A dimension is a structure that categorizes facts and measures in order to enable users to answer business questions. Commonly used dimensions are people, products, place and time.
In a data warehouse, dimensions provide structured labeling information to otherwise unordered numeric measures. The dimension is a data set composed of individual, non-overlapping data elements. The primary functions of dimensions are threefold: to provide filtering, grouping and labelling.
These functions are often described as "slice and dice". Slicing refers to filtering data. Dicing refers to grouping data. A common data warehouse example involves sales as the measure, with customer and product as dimensions. In each sale a customer buys a product. The data can be sliced by removing all customers except for a group under study, and then diced by grouping by product.
Typically dimensions in a data warehouse are organized internally into one or more hierarchies. "Date" is a common dimension, with several possible hierarchies:
Directed by The Malloys, the music video for "Dimension" was first aired in the week of 13 February 2006. Prior to this, the video was featured on the 2006 extended play (EP) Dimensions.
Critical reception
In a review of Wolfmother for Blender, writer Jonah Weiner identified "Dimension" as an example of the band "at [their] hardest", describing it as an "acid anthem".NME reviewer James Jam described the song as "a throb of gonzometal not unlike Black Sabbath playing Motown".
A field k has Krull dimension 0; more generally, k[x1, ..., xn] has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.
Explanation
We say that a chain of prime ideals of the form
has length n. That is, the length is the number of strict inclusions, not the number of primes; these differ by 1. We define the Krull dimension of to be the supremum of the lengths of all chains of prime ideals in .
In biology, a pathogen (Greek:πάθοςpathos “suffering, passion” and -γενής -genēs “producer of”) in the oldest and broadest sense is anything that can produce disease, a term which came into use in the 1880s. Typically the term is used to describe an infectious agent such as a virus, bacterium, prion, fungus, viroid, or parasite that causes disease in its host. The host may be a human, an animal, a plant, a fungus, or even another micro-organism.
There are several substrates including pathways where the pathogens can invade a host. The principal pathways have different episodic time frames, but soil contamination has the longest or most persistent potential for harboring a pathogen. Diseases caused by organisms in humans are known as pathogenic diseases.
Pathogenicity
Pathogenicity is the potential disease-causing capacity of pathogens. Pathogenicity is related to virulence in meaning, but some authorities have come to distinguish it as a qualitative term, whereas the latter is quantitative. By this standard, an organism may be said to be pathogenic or non-pathogenic in a particular context, but not "more pathogenic" than another. Such comparisons are described instead in terms of relative virulence. Pathogenicity is also distinct from the transmissibility of the virus, which quantifies the risk of infection.
The newly developed AI framework, a collaborative effort between mathematicians at the University of Manchester and Oxford, represents a significant leap in pathogen surveillance.
... as well as adaptation to changing climates, local pathogens, and lifestyle innovations. These details, inaccessible using previous methods, add a new dimension to our understanding of human origins.
Nanoparticles have been used in the past to observe changes in biological systems, Pan said, but this is the first time two nanoscale objects in two different dimensions have been deployed to detect an emerging pathogen.
Biohazards became a dominant theme in gaming, with mad scientists and big corporations mucking about with our DNA, weird pathogens, doors to alternate dimensions , or even the gates to hell itself, ...
... correlated with multiple dimensions of ecosystem functions e.g., carbon sequestration and water regulation to plant pathogen control, and antibiotic resistance regulation in urban parks and gardens.
... the world’s most dangerous pathogens ... “Some scientists outside China worry about pathogens escaping, and the addition of a biological dimension to geopolitical tensions between China and other nations.
... the world’s most dangerous pathogens ... “Some scientists outside China worry about pathogens escaping, and the addition of a biological dimension to geopolitical tensions between China and other nations.
To the extent that JenAct has perfected its UVC light solution by developing software which enables the company to match disinfection performance to customer requirements, including air flow and dimensions, as well as specified pathogens.
Bioinformatics as a Tool for Pathogen Genomics Research. Host-pathogen genomics and transcriptomics have strengthened our understanding of human-pathogen interactions and the fast identification of potential diagnostic and prognostic markers.
... feels like it’s exploring overly familiar territory – even though the specter of Covid-19 adds a spooky, all-too-real dimension to the story’s novel pathogen and lockdowns.
has length n. That is, the length is the number of strict inclusions, not the number of primes; these differ by 1. We define the Krull dimension of 
to be the supremum of the lengths of all chains of prime ideals in 
