On the real linear polarization constant problem

The present paper deals with lower bounds for the norm of products of linear forms. It has been proved by J. Arias-de-Reyna [2], that the so-called n(th) linear polarization constant c(n)(C-n) is n(n/2), for arbitrary n is an element of N. The same value for c(n) (R-n) is only conjectured. In a recent work A. Pappas and S. Revesz prove that c(n) (R-n) = n(n/2) for n <= 5. Moreover, they show that if the linear forms are given as f(j)(x) = [x, a(j)),for some unit vectors a(j) (1 <= j <= n), then the product of the f(j)'s attains at least the value n(-n/2) at the normalized signed sum of the vectors having maximal length. Thus they asked whether this phenomenon remains true for arbitrary n is an element of N. We show that for vector systems {a(j)}(j=1)(n) close to an orthonormal system, the Pappas-Revesz estimate does hold true. Furthermore, among these vector systems the only system giving n(-n/2) as the norm of the product is the orthonormal system. On the other hand, for arbitrary vector systems we answer the question of A. Pappas and S. Revesz in the negative when n is an element of N is large enough. We also discuss various further examples and counterexamples that may be instructive for further research towards the determination of c(n)(R-n)

Water footprint of cotton, wheat and rice production in Central Asia

The hydrology of the Aral Sea Basin during the past few decades has been largely determined by the decision to\ud develop irrigated agriculture on a large scale to produce cotton for export in the 1960s. The irrigated area has\ud grown to 8 million hectares, using practically the entire available flow of the two main rivers, the Amu Darya\ud and Syr Darya. Almost two decades after the disintegration of the Soviet Union, the five states of the Aral Sea\ud Basin face the challenge of restoring a sustainable equilibrium while offering development opportunities for an\ud increasing population. Sustainable water management is thus an imperative that will require coordinated\ud political action of all the states involved.\ud The Soviet Union established its cotton-producing areas in Uzbekistan, Turkmenistan, Tajikistan, and\ud Kyrgyzstan. Today, while cotton remains relatively important, cereal production to reduce imports has become a\ud priority in all four nations. The cotton crop area has decreased over the past ten years, while that of winter wheat\ud – the main grain crop – has doubled. At 39 per cent of the total (blue and green) water consumption in\ud agriculture, wheat is the largest water-consuming crop in the five basin states, followed by cotton at 33 per cent.\ud The present study analyses the water footprint of Central Asian cotton (Gossypium hirsutum L.), wheat\ud (Triticum aestivum L.) and rice (Oryza sativa L.) production, differentiating between the green and blue\ud components, in order to know how the scarce water resources in the region are apparently allocated

Experimental Constraints on the Neutralino-Nucleon Cross Section

In the light of recent experimental results for the direct detection of dark matter, we analyze in the framework of SUGRA the value of the neutralino-nucleon cross section. We study how this value is modified when the usual assumptions of universal soft terms and GUT scale are relaxed. In particular we consider scenarios with non-universal scalar and gaugino masses and scenarios with intermediate unification scale. We also study superstring constructions with D-branes, where a combination of the above two scenarios arises naturally. In the analysis we take into account the most recent experimental constraints, such as the lower bound on the Higgs mass, the $b\to s\gamma$ branching ratio, and the muon $g-2$.Comment: References added, bsgamma upper bound improved, results unchanged, Talk given at Corfu Summer Institute on Elementary Particle Physics, August 31-September 20, 200

Further remarks on isospin breaking in charmless semileptonic B decays

We consider the isospin breaking corrections to charmless semileptonic decays of B mesons. Both, the recently measured branching ratios of exclusive decays by the CLEO Collaboration and the end-point reion of the inclusive lepton spectrum in form factor models, can be affected by these corrections. Isospin corrections can affect the determination of |V_ub| from exclusive semileptonic B decays at a level comparable to present statistical uncertainties.Comment: Latex, 7 pages, 1 .ps figure, to appear in Phys. Rev.

Right-handed sneutrino as thermal dark matter

We study an extension of the MSSM with a singlet S with coupling SH1H2 in order to solve the mu problem as in the NMSSM, and right-handed neutrinos N with couplings SNN in order to generate dynamically electroweak-scale Majorana masses. We show how in this model a purely right-handed sneutrino can be a viable candidate for cold dark matter in the Universe. Through the direct coupling to the singlet, the sneutrino can not only be thermal relic dark matter but also have a large enough scattering cross section with nuclei to detect it directly in near future, in contrast with most of other right-handed sneutrino dark matter models.Comment: 5 pages, 2 figures. References added and minor changes. Final version to appear in Phys. Rev.

Mixing of two-level unstable systems

Unstable particles can be consistently described in the framework of quantum field theory. Starting from the full S-matrix amplitudes of B^+ --> (2 pi, 3 pi) l nu decays as examples in the energy region where the rho-omega resonances are dominating, we propose a prescription for the mixing of two quasi `physical' unstable states that differs from the one obtained from the diagonalization of the M -i*Gamma/2 non-hermitian hamiltonian. We discuss some important consequences for CP violation in the K_L - K_S system.Comment: 7 pages, Latex. A factor 1/2 removed from r.h.s. of Eqs. (12)-(15). Conclusions unchange