Applied Mathematics Commons^™

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

A Center Of A Polytope: An Expository Review And A Parallel Implementation, S. K. Sen, Hongwei Du, Donald W. Fausett

Mathematics and System Engineering Faculty Publications

The solution space of the rectangular linear system Ax = b, subject to x ≥ 0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem. © 1993, Hindawi Publishing Corporation. All rights reserved.

Data On Four-Rewriteability In Finite Groups, Sharon A. Kineke

Mathematical Sciences Technical Reports (MSTR)

A four-tuple of elements, (x₁,x₂,x₃,x₄), from a finite group, G, is said to be

rewriteable (see [l], [2], [3]) by p where p is an element of the symmetric group on four symbols, if
x₁x₂x₃x₄ = x_p(l)x_p(2)x_p(3)x_p(4)

The entry at the intersection of the G-th row and j-th column of each table on the succeeding three pages is the number of four-tuples from G which are rewriteable by exactly j permutations in the symmetric group …

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H^1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Mathematics and Statistics Faculty Publications

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

Lyapunov Stability Theory For Dynamic Systems On Time Scales, Billur Kaymakçalan

Mathematics and System Engineering Faculty Publications

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov’s second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

On A Multilevel Controlled Bulk Queueing System Mx/Gr,R/1, Lev M. Abolnikov, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors introduce and study a class of bulk queueing systems with a compound Poisson input modulated by a semi-Markov process, multilevel control service time and a queue length dependent service delay discipline. According to this discipline, the server immediately starts the next service act if the queue length is not less than r; in this case all available units, or R (capacity of the server) of them, whichever is less, are taken for service. Otherwise, the server delays the service act until the number of units in the queue reaches or exceeds level r. The authors establish a necessary …

Extremal Solutions To A Class Of Multivalued Integral Equations In Banach Space, Sergiu Aizicovici, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.

On A First Passage Problem In General Queueing Systems With Multiple Vacations, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled …

Existence Of A Solution Of A Fourier Nonlocal Quasilinear Parabolic Problem, Ludwik Byszewski

Mathematics and System Engineering Faculty Publications

The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder’s theorem is used. The paper is a continuation of papers [l]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

Existence Of Approximate Solution To Abstract Nonlocal Cauchy Problem, Ludwik Byszewski

Mathematics and System Engineering Faculty Publications

The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …

Generalized Two Point Boundary Value Problems. Existence And Uniqueness, K. N. Murty, Seenith Sivasundaram

Mathematics and System Engineering Faculty Publications

An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

Rewriteability In Finite Groups, Judy Leavitt Walker, G. J. Sherman, Mark E. Walker

Department of Mathematics: Faculty Publications

What's the probability that two elements in a finite group commute? A formal answer,

Pr₂(G) = {(x, y) [element of] G² |xy = yx}| / |G|²

begs our next question. How many ordered pairs of elements of a finite group commute?

A Note On The Connectedness Problem For Nest Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

It has been conjectured that a certain operator T belonging to the group ff of invertible elements of the algebra Alg Z of doubly infinite uppertriangular bounded matrices lies outside the connected component of the identity in W. In this note we show that T actually lies inside the connected component of the identity of & .

On Sources In Comparability Graphs, With Applications, Stephan Olariu

Computer Science Faculty Publications

We characterize sources in comparability graphs and show that our result provides a unifying look at two recent results about interval graphs.

A Charming Class Of Perfectly Orderable Graphs, Chinh T. Hoang, Frederic Maffray, Stephan Olariu, Myriam Preissmann

Computer Science Faculty Publications

We investigate the following conjecture of Vašek Chvátal: any weakly triangulated graph containing no induced path on five vertices is perfectly orderable. In the process we define a new polynomially recognizable class of perfectly orderable graphs called charming. We show that every weakly triangulated graph not containing as an induced subgraph a path on five vertices or the complement of a path on six vertices is charming.

Automorphisms Of The Lattice Of Recursively Enumerable Sets: Promptly Simple Sets, Peter Cholak, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

We show that for every coinfinite r.e. set A there is a complete r.e. set B such that ℒ⋆(A)≈ ℒ⋆(B) and that every promptly simple set is automorphic (in f⋆) to a complete set.

Automorphisms Of The Lattice Of Recursively Enumerable Sets: Orbits, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

No abstract provided.

Solution Uniqueness And Stability Criteria For A Model Of Growth Factor Production, J. A. Adam

Mathematics & Statistics Faculty Publications

Uniqueness and stability criteria are established for the steady states of a nonlinear model of growth factor production. A specific expression for the nonlinearity is chosen, containing three parameters which can be adjusted to fit a specific biological context, but much of the analysis applies to a general class of source terms that exhibit the same qualitative behavior.

Temperature And Suction Effects On The Instability Of An Infinite Swept Attachment Line, D. G. Lasseigne, T. L. Jackson, F. Q. Hu

Mathematics & Statistics Faculty Publications

It is known that the incompressible, infinite swept attachment line flow is unstable to streamwise disturbances that originate in the boundary layer when the cross-flow exceeds a critical magnitude. Furthermore, a small degree of suction at the surface has a significant stabilizing influence while a small degree of blowing has a considerable destabilizing influence. This paper investigates the stabilizing and destabilizing effects of, respectively, cooling or heating the plate and the competing or enhancing effects of suction or blowing. A nonorthogonal flow with respect to the attachment line is also considered by adding a component of shear to the mean …

Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In the recent paper [7], it was shown that the solutions of weakly singular Hammerstein equations satisfy certain regularity properties. Using this result, the optimal convergence rate of a standard piecewise polynomial collocation method and that of the recently proposed collocationtype method of Kumar and Sloan [10] are obtained. Superconvergence of both of these methods are also presented. In the final section, we discuss briefly a standard productintegration method for weakly singular Hammerstein equations and indicate its superconvergence property. © 1992 Rocky Mountain Mathematics Consortium.

The Morphology Of Convex Polygons, Stephan Olariu

Computer Science Faculty Publications

A simple polygon P is said to be unimodal if for every vertex of P, the Euclidian distance function to the other vertices of P is unimodal. The study of unimodal polygons has emerged as a fruitful area of computational and discrete geometry. We study unimodality properties of a number of special convex polygons from the morphological point of view. In particular, we establish a hierarchy among three classes of convex polygons in terms of their unimodality properties.

A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu

Computer Science Faculty Publications

A graph G is P₄-sparse if no set of five vertices in G induces more than one chordless path of length three. P₄-sparse graphs generalize both the class of cographs and the class of P₄-reducible graphs. We give several characterizations for P₄-sparse graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P₄-sparse graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

The Hydraulic Performance Of A Vortex Tube Foector, F Mtaro

Tanzania Journal of Engineering and Technology (TJET)

The vorle.r tube silt exrrac/or consists of a pipe, rhe crest of which has a slit and lies flush across lhe canal bed.With minimal warer loss, I.oe bedload is extracted through lhe slil settling canal back ro the river, thus reducing or eliminating the bedload transported in main canal. Ihe resulting swirling flow phenomena is of complex nature and depends on sc conirol paramerers, as a result of which previous empirical design approaches have yielded conflicting guidelines. By means Of a simplified hydraulic system, the flow mechanism and energy in rhe can be determined.

Flood Forecasting In Tanzanian Catchments, Omari Rumambo

Tanzania Journal of Engineering and Technology (TJET)

Floods are still a problem to many countries in the world todate. Floods do cause damages to property and sometimes loss to human life. Flood control measures by structural and non—structural methods are avail able in the literature . However , structural flood control measures are financially infeasible in most developing countries today. Flood forecasting is a non—structural measure for reducing flood damages. It is a means of providing early The Li near f 1 ood warnings to flood prone areas . Perturbation Model has been appl ied for real time flood The Linear forecasting in Tan zanian catchments . …

Experimental Investigations On The Behaviour Of Wood In Transverse Compression, A Mrema

Tanzania Journal of Engineering and Technology (TJET)

Experimental investigations were done to study the behaviour of wood in transverse compress ion. Three key variables were incorporated in the experiments to study their influence on the •nriables were the orthotropic ratio of the behav iour. These material, the geometry of loading and that of the specimen . Deformation measurements were made at selected locations on test specimens by means of strain—gage based clip gages. Results from the experimental measurements were compared to previous deformation predictions made by a finite element analysis (9) . There is a very good agreement between measured values and those obtained trom the finite …

A Finite Element Analysis Of Wood In Transverse Compression, A Mrema

Tanzania Journal of Engineering and Technology (TJET)

A two dimensional finite element analysis is utilized to predict the stress and strain distributions for wood in transverse compression. Important key var iables are incorporated into the ana lysis to define their influence on the stress and strain distributions. These variables are geometry of loading, geometry of specimen and the orthotropic ratio of the material. Based on the finite element analysis results, relationships are arising stress from developed relat ing maximum stress concentrations to the above three variables. possible appl ications of the results from this study relate to the development of more efficient design of connections such as …