The Riccati System and a Diffusion-Type Equation

We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered.Comment: 11 pages, no figure

On the native status of the southern right whale <i>Eubalaena australis</i> in Peru

The native status of the southern right whale in Peruvian waters is now firmly supported by six confirmed sightings, including four cow-calf pairs, the northernmost at Pucusana (12°29’S,76°48’W) and off San Bartolo (12°24’S,77°11’W). An unconfirmed report exist from northern Peru. Five of six observations were shore-based, underscoring the importance of neritic habitat for E. australis also in Pacific South America. As sighting intervals have shortened over a period of two decades (near significant trend, P= 0.054) without indication of improved reporting, a guarded optimism for the recovery of E. australis in Peru may be warranted. However, a near-collision event with a fishing boat warns of conservation challenges ahead. As applies to three other cetacean species, the coast of Peru is proposed as the most boreal habitual range for E. australis on the planet, enabled by the cooling effects of the strongest of eastern boundary currents

The Degenerate Parametric Oscillator and Ince's Equation

We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their connections with dynamical invariants and SU(1,1) group are also discussed.Comment: 10 pages, no figure

Quantum Integrals of Motion for Variable Quadratic Hamiltonians

We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.Comment: 32 pages, no figure

The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys., Special Issue celebrating the 20th anniversary of quantum state engineering (R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Signaling in Secret: Pay-for-Performance and the Incentive and Sorting Effects of Pay Secrecy

Key Findings: Pay secrecy adversely impacts individual task performance because it weakens the perception that an increase in performance will be accompanied by increase in pay; Pay secrecy is associated with a decrease in employee performance and retention in pay-for-performance systems, which measure performance using relative (i.e., peer-ranked) criteria rather than an absolute scale (see Figure 2 on page 5); High performing employees tend to be most sensitive to negative pay-for- performance perceptions; There are many signals embedded within HR policies and practices, which can influence employees’ perception of workplace uncertainty/inequity and impact their performance and turnover intentions; and When pay transparency is impractical, organizations may benefit from introducing partial pay openness to mitigate these effects on employee performance and retention