A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

The interactions of basic proteins and DNA

I. ELECTROPHORESIS OF THE NUCLEIC ACIDS

A zone electrophoresis apparatus using ultraviolet optics has been constructed to study nucleic acids at concentrations less than 0.004%. Native DNA has a mobility about 15% higher than denatured DNA over a range of conditions. Otherwise, the electrophoretic mobility is independent of molecular weight, base composition or source. DNA mobilities change in the expected way with pH but the fractional change in mobility is less than the calculated change in charge. A small decrease in mobility accompanies an increase in ionic strength. RNA’s from various sources have mobilities slightly lower than denatured DNA except for s-RNA which travels slightly faster. The important considerations governing the mobility of nucleic acids appear to be the nature of the hydrodynamic segment, and the binding of counterions. The differences between electrophoresis and sedimentation stem from the fact that all random coil polyelectrolytes are fundamentally free draining in electrophoresis.

II. THE CYTOCHROME C/DNA COMPLEX

The basic protein, cytochrome c, has been complexed to DNA. Up to a cytochrome:DNA mass ratio of 2, a single type of complex is formed. Dissociation of this complex occurs between 0.05F and 0.1F NaCl. The complexing of cytochrome to DNA causes a slight increase in the melting temperature of the DNA, and a reduction of the electrophoretic mobility proportional to the decrease in net charge. Above a cytochrome:DNA mass ratio of 2.5, a different type of complex is formed. The results suggest that complexes such as are formed in the Kleinschmidt technique of electron microscopy would not exist in bulk solution and are exclusively film phenomena.

III. STUDIES OF THE ELECTROPHORESIS AND MELTING BEHAVIOUR OF NUCLEOHISTONES

Electrophoresis studies on reconstituted nucleohistones indicate that the electrophoretic mobility for these complexes is a function of the net charge of the complex. The mobility is therefore dependent on the charge density of the histone complexing the DNA, as well as on the histone/DNA ratio. It is found that the different histones affect the transition from native to denatured DNA in different ways. It appears that histone I is exchanging quite rapidly between DNA molecules in 0.01 F salt, while histone II is irreversibly bound. Histone III-IV enhances the capacity of non-strand separated denatured DNA to reanneal. Studies on native nucleoproteins indicate that there are no gene-sized uncomplexed DNA regions in any preparations studied.

IV. THE DISSOCIATION OF HISTONE FROM CALF THYMUS CROMATIN

Calf thymus nucleoprotein was treated with varying concentrations of NaCl. The identity of the histones associated and dissociated from the DNA at each salt concentration was determined by gel electrophoresis. It was found that there is no appreciable histone dissociation below 0.4 F NaCl. The lysine rich histones dissociate between 0.4 and 0.5 F NaCl. Their dissociation is accompanies by a marked increase in the solubility of the chromatin. The moderately lysine rich histones dissociate mainly between 0.8 and 1.1 F NaCl. There are two arginine rich histone components: the first dissociates between 0.8 F and 1.1 F NaCl, but the second class is the very last to be dissociated from the DNA (dissociation beginning at 1.0 F NaCl). By 2.0 F NaCl, essentially all the histones are dissociated.

The properties of the extracted nucleoprotein were studied. The electrophoretic mobility increases and the melting temperature decreases as more histones are dissociated from the DNA. A comparison with the dissociation of histones from DNA in NaClO₄ shows that to dissociate the same class of histones, the concentration of NaCl required is twice that of NaClO₄.

Extension theorems for functions of vanishing mean oscillation

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in R^d converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.

We consider the similar extension problem pertaining to BMO(ρ) functions; that is, those VMO functions whose mean oscillation over any cube is O(ρ(l(Q))) where l(Q) is the length of Q and ρ is a positive, non-decreasing function with ρ(0⁺) = 0.

We apply these results to obtain sufficient conditions for a Blaschke sequence to be the zeros of an analytic BMO(ρ) function on the unit disc.

On concentrated loads and Green's functions in elastostatics

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.

Computer system support for data analysis

This thesis is an investigation into the nature of data analysis and computer software systems which support this activity.

The first chapter develops the notion of data analysis as an experimental science which has two major components: data-gathering and theory-building. The basic role of language in determining the meaningfulness of theory is stressed, and the informativeness of a language and data base pair is studied. The static and dynamic aspects of data analysis are then considered from this conceptual vantage point. The second chapter surveys the available types of computer systems which may be useful for data analysis. Particular attention is paid to the questions raised in the first chapter about the language restrictions imposed by the computer system and its dynamic properties.

The third chapter discusses the REL data analysis system, which was designed to satisfy the needs of the data analyzer in an operational relational data system. The major limitation on the use of such systems is the amount of access to data stored on a relatively slow secondary memory. This problem of the paging of data is investigated and two classes of data structure representations are found, each of which has desirable paging characteristics for certain types of queries. One representation is used by most of the generalized data base management systems in existence today, but the other is clearly preferred in the data analysis environment, as conceptualized in Chapter I.

This data representation has strong implications for a fundamental process of data analysis -- the quantification of variables. Since quantification is one of the few means of summarizing and abstracting, data analysis systems are under strong pressure to facilitate the process. Two implementations of quantification are studied: one analagous to the form of the lower predicate calculus and another more closely attuned to the data representation. A comparison of these indicates that the use of the "label class" method results in orders of magnitude improvement over the lower predicate calculus technique.

A influência do tratamento periodontal não cirúrgico sobre o perfil lipídico e células sangüíneas de pacientes portadores de periodontite crônica generalizada

O objetivo deste estudo foi verificar se o tratamento periodontal não cirúrgico exercia alguma influência sobre o perfil lipídico, os elementos celulares das séries banca e vermelha do sangue, plaquetas e VHS de pacientes portadores de periodontite crônica generalizada. Dezoito pacientes, com média de idade de 50,6 anos ( 7,6), foram submetidos, previamente ao tratamento periodontal e 30 dias após o mesmo, à coleta de 10ml de sangue periférico, através do qual foram analisados o perfil lipídico, os elementos celulares das séries branca e vermelha, o número de plaquetas e VHS. Destes 18 pacientes, 7, com média de idade de 47,4 anos ( 5,9) também foram reavaliados 90 dias após o término do tratamento. Os parâmetros clínicos utilizados, previamente ao tratamento e nas reavaliações, foram o Índice de Placa (IP), de Silness e Löe (1964), o Índice Gengival (IG), de Löe (1967), Sangramento na Sondagem (SS), Profundidade de Bolsa à Sondagem (PBS) e Nível de Inserção (NI). Foram ainda registrados e classificados os sítios com envolvimento de furca. O tratamento periodontal consistiu de terapia básica não cirúrgica. Após 30 dias do término do tratamento periodontal todos os pacientes foram reavaliados sendo verificada melhora significativa (P<0,05) dos valores de IP, IG, SS e PBS e de NI ≥ 6mm (P=0,05). Sítios com envolvimento de furca classes II e III apresentaram também diminuição significativa (P=0,01). Os 7 pacientes submetidos às reavaliações de 30 e 90 dias pós-tratamento também mostraram melhora significativa (P<0,05) dos valores de IP, IG, SS e PBS entre estas fases. Já o NI entre 4-5mm aumentou de forma significativa (P=0,04) entre o pré-tratamento e 90 dias após o mesmo, enquanto que o NI ≥ 6mm diminui significativamente entre as reavaliações de 30 e 90 dias (P=0,01 e P=0,02, respectivamente). Quando comparados os valores de 30 com os de 90 dias resultados semelhantes aos supracitados foram observados, inclusive o aumento do NI entre 4-5mm (P=0,02). É verificado também entre estas fases um IG aumentado (P=0,07). Quanto aos valores hematológicos ocorreu uma diminuição significativa dos níveis de bastões (P=0,05) e de monócitos (P=0,03) após o tratamento periodontal (30 dias), enquanto que o colesterol total e o LDL apresentaram uma tendência ao aumento (P=0,09 para ambos). Já nos sete pacientes submetidos às duas reavaliações o colesterol total apresentou aumento significativo entre as fases pré-tratamento, 30 (P=0,04) e 90 dias (P=0,02) após terapia, assim como o LDL (P=0,04 e P=0,03, respectivamente). Quando comparados os valores plaquetários entre as fases 30 e 90 dias pós-tratamento, verifica-se uma tendência a sua diminuição (P=0,09). O Índice de Castelli II (relação colesterol/HDL) apresenta entre as fases pré e 30 dias pós-tratamento tendência a aumento (P=0,09). Através desses resultados é possível concluir que o tratamento periodontal exerceu influência sobre bastões e monócitos do sangue, caracterizada pela diminuição dessas células, e sobre o colesterol total e o LDL, representada pelo aumento de seus valores.