Construction of the Best Monotone Approximation on Lp [0, 1]

(First paragraph) For 1 ≤ p \u3c ∞, let Lp, denote the Banach space of pth power Lebesgue integrable functions on [0, l] ∥ƒ∥p = (∫¹₀∣ƒ∣ p)1/p Let Mp denote the set of nondecreasing functions in Lp. For l \u3c p \u3c ∞ , each ƒ∊Lp has a unique best approximation from Mp, while, for p = 1, existence of a best approximation from M1 follows from Proposition 4 of [6]

Hamiltonian systems with symmetry, coadjoint orbits and plasma physics

The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the Lie-Poisson structure on the dual of a Lie algebra. These results are applied to plasma physics. We show in three steps how the Maxwell-Vlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. First, the Poisson-Vlasov equations are shown to be in Hamiltonian form relative to the Lie-Poisson bracket on the dual of the (nite dimensional) Lie algebra of innitesimal canonical transformations. Then we write Maxwell's equations in Hamiltonian form using the canonical symplectic structure on the phase space of the electromagnetic elds, regarded as a gauge theory. In the last step we couple these two systems via the reduction procedure for interacting systems. We also show that two other standard models in plasma physics, ideal MHD and two- uid electrodynamics, can be written in Hamiltonian form using similar group theoretic techniques

Observation and interpretation of motional sideband asymmetry in a quantum electro-mechanical device

Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up and down frequency-conversion of microwave photons. Due to quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radio-frequency mechanical mode, cooled near the ground state of motion. We also discuss the subtle origin of this imbalance: depending on the measurement scheme, the imbalance is most naturally attributed to the quantum fluctuations of either the mechanical mode or of the electromagnetic field

On Deusons or Deuteronlike Meson-Meson Bound States

The systematics of deuteronlike two-meson bound states, {\it deusons}, is discussed. Previous arguments that many of the present non-$q\bar q$ states are such states are elaborated including, in particular, the tensor potential. For pseudoscalar states the important observation is made that the centrifugal barrier from the P-wave can be overcome by the $1/r^2$ and $1/r^3$ terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteron-like $B\bar B^*$ and $B^*\bar B^*$ composites bound by approximately 50 MeV, while $D\bar D^*$ and $D^*\bar D^*$ states are expected near the threshold.Comment: Invited talk at the Hadron93 International Conf. on Hadron Spectroscopy, Como, Italy 22.-25.6. 1993. 5 pages in LATEX HU-SEFT R 1993-13

A unified approach to estimating demand and welfare

The measurement of price changes, economic welfare, and demand parameters is currently based on three disjoint approaches: macroeconomic models derived from time-invariant utility functions, microeconomic estimation based on time-varying utility (demand) systems, and actual price and real output data constructed using formulas that differ from either approach. The inconsistencies are so deep that the same assumptions that form the foundation of demand-system estimation can be used to prove that standard price indexes are incorrect, and the assumptions underlying standard exact and superlative price indexes invalidate demand-system estimation. In other words, we show that extant micro and macro welfare estimates are biased and inconsistent with each other as well as the data. We develop a unified approach to demand and price measurement that exactly rationalizes observed micro data on prices and expenditure shares while permitting exact aggregation and meaningful macro comparisons of welfare over time. We show that all standard price indexes are special cases of our approach for particular values of the elasticity of substitution, constant preferences for each good, and a constant set of goods. In contrast to these standard index numbers, our approach allows us to compute changes in the cost of living that take into account both changes in the preferences for individual goods and the entry and exit of goods over time. Using barcode data for the U.S. consumer goods industry, we show that allowing for the entry and exit of products, changing preferences for individual goods, and a value for the elasticity of substitution estimated from the data yields substantially different conclusions for changes in the cost of living from standard index numbers

Quantum squeezing of motion in a mechanical resonator

As a result of the quantum, wave-like nature of the physical world, a harmonic oscillator can never be completely at rest. Even in the quantum ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. In this work, using microwave frequency radiation pressure, we both prepare a micron-scale mechanical system in a state near the quantum ground state and then manipulate its thermal fluctuations to produce a stationary, quadrature-squeezed state. We deduce that the variance of one motional quadrature is 0.80 times the zero-point level, or 1 dB of sub-zero-point squeezing. This work is relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultra-sensitive sensing of force and motion

Extracting the Mass Dependence and Quantum Numbers of Short-Range Correlated Pairs from A(e,e'p) and A(e,e'pp) Scattering

The nuclear mass dependence of the number of short-range correlated (SRC) proton-proton (pp) and proton-neutron (pn) pairs in nuclei is a sensitive probe of the dynamics of short-range pairs in the ground state of atomic nuclei. This work presents an analysis of electroinduced single-proton and two-proton knockout measurements off 12C, 27Al, 56Fe, and 208Pb in kinematics dominated by scattering off SRC pairs. The nuclear mass dependence of the observed A(e,e'pp)/12C(e,e'pp) cross-section ratios and the extracted number of pp- and pn-SRC pairs are much softer than the mass dependence of the total number of possible pairs. This is in agreement with a physical picture of SRC affecting predominantly nucleon-nucleon pairs in a nodeless relative-S state of the mean-field basis.Comment: 6 pages, 3 figure

Calculus I

Preface: The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition...

All-optical generation and photoassociative probing of sodium Bose-Einstein condensates

We demonsatrate an all optical technique to evaporatively produce sodium Bose-Einstein condensates (BEC). We use a crossed-dipole trap formed from light near 1060 nm, and a simple ramp of the intensity to force evaporation. In addition, we introduce photoassociation as diagnostic of the trap loading process, and show that it can be used to detect the onset of Bose-Einstein condensation. Finally, we demonstrate the straightforward production of multiple traps with condensates using this technique, and that some control over the spinor state of the BEC is achieved by positioning the trap as well.Comment: 8 pages, 10 figure