8,807 research outputs found
On complex oscillation theory, quasi-exact solvability and Fredholm Integral Equations
Biconfluent Heun equation (BHE) is a confluent case of the general Heun
equation which has one more regular singular points than the Gauss
hypergeometric equation on the Riemann sphere . Motivated by
a Nevanlinna theory (complex oscillation theory) approach, we have established
a theory of \textit{periodic} BHE (PBHE) in parallel with the Lam\'e equation
verses the Heun equation, and the Mathieu equation verses the confluent Heun
equation. We have established condition that lead to explicit construction of
eigen-solutions of PBHE, and their single and double orthogonality, and a
related first-order Fredholm-type integral equation for which the corresponding
eigen-solutions must satisfy. We have also established a Bessel polynomials
analogue at the BHE level which is based on the observation that both the
Bessel equation and the BHE have a regular singular point at the origin and an
irregular singular point at infinity on the Riemann sphere ,
and that the former equation has orthogonal polynomial solutions with respect
to a complex weight. Finally, we relate our results to an equation considered
by Turbiner, Bender and Dunne, etc concerning a quasi-exact solvable
Schr\"odinger equation generated by first order operators such that the second
order operators possess a finite-dimensional invariant subspace in a Lie
algebra of Comment: This paper has been withdrawn by the authors due to a new version
with different title "Galoisian approach to complex oscillation theory of
Hill equations" and many contents change
Is the financial crisis over? a yield spread perspective
Our finding is consistent with some recent, substantial volatility in the U.S. corporate bond market and leaves open a possibility that additional, future shocks to default premia may have long-lived effects.Financial crises
Taming the long-term spreads
Given the size of the underlying markets, cutting the cost of capital to firms and households by reducing the yields required on long-term corporate bonds and mortgages is a key policy objective.Government securities ; Monetary policy ; Interest rates
Why HARM the subprime borrower?
Hybrid adjustable rate mortgages (HARM) were designed to be refinanced by the reset date, when the interest rate would jump. These mortgages worked out well for many people who were credit risks - but only as long as housing prices continued to rise.Subprime mortgage
- …