A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION

In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint locations. Scaled coordinates may be introduced, so that these maximizing paths, or polymers, now cross unit distances with unit-order fluctuations, and have scaled energy, or weight, of unit order. In this article, we consider Brownian last passage percolation in these scaled coordinates. In the narrow wedge case, when one endpoint of such polymers is fixed, say at $(0,0)\in \mathbb{R}^{2}$ , and the other is varied horizontally, over $(z,1)$ , $z\in \mathbb{R}$ , the polymer weight profile as a function of $z\in \mathbb{R}$ is locally Brownian; indeed, by Hammond [‘Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation’, Preprint (2016), arXiv:1609.02971, Theorem 2.11 and Proposition 2.5], the law of the profile is known to enjoy a very strong comparison to Brownian bridge on a given compact interval, with a Radon–Nikodym derivative in every $L^{p}$ space for $p\in (1,\infty )$ , uniformly in the scaling parameter, provided that an affine adjustment is made to the weight profile before the comparison is made. In this article, we generalize this narrow wedge case and study polymer weight profiles begun from a very general initial condition. We prove that the profiles on a compact interval resemble Brownian bridge in a uniform sense: splitting the compact interval into a random but controlled number of patches, the profile in each patch after affine adjustment has a Radon–Nikodym derivative that lies in every $L^{p}$ space for $p\in (1,3)$ . This result is proved by harnessing an understanding of the uniform coalescence structure in the field of polymers developed in Hammond [‘Exponents governing the rarity of disjoint polymers in Brownian last passage percolation’, Preprint (2017a), arXiv:1709.04110] using techniques from Hammond (2016) and [‘Modulus of continuity of polymer weight profiles in Brownian last passage percolation’, Preprint (2017b), arXiv:1709.04115].

From unit-and-ten to ten-before-unit order in the history of English numerals

In the course of its history, English underwent a significant structural change in its numeral system. The number words from 21 to 99 switched from the unit-and-ten to the ten-before-unit pattern. This change is traced on the basis of more than 800 number words. It is argued that this change, which took seven centuries to complete and in which the Old English pattern was highly persistent, can be broken down into two parts—the reordering of the units and tens and the loss of the conjoining element. Although the two steps logically belong to the same overall change, they display a remarkably disparate behavior. Whereas the reordering process affected the least frequent number words first, the deletion process affected the most frequent words first. This disparity lends support to the hypothesis that the involvement or otherwise of low-level aspects of speech determines the role of frequency in language change (Phillips, 2006). Finally, the order change is likely to be a contact-induced phenomenon and may have been facilitated by a reduction in mental cost.

Oxidation of Chalcones by Morpholinium Chlorochromate with Oxalic Acid as Catalyst: Kinetic and Mechanistic Study

The kinetics of oxidation of chalcones by morpholinium chlorochromate (MCC) has been studied in 55% acetic acid-water (v/v) medium. The reaction showed unit order dependence each with respect to oxidant and catalyst and fractional order with respect to substrate and H+ion. Increased ionic strength has no effect on the reaction rate. In the case of substituted chalcones, the order with respect to substrate varies depending upon the nature of the substituent present in the ring. In general, the electron withdrawing substituents retard the reaction rate while the electron releasing substituents enhance the rate of the reaction. From the kinetic data obtained, the activation parameters have been calculated and a suitable mechanism has been proposed.

Mechanistic Aspects of Osmium(VIII) Catalyzed Oxidation of L-Tryptophan by Diperiodatocuprate(III) in Aqueous Alkaline Medium: A Kinetic Model

In presence of osmium(VIII), the reaction between L-tryptophan and diperiodatocuprate(III) DPC in alkaline medium exhibits 1:4 stochiometry (L-tryptophan:DPC). The reaction shows first-order dependence on [DPC] and [osmium(VIII)], less than unit order in both [L-tryptophan] and [alkali], and negative fractional order in [periodate]. The active species of catalyst and oxidant have been identified. The main products were identified by spectral studies and spot test. The probable mechanism was proposed and discussed.

A Computerized Intensive Care Unit Order-Writing Protocol

OBJECTIVE: To present a computerized intensive care unit order-writing protocol. DESIGN: Descriptive report. SETTING: Eight-bed surgical intensive care unit, Department of Surgery, Department of Veterans Affairs Medical Center, Bronx, NY. METHODS: IBM-based, computer network program that provides user-friendly, logical, and comprehensive organ-system order sequences for patient management. RESULTS: Since July 1988, an order program that stresses (1) improved and more efficient patient care, (2) the use of program-integrated automatic safety features, (3) the substitution of computer entry for handwriting, and (4) the assurance that physicians deliver obligatory care in a logical organ-system—based progression has been implemented. CONCLUSIONS: The order protocol system presented is simple to introduce and operate, has minimal training and technical requirements, and is demonstrably reliable.

FT8: A High Performance Industrial and Marine Gas Turbine Derived From the JT8D Aircraft Engine

This paper describes the FT8 gas turbine, which has been introduced by Turbo Power and Marine Systems (TPM). The FT8 is derived from the Pratt & Whitney JT8D aircraft engine and the TPM FT4 industrial gas turbine. The FT8 has been launched with a collaboration program between TPM and the China National Aerotechnology Import-Export Corporation (CATIC) of the People’s Republic of China. The collaboration program includes co-production of certain components and a 37-unit order from CATIC over a 10-year period for marine and industrial applications.