Computer-aided heuristic analysis of fluid models

A new kind of symbolic program to aid the heuristic simplification of fluid models is presented. The program, AOM, employs order of magnitude analysis and method of dominant balance to generate simplified models. It has two novel features: (1) it uses heuristic techniques to decide what equations to solve and what algebra to do, and (2) it explains its deduction steps. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i.e., terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels to simplify complicated fluid models such as the triple-deck equations. Three annotated examples are presented to explain the operations of AOM. The implications for the development of computer-aided analysis programs for fluid dynamics and education are discussed.This research was funded in part by NSF NYI Award ECS-9357773 and CCR-9109567.     

An improved optical TE-TM mode splitter and modulator using a Ti-LiNbO3 Y-junction waveguide

An optical TE-TM mode splitter and modulator with an improved design using a Y-junction waveguide by Ti-diffusion in a Y-cut LiNbO₃ substrate has been fabricated and characterized. Improvements in fabrication and measurement techniques are discussed. Experimental results on the device characteristics are presented.     

Congruence and Conjunctivity of Matrices

Congruence of arbitrary square matrices over an arbitrary field is treated here by elementary classical methods, and likewise for conjunctivity of arbitrary square matrices over an arbitrary field with involution. Uniqueness results are emphasized, since they are largely neglected in the literature. In particular, it is shown that a matrix S is congruent [conjunctive] to S₀⊕S₁ with S₁ nonsingular, and that if S₁ here is of maximal size among all nonsingular matrices R₁ for which R₀⊕R₁ is congruent [conjunctive] to S, then the congruence [conjunctivity] class of S determines that of S₁. Partially canonical forms (most of them already known) are derived, to the extent that they do not depend on the field. Nearly canonical forms are derived for “neutral” matrices (those congruent or conjunctive with block matrices $\text{O}\text{N}\text{M}\text{O}$ with the two zero blocks being square). For a neutral matrix S over a field F,the F-congruence [F-conjunctivity] class of S is determined by the F-equivalence class of the pencil S+tS' [S+tS¹] and, if the pencil is nonsingular, by the F[t]-equivalence class of S+tS' [S+tS¹].     

Lectin-based electrophoretic analysis of the expression of the 35 kDa inter-alpha-trypsin inhibitor heavy chain H4 fragment in sera of patients with five different malignancies

A 35 kDa glycoprotein whose abundance was previously demonstrated to be enhanced in sera of patients with endometrial adenocarcinoma (n = 12), was isolated from pooled sera of three of the cancer patients using champedak galactose-binding lectin affinity chromatography in the present study. Subjecting it to 2-DE and MS/MS, the glycoprotein was identified as the O-glycosylated fragment of inter-alpha-trypsin inhibitor heavy chain H4 (ITIH4). When compared to control sera (n = 17), expression of the 35 kDa ITIH4 cleavage fragment was demonstrated to be significantly enhanced in sera of patients with breast carcinoma (n = 10), epithelial ovarian carcinoma (n = 10), and germ cell ovarian carcinoma (n = 10) but not in patients with nasopharyngeal carcinoma (n = 13) and osteosarcoma (n = 7). The lectin-based electrophoretic bioanalytical method adopted in the present study may be used to assess the physiological relevance of ITIH4 fragmentation and its correlation with different malignancies, their stages and progression.     

Crystallographic evidence of an unusual, pentagon-shaped folding pattern in a circular aromatic pentamer

Introduction of a continuous hydrogen-bonding network suppressed the conformational flexibility of an oligomeric backbone. Cyclization of a rigidified, suitably sized oligomer led to a circular aromatic pentamer. Its crystal structure determined by X-ray crystallography reveals a pseudo five-fold symmetric planarity in the solid state, which is quite unusual among all the previously described shape-persistent macrocycles and synthetic foldamers with biased conformations enforced by noncovalent forces.