On Some Inequalities Involving Harmonic Mean and Moments

We derive bounds on the second order moment of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered and it is shown that the present bounds provide refinements of the bounds which exist in literature. As an application we obtain a lower bound for the spread of a positive definite matrix A in terms of traces of A, A-1 and A2. Our results compare favourably with those obtained by Wolkowicz and Styan (Bounds for eigenvalues using traces, Lin. Alg. Appl. 29, 471-506, 1980)

An Integrated Model with Variable Production and Demand Rate under Inflation

AbstractIn this article, an integrated model is developed in which a manufacturer purchases raw materials from a supplier, and then produces finished products/goods, after that delivers them to a buyer. In the intended model production rate is assumed as a function of demand rate and customer demand rate is time dependent. To make the model more realistic the effect of inflation and time value of money is also taken into consideration. The concept of the model is illustrated through the numerical example and sensitivity analysis with respect to the system parameters is also performed

Abscisic acid analogues for enhanced stress tolerance and size control of tomato seedlings

Non-Peer ReviewedTransplanting shock is a common problem during establishment of horticultural crops like vegetables and ornamental bedding plants. The marketing period of nursery raised seedlings is limited due to the loss of aesthetic quality associated with undesirable growth and accelerated moisture loss during storage and handling. Two synthetic analogues (PBI 365 and PBI 429) of the plant hormone abscisic acid (S. Abrams PBI/NRC) were evaluated in a number of greenhouses and field trials at the University of Saskatchewan, for their potential to alter the stress tolerance and growth of horticultural crops. Pre-planting application of analogues, at 10-4 M, enhanced the tomato transplants survival under moisture stress in field conditions. Under greenhouse conditions, the ABA analogues slowed the moisture use and growth of seedlings without deteriorating the visual quality. Thus, ABA analogues could be used in horticultural crops for enhanced stand establishment as well as to hold seedlings at a particular stage thereby allowing their storage and extending the marketing period

Biochemically Induced Variations During Some Phenological Stages in Thompson Seedless Grapevines Grafted on Different Rootstocks

Phenological variation in Thompson Seedless grapevines grafted on different rootstocks and own rootedvines was assessed for two consecutive years and the reasons for such variations were studied throughbiochemical analysis. Uniform and early bud sprouting was recorded in the vines grafted on 110Rrootstock and on own roots, which was attributed to increased peroxidase activity and protein content inthe buds before bud burst. Increased fruitfulness on 110R rootstock and own rooted vines was attributedto the increased phosphorus and protein content of those vines and reduced vegetative vigour measuredin terms of shoot length, cane diameter and pruned biomass. Thompson Seedless grafted on Dogridgerootstock recorded the highest nitrogen content, increased shoot length, cane diameter and increasedpruned biomass attributing to reduced fruitfulness. The highest concentration of phenolic compoundsand amino acids was recorded in the fruits produced on 110R rootstock, while it was least on St. Georgeand own roots. Significant variation in the accumulation pattern of amino acids (especially proline andarginine) was observed, with the least proline/arginine ratio recorded on 110R rootstocks at the time ofharvest, indicating the variation in the days taken for fruit ripening on different rootstocks

Phase Separation Based on U(1) Slave-boson Functional Integral Approach to the t-J Model

We investigate the phase diagram of phase separation for the hole-doped two dimensional system of antiferromagnetically correlated electrons based on the U(1) slave-boson functional integral approach to the t-J model. We show that the phase separation occurs for all values of J/t, that is, whether $0 < J/t < 1$ or $J/t \geq 1$ with J, the Heisenberg coupling constant and t, the hopping strength. This is consistent with other numerical studies of hole-doped two dimensional antiferromagnets. The phase separation in the physically interesting J region, $0 < J/t \lesssim 0.4$ is examined by introducing hole-hole (holon-holon) repulsive interaction. We find from this study that with high repulsive interaction between holes the phase separation boundary tends to remain robust in this low $J$ region, while in the high J region, J/t > 0.4, the phase separation boundary tends to disappear.Comment: 4 pages, 2 figures, submitted to Phys. Rev.

Effect of Ferroelectric Nanopowder on Electrical and Acoustical Properties of Cholesteric Liquid Crystal

Ferroelectric nano-materials are very sensitive to several external stimuli and have attracted great deal of attention due to their property of improving various properties such as photoluminescence, higher polarization, fast response time, low operating voltage and improved conductivity. For enhancing the physical properties, a proper selection of nano-materials for liquid crystals depends upon various factors such as size, shape, preparation methods, surfactant concentration and amount of doping materials. In the present study an attempt is made to study  electrical and acoustical properties of cholesteric liquid crystal after dispersing ferroelectric nano-powder of Barium Titanate (BaTiO3). In addition with this particle size and surface area of pure and nono-particle dispersed liquid crystal were also measured. Our investigation shows increase in Rao’s constant or molar sound velocity, which indicates increase in molecular density indicating a close packing of the material. The measurement of dielectric relaxation at different frequencies gives information about the dynamics of polar groups and molecular motion

Studies on Anatomical and Physico-Mechanical Properties of Candidate Plus Culms (CPCs) of Dendrocalamus strictus for Planting Stock Improvement Programme

Five candidate plus culms (CPCs) of about 2-year-old Dendrocalamus strictus (namely 16, 17, 21, 55 and 110) were collected from Sirsi, Karnataka, India, for investigations on anatomical, physical and mechanical properties. Various morphological (inter-nodal length, culm diameter and culm wall thickness), anatomical (fibre length, fibre diameter, fibre lumen diameter, fibre wall thickness and vascular bundles), physical (moisture content and specific gravity) and mechanical (fibre stress at elastic limit-FS at EL, modulus of rupture-MOR and modulus of elasticity-MOE) properties were evaluated for inter-comparison among the CPCs. Among all the CPCs, specific gravity was maximum in CPC 55 and minimum in CPC 17. A comparison of different properties was carried out at 2nd and 4th internode for all the five CPCs. The results indicate that the internodal length was lower in 2nd than 4th internodes with maximum and minimum values observed in CPC 55 and CPC 16 respectively. The culm diameter and culm wall thickness was higher in the 2nd internode than 4th internode. The maximum value of culm wall thickness was observed in CPC 110 and minimum in CPC 21 whereas culm diameter was maximum in CPC 16 and minimum in CPC 17. The fibre morphology did not show significant variation between 2nd and 4th internode among all the CPCs. However, the number of vascular bundles remained more in 4th internode of all the CPCs compared to 2nd internode. While FS at EL was maximum in CPC 55, the minimum corresponding values were found in CPC 110. Similarly, the MOR was maximum in CPC 55 and minimum in CPC 110. The maximum value of MOE was observed in CPC 55 while minimum values was in CPC 16. The data analysis shows that CPCs 55 having superior strength properties is comparatively more suitable for structural applications. CPCs 16 showed most of the anatomical parameters in the higher range and may be utilized for general applications including pulp and paper. The data generated on CPCs may be of use for bamboo improvement program and bamboo plantations which can produce quality product

Two temperature viscous accretion flows around rotating black holes: Description of under-fed systems to ultra-luminous X-ray sources

We discuss two temperature accretion disk flows around rotating black holes. As we know that to explain observed hard X-rays the choice of Keplerian angular momentum profile is not unique, we consider the sub-Keplerian regime of the disk. Without any strict knowledge of the magnetic field structure, we assume the cooling mechanism is dominated by bremsstrahlung process. We show that in a range of Shakura-Sunyaev viscosity parameter 0.2\gsim\alpha\gsim0.0005, flow behavior varies widely, particularly by means of the size of disk, efficiency of cooling and corresponding temperatures of ions and electrons. We also show that the disk around a rotating black hole is hotter compared to that around a Schwarzschild black hole, rendering a larger difference between ion and electron temperatures in the former case. With all the theoretical solutions in hand, finally we reproduce the observed luminosities ($L$) of two extreme cases -- the under-fed AGNs and quasars (e.g. Sgr $A^*$) with L\gsim 10^{33} erg/sec to ultra-luminous X-ray sources with $L\sim 10^{41}$ erg/sec, at different combinations of mass accretion rate, ratio of specific heats, Shakura-Sunyaev viscosity parameter and Kerr parameter, and conclude that Sgr $A^*$ may be an intermediate spinning black hole.Comment: 21 pages including 5 figures; few typos corrected; to appear in New Astronom