A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

An Interactive Theorem Prover for First-Order Dynamic Logic

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs. The method of proving correctness of properties of a computer program using the well-known Hoare Logic can be implemented by utilizing the robustness of dynamic logic. For a very broad range of languages and applications in program veri cation, a theorem prover named KIV (Karlsruhe Interactive Veri er) Theorem Prover has already been developed. But a high degree of automation and its complexity make it di cult to use it for educational purposes. My research work is motivated towards the design and implementation of a similar interactive theorem prover with educational use as its main design criteria. As the key purpose of this system is to serve as an educational tool, it is a self-explanatory system that explains every step of creating a derivation, i.e., proving a theorem. This deductive system is implemented in the platform-independent programming language Java. In addition, a very popular combination of a lexical analyzer generator, JFlex, and the parser generator BYacc/J for parsing formulas and programs has been used.

First Field Artillery Brigade Observer, 1 July 1918

The report mentions that General Pershing presented Distinguished Service Crosses to soldiers in the First Field Artillery Brigade. It also describes a Sergeant and 3 men finding an enemy soldier asleep with a machine gun. They brought him back to the American lines. Also included is a list of destruction that took place over the the last three days.

A study of the thermal decomposition of allyl t-butyl peroxide and 3-hydroperoxy-1-propene (allyl hydroperoxide) in toluene /|nby Krishnankutty Nair V. G. -- 260 St. Catharines [Ont. : s. n.],

Kinetics and product studies of the decompositions of allyl-t-butyl peroxide and 3-hydroperoxy- l-propene (allyl hydroperoxide ) in tolune were investigated. Decompositions of allyl-t-butyl peroxide in toluene at 130-1600 followed first order kinetics with an activation energy of 32.8 K.cals/mol and a log A factor of 13.65. The rates of decomposition were lowered in presence of the radical trap~methyl styrene. By the radical trap method, the induced decomposition at 1300 is shown to be 12.5%. From the yield of 4-phenyl-l,2- epoxy butane the major path of induced decomposition is shown to be via an addition mechanism. On the other hand, di-t-butYl peroxyoxalate induced decomposition of this peroxide at 600 proceeded by an abstraction mechanism. Induced decomposition of peroxides and hydroperoxides containing the allyl system is proposed to occur mainly through an addition mechanism at these higher temperatures. Allyl hydroperoxide in toluene at 165-1850 decomposes following 3/2 order kinetics with an Ea of 30.2 K.cals per mole and log A of 10.6. Enormous production of radicals through chain branching may explain these relatively low values of E and log A. The complexity of the reaction is indicated a by the formation of various products of the decomposition. A study of the radical attack of the hydro peroxide at lower temperatures is suggested as a further work to throw more light on the nature of decomposition of this hydroperoxide.

The kinetics and solvent effects on the thermal decomposition of isopropyl peroxide and 1, 2-dioxane

Rates of H2 formation have been determined for the thermal decomposition of isopropyl peroxide at l30o-l50oC in toluene and methanol and at l400C in isopropyl alcohol and water. Product studies have been carried out at l400C in these solvents. The decomposition of isopropyl peroxide was shown to be unimolecular with energies of activation in toluene, and methanol of 39.1, 23.08 Kcal/mole respectively. It has been shown that the rates of H2 formation in decomposition of isopropyl peroxide are solvent dependent and that the ~ vs "'2';' values (parameters for solvent polarity) givesastraight line. Mechanisms for hydrogen production are discussed which satisfactorily explain the stabilization of the six-centered transition state by the solvent. One possibility is that of conformation stabilization by solvent and the other, a transition state with sufficient ionic character to be stabilized by a polar solvent. Rates of thermal decomposition of 1,2-dioxane in tert-butylbenzene at l40o-l70oC have been determined. The activation energy was found to be 33.4 Kcal/mole. This lower activation energy, compared to that for the decomposition of isopropyl peroxide in toluene (39.1 Kcal/mole) has been explained in terms of ring strain. Decomposition of 1,2 dioxane in MeOH does not follow a first order reaction. Several mechanisms have been suggested for the products observed for decomposition of 1;2-dioxane in toluene and methanol.

Autonomy and Relatedness in Mainland Chinese Adolescents: Social or Personal? Accommodation or Distinctiveness?

Three studies comprised the current research program, in which the major goals were to propose and validate empirically the proposed two-level (universal and culture-specific) model of both autonomy and relatedness, as well as to develop reliable and valid measures for these two constructs. In Study 1, 143 mainland Chinese adolescents were asked open-ended questions about their understanding of autonomy and relatedness in three social contexts (peer, family, school). Chinese youth’s responses captured universal and culturally distinctive forms of autonomy (personal vs. social) and relatedness (accommodation vs. distinctiveness), according to a priori criteria based on the theoretical frameworks. Also, scenarios designed to reflect culture-specific forms of autonomy and relatedness suggested their relevance to Chinese adolescents. With a second sample of 201 mainland Chinese youth, in Study 2, the obtained autonomy and relatedness descriptors were formulated into scale items. Those items were subject to refinement analyses to examine their psychometric properties and centrality to Chinese youth. The findings of Study 1 scenarios were replicated in Study 2. The primary goal of Study 3 was to test empirically the proposed two-level (universal and culture-specific) models of both autonomy and relatedness, using the measures derived from Studies 1 and 2. A third sample of 465 mainland Chinese youth completed a questionnaire booklet consisting of autonomy and relatedness scales and scenarios and achievement motivation orientations measures. A series of confirmatory factor analysis (CFA) autonomy and relatedness measurement models (first-order and second-order), as well as structural models linking culture-specific forms of autonomy and relatedness and achievement motivation orientations, were conducted. The first-order measurement models based on scale and scenario scores consistently confirmed the distinction between personal autonomy and social autonomy, and that of accommodation and distinctiveness. Although the construct validity of the two culture-specific forms of autonomy gained additional support from the structural models, the associations between the two culture-specific forms of relatedness and achievement motivation orientations were relatively weak. In general, the two-level models of autonomy and relatedness were supported in two ways: conceptual analysis of scale items and second-order measurement models. In addition, across the three studies, I explored potential contextual and sex differences in Chinese youth’s endorsement of the diverse forms of autonomy and relatedness. Overall, no substantial contextual variability or sex differences were found. The current research makes an important theoretical contribution to the field of developmental psychology in general, and autonomy and relatedness in particular, by proposing and testing empirically both universal and culture-specific parts of autonomy and relatedness. The current findings have implications for the measurement of autonomy and relatedness across social contexts, as well as for socialization and education practice.

Reactivity characteristics of cytochrome c, cytochrome oxidase and the electrostatic cytochrome c - cytochrome oxidase complex /

The mechanism whereby cytochrome £ oxidase catalyses elec-. tron transfer from cytochrome £ to oxygen remains an unsolved problem. Polarographic and spectrophotometric activity measurements of purified, particulate and soluble forms of beef heart mitochondrial cytochrome c oxidase presented in this thesis confirm the following characteristics of the steady-state kinetics with respect to cytochrome £: (1) oxidation of ferrocytochrome c is first order under all conditions. -(2) The relationship between sustrate concentration and velocity is of the Michaelis-Menten type over a limited range of substrate. concentrations at high ionic strength. (3) ~he reaction rate is independent from oxygen concentration until very low levels of oxygen. (4) "Biphasic" kinetic plots of enzyme activity as a function of substrate concentration are found when the range of cytochrome c concentrations is extended; the biphasicity ~ is more apparent in low ionic strength buffer. These results imply two binding sites for cytochrome £ on the oxidase; one of high affinity and one of low affinity with Km values of 1.0 pM and 3.0 pM, respectively, under low ionic strength conditions. (5) Inhibition of the enzymic rate by azide is non-c~mpetitive with respect to cytochrome £ under all conditions indicating an internal electron transfer step, and not binding or dissociation of £ from the enzyme is rate limiting. The "tight" binding of cytochrome '£ to cytochrome c oxidase is confirmed in column chromatographic experiments. The complex has a cytochrome £:oxidase ratio of 1.0 and is dissociated in media of high ionic strength. Stopped-flow spectrophotometric studies of the reduction of equimolar mixtures and complexes of cytochrome c and the oxidase were initiated in an attempt to assess the functional relevance of such a complex. Two alternative routes -for reduction of the oxidase, under conditions where the predominant species is the £ - aa3 complex, are postulated; (i) electron transfer via tightly bound cytochrome £, (ii) electron transfer via a small population of free cytochrome c interacting at the "loose" binding site implied from kinetic studies. It is impossible to conclude, based on the results obtained, which path is responsible for the reduction of cytochrome a. The rate of reduction by various reductants of free cytochrome £ in high and low ionic strength and of cytochrome £ electrostatically bound to cytochrome oxidase was investigated. Ascorbate, a negatively charged reagent, reduces free cytochrome £ with a rate constant dependent on ionic strength, whereas neutral reagents TMPD and DAD were relatively unaffected by ionic strength in their reduction of cytochrome c. The zwitterion cysteine behaved similarly to uncharged reductants DAD and TI~PD in exhibiting only a marginal response to ionic strength. Ascorbate reduces bound cytochrome £ only slowly, but DAD and TMPD reduce bound cytochrome £ rapidly. Reduction of cytochrome £ by DAD and TMPD in the £ - aa3 complex was enhanced lO-fold over DAD reduction of free £ and 4-fold over TMPD reduction of free c. Thus, the importance of ionic strength on the reactivity of cytochrome £ was observed with the general conclusion being that on the cytochrome £ molecule areas for anion (ie. phosphate) binding, ascorbate reduction and complexation to the oxidase overlap. The increased reducibility for bound cytochrome £ by reductants DAD and TMPD supports a suggested conformational change of electrostatically bound c compare.d to free .£. In addition, analysis of electron distribution between cytochromes £ and a in the complex suggest that the midpotential of cytochrome ~ changes with the redox state of the oxidase. Such evidence supports models of the oxidase which suggest interactions within the enzyme (or c - enzyme complex) result in altered midpoint potentials of the redox centers.

Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

Kinetic and mechanistic studies for the molybdenum- catalyzed oxidation of organic sulfides and olefins by t- DuO2H

This research was focussed on the effects of light, solvent and substituents in the molybdenum-catalyzed oxidation of phenylmethyl sulfides with t-Bu02H and on the effect of light in the molybdenum-catalyzed epoxidation of l-octene with t-Bu02H. It was shown that the Mo(CO)6-catalyzed oxidation of phenylmethyl sulfide with t-Bu02H~ at 35°C, proceeds 278 times faster underUV light than under laboratory lighting, whereas the Mo02(acac)2-catalyzed oxidation proceeds only 1.7 times faster under UV light than under normal laboratory lighting. The difference between the activities of both catalysts was explained by the formation of the catalytically active species, Mo(VI). The formation of the Mo(VI) species, from Mo(CO)6 was observed from the IR spectrum of Mo(CO)6 in the carbonyl region. The Mo(CO)6-catalyzed epoxidation of l-octene with t-Bu02H showed that the reaction proceeded 4.6 times faster under UV light than in the dark or under normal laboratory lighting; the rates of epoxidations were found to be the same in the dark and under normal laboratory lighting. The kinetics of the epoxidations of l-octene with t-Bu02H, catalyzed by Mo02(acac)2 were found to be complicated; after fast initial rates, the epoxidation rates decreased with time. The effect of phenylmethyl sulfide on the Mo(CO)6-catalyzed epoxidation of l-octene waS studied. It was shown that instead of phenylmethyl sulfide, phenylmethyl sulfone, which formed rapidly at 85°C, lowered the reaction rate. The epoxidation of l-octene was found to be 2.5 times faster in benzene than in ethanol. The substituent effect on the Mo02(acac)2-catalyzed oxidations of p-OH, p-CHgO, P-CH3' p-H, p-Cl, p-Br, p-CHgCO, p-HCO and P-N02 substituted phenylmethyl sulfides were studied. The oxidations followed second order kinetics for each case; first order dependency on catalyst concentration was also observed in the oxidation of p-CHgOPhSMeand PhSMe. It was found that electron-donating groups on the para position of phenylmethyl sulfide increased the rate of reaction, while electronwithdrawing groups caused the reaction rate to decrease. The reaction constants 0 were determined by using 0, 0- and 0* constants. The rate effects were paralleled by the activation energies for oxidation. The decomposition of t-Bu02H in the presence of M.o (CO)6, Mo02 (acac)2 and VO(acac)2 was studied. The rates of decomposition were found to be very small compared to the oxidation rates at high concentration of catalysis. The relative rates of the Mo02(acac)2-catalyzed oxidation of p-N02PhSMe by t-Bu02H in the presence of either p-CH30PhSMe or PhSMe clearly show that PhSMe and p-CHgOPhSMe act as co-catalysts in the oxidation of p-N02PhSMe. Benzene, mesity1ene and cyclohexane were used to determine the effect of solvent in the Mo02 (acac)2 and Mo(CO)6-catalyzed oxidation of phenylmethyl sulfide. The results showed that in the absence of hydroxylic solvent, a second molecule of t-Bu02H was involved in the transition state. The complexation of the solvent with the catalyst could not be explained.The oxidations of diphenyl sulfoxide catalyzed by VO(acac)2, Mo(CO)6 and Mo02(acac)2 showed that VO(acac)2 catalyzed the oxidation faster than Mo(CO)6 and Mo02 (acac)2_ Moreover, the Mo(CO)6-catalyzed oxidation of diphenyl sulfoxide proceeded under UV light at 35°C.

Solute effects on the production and decay of primary species in the flash photolysis of indole

Maximum production rates ofs and decay kinetics for the hydrated electron, the indolyl neutral radical and the indole triplet state have been obtained in the microsecond, broadband (X > 260 nm) flash photolysis of helium-saturated, neutral aqueous solutions of indole, in the absence and in the presence of the solutes NaBr, BaCl2*2H20 and CdSCV Fluorescence spectra and fluorescence lifetimes have also been obtained in the absence and in the presence of the above solutes, The hydrated electron is produced monophotonically and biphotonically at an apparent maximum rate which is increased by BaCl2*2H20 and decreased by NaBr and CdSOif. The neutral indolyl radical may be produced monophotonically and biphotonically or strictly monophotonically at an apparent maximum rate which is increased by NaBr and CdSO^ and is unaffected by BaCl2*2H20. The indole triplet state is produced monophotonically at a maximum rate which is increased by all solutes. The hydrated electron decays by pseudo first order processes, the neutral indolyl radical decays by second order recombination and the indole triplet state decays by combined first and second order processes. Hydrated electrons are shown to react with H , H2O, indole, Na and Cd"*""1"". No evidence has been found for the reaction of hydrated electrons with Ba . The specific rate of second order neutral indolyl radical recombination is unaffected by NaBr and BaCl2*2H20, and is increased by CdSO^. Specific rates for both first and second order triplet state decay processes are increased by all solutes. While NaBr greatly reduced the fluorescence lifetime and emission band intensity, BaCl2*2H20 and CdSO^ had no effect on these parameters. It is suggested that in solute-free solutions and in those containing BaCl2*2H20 and CdSO^, direct excitation occurs to CTTS states as well as to first excited singlet states. It is further suggested that in solutions containing NaBr, direct excitation to first excited singlet states predominates. This difference serves to explain increased indole triplet state production (by ISC from CTTS states) and unchanged fluorescence lifetimes and emission band intensities in the presence of BaCl2*2H20 and CdSOt^., and increased indole triplet state production (by ISC from S^ states) and decreased fluorescence lifetime and emission band intensity in the presence of NaBr. Evidence is presented for (a) very rapid (tx ^ 1 us) processes involving reactions of the hydrated electron with Na and Cd which compete with the reformation of indole by hydrated electron-indole radical cation recombination, and (b) first and second order indole triplet decay processes involving the conversion of first excited triplet states to vibrationally excited ground singlet states.

Proceedings of the Court Martial Held by Order of Major Merritt

Proceedings of the court martial held by order of Major Merritt (1 double-sided page, handwritten): Captain Hamilton gave evidence against Caleb Cook (a private in Major Merritt’s Company of Light Dragoons) for disobedience and leaving quarters without leave of absence. Cook was fined and ordered to spend one month in prison. The document is stained and has holes in it along the middle fold. This does not affect the text, Aug. 7, 1812.