In this report, we define an algebra of dyadic intervals. Thereupon, we present a formalization of a generalized theory of interval differentiation and investigate into some of the analytic and algebraic properties thereof.

By means of the most fundamental logical concepts of quantification theory, the notion of interval dependency is axiomatized and its fundamental properties are deduced.

In this report, we study some of the order-theoretic and algebraic aspects of interval mathematics.

In this report, we set up an axiomatic system of algorithmic differentiation and deduce its fundamental algebraic properties.

The aim of this paper is to provide a metamathematical investigation of the theory of intervals with the requisite predicate calculi and axiomatic set theory.

The dynamically combined deductive and hypothetico-deductive method has been available to objective investigators since ancient times. Only in the last half-century has it been taught in courses on scientific method and critical thinking. The below chart for teaching and applying it is only about thirty years old.

Pimprinine and streptochlorin are indole alkaloids derived from marine or soil microorganisms. In our previous study, they were promising lead compounds due to their potent bioactivity in preventing many phytopathogens, but further structural modifications are required to improve their antifungal activity. In this study, pimprinine and streptochlorin were used as parent structures with the combination strategy of their structural features. Three series of target compounds were designed and synthesized. Subsequent evaluation for antifungal activity against six common phytopathogenic fungi showed that some of thee compounds possessed excellent effects, and this is highlighted by compounds 4a and 5a, displaying 99.9% growth inhibition against Gibberella zeae and Alternaria Leaf Spot under 50 μg/mL, respectively. EC50 values indicated that compounds 4a, 5a, 8c, and 8d were even more active than Azoxystrobin and Boscalid. SAR analysis revealed the relationship between 5-(3′-indolyl)oxazole scaffold and antifungal activity, which provides useful insight into the development of new target molecules. Molecular docking models indicate that compound 4a binds with leucyl-tRNA synthetase in a similar mode as AN2690, offering a perspective on the mode of action for the study of its antifungal activity. These results suggest that compounds 4a and 5a could be regarded as novel and promising antifungal agents against phytopathogens due to their valuable potency.

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