On time changes in a digraph technical report no. 3

Mathematical model for analyzing changes through time in binary dyadic relation - probability theor

Stochastic models for multi-valued, multi- dimensional relations Semiannual status report, Jun. 16, 1966 - Jan. 15, 1967

Covered space, Riemann geometry extension, and partition function research on stochastic models for multivalued, multidimensional relation

Appraisal of the Quality of Ground Waters in the Arid Zone of Rajasthan and Kutch

A survey and analyses of waters of arid zones of Western Rajasthan and Kutch have been presented. The data on physico-chemical characteristics of about 2000 ground water samples indicate that according to International Standards of drinking water as devised by WHO, 9 per cent waters in Rajasthan and 19 per cent in Kutch conform to permissible limits (TDS < 500 mg/l) and are suitable for drinking. Considering 2000 mg/l TDS, as maximum permissible level, 46 per cent of available waters in Western Rajasthan and 71 per cent in Kutch are potable. 38 and 57 per cent of waters have electrical conductivity less than 2250 micromhos/cm in Rajasthan and Kutch respectively. Salinity and toxicological studies of brackish waters and their remedial measures are also discussed. A tentative correlation between prevailing water-borne diseases, kidney diseases and fluorosis and dissolved solids in waters of Western Rajasthan has also been shown. The waters have been classified into various suitability classes depending upon their composition

What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

Mechanisms of rolling contact spalling

The results of a study aimed at analyzing the mechanical material interactions responsible for rolling contact spalling of the 440 C steel, high pressure oxygen turbopump bearings are presented. A coupled temperature displacement finite element analysis of the effects of friction heating under the contact is presented. The contact is modelled as a stationary, heat generating, 2 dimensional indent in an elastic perfectly plastic half-space with heat fluxes up to 8.6 x 10000 KW/m sq comparable to those generated in the bearing. Local temperatures in excess of 1000 C are treated. The calculations reveal high levels of residual tension after the contact is unloaded and cools. Efforts to promote Mode 2/Mode 3 fatigue crack growth under cyclic torsion in hardened 440 C steel are described. Spalls produced on 440 C steel by a 3 ball/rod rolling contact testing machine were studied with scanning microscopy. The shapes of the cyclic, stress strain hysteresis loops displayed by hardened 440 C steel in cyclic torsion at room temperature are defined for the plastic strain amplitudes encountered in rolling/sliding contact. Results of these analyses are discussed in detail

Mathematical Models in Management Sciences. (1) - Consumer Behaviour as a Markov Process

Mathematical models based on Markov processes for consumer purchasing behavio

Random Graphs and Probability Models

Preliminary results concerning random graphs, digraphs, time dependent processes, and probability model

Role of ABA Signaling in Regulation of Stem Sugar Metabolism and Transport under Post- Flowering Drought Stress in Sweet Sorghum

Sugar remobilization from vegetative to reproductive tissues is an important process that determines grain yield in crops. Sweet sorghum stems store sugar and introgression of Stay green1 (Stg 1) locus from the grain sorghum genotype B35 into the sweet sorghum genotype S35 was previously shown to bring about a 2-fold higher stem sugar accumulation in the near-isogenic line (NIL) S35SG06040. We hypothesized that remobilization of stem sugar augments grain yield on exposure to drought stress and that the phytohormone abscisic acid (ABA) has a role to play in this process. ABA levels were three times higher in the NIL as compared to those in S35 on drought stress exposure. Remobilization of stem sugars in the NIL was evident by the observed decrease in reducing sugar content in the stem but not in the peduncle in response to prolonged drought stress exposure. Drought-induced expression of some ABA response factors (ABFs) as well as invertase and sucrose transporter genes was seen to be higher in the NIL as compared to S35. An over-representation of ABA-responsive elements (ABREs) and sugar signaling motifs in the differentially expressed genes indicated the involvement of ABA and sugar signaling in regulation of their expression. Two ABF genes located on the Stg1 locus showed single nucleotide polymorphism, which possibly accounted for their differential regulation in S35 and the NIL. The results suggest that ABA signaling plays an important role in post-flowering drought-induced remobilization of sugars to the reproductive sinks

Electron- and Hole-Doping Effects on AA-site Ordered NdBaMn2_2O6_6

We have investigated electron- and hole-doping effects on $A$-site ordered perovskite manganite NdBaMn$_2$O$_6$, which has the $A$-type (layered) antiferromagnetic (AFM) ground state. Electrons (holes) are introduced by partial substitution of Ba$^{2+}$ (Nd$^{3+}$) with Nd$^{3+}$ (Ba$^{2+}$). Electron-doping generates ferromagnetic (FM) clusters in the $A$-type AFM matrix. With increasing the electron-doping level, the volume fraction of the FM phase or the number of the FM clusters is abruptly increasing. In contrast, the $A$-type AFM phase is robust against the hole-doping, and no FM correlation is observed in the hole-doped NdBaMn$_2$O$_6$.Comment: 8 pages, 5 figures, to be published in Journal of the Physical Society of Japa