OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Performance Improvement of Fuzzy and Neuro Fuzzy Systems: Prediction of Learning Disabilities in School-age Children

Learning Disability (LD) is a classification including several disorders in which a child has difficulty in learning in a typical manner, usually caused by an unknown factor or factors. LD affects about 15% of children enrolled in schools. The prediction of learning disability is a complicated task since the identification of LD from diverse features or signs is a complicated problem. There is no cure for learning disabilities and they are life-long. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. The aim of this paper is to develop a new algorithm for imputing missing values and to determine the significance of the missing value imputation method and dimensionality reduction method in the performance of fuzzy and neuro fuzzy classifiers with specific emphasis on prediction of learning disabilities in school age children. In the basic assessment method for prediction of LD, checklists are generally used and the data cases thus collected fully depends on the mood of children and may have also contain redundant as well as missing values. Therefore, in this study, we are proposing a new algorithm, viz. the correlation based new algorithm for imputing the missing values and Principal Component Analysis (PCA) for reducing the irrelevant attributes. After the study, it is found that, the preprocessing methods applied by us improves the quality of data and thereby increases the accuracy of the classifiers. The system is implemented in Math works Software Mat Lab 7.10. The results obtained from this study have illustrated that the developed missing value imputation method is very good contribution in prediction system and is capable of improving the performance of a classifier.

Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from f+; g. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Brachyuran Crabs of Cochin Backwaters- Diversity, Habitat Ecology and Systematics, with special emphasis to Genus Scylla

Among the decapod crustaceans, brachyuran crabs or the true crabs occupy a very significant position due to their ecological and economic value. Crabs support a sustenance fishery in India, even though their present status is not comparable to that of shrimps and lobsters. They are of great demand in the domestic market as well as in the foreign markets. In addition to this, brachyuran crabs are of great ecological importance. They form the conspicuous members of the mangrove ecosystems and play a significant role in detritus formation, nutrient recycling and dynamics of the ecosystem. Considering all these factors, crabs are often considered to be the keystone species of the mangrove ecosystem. Though several works have been undertaken on brachyuran crabs world –wide as well as within the country, reports on the brachyuran crabs of Kerala waters are very scanty. Most of the studies done on brachyuran fauna were from the east coast of India and a very few works from the west coast. Among the edible crabs, mud crabs belonging to genus Scylla forms the most important due to their large size and taste. They are being exported on a large scale to the foreign markets like Singapore, Malaysia and Hong Kong. Kerala is the biggest supplier of live mud crabs and Chennai is the major centre of live mud crab export. However, there exists considerable confusion regarding the identification of mud crabs because of the subtle morphological differences between the species.In this context, an extensive study was undertaken on the brachyuran fauna of Cochin Backwaters, Kerala, India, to have a basic knowledge on their diversity, habitat preference and systematics. The study provides an attempt to resolve the confusion pertaining in the species identification of mud crabs belonging to Genus Scylla. Diversity study revealed the occurrence of 23 species of brachyuran crabs belonging to 16 genera and 8 families in the study area Cochin Backwaters. Among the families, the highest number of species was recorded from Family Portunidae .Among the 23 crab species enlisted from the Cochin backwaters, 5 species are of commercial importance and contribute a major share to the crustacean fishery of the Cochin region. It was observed that, the Cochin backwaters are invaded by certain marine migrant species during the Post monsoon and Pre monsoon periods and they are found to disappear with the onset of monsoon. The study reports the occurrence of the ‘herring bow crab’ Varuna litterata in the Cochin backwaters for the first time. Ecological studies showed that the substratum characteristics influence the occurrence, distribution and abundance of crabs in the sampling stations rather than water quality parameters. The variables which affected the crab distribution the most were Salinity, moisture content in the sediment, organic carbon and the sediment texture. Besides the water and sediment quality parameters, the most important factor influencing the distribution of crabs is the presence of mangroves. The study also revealed that most of the crabs encountered from the study area preferred a muddy substratum, with high organic carbon content and high moisture content. In the present study, an identification key is presented for the brachyuran crabs occurring along the study area the Cochin backwaters and the associated mangrove patches, taking into account the morphological characters coupled with the structure of third maxillipeds, first pleopods of males and the shape of male abdomen. Morphological examination indicated the existence of a morphotype which is comparable with the morphological features of S. tranquebarica, the morphometric study and the molecular analyses confirmed the non existence of S. tranquebarica in the Cochin backwaters.