concepts of I-convergence, I^∗-convergence and I-Cauchy sequence for sequences of fuzzy numbers where I denotes the ideal of subsets of N, the set of positive integers.     

Multi-objective semi-supervised clustering of tissue samples for cancer diagnosis

In the domain of bioinformatics, the clustering of gene expression profiles of different tissue samples over different experimental conditions has gained importance with the invention of micro-array based technology. This study also has some impact on cancer diagnosis. The proper classification of cancer tissue samples generated using the micro-array technology helps in detecting cancers in an automated way. In the current paper we have developed a semi-supervised clustering technique for proper partitioning of these gene expression data sets. Semi-supervised clustering is a combination of unsupervised and supervised classification techniques. It uses some amount of supervised information and a large collection of unsupervised data. Here a multi-objective based semi-supervised clustering technique is developed for solving the cancer tissue classification problem. Different combinations of objective functions are used. As the supervised information we assume that class labels of 10 % data are available. The proposed technique is evaluated for three open source benchmark cancer data sets (brain tumor data set, adult malignancy and small round blood cell tumors). Two classification quality measures, viz., Adjusted Rand Index and Classification Accuracy are used to measure the goodness of the obtained partitionings. Obtained results are compared with several state-of-the-art clustering techniques. Moreover, significant gene markers have been identified and demonstrated visually from the clustering solutions obtained.     

Synthesis of ribbon type carbon nanostructure using LiFePO4 catalyst and their electrochemical performance

Ribbon type of carbon nanostructure has been synthesized by chemical vapor deposition using a new catalyst (LiFePO₄) introduced for the first time and its electrochemical behavior has been determined from charge/discharge characteristics. The synthesized material characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy and by Raman spectroscopy confirms the graphitic structure and ribbon type morphology of material. The performance of the single cell using purified carbon nanoribbon as the anode has been studied and the reversible lithium intercalation capacity has been found about 345 mAh/g, of which 335 mAh/g remain after 14th cycle. The columbic efficiency has been stabilized at approximately 98% from the 5th cycle.     

Synthesis of conducting ferromagnetic nanocomposite with improved microwave absorption properties

The present paper reports the synthesis of polyaromatic amine–ferromagnetic composite with nanosize TiO₂ (～70–90 nm) and γ-Fe₂O₃ (～10–15 nm) particles via in situ emulsion polymerization. Magnetic and conductivity studies demonstrate that the conducting ferromagnetic composite possesses saturation magnetization (M_S) value of 26.9 emu g^?1 and conductivity of the order of 0.46 S cm^?1, which are measured by vibrating sample magnetometer and four-probe technique, respectively. It is observed that the presence of the nanosized γ-Fe₂O₃ in the polyaniline–TiO₂ matrix affects the electromagnetic shielding property of the composite. Polyaniline–TiO₂–γ-Fe₂O₃ nanocomposite has shown better shielding effectiveness due to absorption (SE_A ～ 45 dB) than the polyaniline-γ-Fe₂O₃ (SE_A ～ 8.8 dB) and polyaniline–TiO₂ (SE_A ～ 22.4 dB) nanocomposite. The polymer composites were further characterized by high resolution transmission electron microscopy (HRTEM) and X-ray diffraction (XRD) technique.