Fixing number of co-noraml product of graphs

An automorphism of a graph $G$ is a bijective mapping from the vertex set of $G$ to itself which preserves the adjacency and the non-adjacency relations of the vertices of $G$. A fixing set $F$ of a graph $G$ is a set of those vertices of $G$ which when assigned distinct labels removes all the automorphisms of $G$, except the trivial one. The fixing number of a graph $G$, denoted by $fix(G)$, is the smallest cardinality of a fixing set of $G$. The co-normal product $G_1\ast G_2$ of two graphs $G_1$ and $G_2$, is a graph having the vertex set $V(G_1)\times V(G_2)$ and two distinct vertices $(g_1, g_2), (\acute{g_1}, \acute{g_2})$ are adjacent if $g_1$ is adjacent to $\acute{g_1}$ in $G_1$ or $g_2$ is adjacent to $\acute{g_2}$ in $G_2$. We define a general co-normal product of $k\geq 2$ graphs which is a natural generalization of the co-normal product of two graphs. In this paper, we discuss automorphisms of the co-normal product of graphs using the automorphisms of its factors and prove results on the cardinality of the automorphism group of the co-normal product of graphs. We prove that $max\{fix(G_1), fix(G_2)\}\leq fix(G_1\ast G_2)$, for any two graphs $G_1$ and $G_2$. We also compute the fixing number of the co-normal product of some families of graphs.Comment: 13 page

Computer-supported collaborative learning performance and satisfaction: A muiti-stage study

Research in computer-supported cooperative learning provides evidence that collaborative technology can enhance learning performance and increase affective experiences in the context of cooperative learning. Most studies, however, have examined the learning performance only during the middle and end of the process. It is not clear how information technology continuously facilitates and improves student performance and learning experience over time. By employing a multidisciplinary approach, the research presented in this article drew research findings in the fields of communication, information systems, and education to examine cooperative learning processes with a continuous, longitudinal study. Based on a descriptive model of computer-supported cooperative learning, this research examined the effect of a collaborative technology on the accumulation of learning performance and learning satisfaction on group members. Three sets of hypotheses regarding learning performance, perceived learning performance, and group member satisfaction are examined

Comparative study of radio pulses from simulated hadron-, electron-, and neutrino-initiated showers in ice in the GeV-PeV range

High energy particle showers produce coherent Cherenkov radio emission in dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT simulation tools, we make a comparative study among electromagnetic (EM) and hadronic showers initiated by single particles and neutrino showers initiated by multiple particles produced at the neutrino-nucleon event vertex. We include all the physics processes and do a complete 3-D simulation up to 100 TeV for all showers and to 1 PeV for electron and neutrino induced showers. We calculate the radio pulses for energies between 100 GeV and 1 PeV and find hadron showers, and consequently neutrino showers, are not as efficient below 1 PeV at producing radio pulses as the electromagnetic showers. The agreement improves as energy increases, however, and by a PeV and above the difference disappears. By looking at the 3-D structure of the showers in time, we show that the hadronic showers are not as compact as the EM showers and hence the radiation is not as coherent as EM shower emission at the same frequency. We show that the ratio of emitted pulse strength to shower tracklength is a function only of a single, coherence parameter, independent of species and energy of initiating particle.Comment: a few comments added, to bo published in PRD Nov. issue, 10 pages, 3 figures in tex file, 3 jpg figures in separate files, and 1 tabl

Phenotypes of Alpha 1 Antitrypsin in Karachi, Pakistan

Objective: To determine serum level of the protease inhibitor, to identify phenotypes and determine their frequencies. Study Design: A prospective study. Setting: PMRC Research Centre, JPMC and the Aga Khan University Hospital Karachi. Subjects: Healthy aduIts without history ol peptic ulcer disease and a normal endoscopy. Methodology: Quantitive measurement of serum alpha 1 AT was carried out by radial immunodiffusion. phenotyping by iso-electric focusing and confirmation of phenotypes by immunofixation and DNA analysis technique. Results:Serum alpha I AT was low in 13.4% of the subjects. Ni MM phenotype predominated followed by SZ SS, MZ and ZZ. DNA diagnosis accurately resolved the phenotypes as S and Z. Conclusion: Frequency by phenotype associated with total and intermediate deficiency is less in the populatio

A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate level-solve packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (PTC). We analyze the magnitude of the PTC parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the partial temperature scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. (Abridged)Comment: 46 pages, 14 figures, accepted to JC

Diagnostic evaluation of fine Needle aspiration cytology in the management of palpable Breast lesions

A total of 113 fine needle aspirates of the breast masses were evaluated in which the subsequent biopsy or mastectomy specimen were also available for histological examination. The age ranged from 16 to 80 years with a mean of 42 years. In benign conditions the mean age was 34.7 years while in malignant cases it was 48 years. The cytological diagnoses were compared with the histological results which revealed that the specificity and sensitivity of fine needle aspiration cytology in the palpable breast lesions was 86.1% and 89.2% respectively with a positive predictive value of 93% and efficiency of 88.2%. Similar statistics from other series in which the cytological results of breast lesions were compared with histological results, revealed almost same results which suggest that fine needle aspiration cytology is an effective and accurate technique for the diagnosis and management of palpable breast lumps

Synthesis and characterisation of potassium polytitanate for photocatalytic degradation of crystal violet

© 2014 . Potassium titanate nanostructures were synthesised by hydrothermal treatment of TiO2 (P25) in KOH and H2O2. As-produced powders were characterised by scanning electron microscopy, energy-dispersive X-ray spectroscopy, transmission electron microscopy, X-ray diffraction, and nitrogen adsorption-desorption methods. Longitudinally-oriented-wire-like structures with a length up to several micrometres and diameters ranging from 10 to 30nm were obtained. Larger size fibrous nanowires resulting from the hydrothermal treatment showed high affinity in adsorbing crystal violet (CV), which was mainly due to their high surface area. The photocatalytic bleaching of CV solution revealed that the wires are photoactive under ultraviolet light irradiation. Macroporous nanowires are considered as effective adsorbents of CV, capable of photocatalytic degradation, and they can be easily separated from the solution by settling

Morphological pattern of salivary gland tumours

Objective: To delineate the spectrum of salivary gland tumors in our setup. Setting: The Aga Khan University Medical Centre, Karachi. Method: Tumors were analysed considering histological type, age and sex of the patients and anatomic location. The diagnosis of individual tumours was based on the 1991 World Health Organisation Classification. Results: During the span of eight years (1991-1998), 379 cases of salivary gland tumours were diagnosed. Of these, 205 (65.7%) were male and 174 (34.3%) were female. The median age at the time of diagnosis was 35 years. The median age for patients with malignant lesions (44 years) was 12 years older than those with benign tumours (34 years). Overall, malignant tumours were seen more frequently in males, however benign tumours were distributed equally between the two sexes. The most common site was parotid gland (82.85%). Only five cases of minor salivary gland tumours were seen. The most frequently diagnosed benign salivary gland neoplasm was pleomorphic adenoma (84.5%), followed by Warthin’s tumours (6.18%), Mucoepidermoid carcinoma was the most commonly encountered malignant lesion (56.9%), followed by adenoid cystic carcinoma (19.6%). Conclusion: Plemorphic adenoma was the most common benign salivary gland tumour and mucoepidermoid carcinoma was the most frequent malignant neoplasm. Parotid gland was the most common site of origin in both benign and malignant tumours. The overall relative frequency of salivary gland tumours in this series correlates with that reported in the international literature

Nutrient Composition of Selected Cooked and Processed Snack Foods

Nutrient composition of 27 cooked snack foods and 19 processed snacks was determined. The cooked foods were mostly cereal based, made from wheat flour, rice or rice flour, and almost all of them were traditional Malaysian kuih or dishes. The processed snacks studied were chocolate, cereal, tuber, fish and prawn products. The levels of 19 nutrients were tabulated, expressed as per 100 g edible portion. Selected nutrients in each serving or packet of the foods were also presented. The paper is intended as a contribution to the knowledge on nutrient composition of local snack foods, for which information is still greatly lacking. The number of foods studied is only a fraction of the total number available. More work in this area will have to be carried out, to meet the increasing demand for such data