Time-reversal and parity conservation for gravitating quarks

The complex mass term of a quark does not violate time-reversal or parity in gravitational interactions, in spite of an axial anomaly.Comment: 4 pages, to appear in Classical and Quantum Gravit

Set covering and set partitioning: a collection of test problems

It is now well established that set covering and set partitioning models play a central role in many scheduling applications. There are many algorithms which solve these problems. In order to test and validate such implementations we have collected a range of test problems taken from different contexts. A brief description of these models, their applications and summary model data, are supplied in this paper

A tree search approach for the solution of set problems using alternative relaxations

A number of alternative relaxations for the family of set problems (FSP) in general and set covering problems (SCP) in particular are introduced and discussed. These are (i) Network flow relaxation, (ii) Assignment relaxation, (iii) Shortest route relaxation, (iv) Minimum spanning tree relaxation. A unified tree search method is developed which makes use of these relaxations. Computational experience of processing a collection of test problems is reported

Quantum Information Paradox: Real or Fictitious?

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of Black Hole (BH) evaporation or accretion. Let us recall that Quantum Mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH would exist, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction of QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an INTEGRATION CONSTANT of Einstein equations. And it has been shown that the value of this integration constant is actually zero. Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an "Eternally Collapsing Object" which is a ball of hot plasma and which is asymptotically approaching the true BH state with M=0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by highest QM acceleration. In any case no EH is ever formed and in reality, there is no quantum information paradox.Comment: 8 pages in Pramana Style, 6 in Revtex styl

Three-point Green function of massless QED in position space to lowest order

The transverse part of the three-point Green function of massless QED is determined to the lowest order in position space. Taken together with the evaluation of the longitudinal part in arXiv:0803.2630, this gives a relation for QED which is analogous to the star-triangle relation. We relate our result to conformal-invariant three-point functions.Comment: 8 page

Complex fermion mass term, regularization and CP violation

It is well known that the CP violating theta term of QCD can be converted to a phase in the quark mass term. However, a theory with a complex mass term for quarks can be regularized so as not to violate CP, for example through a zeta function. The contradiction is resolved through the recognition of a dependence on the regularization or measure. The appropriate choice of regularization is discussed and implications for the strong CP problem are pointed out.Comment: REVTeX, 4 page

Ranking Investment Projects

This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period.