Physical Sciences and Mathematics Commons^™

Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A² (G\K) and A²(G) be the Bergman spaces on G\K, respectively G and define N = A²(G\K) Ɵ A² (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator C_f = P_NT_f│N, where f ϵ C(G) …

A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

The existence of difference sets in abelian 2-groups is a recently settled problem [5]; this note extends the abelian constructs of difference sets to nonabelian groups of order 64.

A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott

Department of Math & Statistics Faculty Publications

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets.

Insecticides Based On Differences In Metabolic Pathways, Richard T. Mayer, G N. Cunningham, John T. Gupton

Chemistry Faculty Publications

Insects have been major pests of humankind at least since the beginning of recorded history. To this day insects continue to cause problems in domestic, agricultural, and health situations. It is no wonder that people have continually sought new solutions to controlling insect pests. Even when new control methods are discovered and established, insects evolve into resistant species so that the method is only of real value for a few brief years. Modern science and technology are now enabling scientists to tear away the fabric that has so long masked physiological and biochemical events critical to insects. Armed with this …

On Uniform And Relative Distribution In The Brauer Group, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

In this progress/technical report our objective is twofold. First, to formalize and expand upon remarks appearing in [7] concerning the relativization of the fundamental identity in the setting of the Brauer group of a ring, and second to exhibit a construction which shows how to interpret uniform distribution as a homological phenomenon.

Partially Confluent Maps And N-Ods, Van C. Nall

Department of Math & Statistics Faculty Publications

Let f : X-->Y be a map between topological spaces. A Wf-set in Y is a continuum in Y which is the image under f of a continuum in X. The map f is partially confluent if each continuum in Y is the union of a finite number of Wf-sets, and n-partially confluent if each continuum in Y is the union of n Wf-sets. In this paper, it is shown that every partially confluent map onto an n-cell is weakly confluent. Also, the relationship between partially confluent maps and continua which …

Maps Which Preserve Graphs, Van C. Nall

Department of Math & Statistics Faculty Publications

In 1976 Eberhart, Fúgate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.

In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.

Some Useful Synthetic Applications Of Gold's Reagent, John T. Gupton

Chemistry Faculty Publications

While looking for some appropriate research projects, I had been impressed by and interested in the work of Danishefsky¹ and others² regarding the use of "Eschenmoser's salt" (1). During the course of a literature search on an industrial project, we came across an article by Gold,³ which described the preparation of a rather interesting vinylogous iminium salt (2). The name assigned to this compound was [3-(dimethylamino)-2-azaprop-2-en-1-ylidene]dimethylammonium chloride. This terminology seemed a little cumbersome for routine discussions so we adopted the name "Gold's Reagent" for compound 2. Although the reagent had been prepared³ in 1960, very little …

Weak Confluence And W-Sets, Van C. Nall

Department of Math & Statistics Faculty Publications

A mapping between continua is weakly confluent if for each subcontinuum K of the range some component of the preimage of K maps onto K. Class [W] is the class of all continua which are the images of weakly confluent maps only. The notion of Class [W] was introduced by Andrej Lelek in 1972. Since then it has been widely explored and some characterizations of these continua have been given. J. Grispolakis and E. D. Tymchatyn have given a characterization in terms of hyperspaces [4]. J. Davis has shown that acyclic atriodic continua are in Class [W]i therefore, atriodic tree-like …

Method For Direct Preparation For 1,2,4-Triazole From Hydrazine And Formamide, Harris E. Petree, Joseph R. Pociask, John T. Gupton

Chemistry Faculty Publications

Process for the preparation of 1,2,4-triazole comprises contacting hydrazine or its aqueous solutions with at least about 2.5 moles of formamide at a temperature of 140° to 210° C. and then recovering the resultant 1,2,4- triazole in yields of 92-98% with 94-98% purity. The formamide is maintained in an excess over about the 2.5 molar amount consumed in the reaction with the hydrazine. Recovery steps for isolating the 1,2,4-triazole are disclosed.

A Process For The Production Of 2-Alkyl Or 2-Cycloalkyl-4-Methyl-6-Hydroxypyrimidines, Joseph T. Blackwell Iii, John T. Gupton, Teruko U. Miyazaki, James B. Nabors, Joseph R. Pociask

Chemistry Faculty Publications

Production of 2-alkyl- or cycloalkyl-4-methyl-6- hydroxypyrimidines by first neutralizing an alkyl imidate ester hydrochloride with a base in the presence of a water-immiscible solvent for the alkyl imidate ester to be freed thereby; condensing the alkyl imidate ester with diketene to form an oxazinone intermediate, which is then reacted in organic solution with gaseous ammonia and recovering the desired substituted 6-hydroxypyrimidine.

Process For The Production Of 2-Alkyl Or 2-Cycloalkyl-4-Methyl-6-Hydroxypyrimidines, J. Thomas Blackwell, John T. Gupton, Jim B. Narbors

Chemistry Faculty Publications

Production of 2-alkyl or 2-cycloalkyl-4-methyl-6-hydroxy pyrimidines by sequentially reacting without isolation of any intermediates in an organic solvent (1) diketene and ammonia to produce .beta.-aminocrotonamide and (2) .beta.-aminocrotonamide, after water removal therefrom, a lower alkanoic or cycloalkanoic acid ester and an alkali metal alkoxide.

Process For The Production Of 2-Alkyl Or 2-Cycloalkyl-4-Methyl-6-Hydroxypyrimidines, John T. Gupton, Alex M. Jelenevsky, Teruko U. Miyazaki, Harris E. Petree

Chemistry Faculty Publications

Production of 2-alkyl or 2-cycloalkyl-4-methyl-6-hydroxy pyrimidines by first reacting diketene and lower alkanoic or cycloalkanoic acid amides in the presence of catalytic amounts of Lewis bases or Lewis or Bronsted acids, followed by treating the N-acetoacetyl (lower) alkanoic or cycloalkanoic acid amide intermediates with ammonia in the presence of acid catalysts.

Approximation Of Compact Homogeneous Maps, John R. Hubbard

Department of Math & Statistics Faculty Publications

Within the clasp of continuous homogeneous maps between Banach spaces, it is proved that every compact map can be uniformly approximated by finite-rank maps. This result is obtained by means of the classical metric projection on Banach spaces.

Photochemical Rearrangements Of 6/5 -Fused Cross-Conjugated Cyclohexadiensnes In Protic Solvents, Drury Caine, John T. Gupton, Ko Ming, William J. Powers Iii

Chemistry Faculty Publications

Irradiation of the ring A unsubstituted 6/5-fused cross-conjugated cyclohexadienone (1a) and its 2-methyl derivative (1b) in methanolic acetic acid yields, in addition to other products, novel tricyclononane derivatives which have been assigned the structures (3a) and (3b).