Revisiting conserved currents in F(R) theory of gravity via Noether symmetry

Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \propto R^{3/2} along with the conserved current \frac{d}{dt}(a\sqrt R) in Robertson-Walker metric and nothing else. Still some authors recently claimed to have obtained four conserved currents setting F(R) \propto R^{3/2} a-priori, taking time translation along with a gauge term. We show that the first one of these does not satisfy the field equations and the second one is the Hamiltonian which is constrained to vanish in gravity and thus a part and parcel of the field equations. We also show that the other two conserved currents, which do not contain time translation are the same in disguise and identical to the one mentioned above. Thus the claim is wrong.Comment: 8 page

Target Tracking in Non-Gaussian Environment

Masreliez filter which is a Kalman type of recursive filter is implemented and validated. The main computation in Masreliez filter is to evaluate the score function which directly influences the estimates of the target states. Scalar approximation for score function evaluation is extended to vector observations, implemented and validated. The simulation studies have shown that the performance of the Masreliez filter is relatively better than that of the conventional Kalman filter in the presence of significant glint noise in the observation

Are agricultural markets location-optimal? A case study of Gaya District (Bihar)

The thesis of efficiency and optimality of Indian agricultural system has several facets that have called for attention of a number of scholars. Some have proved allocative optimality of resource utilization, the others have proved optimality of distribution of gains from agriculture, while still others have come up with the cases of marketing optimality. However, there is hardly any work that studies location optimality of market centers in any region of India. In this paper we examine if the empirically observed market locations are optimal and as a case study take up the agricultural markets located in Gaya district of Bihar. We have used the location-allocation model for optimality analysis. Our findings reveal that existing locations and arrivals of merchandise at the agricultural markets of Gaya are very close to what might have been if they had been located on the principle of optimality. There are minor deviations, of course. However, as the existing markets have developed in an open region, unlike our cost-optimal locations searched out in a closed region, a discount must be made in favour of the existing locations, and we do not have enough reasons and evidence to conclude that the existing markets are sub-optimally located. We conclude, therefore, that market forces automatically establish location optimality and assert that the existing agricultural markets in Gaya district are location-optimal

Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.Comment: 6 Pages, Comments are welcom

On the equivalence between different canonical forms of F(R) theory of gravity

Classical equivalence between Jordan's and Einstein's frame counterparts of F(R) theory of gravity has recently been questioned, since the two produce different Noether symmetries, which couldn't be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time-time component of Einstein's equation, through a Lagrange multiplier to the existence condition for Noether symmetry to show that all the three different canonical structures of F(R) theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence amongst all the three.Comment: 10 pages, o figure

Spontaneous Bacterial Peritonitis Presenting as Acute Abdomen in a Patient with Chronic Kidney Disease

Spontaneous bacterial peritonitis (SBP) is a relatively common problem in adult patients with liver cirrhosis. The complication of SBP in adults with chronic kidney disease on maintenance hemodialysis is, however, extremely rare. To best of our knowledge this is probably the first case report