A study of nozzle and ejector flow problems by the method of integral relations

The application of the method of integral relations to nozzle and ejector flow problems was examined. For nozzle flow problems, the general formulation is that the approaching flow may be rotational. Particular attention was given to the phenomenon of choking under nonuniform flow conditions. Numerical integration of the governing ordinary differential equations was also investigated. This scheme of analysis was also applied to study the interacting flow field within an ejector system

Reflections in abstract Coxeter groups

Let $W$ be a Coxeter group and $r\in W$ a reflection. If the group of order 2 generated by $r$ is the intersection of all the maximal finite subgroups of $W$ that contain it, then any isomorphism from $W$ to a Coxeter group $W'$ must take $r$ to a reflection in $W'$. The aim of this paper is to show how to determine, by inspection of the Coxeter graph, the intersection of the maximal finite sugroups containing $r$. In particular we show that the condition above is satisfied whenever $W$ is infinite and irreducible, and has the property that all rank two parabolic subgroups are finite. So in this case all isomorphisms map reflections to reflections.Comment: 25 pages, 0 figure

CL 510 Formation for United Methodist Ordained Ministry

• Hunt, Richard, Christian As Minister: Ministry Inquiry Process: The United Methodist Church (Nashville: General Board of Higher Education and Ministry, 1997). • Hunt, Richard A., Candidacy Guidebook: For Deacons, Elders, and Local Pastors: The United Methodist Church, 2001 edition (Nashville: General Board of Higher Education and Ministry, 2001).https://place.asburyseminary.edu/syllabi/2563/thumbnail.jp

On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page

Herbivory on planted dipterocarp seedlings in secondary logged forests and primary forests of Sabah, Malaysia

Journal ArticleLeaf defences, leaf nutritional quality and leaf expansion rates may vary with resource availabilities to plants. Such variation could affect rates of leaf loss to herbivores, particularly along the steep resource gradients in disturbed forests. Intraspecific and interspecific variation in leaf damage and leaf expansion rates were measured on dipterocarp seedlings planted into secondary forests 1, 5 and 15 y after logging, and in adjacent primary forest of Sabah, Malaysia. Herbivory rates or amounts of leaf damage were compared across habitats and species for expanding, recently expanded, and mature leaves of Shorea leprosula and Dryobalanops lanceolata (Dipterocarpaceae). In all four habitats, leaves of the faster growing S. leprosula sustained higher rates and amounts of leaf-area loss than did the tougher leaves of slower growing D. lanceolata. Expanding leaves accumulated more leaf-area loss per week than did mature leaves. In all habitats and in both species, more than 25% of expanding leaves disappeared entirely. Rates of leaf-area loss per week differed among habitats for expanding leaves but not for mature leaves. In a relatively open, 1-y-old logged forest, faster leaf expansion reduced the time leaves spent in the most vulnerable stage; however, in S. leprosula a greater rate of leaf area loss countered the shorter expansion time. Thus, leaves accumulated similar total damages across habitats, and herbivory did not produce differences among habitats in seedling growth or mortality. High levels of resources may increase both leaf palatability and leaf expansion rates, with counteracting effects on herbivory

Environmental problems, uncertainty, and mathematical modeling

In this paper we discuss three rather special characteristics shared by many environmental problems. Namely, that (i) the environmental variables in which we are most interested constitute a stochastic process; (ii) the long-term or limiting behavior and the short-term or transient behavior are often both important; and (iii) the underlying probability distributions are likely to be influenced by the environmental policies or remedies that we choose to impose. This third characteristic implies the need to understand the impact of technologies and controls that influence the dynamics of the system. The control theoretic perspective of environmental engineering problems has, we believe, received less attention than it deserves in the literature. Consequently, after a brief discussion of the exogenous, control-independent case we focus on illustrating some special challenges and opportunities embedded in the control-dependent situations