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.

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.

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.

The determination of sinigrin in Brassica, and investigations into the use of allyl-isothiocyanate as a nematicide

The goal of this thesis was to study factors related to the development of Brassica juncea as a sustainable nematicide. Brassica juncea is characterized by the glycoside (glucosinolate) sinigrin. Various methods were developed for the determination of sinigrin in Brassica juncea tissue extracts. Sinigrin concentrations in plant tissues at various stages of growth were monitored. Sinigrin enzymatically breaks down into allylisothiocyanate (AITC). AITC is unstable in aqueous solution and degradation was studied in water and in soil. Finally, the toxicity of AITC against the root-lesion nematode (Pratylenchus penetrans) was determined. A method was developed to extract sinigrin from whole Brassica j uncea tissues. The optimal time of extraction wi th boiling phosphate buffer (0.7mM, pH=6.38) and methanol/water (70:30 v/v) solutions were both 25 minutes. Methanol/water extracted 13% greater amount of sinigrin than phosphate buffer solution. Degradation of sinigrin in boiling phosphate buffer solution (0.13%/minute) was similar to the loss of sinigrin during the extraction procedure. The loss of sinigrin from boiling methanol/water was estimated to be O.Ol%/minute. Brassica juncea extract clean up was accomplished by an ion-pair solid phase extraction (SPE) method. The recovery of sinigrin was 92.6% and coextractive impurities were not detected in the cleaned up extract. Several high performance liquid chromatography (HPLC) methods were developed for the determination of sinigrin. All the developed methods employed an isocratic mobile phase system wi th a low concentration of phosphate buffer solution, ammonium acetate solution or an ion-pair reagent solution. A step gradient system was also developed. The method involved preconditioning the analytical column with phosphate buffer solution and then switching the mobile phase to 100% water after sample injection.Sinigrin and benzyl-glucosinolate were both studied by HPLC particle beam negative chemical ionization mass spectrometry (HPLCPB- NCI-MS). Comparison of the mass spectra revealed the presence of fragments arising from the ~hioglucose moiety and glucosinolate side-chain. Variation in the slnlgrin concentration within Brassica juncea plants was studied (Domo and Cutlass cuItivars). The sinigrin concentration in the top three leaves was studied during growth of each cultivar. For Cutlass, the minimum (200~100~g/g) and maximum (1300~200~g/g) concentrations were observed at the third and seventh week after planting, respectively. For Domo, the minimum (190~70~g/g) and maximum (1100~400~g/g) concentrations were observed at the fourth and eighth week after planting, respectively. The highest sinigrin concentration was observed in flower tissues 2050±90~g/g and 2300±100~g/g for Cutlass and Domo cultivars, respectively. Physical properties of AITC were studied. The solubility of AITC in water was determined to be approximately 1290~g/ml at 24°C. An HPLC method was developed for the separation of degradation compounds from aqueous AITC sample solutions. Some of the degradation compounds identified have not been reported in the literature: allyl-thiourea, allyl-thiocyanate and diallyl-sulfide. In water, AITC degradation to' diallyl-thiourea was favored at basic pH (9.07) and degradation to diallyl-sulfide was favored at acidic pH (4 . 97). It wap necessary to amend the aqueous AITC sample solution with acetonitrile ?efore injection into the HPLC system. The acetonitrile amendment considerably improved AITC recovery and the reproducibility of the results. The half-life of aqueous AITC degradation at room temperature did not follow first-order kinetics. Beginning with a 1084~g/ml solution, the half-life was 633 hours. Wi th an ini tial AITC concentration of 335~g/ml the half-life was 865 hours. At 35°C the half-life AITC was 76+4 hours essentially independent of the iiisolution pH over the range of pH=4.97 to 9.07 (1000~g/ml). AITC degradation was also studied in soil at 35°C; after 24 hours approximately 75% of the initial AITC addition was unrecoverable by water extraction. The ECso of aqueous AITC against the root-lesion nematode (Pratylenchus penetrans) was determined to be approximately 20~g/ml at one hour exposure of the nematode to the test solution. The toxicological study was also performed with a myrosinase treated Brassica juncea extract. Myrosinase treatment of the Brassica juncea extract gave nearly quantitative conversion of sinigrin into AITC. The myrosinase treated extract was of the same efficacy as an aqueous AITC solution of equivalent concentration. The work of this thesis was focused upon understanding parameters relevant to the development of Brassica juncea as a sustainable nematicide. The broad range of experiments were undertaken in support of a research priority at Agriculture and Agri-Food Canada.

The Effects of Annealing URu2Si2 on the Resistivity and Meissner Effect

The enigmatic heavy fermion URu2Si2, which is the subject of this thesis, has attracted intensive theoretical and experimental research since 1984 when it was firstly reported by Schlabitz et al. at a conference [1]. The previous bulk property measurements clearly showed that one second order phase transition occurs at the Hidden Order temperature THO ≈ 17.5 K and another second order phase transition, the superconducting transition, occurs at Tc ≈ 1 K. Though twenty eight years have passed, the mechanisms behind these two phase transitions are still not clear to researchers. Perfect crystals do not exist. Different kinds of crystal defects can have considerable effects on the crystalline properties. Some of these defects can be eliminated, and hence the crystalline quality improved, by annealing. Previous publications showed that some bulk properties of URu2Si2 exhibited significant differences between as-grown samples and annealed samples. The present study shows that the annealing of URu2Si2 has some considerable effects on the resistivity and the DC magnetization. The effects of annealing on the resistivity are characterized by examining how the Residual Resistivity Ratio (RRR), the fitting parameters to an expression for the temperature dependence of the resistivity, the temperatures of the local maximum and local minimum of the resistivity at the Hidden Order phase transition and the Hidden Order Transition Width ∆THO change after annealing. The plots of one key fitting parameter, the onset temperature of the Hidden Order transition and ∆THO vs RRR are compared with those of Matsuda et al. [2]. Different media used to mount samples have some impact on how effectively the samples are cooled because the media have different thermal conductivity. The DC magnetization around the superconducting transition is presented for one unannealed sample under fields of 25 Oe and 50 Oe and one annealed sample under fields of 0 Oe and 25 Oe. The DC field dependent magnetization of the annealed Sample1-1 shows a typical field dependence of a Type-II superconductor. The lower critical field Hc1 is relatively high, which may be due to flux pinning by the crystal defects.