I will prove the so-called Frisch-Parisi conjecture, showing that behind this chaotic behavior there is an underlying

algebraic structure that controls the dynamics.

The interesting, but restrictive,

algebraic structure of the model, containing a 3-algebra with antisymmetric structure constants, turned out to have only one finite-dimensional realization [24,25], possible to interpret in terms of two M2-branes [26,27] (see, however, [28-30] dealing with the infinite-dimensional solution related to volume-preserving diffeomorphisms in three dimensions).

An Abel- Grassmann's groupoid, abbreviated as an AG-groupoid (or in some papers left almost semigroup), is a non-associative

algebraic structure mid way between a groupoid and a commutative semigroup.

Studying such polynomial equations in the multivariate setting is more complicated due to the much more complex

algebraic structure of the ring of multivariate polynomials.

One challenge of the research is the matching of the

algebraic structure to the data and problems at hand," Albanese said.

As a consequence, it is decided that "top-level" language will not become "yet another specification language" but rather another

algebraic structure suitable for the following experiments:

It seems that, even after being taught structural aspects of numerical expressions, a considerable amount of students did not perceive numerical expressions with the same

algebraic structure as algebraically the same.

He was awarded a $50,000 scholarship for his research that classifies certain fusion categories of mathematics, a recently discovered type of

algebraic structure with applications to areas of theoretical physics, computer science and mathematics, such as string theory, quantum computation and knot theory.

The featured projects include a Quilted Mobius Band (making a mobius quilt); Diphantine Equations (making a bi-directional hat); Sierpinski Variatins (making a Sierpinski shawl); a Two Knit Stiches Tours; Symmetry Patterns in Cross-Stitch;

Algebraic Structure (making algebraic socks); Fortunatus's Purse; (K)Not Cables and Braids (making a pillow of Braid Equivalence); The Graph Theory of Blackwork Embroidery (embroidering a Holbeinian Graph); and making Hyperbolic Pants.

By using a direct product of bilinear groups, it is possible to construct "dual pairing vector spaces" with a richer

algebraic structure than that of a bilinear group itself.

An

algebraic structure (Q, + , x) is called a quasi-near-ring (or a right quasi-near-ring) if it satisfies the following three conditions:

Among the topics are nearby cycles and periodicy in cyclic homology, the Gauss-Bonnet theorem for the noncommutative two torus, zeta phenomenology, absolute modular forms, the transcendence of values of transcendental functions at algebraic points, and the Hopf

algebraic structure of perturbative quantum gauge theories.