Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group

A new set of elementary symplectic elements is described, It is shown that these also generate the elementary symplectic group {\rm ESp}$_{2n}(R)$. These generators are more symmetrical than the usual ones, and are useful to study the action of the elementary symplectic group on unimodular rows. Also, an alternate proof of, {\rm ESp}$_{2n}(R)$ is a normal subgroup of {\rm Sp}$_{2n}(R)$, is shown using the Local Global Principle of D. Quillen for the new set of generators.Comment: 14 pages, few typos corrected. To appear in Ramanujan Math. Soc. Lect. Notes Se

Improving Volumetric Accuracy of AM Part Using Adaptive Slicing of Octree Based Structure

In Additive Manufacturing (AM) processes, the layer-by-layer fabrication of complex geometries may lead to stair casing and thus error resulting in volumetric inaccuracies in the model. Using thinner slices reduces the staircase error and improves part accuracy but there is a tradeoff between number of layers and the build time for manufacturing part. This paper presents a octree based structure to improve the accuracy as well as reduces the build time. In the current work, firstly converting STL file into a modified boundary octree data structure (MBODS) and then calculating the non-uniform slice thicknesses (adaptive slicing) from the octree representation. This slice thickness at any height is computed from the AM machine parameters and the smallest octree size at that available height. After the computation of the variable slice thicknesses has been completed, the part is virtually manufactured and the part errors are calculated. The virtually manufactured part and physical models are inspected to evaluate the volumetric errors. This algorithm uses an octree approach to improve the volumetric accuracy. And build time for the two different case studies are also done.Mechanical Engineerin

Estimates of genetic components and regression analysis for grain yield and various morphological traits in bread wheat (Triticum aestivum L.)

The present study was conducted to estimate the gentic components and regression analysis for grain yield and various morphological traits in bread wheat involving 10 parents and their 45 F1s (half diallel) during 2012- 13 and 2013-14. Significant additive (D) and dominance (H1) variance for the traits indicated that expression of these traits is control by both additive and dominance gene action. Average degree of dominance (H1/D)1/2 were more than unity for the traits (peduncle length, flag leaf area, productive tillers, biological yield, grain yield, harvest index) indicating the preponderance of over dominance gene action. The estimates of h2 were positive and significant for days to ear emergence, peduncle length, productive tillers, biological yield and grain yield indicated dominance of genetic components in F1s. Positive and significant values of F were estimated for days to ear emergence, days to 50% flowering, spike length, flag leaf area and grain yield in F1s indicating the preponderance of dominance and positive genes in the parents involved. The theoretical value (0.25) of (H2/4H1) for all the traits indicated asymmetrical distribution of positive and negative genes. The proportion of dominant and recessive alleles indicated presence of dominant alleles in the parents. The traits showing more than 30% narrow sanse heritability could be rewarding for further improvement in grain yield in bread wheat. Regression analysis indicated that the traits (days to ear emergence, days to 50% flowering, peduncle length, flag leaf area, productive tillers, harvest index, biological yield and grain yield) control by over dominance type of gene action. The parent RAJ 4246 contained maximum dominant genes for days to ear emergence and days to 50% flowering; HD 2733 for spike length and flag leaf area and HD 2824 for productive tillers, biological yield and grain yield used as donors in multiple traits breeding programme to develop high yielding wheat genotypes

Minimization of Volumetric Errors in CAD Medical Models Using 64 Slice Spiral CT Scanner

Sixty four slice spiral Computed Tomography (CT) scanner is one of the advanced CT scanners to capture the large volume of tissues and improved longitudinal resolution. The CT images are used to develop a 3-Dimensional (3D) Computer Aided Design (CAD) medical model. While developing a 3D CAD medical model volumetric errors occur due to partial volume or volume averaging effect. In order to study, various CT image construction parameters were considered to minimize the volumetric errors in 3D CAD medical models, a human dry mandible has been selected as a phantom. A Taguchi technique was used to find optimal CT image construction parameters. A L9 orthogonal array was used to optimize the CT image construction parameters constituting slice thickness, slice increment and Field of View (FOV) while performing CT image construction. The resultant optimal parameters are scrutinized using analysis of variance (ANOVA) method for its influence on the CT image construction. In this work, it has been found that there is a volumetric error of a 3D CAD medical model (STL file) from CT images of a dry mandible was 1978 mm3 (6.11%).Mechanical Engineerin

Identification of heterotic cross combinations for various agromorphological and some quality traits in bread wheat (Triticum aestivum L.)

A study was conducted to identify the best heterotic cross for various agromorphological and some quality traits involving 10 parents and their 45 F1s excluding reciprocals during 2012-13 and 2013-14. The higher magnitude of heterosis for all the agromorphological and quality traits was not expressed in a single cross combination. It varied from cross to cross due to diverse genetic background of their parents. The highest heterobeltiosis (35.68%, 11.11%, 11.44%), average heterosis (38.97%, 9.13%, 10.26%) and standard heterosis (31.09%, 7.84%, 10.41%) for grain yield, spikelets per spike and grains per spike respectively, was showed by HD 3095 x RAJ 4246 and this cross also showed highly significant (at <1% level of significant) heterosis for biological yield, flag leaf area, spike length and productive tillers. Whereas PBW 435 x RAJ 4246 were common for gluten content (8.52% and 7.72%), grain yield (33.11% and 33.64%), productive tillers (16.15% and 13.53%) and biological yield (36.27% and 21.98%) which showed superior average heterosis and heterobeltiosis respectively, therefore, these crosses may be exploit-ed in a national hybrid wheat breeding programme may offer genetic improvement in breeding for higher grain yield, agromorphological and quality traits in bread wheat. The presence of high heterosis for yield contributing compo-nents is not only for developing hybrids through exploitation of heterosis but also helps to produce transgressive segregants for developing of superior homozygous lines