A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

Functions f(z)= z+E°2 anzn that are analytic in the unit disk and satisfy the differential equation f'(z) + azf"(z)+yz2f"(z) = g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z) = (10(10G(ztμsν�t−μs−νds dt with G" subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h

Exit Consents in Sovereign Bond Exchanges

The external debt of emerging market sovereign borrowers is now mainly in the form of bonds held by numerous institutional and individual bondholders. Many of these bonds are governed by the law of the state of New York. As a matter of drafting convention, bonds for sovereign issuers governed by New York law prohibit amendments to the payment terms of the instruments (the amount and the due dates of payments) without the consent of each affected bondholder. If a sovereign issuer finds it necessary to seek a restructuring of its bond indebtedness, it must therefore implement the restructuring by offering to exchange its old bonds for new debt instruments that reflect the new financial terms; a technique that inevitably risks leaving behind holdout creditors who may refuse to accept the proposed restructuring. Holdouts pose a litigation threat to the sovereign and may even jeopardize the sovereign\u27s ability to service the new bonds it has issued to the other creditors participating in the exchange. A number of ideas - ranging from international bankruptcy codes and stays of creditor legal remedies administered by the International Monetary Fund (IMF), to reforming the explicit terms of sovereign bond contracts - have been suggested as a means of dealing with the holdout creditor threat. This article suggests a less radical, and more immediately applicable, alternative; allowing the majority creditors to use the amendment clauses in their existing bonds to change certain nonpayment terms contained in those bonds (such as financial covenants or waivers of sovereign immunity) as a means of encouraging prospective holdouts to participate in the exchange. Because the sovereign issuer solicits the consent of its creditors to amend the old bonds just as those lenders exchange their bonds for the sovereign\u27s new debt instruments, this techinque is referred to as an exit consent

Searching for physics beyond the Standard Model through the dipole interaction

The magnetic dipole interaction played a central role in the development of QED, and continued in that role for the Standard Model. The muon anomalous magnetic moment has served as a benchmark for models of new physics, and the present experimental value is larger than the standard-model value by more than three standard deviations. The electric dipole moment (EDM) violates parity ({$P$}) and time-reversal ({$T$}) symmetries, and in the context of the $CPT$ theorem, the combination of charge conjugation and parity ($CP$). Since a new source of {$CP$} violation outside of that observed in the $K$ and $B$ meson systems is needed to help explain the baryon asymmetry of the universe, searches for EDMs are being carried out worldwide on a number of systems. The standard-model value of the EDM is immeasurably small, so any evidence for an EDM would signify the observation of new physics. Unique opportunities exist for EDM searches using polarized proton, deuteron or muon beams in storage rings. This talk will provide an overview of the theory of dipole moments, and the relevant experiments. The connection to the transition dipole moment that could produce lepton flavor violating interactions such as $\mu^+ \rightarrow e^+ \gamma$ is also mentioned.Comment: Invited Plenary talk at the 19th International Spin Physics Symposium, Juelic

Ultra-High Energy Neutrino Fluxes: New Constraints and Implications

We apply new upper limits on neutrino fluxes and the diffuse extragalactic component of the GeV gamma-ray flux to various scenarios for ultra high energy cosmic rays and neutrinos. As a result we find that extra-galactic top-down sources can not contribute significantly to the observed flux of highest energy cosmic rays. The Z-burst mechanism where ultra-high energy neutrinos produce cosmic rays via interactions with relic neutrinos is practically ruled out if cosmological limits on neutrino mass and clustering apply.Comment: 10 revtex pages, 9 postscript figure

A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

Functions f(z)=z+∑2∞‍anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z)=∫01∫01‍G(ztμsν)t-μs-νds dt with G' subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h