Create your page here

back to playlist

**Degree** may refer to:

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Degree

In abstract algebra, **field extensions** are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set **Q**(√2) = {*a* + *b*√2 | *a*, *b* ∈ **Q**} is the smallest extension of **Q** that includes every real solution to the equation *x*^{2} = 2.

Let *L* be a field. A **subfield** of *L* is a subset *K* of *L* that is closed under the field operations of *L* and under taking inverses in *L*. In other words, *K* is a field with respect to the field operations inherited from *L*. The larger field *L* is then said to be an **extension field** of *K*. To simplify notation and terminology, one says that *L* / *K* (read as "*L* over *K*") is a **field extension** to signify that *L* is an extension field of *K*.

If *L* is an extension of *F* which is in turn an extension of *K*, then *F* is said to be an **intermediate field** (or **intermediate extension** or **subextension**) of the field extension *L* / *K*.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Field_extension

The **degree of an algebraic variety** in mathematics is defined, for a projective variety *V*, by an elementary use of intersection theory.

For *V* embedded in a projective space *P*^{n} and defined over some algebraically closed field *K*, the degree *d* of *V* is the number of points of intersection of *V*, defined over *K*, with a linear subspace *L* in general position, when

Here dim(*V*) is the dimension of *V*, and the codimension of *L* will be equal to that dimension. The degree *d* is an extrinsic quantity, and not intrinsic as a property of *V*. For example the projective line has an (essentially unique) embedding of degree *n* in *P*^{n}.

The degree of a hypersurface *F* = 0 is the same as the total degree of the homogeneous polynomial *F* defining it (granted, in case *F* has repeated factors, that intersection theory is used to count intersections with multiplicity, as in Bézout's theorem).

For a more sophisticated approach, the linear system of divisors defining the embedding of *V* can be related to the line bundle or invertible sheaf defining the embedding by its space of sections. The tautological line bundle on *P*^{n} pulls back to *V*. The degree determines the first Chern class. The degree can also be computed in the cohomology ring of *P*^{n}, or Chow ring, with the class of a hyperplane intersecting the class of *V* an appropriate number of times.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Degree_of_an_algebraic_variety

**Solar** may refer to:

- A solar telescope is a special purpose telescope used to observe the Sun
- A device that utilizes solar energy (e.g. "solar panels")
- Solar calendar, a calendar whose dates indicate the position of the earth on its revolution around the sun

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Solar

**Generic top-level domains** (**gTLDs**) are one of the categories of top-level domains (TLDs) maintained by the Internet Assigned Numbers Authority (IANA) for use in the Domain Name System of the Internet. A top-level domain is the last label of every fully qualified domain name. They are called generic for historic reasons; initially, they were contrasted with country-specific TLDs in RFC 920.

The core group of generic top-level domains consists of the `com`, `info`, `net`, and `org` domains. In addition, the domains `biz`, `name`, and `pro` are also considered *generic*; however, these are designated as *restricted*, because registrations within them require proof of eligibility within the guidelines set for each.

Historically, the group of generic top-level domains included domains, created in the early development of the domain name system, that are now sponsored by designated agencies or organizations and are restricted to specific types of registrants. Thus, domains `edu`, `gov`, `int`, and `mil` are now considered sponsored top-level domains, much like the *themed* top-level domains (e.g., `jobs`). The entire group of domains that do not have a geographic or country designation (see country-code top-level domain) is still often referred to by the term *generic* TLDs.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Generic_top-level_domain

The **solar** was a room in many English and French medieval manor houses, great houses and castles, generally situated on an upper storey, designed as the family's private living and sleeping quarters. In such houses, the main ground-floor room was known as the Great Hall, in which all members of the household, including tenants, employees and servants, would eat. Those of highest status would be at the end, often on a raised dais, and those of lesser status further down the hall. But a need was felt for more privacy to be enjoyed by the head of the household, and, especially, by the senior women of the household. The solar was a room for their particular benefit, in which they could be alone and away from the hustle, bustle, noise and smells (including cooking smells) of the Great Hall.

The solar was generally smaller than the Great Hall, because it was not expected to accommodate so many people, but it was a room of comfort and status, and usually included a fireplace and often decorative woodwork or tapestries/wall hangings.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Solar_(room)

The lights go down now. I'm one thousand miles away from you. My only thoughts now are the one thousand smiles I took from you. This room is such a lonely place without the presence of your face. I dread the thought of every minute I spend without you. I can't sleep without you snoring. I can't speak without you ignoring. Every word that I slur with a grin. 'Cause what's a drunked word without a wasted ear to take it in. Late nights and too much smoke is starting to catch up with me. My voice is almost broke. You're the only thing that gets it out of me. It's been six weeks now since I drank the night away with you. Now I'm drinking by myself to try and keep my thoughts away from you. I'd drive all night on three hours sleep to make sure you last another day. The things we do somehow just make my life complete, and I know you'll make my bed someday. I'm like a wino staring at an empty bottle. Looking at pictures of me and you. If I don't get a taste of you tomorrow, God only knows what I will do.

© WN 2018

- Connect:
- CHAT

×

Share this video with your family and friends