A Machian Model of Dark Energy

Einstein believed that Mach's principle should play a major role in finding a meaningful spacetime geometry, though it was discovered later that his field equations gave some solutions which were not Machian. It is shown, in this essay, that the kinematical $\Lambda$ models, which are invoked to solve the cosmological constant problem, are in fact consistent with Mach's ideas. One particular model in this category is described which results from the microstructure of spacetime and seems to explain the current observations successfully and also has some benefits over the conventional models. This forces one to think whether the Mach's ideas and the cosmological constant are interrelated in some way.Comment: Received an Honorable mention in the Essay Contest-2002 sponsored by the Gravity Research Foundation; A paragraph added on how the model can explain the CMB anisotropy observations; To appear in the Classical and Quantum Gravit

Non-monotonic diffusion rates in atom-optics L\'{e}vy kicked rotor

The dynamics of chaotic Hamiltonian systems such as the kicked rotor continues to guide our understanding of transport and localization processes. The localized states of the quantum kicked rotor decay due to decoherence effects if subjected to stationary noise. The associated quantum diffusion increases monotonically as a function of a parameter characterising the noise distribution. In this work, for the Levy kicked atom-optics rotor, it is experimentally shown that by tuning a parameter characterizing the Levy distribution, quantum diffusion displays non-monotonic behaviour. The parameters for optimal diffusion rates are analytically obtained and they reveal a good agreement with the cold atom experiments and numerics. The non-monotonicity is shown to be a quantum effect that vanishes in the classical limit.Comment: 5 pages, revte

Modeling Repulsive Gravity with Creation

There is a growing interest in the cosmologists for theories with negative energy scalar fields and creation, in order to model a repulsive gravity. The classical steady state cosmology proposed by Bondi, Gold and Hoyle in 1948, was the first such theory which used a negative kinetic energy creation field to invoke creation of matter. We emphasize that creation plays very crucial role in cosmology and provides a natural explanation to the various explosive phenomena occurring in local (z<0.1) and extra galactic universe. We exemplify this point of view by considering the resurrected version of this theory - the quasi-steady state theory, which tries to relate creation events directly to the large scale dynamics of the universe and supplies more natural explanations of the observed phenomena. Although the theory predicts a decelerating universe at the present era, it explains successfully the recent SNe Ia observations (which require an accelerating universe in the standard cosmology), as we show in this paper by performing a Bayesian analysis of the data.Comment: The paper uses an old SNeIa dataset. With the new improved data, for example the updated gold sample (Riess et al, astro-ph/0611572), the fit improves considerably (\chi^2/DoF=197/180 and a probability of goodness-of-fit=18%

Inequalities for totally nonnegative matrices: Gantmacher--Krein, Karlin, and Laplace

A real linear combination of products of minors which is nonnegative over all totally nonnegative (TN) matrices is called a determinantal inequality for these matrices. It is referred to as multiplicative when it compares two collections of products of minors and additive otherwise. Set theoretic operations preserving the class of TN matrices naturally translate into operations preserving determinantal inequalities in this class. We introduce set row/column operations that act directly on all determinantal inequalities for TN matrices, and yield further inequalities for these matrices. These operations assist in revealing novel additive inequalities for TN matrices embedded in the classical identities due to Laplace $[$Mem$.$ Acad$.$ Sciences Paris $1772]$ and Karlin $(1968).$ In particular, for any square TN matrix $A,$ these derived inequalities generalize -- to every i^{\mbox{th}} row of $A$ and j^{\mbox{th}} column of ${\rm adj} A$ -- the classical Gantmacher--Krein fluctuating inequalities $(1941)$ for $i=j=1.$ Furthermore, our row/column operations reveal additional undiscovered fluctuating inequalities for TN matrices. The introduced set row/column operations naturally birth an algorithm that can detect certain determinantal expressions that do not form an inequality for TN matrices. However, the algorithm completely characterizes the multiplicative inequalities comparing products of pairs of minors. Moreover, the underlying row/column operations add that these inequalities are offshoots of certain ''complementary/higher'' ones. These novel results seem very natural, and in addition thoroughly describe and enrich the classification of these multiplicative inequalities due to Fallat--Gekhtman--Johnson $[$Adv$.$ Appl$.$ Math$.$ $2003]$ and later Skandera $[$J$.$ Algebraic Comb$.$ $2004].$Comment: 2 figures, 39 pages, and minor adjustments in the expositio

Effect of various pre-harvest treatments on shelf life and morphological characteristics of fruits of mango (Mangifera indica L.) var. ‘Amrapali’

The mango is considered as ‘king of fruits’ in India due to its delicious taste and nutritional status. Extension of fruit shelf life is a prime importance for availability of fresh fruit in market for longer duration and distance transportation. India is the largest producer and a prominent exporter of mango in the world.In this context, the study was conducted to evaluate the effect of preharvest spray of different chemicals and plant growth regulators (PGRs) on mango var. ‘Amrapali’ for shelf life and its quality. As ‘Amrapali’ has regular bearer with very good flavor and taste with a late maturing character, selected for shelf life studies. The fruits of mango weresprayed with chemicals viz. CaCl2 1%, CaCl2 2%, Ca(NO3)2 1%, Ca(NO3)2 2%, KNO3 1%, KNO3 2%, GA3 25 mg/l, GA3 50 mg/l, Ethrel 0.1 ml/l and Ethrel 0.2 ml/l prior to harvest. After harvesting, fruits were stored under ambient storage condition. Among all the treatments, GA3 25 mg/l treatment recorded significantly highest fruit length, fruit diameter, fruit volume and fruit weight at harvest and at fully ripe stage. Application of CaCl22% resulted in significantly minimum physiological loss in weight consistently from 2nd day to 16th day of storage besides significantly highest shelf life and quality. Hence, this intervention can contribute in preserving physical and chemical quality attributes for maximum acceptance by consumers

Inhibition of Formalin Induced Paw Edema in Rats by Various Fractions/Extracts of Bryophyllum pinnatum

Traditionally, Bryophyllum pinnatum is used in the management of arthritis and inflammatory diseases. However, B. pinnatum has not been analysed previously for anti-inflammatory activity. Hence, this study is designed to determine the anti-inflammatory effects of various fractions of B. pinnatum leaf extract using rat model of formalin-induced paw edema. Treatment with various fractions showed marked decrease in formalin-induced paw volume and edema in rats. The results of BPAAF treatment were comparable to standard drug, diclofenac. These results indicate that B. pinnatum could be developed as ant-inflammatory drug after further studies