Ultrasonic diffraction grating spectroscopy and characterization of fluids and slurries

The ultrasonic diffraction grating is formed by machining triangular grooves, 300 microns apart, on a stainless steel surface. The grating surface is in contact with the liquid or slurry. The ultrasonic beam, traveling in the solid, strikes the back of the grating and produces a transmitted m=1 beam in the liquid. The angle of this beam in the liquid increases with decreasing frequency and the critical frequency FCR occurs when the angle is 90 degrees. At frequencies below FCR, this m=1 wave does not exist and its energy is shared with other types of waves. The signal of the reflected m=0 wave is observed and an increase is observed at FCR. This information yields the velocity of sound in the liquid and particle size.     

Statistical quality control of PCDD/PCDF analysis using a total measuring data set

 A random error and accuracy estimation approach for polychlorinated dibenzo-p-dioxins (PCDD) and dibenzofurans (PCDF) analysis is presented based on statistical treatment of all the data set registered in a run or in a bunch of uniform runs. Received: 18 August 1998 / Accepted: 21 October 1998     

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as . Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains “hidden color” states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which show that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Work supported by Department of Energy contract DE-AC02-76SF00515     

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons

The predictions of quantum chromodynamics for meson form factors at large momentum transfer are given. Evolution equations are derived which determine the structure of hadronic wavefunctions at short distances from their form at large distances. The eigenvalues of the evolution equations appear as exponents in anomalous logarithm corrections to the nominal power law of form factors determined by dimensional counting. The results lead to detailed tests of the spin and scaling structure of QCD at short distances. The predictions for the charged pion, kaon and rho form factors and the γ → π⁰ transition form factor of the photon are absolutely normalized at asymptotic momentum transfer.     

A Theory of Stationary Trees and the Balanced Baumgartner–Hajnal–Todorcevic Theorem for Trees

Building on early work by Stevo Todorcevic, we develop a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize arbitrary subsets of a non-special tree as being either stationary or non-stationary. We then use this theory to prove the following partition relation for trees: Main Theorem. Let \({\kappa}\) be any infinite regular cardinal, let ξ be any ordinal such that \({2^{|\xi|} < \kappa}\) , and let k be any natural number. Then $$non-(2^{<\kappa})-special\, tree \rightarrow (\kappa + \xi)^{2}_k.$$ This is a generalization to trees of the Balanced Baumgartner–Hajnal–Todorcevic Theorem, which we recover by applying the above to the cardinal \({(2^{< \kappa})^{+}}\) , the simplest example of a non- \({(2^{< \kappa})}\) -special tree. As a corollary, we obtain a general result for partially ordered sets: Theorem. Let \({\kappa}\) be any infinite regular cardinal, let ξ be any ordinal such that \({2^{|\xi|} < \kappa}\) , and let k be any natural number. Let P be a partially ordered set such that \({P \rightarrow (2^{< \kappa})^{1}_{2^{< \kappa}} }\) . Then $$P \rightarrow (\kappa + \xi)^{2}_{k}.$$      

Sequential change-point detection for mixing random sequences under composite hypotheses

The problem of sequential detection of a change-point in the density function of one-dimensional distribution of observations from a mixing random sequence is considered when both before and after a change-point this density function belongs to a certain family of distributions, i.e. in the situation of composite hypotheses. A new quality criterion for change-point detection is proposed. The asymptotic a priori lower bound for this criterion is proved for wide class of methods of change-point detection. An asymptotically optimal method of change-point detection is proposed for which this lower bound is attained asymptotically. In particular, for the case of a simple hypothesis before a change-point, this method coincides with the generalized cumulative sums (CUSUM) method.