Paving tropical ideals

Tropical Varieties, Ideals and an Algebraic Nullstellensatz

The objective of this paper is to introduce the fundamental algebro-geometric constructions over the extended tropical semi-ring. The study of tropical varieties, co-varieties and ideals over this extension eventually yields the theorem of the weak tropical Nullstellensatz and gives an algebraic interpretation of the tropical Nullstellensatz.

Tropical Algebraic Sets, Ideals and an Algebraic Nullstellensatz

This paper introduces the foundations of the polynomial algebra and basic structures for algebraic geometry over the extended tropical semiring. Our development, which includes the tropical version for the fundamental theorem of algebra, leads to the reduced polynomial semiring – a structure that provides a basis for developing a tropical analogue to the classical theory of commutative algebra....

Crazy paving pattern

Crazy paving pattern is the name given to characteristic polygonal pattern of interlobular thickening on computed tomography (CT scan) of the lung, which results from accumulation of collagen, interstitial fluid, cell, or other pathology and may be seen in multiple clinical conditions including metastatic cancer as described in this case.

The asphalt paving process

Language: English The Challenge At the outset the asphalt paving process seems to be simple. Trucks deliver hot mix asphalt from plants to the construction site. There the asphalt is loaded on asphalt pavers that evenly spread the asphalt. Finally, compactors compact the asphalt to its required density. Despite this relatively structured process our research shows that there are significant dis...

Primary Ideals and Valuation Ideals