On Krasner's Constant

AbstractLetvbe a henselian valuation of any rank of a fieldKandv̄be the extension ofvto a fixed algebraic closureK̄ofK. Let α∈K̄\Kbe separable overK. In this paper the author investigates the condition under which Krasner's constant ωK(α) given by max{v̄(α−α′)|α′≠α runs overK-conjugates of α}, is equal to min{v̄(α−α′): α′ runs overK-conjugates of α}; this is the condition for α to be equidistant from all of itsK-conjugates

Optimality and Construction of Designs with Generalized Group Divisible Structure

This thesis is an investigation of the optimality and construction problems attendant to the assignment of v treatments to experimental units in b blocks of size k, paying special attention to settings for which equal replication of the treatments is not possible. The model is that of one way elimination of heterogeneity, in which the expectation of an observation on treatment i in block j is Ti + βj (treatment effect + block effect), where Ti and βj are unknown constants, 1 ≤ i ≤ v and 1 ≤ j ≤ b. All observations are assumed to be uncorrelated with same variance. The generalized group divisible design with s groups, or GGDD(s), is defined in terms of the elements of the information matrix, instead of in terms of the elements of the concurrence matrix as done by Adhikary (1965) and extended by Jacroux (1982). This definition extends the class of designs to include non-binary members, and allows for broader optimality results. Some sufficient conditions are derived for GGDD(s) to be E- and MV-optimal. It is also shown how augmentation of addition blocks to certain GGDD(s)s produces other nonbinary, unequally replicated E- and MV-optimal block designs. Where nonbinary designs are found, they are generally preferable to binary designs in terms of interpretability, and often in terms of one or more formal optimality criteria as well. The class of generalized nearly balanced incomplete block designs with maximum concurrence range l, or NBBD(l), is defined. This class extends the nearly balance incomplete block designs as defined by Cheng & Wu (1981), and the semi-regular graph designs as defined by Jacroux (1985), to cases where off-diagonal entries of the concurrence matrix differ by at most the positive integer l. Sufficient conditions are derived for a NBBD(2) to be optimal under a given type-I criterion. The conditions are used to establish the A- and D-optimality of an infinite series of NBBD(2)s having unequal numbers of replicates. Also, a result from Jacroux (1985) is used to establish the A-optimality of a new series of NBBD(1)s. Several methods of construction of GGDD(s)s are developed from which many infinite series of designs are derived. Generally these designs satisfy the obtained sufficient conditions for E- and MV-optimality. Finally, in the nested row-column setting, the necessary conditions for existence of 2 x 2 balanced incomplete block designs with nested rows and columns (BIBRCs) are found to be sufficient. It is also shown that, sufficient for a BIBRC with p=q to generally balanced, is that the row and column classifications together form a balanced incomplete block design, as does the block classification. All of the 2 x 2 BIBRCs are constructed to have this property

EXPLORING PSYCHO-SOMATIC IMPLICATIONS OF YOGA PRACTICES – A STRATEGIC INQUIRY

Benefits of yogic practices are well documented, and its popularity is increasing day by day across the world. Yoga has gained new avenues and has started to explore the new facts and hidden benefits by objectively testing the potential benefits of yogic practices for human well-being and holistic health. The present research adopts a philosophical descriptive approach to analyze the popular belief regarding the psychosomatic qualities developed through yogic practices. An opinionnaire consisting to two broad themes was designed to obtain the responses from the surveyed yoga practitioners (N=400: Male=200 and Female=200), aged 18 to 25 years. Data was statistically analyzed to find out the somatic and psychological qualities that the subjects perceived were developed through yoga practices. The results indicated that the female participants believed that yoga practices will much contribute to their Stability and Balance, while the male subjects believed it will help them in developing their Core Strength. With regard to the psychological qualities, both male and female subjects listed Self-Confidence as their first preference. Overall, the subjects believed that the yogic practices can be quite useful to promote somatic qualities of stability and balance, and core strength. Regarding the psychological qualities, self-confidence and mental rejuvenation were found to be most favorable reasons to practice yoga. Implications of the study have been discussed and the recommendations for future research have been made.  Article visualizations

3D Localisation of Target using Elevation Angle Algorithm with the use of Ground Radars

A new novel method based on elevation angle algorithm (EAA) is proposed in this paper, to obtain 3D position of target using range and azimuth measurements of two ground 2D radars. The EAA estimates optimal target elevation angle wrt contributing radar by solving a non-linear optimisation problem using Levenberg-Marquardt method in geo-centric frame such as earth-centred-earth-fixed. The target position in geodetic frame (WGS84) is then obtained using slant range, azimuth and estimated elevation angle. The proposed method is evaluated using simulated but realistic radar data and accuracy of estimated position is found to be comparable with true position (error within acceptable limit). The method is also evaluated with real data from actual ground 2D radars and estimated target position is found to be comparable with reference navigation data (GPS) on-board of target. For each radar, corresponding Extended Kalman filter (EKF) is used to handle noisy, asynchronous measurements and to provide estimated range and azimuth at common reference time for altitude estimation using proposed EAA method. In case of real data, the estimated altitude is found to be comparable GPS altitude with error less than 5 % of true altitude. From the study, it is found that EAA is suitable to estimate target position using measurements from only two contributing asynchronous 2D radars in real-time as compared to some other techniques such triangulation and Trilateration where at-least three radars are required to get the position of target. This method can be useful to utilise network of vintage long range 2D radars to determine target position and to fill the gap wherever/whenever target is out of detection range of 3D radars. In addition, EAA method is compared with commonly used methodology such range only localisation and results are presented

Cloning and Expression of the PHA Synthase Gene From a Locally Isolated Chromobacterium sp. USM2

Chromobacterium sp. USM2, a locally isolated bacterium was found to synthesize poly(3-hydroxybutyrate-co-3-hydroxyvalerate), P(3HB-co-3HV) copolymer with high 3HV monomer composition. The PHA synthase gene was cloned and expressed in Cupriavidus necator PHB¯4 to investigate the possibilities of incorporating other monomer. The recombinant successfully incorporated 3-hydroxyhexanoate (3HHx) monomer when fed with crude palm kernel oil (CPKO) as the sole carbon source. Approximately 63 ± 2 wt% of P(3HB-co-3HHx) copolymer with 4 mol% of 3HHx was synthesized from 5 g/L of oil after 48 h of cultivation. In addition, P(3HB-co-3HV-co-3HHx) terpolymer with 9 mol% 3HV and 4 mol% 3HHx could be synthesized with a mixture of CPKO and sodium valerate. The presence of 3HV and 3HHx monomers in the copolymer and terpolymer was further confirmed with +H-NMR analysis. This locally isolated PHA synthase has demonstrated its ability to synthesize P(3HB-co-3HHx) copolymer from a readily available and renewable carbon source; CPKO, without the addition of 3HHx precursors