Volume 4 Issue 3 December 2005

0
0

0
0
0

https://doi.org/10.33697/ajur.2005.018

Editorial: AJUR and the Flat World

https://doi.org/10.33697/ajur.2005.019

Author(s):

C. C. Chancey

Affiliation:

American Journal of Undergraduate Research, University of Northern Iowa, Cedar Falls, Iowa 50614-0150 USA


Aggregation of Cyanine Dye in Bilayer Vesicles of Phospholipids

https://doi.org/10.33697/ajur.2005.020

Author(s):

Casey McCullough, Matthew Heywood, and Hussein Samha

Affiliation:

Division of Chemistry, Southern Utah University, 351 W. Center Street, SC 215, Cedar City, Utah 84720 USA

ABSTRACT:

The effect of phospholipid, 1,2-Dipalmitoyl-sn-glycero-3-Phosphocholine (DPPC) on the spectroscopy of the cyanine dye, 1-ethyl-1’-octadecyl-2,2’-cyanine iodide (PIC-18), has been investigated using UV-Vis spectroscopy. Vesicles of DPPC containing PIC-18 in the molar ratio of 1:3 (dye/phospholipids) were prepared in aqueous solution. J-aggregates of PIC-18 were detected in the bilayer wall of the vesicles. When an aqueous solution of mixed PIC-18/DPPC vesicles is treated with excess DPPC vesicles that are prepared separately, the dye molecules in the mixed vesicles underwent a rapid (aggregate)n’ n (monomer) equilibrium as the  appearance of only one isosbestic point in the absorbance of the dye indicates. The equilibrium constant was calculated at room temperature (Keq = 6.7×10-2). An aggregation number of 4 was calculated for the dye in the bilayer vesicles.


JAR1, a Dominant Gene Conferring Resistance to Amphotericin B in Saccharomyces cerevisiae

https://doi.org/10.33697/ajur.2005.021

Author(s):

Joyce Iwema, Katherine Force, and Robin Pals-Rylaarsdam

Affiliation:

Biology Department, Trinity Christian College, 6601 West College Drive, Palos Heights, Illinois 60463 USA

ABSTRACT:

Infectious diseases are the cause of death for over 1 million people a year in the United States alone. Drug resistance in infectious microbes is an increasing problem. This study focuses on antibiotic resistance in fungal infections, using Saccharomyces cerevisiae as the model of study. Spontaneous mutations in this yeast resulted in a yeast strain with the ability to grow in the presence of the antifungal drug amphotericin B. This yeast isolate, named JAR1, was genetically analyzed to determine how many mutated genes were responsible for the resistant phenotype, and whether the allele was dominant or recessive. The results indicate that the ability of JAR1 to grow in the presence of amphotericin B is due to a single dominant mutation.


Construction of Higher Orthogonal Polynomials Through a New Inner Product, ‹·,·›p, In a Countable Real Lp-space

https://doi.org/10.33697/ajur.2005.022

Author(s):

Femi O. Oyadare

Affiliation:

Department of Mathematics, University of Ibadan, Ibadan, Oyo State, NIGERIA

ABSTRACT:

This research work places a new and consistent inner product ‹·,·›p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for ‹·,·›p provides a construction of a specie of Higher Orthogonal Polynomials in these inner-product–admissible function spaces, and ultimately brings us to a study of the Generalized Fourier Series Expansion in terms of these polynomials. First, the reputation of this new inner product is established by the proofs of various inequalities and identities, all of which are found to be generalizations of the classical inequalities of functional analysis. Thereafter two orthogonalities of ‹·,·›p (which coincide at p = 2) are defined while the Gram-Schmidt orthonormalization procedure is considered and lifted to accommodate this product, out of which emerges a set of higher orthogonal polynomials in Lp[-1,1] that reduce to the Legendre Polynomials at p = 2. We argue that this inner product provides a formidable tool for the investigation of Harmonic Analysis on the real Lp function spaces for p other than p = 2, and a revisit of the various fields where the theory of inner product spaces is indispensable is recommended for further studies.


Noetherian Rings—Dimension and Chain Conditions

https://doi.org/10.33697/ajur.2005.023

Author(s):

Abhishek Banerjee

Affiliation:

57/1/C, Panchanantala Lane, Behala, Calcutta 700034, INDIA

ABSTRACT:

In this paper we look at the properties of modules and prime ideals in finite dimensional noetherian rings. This paper is divided into four sections. The first section deals with noetherian one-dimensional rings. Section Two deals with what we define a “zero minimum rings” and explores necessary and sufficient conditions for the property to hold. In Section Three, we come to the minimal prime ideals of a noetherian ring. In particular, we express noetherian rings with certain properties as finite direct products of noetherian rings with a unique minimal prime ideal, as an analogue to the expression of an artinian ring as a finite direct product of artinian local rings. Besides, we also consider the set of ideals I in R such that M ≠ I M for a given module M and show that a maximal element among these is prime. In Section Four, we deal with dimensions of prime ideals, Krull’s Small Dimension Theorem and generalize it (and its converse) to the case of a finite set of prime ideals. Towards the end of the paper, we also consider the sets of linear dependencies that might hold between the generators of an ideal and consider the ideals generated by the coefficients in such linear relations.