Evolution of Bridge Live Load Models and Truck Weight Limits:The Case of Manitoba, Canada

Truck size and weight regulations have been a key instrument used to improve trucking productivity, safety, and operational performance in Canada. In response to these changes, bridge design codes undergo modifications to envelop the potential range of trucks in operation. A five-decade timeline is presented: (1) to document how bridge codes and their live load models have evolved, with a focus on the Manitoba-specific HSS-25 truck, and (2) to discuss how responsive bridge design codes have historically been to changes in truck size and weight regulations. While at times bridge codes are released in conjunction with expected regulation changes, there is often delay in the issuance of revised bridge design and evaluation codes. Assessments of the current truck fleet, which now includes long combination vehicles (LCVs), may be a consideration for future bridge design live load models.

Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives

We upper-bound the number of common zeros over a finite grid of multivariate polynomials and an arbitrary finite collection of their consecutive Hasse derivatives (in a coordinate-wise sense). To that end, we make use of the tool from Gröbner basis theory known as footprint. Then we establish and prove extensions in this context of a family of well-known results in algebra and combinatorics. These include Alon's combinatorial Nullstellensatz [1], existence and uniqueness of Hermite interpolating polynomials over a grid, estimations of the parameters of evaluation codes with consecutive derivatives [20], and bounds on the number of zeros of a polynomial by DeMillo and Lipton [8], Schwartz [25], Zippel [26, 27] and Alon and Füredi [2]. As an alternative, we also extend the Schwartz-Zippel bound to weighted multiplicities and discuss its connection to our extension of the footprint bound.

Some bounds for the relative generalized Hamming weights of some evaluation codes

In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori Tn₁-1 and Tn₂-1.