Experimental and numerical study of mixed convection with flow reversal in coaxial double-duct heat exchangers

Velocity vectors in a vertical coaxial double-duct heat exchanger for parallel ascending flow of water under conditions of laminar mixed convection have been determined experimentally using the particle image velocimetry technique. The measured velocity distributions for large annular flow rates, resulting in an essentially isothermal environment for the stream in the inner tube, are in very good agreement with corresponding numerical predictions. For flow rates of the same order of magnitude in the inner tube and the annulus, and corresponding temperature differences of about 20 °C, experimental observations show that flow reversal occurs simultaneously in both streams over large axial distances for both heating and cooling of the flow in the inner tube.     

Examining and developing fourth grade children’s area estimation performance

This study explored children’s area estimation performance. Two groups of fourth grade children completed area estimation tasks with rectangles ranging from 5 to 200 square units. A randomly assigned treatment group completed instructional sessions that involved a conceptual area measurement strategy along with numerical feedback. Children tended to underestimate areas of rectangles. Furthermore, rectangle size was related to performance such that estimation error and variability increased as rectangle size increased. The treatment group exhibited significantly improved area estimation performance in terms of accuracy, as well as reduced variability and instances of extreme responses. Area measurement estimation findings are related to a Hypothetical Learning Trajectory for area measurement.     

Dynamical supersymmetry breaking in supersymmetric QCD

The massless limit of supersymmetric QCD with $\text{N}{}_{\mathrm{?}}$ flavors and N colors is analyzed in detail. For $\text{N}{}_{\mathrm{?}}\text{< N}$ there is a unique superpotential which might be generated by non-perturbative effects. We show that it indeed appears, thus violating the non-renormalization theorems. For $\text{N}{}_{\mathrm{?}}\text{= N ? 1}$ instantons produce the superpotential. For $\text{N}{}_{\mathrm{?}}\text{< N ? 1}$ it is again generated, provided that a mild assumption about the dynamics of pure supersymmetric gauge theories is correct. For $\text{N}{}_{\mathrm{?}}\text{? N}$ no invariant superpotential exists; the classical vacuum degeneracy is a property of the full quantum theory. When a small quark mass term is added to the theory $\text{(}\text{for}\text{N}{}_{\mathrm{?}}\text{< N), N}$ supersymmetric ground states, identified with those found by Witten exist. As m → 0 these N vacua wander to infinity, leaving the massless theory without a ground state.     

The thioacetate approach to the synthesis of the side chain of vitamin D metabolites and analogues

We describe an efficient synthesis of thia analogues of the vitamin D side chain that is based on the in situ generation of a thiolate anion and its alkylation with electrophiles.     

IN-SITU SYNTHESES OF ALKYLLITHIUM COMPOUNDS UNDER ULTRASONIC IRRADIATION

Abstract

The syntheses of organometallics such as alkyllithium compounds are performed. Furan and thiophene derivatives were prepared. Parameters which influence the yield have been optimized. The more important were the physical states of lithium and its sodium content and the nature of the substrate.     

Nonlinear boundary conditions derived by singular pertubation in age structured population dynamics model

In this article, we derive Ricker&rsquo;s [22, 23] type nonlinear boundary&nbsp;condition for an age structured population dynamic model by using a singular&nbsp;perturbation. The question addressed in this paper is the convergence of the&nbsp;singularly perturbed system. We first obtain a finite time convergence for a&nbsp;fixed initial distribution. Then we focus on the convergence uniformly of the&nbsp;singularly perturbed system with respect to the initial distribution in bounded&nbsp;sets.