Voting power in a system of compound majority rule

In 1973, the United States Supreme Court ruled that a water district's voting scheme that apportioned votes on the basis of the assessed valuation of acreage in the district was constitutional. Among the justifications for the constitutionality of this scheme was the concurrent requirement that legislation be approved by a majority of voters as well as by a majority of weighted votes. However, analysis of this voting scheme in game-theoretic terms indicates that this justification is only partial: when two sets of winning coalitions must form simultaneously in order to pass legislation, the voting power of each voter in the combined system equals the mean of the voting power afforded each voter in each simple system. The results can be generalized to three or more concurrent requirements.     

Potential variability of decisional skills in uncertain dichotomous choice situations

The main concern of this paper is the selection of optimal decision rules for groups of individuals with identical preferences but diverse and potentially variable independent decisional skills. Employing the uncertain dichotomous choice model the main results illustrate how optimality and sensitivity analysis can be pursued while explicitly recognizing decision-making costs associated with potential variability of decisional skills. For panels of experts consisting of three members our analysis focuses on three special cases of potential variability in individual skills. The extended optimality problem is analyzed resolving the dilemma which of the two common rules, the simple majority rule or the expert rule, is the better selection for the group. The sensitivity of the two rules to variability of decisional skills is also investigated.     

Gromov-Witten invariants on Grassmannians

We prove that any three-point genus zero Gromov-Witten invariant on a type Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step flag variety is replaced by a sub-maximal isotropic Grassmannian. Our theorems are applied, in type , to formulate a conjectural quantum Littlewood-Richardson rule, and in the other classical Lie types, to obtain new proofs of the main structure theorems for the quantum cohomology of Lagrangian and orthogonal Grassmannians.

     

Relative Frequency and Probability in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics

The existence of probability in the sense of the frequency interpretation, i.e., probability as long term relative frequency, is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.     

Laplace and Segal-Bargmann transforms on Hermitian symmetric spaces and orthogonal polynomials

Let be a complex bounded symmetric domain of tube type in a complex Jordan algebra V and let be its real form in a formally real Euclidean Jordan algebra J⊂V; is a bounded realization of the symmetric cone in J. We consider representations of H that are gotten by the generalized Segal-Bargmann transform from a unitary G-space of holomorphic functions on to an L²-space on . We prove that in the unbounded realization the inverse of the unitary part of the restriction map is actually the Laplace transform. We find the extension to of the spherical functions on and find their expansion in terms of the L-spherical polynomials on , which are Jack symmetric polynomials. We prove that the coefficients are orthogonal polynomials in an L²-space, the measure being the Harish-Chandra Plancherel measure multiplied by the symbol of the Berezin transform. We prove the difference equation and recurrence relation for those polynomials by considering the action of the Lie algebra and the Cayley transform on the polynomials on . Finally, we use the Laplace transform to study generalized Laguerre functions on symmetric cones.     

Activity Coefficients of HCl + GdCl3 + H2O System from 5 to 55°C. Application of Pitzer Formalism

The emf of the cell

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

In this paper, using the Exact Quantization Rule, we present approximate analytical solutions of the radial Schrödinger equation with non-zero l values for the Hulthén potential in the frame of an approximation to the centrifugal potential for any l states. The energy levels of all bound states can be easily calculated from the Exact Quantization Rule. Specifically, the normalized analytical wave functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by other methods such as asymptotic iteration, supersymmetry, numerical integration methods, and the schroedinger Mathematica package.     

基于麦克斯韦方程的矿山岩爆现象研究

基于麦克斯韦方程，本文对岩爆过程中产生的电磁辐射在煤层、岩石中的传播规律进行了理论计算．分析与研究结果显示：一方面，岩爆过程中产生的电磁辐射信号符合麦克斯韦方程；另一方面，数值模拟破裂过程电磁辐射在煤层、岩石中的传播时可将电磁辐射产生源理想化为水平电偶极子和水平磁偶极子的叠加；并得出了电磁辐射源产生的场在煤层、岩石中空间分布的解析计算式．麦克斯韦方程的应用对于岩爆等动力灾害预测的电磁辐射监测仪的研制和定向定位监测具有重要的理论和实际意义．     

On the Measurement Problem for a Two-level Quantum System

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented.     

Manifestation of a size effect in the behavior of the intrinsic absorption edge of nanostructured polycrystalline zinc oxide thin films

We have studied the behavior of the intrinsic absorption edge in zinc oxide thin films in the temperature range 80–300 K. We have observed that the intrinsic absorption edge in films with crystal sizes of ≈45 nm or larger is described by the empirical Urbach’s rule, while in films with crystallite sizes of ≈15 nm, it is described by a modified Urbach’s rule. We have calculated the effective frequency of phonons taking part in formation of the absorption edge. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 275–277, March–April, 2007.