A quantity, called the linking number, is defined, which specifies the total number of t,wists in a circular helix. The linking number is invariant under continuous deformations of the ring and therefore enables one to calculate the influence of superhelical structures on the secondary helix of a circular molecule. The linking number can be determined by projecting the helix into a plane and co...

Abstract. Given a lattice polytope, the secondary fan is a combinatorial structure on the space of all tropical polynomials supported on the polytope. We consider rationally weighted formal sums of cones in the secondary fan as an approximation to a tropical variety. By using tropical intersection theory, we are able to intersect these formal sums with point-condition-imposing hyperplanes. Form...

Given the extraordinary ability of humans and animals to recognize communication signals over a background of noise, describing noise invariant neural responses is critical not only to pinpoint the brain regions that are mediating our robust perceptions but also to understand the neural computations that are performing these tasks and the underlying circuitry. Although invariant neural response...

The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah–Patodi–Singer eta-invariant, the Chern–Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensi...

Homotopy groups of a connective ring spectrum R form an Ngraded algebra π∗R which is commutative if R is commutative. We describe a secondary algebra π∗,∗R which enriches the structure of the algebra π∗R in a new unexpected way. The algebra π∗,∗R encodes secondary homotopy operations in π∗R, such as Toda brackets, and the first Postnikov invariant of R as a ring spectrum. Moreover, π∗,∗R repres...

We prove that if $\Gamma$ is a group of polynomial growth, then each delocalized cyclic cocycle on the algebra has representative growth. For cocycle, we thus define higher analogue Lott’s eta invariant and its convergence for invertible differential operators. also use determinant map construction Xie Yu to there well-defined pairing between cocycles $K$-theory classes $C^\*$-algebraic seconda...

we introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...