Pair correlation functions and limiting distributions of iterated cluster point processes

We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier work by Felsenstein and Shimatani describing a reproducing population. We discuss when closed term expressions of the first and second order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument

Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters $M$ (mass), $Q$ (charge), $a$ (rotation) and $L$ (NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\o}ller in the framework of Weitzenb$\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction.Comment: Latex. Will appear in IJMP

Minimal surface singularities are Lipschitz normally embedded

Any germ of a complex analytic space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the ambient space and the {\it inner metric}, which is the associated riemannian metric on the germ. We show that minimal surface singularities are Lipschitz normally embedded (LNE), i.e., the identity map is a bilipschitz homeomorphism between outer and inner metrics, and that they are the only rational surface singularities with this property.Comment: This paper is a major revision of the 2015 version. It now builds on the paper arXiv:1806.11240 by the same authors which gives a general characterization of Lipschitz normally embedded surface singularitie

Non-Preferential Clubs.

This paper examines the welfare implications of non-discriminatory tariff reforms by a subset of countries, which we term a non-preferential trading club. We show that there exist coordinated tariff reforms, accompanied by appropriate income transfers between these countries, that unambiguously increase the welfare of these member countries while leaving the welfare of non-members unaltered. These tariff reforms are chosen to maintain world prices at their pre-club levels and, in this respect, the trading clubs act in a Kemp-Wan-like manner. In terms of economic policy implications, our results show that there exist regional, MFN-consistent arrangements that lead to Pareto improvements in world welfare. Open regionalism is an example of such trading arrangements.

Non-Preferential Trading Clubs

This paper examines the welfare implications of non-discriminatory tariff reforms by a subset of countries, which we term a nonpreferential trading club. We show that there exist coordinated tariff reforms, accompanied by appropriate income transfers between these countries, that unambiguously increase the welfare of these member countries while leaving the welfare of non-members unaltered. These tariff reforms are chosen to maintain world prices at their pre-club levels and, in this respect, the trading clubs act in a Kemp-Wan-like manner. In terms of economic policy implications, our results show that there exist regional, MFN-consistent arrangements that lead to Pareto improvements in world welfare. Open regionalism is an example of such trading arrangements.trading clubs, non-preferential tariff reform, open regionalism, Kemp-Wan proposition, customs unions

Steepest Ascent Tariff Reforms

This paper introduces the concept of a steepest ascent tariff reform for a small open economy. By construction, it is locally optimal in that it yields the highest gain in utility of any feasible tariff reform vector of the same length. Accordingly, it provides a convenient benchmark for the evaluation of the welfare effectiveness of other well known tariff reform rules, as e.g. the proportional and the concertina rules. We develop the properties of this tariff reform, characterize the sources of the potential welfare gains from tariff reform, use it to establish conditions under which some existing reforms are locally optimal, provide geometric illustrations and compare welfare effectiveness of reforms using numerical examples. Moreover, being a general concept, we apply it to the issue of market access and examine its implications. Overall, the paper’s contribution lies in presenting a theoretical concept where the focus is upon the size of welfare gains accruing from tariff reforms rather than simply with the direction of welfare effects that has been the concern of the literature.steepest ascent tariff reforms, piecemeal tariff policy, welfare, market access, small open economy

Measuring Tax Efficiency: A Tax Optimality Index

This paper introduces an index of tax optimality that measures the distance of a current tax structure from the optimal tax structure in the presence of public goods. In doing so, we derive a [0,1] number that reveals immediately how far the current tax configuration is from the optimal one and, thereby, the degree of efficiency of a tax system. We call this number the Tax Optimality Index. We show how the basic method can be altered in order to derive a revenue equivalent uniform tax, which measures the size of the public sector. A numerical example is used to illustrate the method developed.tax optimality index, excess burden, distance function

Reciprocity, World Prices and Welfare

We examine in detail the circumstances under which reciprocity, as defined in Bagwell and Staiger (1999), leads to fixed world prices. We show that a change of tariffs satisfying reciprocity does not necessarily imply constant world prices in a world of many goods and countries. While it is possible to find tariff reforms that are consistent with both reciprocity and constant world prices, these reforms do not follow from the reciprocity condition, but rather from the requirement of unchanged world prices. We propose an alternative reciprocity rule that is guaranteed to raise the welfare of all countries, independently of whether world prices change and independently of the relative numbers of goods and countries.GATT, reciprocity, fixed world prices

Transverse radiation force in a tailored optical fiber

We show, by means of simple model calculations, how a weak laser beam sent through an optical fiber exerts a transverse radiation force if there is an azimuthal asymmetry present in the fiber such that one side has a slightly different refractive index than the other. The refractive index difference $\Delta n$ needs only to be very small, of order $10^{-3}$, in order to produce an appreciable transverse displacement of order 10 microns. We argue that the effect has probably already been seen in a recent experiment of She et al. [Phys. Rev. Lett. 101, 243601 (2008)], and we discuss correspondence between these observations and the theory presented. The effect could be used to bend optical fibers in a predictable and controlled manner and we propose that it could be useful for micron-scale devices.Comment: 4 pages, 3 figures. Accepted for publication as Rapid Communication in Phys. Rev.

Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory

An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters ``$$the gravitational mass $M$, the charge parameter $Q$ and the rotation parameter $a$" and its associated metric gives Kerr-Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then, calculate the total energy using the gravitational energy-momentum. The energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no energy is shared by the exterior of the Kerr-Newman black hole.Comment: 11 pages, Latex. Will appear in Mod. Phys. Lett.