In this lecture, we will describe a strongly polynomial time algorithm for the minimum cost perfect matching problem in a general graph. Using a simple reduction discussed in lecture 9, one can also obtain an algorithm for the maximum weight matching problem. We also note that when discussing perfect matching, without loss of generality, we can assume that all weights/costs are non-negative (wh...

The main goal of the paper is to find the discrete analogue of the Bianchi system in spaces of arbitrary dimension together with its geometric interpretation. We show that the proper geometric framework of such generalization is the language of dual quadrilateral lattices and of dual congruences. After introducing the notion of the dual Koenigs lattice in a projective space of arbitrary dimensi...

Conditions on the existence of self-dual θ-codes defined over a finite field IFq are studied for θ automorphism of IFq. When q ≡ 1 (mod 4) it is proven that there always exists a self-dual θ-code in any dimension and that self-dual θ-codes of a given dimension are either all θ-cyclic or all θ-negacyclic. When q ≡ 3 (mod 4), there does not exist a selfdual θ-cyclic code and a necessary and suffi...

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

A connected graph G is called t-perfect if its stable set polytope is determined by the non-negativity, edge and odd-cycle inequalities. Moreover, G is called strongly t-perfect if this system is totally dual integral. It is an open problem whether t-perfection is equivalent to strong t-perfection. We prove the equivalence for the class of claw-free graphs.

this paper presents an e-ring shaped printed monopole antenna for uwb applications with dual notched bands performance. in order to generate single frequency band notch function, we applied a u-ring shaped monopole antenna, and by inserting a rectangular ring in the centre of it an e-ring shaped radiating patch created and a dual band-notch function can be achieved. the measured bandwidth of th...

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization themselves are only partially understood. A nonlinear map on space unitary was proposed in PRL.~125, 070501 (2020) that results being arbitrarily close to dual unitaries. Here we study analytically...