On a general solution of Hill's equation

i. ON A GENERAL SOLUTION OF HILL'S EQUATION. BY E. LINDSAY INCE. Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol. LXIV. No. 5. • ii. NOTES ON THE GENERAL SOLUTION OF HILL'S EQUATION. BY E. LINDSAY INCE. Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol. LXXVI. No. 5. • iii. FURTHER NOTES ON THE GENERAL SOLUTION OF HILL'S EQUATION. BY E. LINDSAY INCE. Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol. LXXVIII. No. 2. • iv. On the continued fractions associated with the hypergenerative equatio

On \mu-Compatible Metrics and Measurable Sensitivity

We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.Comment: Many improvements in exposition, a technical assumption removed, as suggested by the reviewe

Exact real-time dynamics of the quantum Rabi model

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of and for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.Comment: 8 pages, 7 figures, published versio

Penrose Limit and String Theories on Various Brane Backgrounds

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.Comment: 41 pages, Latex, minor correction

It\u27s a \u27Criming Shame\u27: Moving from Land Use Ethics to Criminalization of Behavior Leading to Permits and Other Zoning Related Acts

In the past, land use ethics inquiries predominately involved conflicts of interest or an official holding public office while engaging in a previously held business or law practice. Now, prosecutors are looking at the underlying criminality of the unethical acts carried out in the context of land use decisions. With a wide array of criminal statutes in the hands of federal prosecutors, almost all forms of unethical conduct could in some way also violate a federal criminal statute.Part II of this article reviews the federal statutes most often used by federal prosecutors and provides some examples of recent reported cases in which the underlying illegal or unethical conduct involved alleged criminal activity. Part III offers some examples of recent reported state court cases in which criminal acts involving land use permitting or decision-making were the underlying cause of the subsequent or reported court action. Part IV concludes with the caveat that municipal attorneys and public officials can no longer simply view ethical issues in land use as a local or state civil matter, and those who work in and advise those in the public sector should be mindful of the tools at the disposal of federal investigators and prosecutors

It\u27s a \u27Criming Shame\u27: Moving from Land Use Ethics to Criminalization of Behavior Leading to Permits and Other Zoning Related Acts

In the past, land use ethics inquiries predominately involved conflicts of interest or an official holding public office while engaging in a previously held business or law practice. Now, prosecutors are looking at the underlying criminality of the unethical acts carried out in the context of land use decisions. With a wide array of criminal statutes in the hands of federal prosecutors, almost all forms of unethical conduct could in some way also violate a federal criminal statute.Part II of this article reviews the federal statutes most often used by federal prosecutors and provides some examples of recent reported cases in which the underlying illegal or unethical conduct involved alleged criminal activity. Part III offers some examples of recent reported state court cases in which criminal acts involving land use permitting or decision-making were the underlying cause of the subsequent or reported court action. Part IV concludes with the caveat that municipal attorneys and public officials can no longer simply view ethical issues in land use as a local or state civil matter, and those who work in and advise those in the public sector should be mindful of the tools at the disposal of federal investigators and prosecutors

Forest Carbon Sequestration under the U.S. Biofuel Energy Policies

This paper analyzes impacts of the U.S. biofuel energy policies on the carbon sequestration by forest products, which is expressed as Harvested Wood Products (HWP) Contribution under the United Nations Framework Convention on Climate Change. Estimation for HWP Contribution is based on tracking carbon stock stored in wood and paper products in use and in solid-waste disposal sites (SWDS) from domestic consumption, harvests, imports, and exports. For this analysis, we hypothesize four alternative scenarios using the existing and pending U.S. energy policies by requirements for the share of biofuel to total energy consumption, and solve partial equilibrium for the U.S. timber market by 2030 for each scenario. The U.S. Forest Products Module (USFPM), created by USDA Forest Service Lab, operating within the Global Forest Products Model (GFPM) is utilized for projecting productions, supplies, and trade quantities for the U.S. timber market equilibrium. Based on those timber market components, we estimate scenario-specific HWP Contributions under the Production, the Stock Change, and the Atmospheric Approach suggested by Intergovernmental Panel on Climate Change (IPCC) Guidelines for National Greenhouse Gas Inventories using WOODCARB II created by VTT Technical Research Centre of Finland and modified by USDA Forest Service Lab. Lastly, we compare estimated results across alternative scenarios. Results show that HWP Contributions for the baseline scenario in 2009 for all approaches are estimated higher than estimates reported by U.S. Environmental Protection Agency in 2011, (e.g., 22.64 Tg C/ year vs 14.80 Tg C/ year under the Production Approach), which is due to the economic recovery, especially in housing construction, assumed in USFPM/GFPM. Projected HWP Contribution estimates show that the Stock Change Approach, which used to provide the highest estimates before 2009, estimate HWP Contribution lowest after 2009 due to the declining annual net imports. Though fuel wood consumption is projected to be expanded as an alternative scenario requires higher wood fuel share to total energy consumption, the overall impacts on the expansion in other timber products are very modest across scenarios in USFPM/GFPM. Those negligible impacts lead to small differences of HWP Contribution estimates under all approaches across alternative scenarios. This is explained by the points that increasing logging residues are more crucial for expansion in fuel wood projections rather than the expansion of forest sector itself, and that the current HWP Contribution does not include carbon held in fuel wood products by its definition.Forest Products, Carbon Sequestration, Biofuel Policies, HWP Contribution, Resource /Energy Economics and Policy,

Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow

Hollerbach and Rudiger have reported a new type of magnetorotational instability (MRI) in magnetized Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields. The salient advantage of this "helical'' MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize than standard MRI (axial field only). We confirm their results, calculate HMRI growth rates, and show that in the resistive limit, HMRI is a weakly destabilized inertial oscillation propagating in a unique direction along the axis. But we report other features of HMRI that make it less attractive for experiments and for resistive astrophysical disks. Growth rates are small and require large axial currents. More fundamentally, instability of highly resistive flow is peculiar to infinitely long or periodic cylinders: finite cylinders with insulating endcaps are shown to be stable in this limit. Also, keplerian rotation profiles are stable in the resistive limit regardless of axial boundary conditions. Nevertheless, the addition of toroidal field lowers thresholds for instability even in finite cylinders.Comment: 16 pages, 2 figures, 1 table, submitted to PR

Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys

Nonlocal symmetries of Riccati and Abel chains and their similarity reductions

We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal symmetry. The similarity reduced $N^{th}$ order ordinary differential equation (ODE), $N=2, 3,4,...$, in this chain yields $(N-1)^{th}$ order ODE in the same chain. All the equations in the Abel chain also share the same form of nonlocal symmetry (which is different from the one that exist in Riccati chain) but the similarity reduced $N^{th}$ order ODE, $N=2, 3,4,$, in the Abel chain always ends at the $(N-1)^{th}$ order ODE in the Riccati chain. We describe the method of finding general solution of all the equations that appear in these chains from the nonlocal symmetry.Comment: Accepted for publication in J. Math. Phy