Enumeration of idempotents in planar diagram monoids

We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms of certain vertex- and edge-coloured graphs associated to Motzkin diagrams. The enumeration is necessarily algorithmic in nature, and is based on parameters associated to cycle components of these graphs. We compare our algorithms to existing algorithms for enumerating idempotents in arbitrary (regular *-) semigroups, and give several tables of calculated values.Comment: Majorly revised (new title, new abstract, one additional author), 24 pages, 6 figures, 8 tables, 5 algorithm

Pathways for Nutrient Loss to Water; Slurry and Fertilizer Spreading

End of project reportThere are almost 150,000 farms in Ireland and these contribute substantial quantities of N and P to inland and coastal waters. Some of these nutrients are carried from wet soils by overland flow and by leaching from dry soils. Farm practice can reduce the loss from farms by judicious management of nutrients. Improvements are required to diminish export of nutrients without impairing operations on the farm. Literature regarding nutrient loss from agriculture was reviewed in this project and maps were prepared to predict best slurry spreading times around Ireland. Two further maps were prepared to show slurry storage requirement on farms

Successful Fusion Of Information Systems Concepts With Complementary Technical Skill

This paper addresses the integration of technical skills with information systems concepts required in an introductory MIS course, specifically focusing on the laptop inclusion initiative at our university.  We will show the working relationship between the concepts and application segment of MIS, and how a laptop inclusion program combined with the use of e-Learning methodologies successfully combine the two

Geometrically exact planar beams with initial pre-stress and large curvature: Static configurations, natural frequencies, and mode shapes

AbstractWithin this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler–Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures

WASM-MUTATE: Fast and Effective Binary Diversification for WebAssembly

WebAssembly has is renowned for its efficiency and security in browser environments and servers alike. The burgeoning ecosystem of WebAssembly compilers and tools lacks robust software diversification systems. We introduce WASM-MUTATE, a compiler-agnostic WebAssembly diversification engine. It is engineered to fulfill the following key criteria: 1) the rapid generation of semantically equivalent yet behaviorally diverse WebAssembly variants, 2) universal applicability to any WebAssembly programs regardless of the source programming language, and 3) the capability to counter high-risk security threats. Utilizing an e-graph data structure, WASM-MUTATE is both fast and effective. Our experiments reveal that WASM-MUTATE can efficiently generate tens of thousands of unique WebAssembly variants in a matter of minutes. Notably, WASM-MUTATE can protect WebAssembly binaries against timing side-channel attacks, specifically, Spectre