The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.

We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

This study investigates the relationship between the level to which a person feels connected to Nature and that person's ability to perceive the restorative value of a natural environment. We assume that perceived restorativeness may depend on an individual's connection to Nature and this relationship may also vary with the biophilic quality of the environment, i.e., the functional and aestheti...

A natural algebraic approach to the KdV hierarchy and its algebro-geometric finite-gap solutions is developed. In addition, a new derivation of associated higher-order trace formulas in connection with one-dimensional Schrödinger operators is presented.

The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.

In a system of sequents for intuitionistic predicate logic a theorem, which corresponds to Prawitz’s Normal Form Theorem for natural deduction, are proved. In sequent derivations a special kind of cuts, maximum cuts, are defined. Maximum cuts from sequent derivations are connected with maximum segments from natural deduction derivations, i.e., sequent derivations without maximum cuts correspond...

the present study sets out to integrate the performance-based seismic design approach with the connection topology optimization method. performance-based connection topology optimization concept aims to simultaneously optimize the size of members and the type of connections with respect to the framework of performance-based seismic design. this new optimization concept is carried out for unbrac...

Entailment relations are of central importance in the enterprise of natural language semantics. In modern logic, entailment relations are characterized from two viewpoints: the modeltheoretic and proof-theoretic ones. By contrast, most approaches to formalizing entailment relations in natural languages have been solely based on model-theoretic conceptions. Thus, the notion of validity is only c...