envelope

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envelope

1. Biology any enclosing structure, such as a membrane, shell, or skin
2. the bag enclosing the gas in a balloon
3. Maths a curve or surface that is tangent to each one of a group of curves or surfaces
4. Electronics the sealed glass or metal housing of a valve, electric light, etc.
5. Telecomm the outer shape of a modulated wave, formed by the peaks of successive cycles of the carrier wave

Envelope

The boundary that separates a building’s conditioned and unconditioned spaces. The term usually refers to heat and air transfer, such as through walls, windows, and the roof. All of these are part of the building’s envelope. Also, the imaginary shape of a building indicating its maximum volume; used primarily to check the plan, setback, and other restrictions regarding zoning regulations.

Envelope

of a family of curves in a plane (or of surfaces in space), a curve (or surface) that touches at each of its points a single curve (or surface) of the family and is geometrically different from that curve (or surface) in an arbitrarily small neighborhood of the point of contact. The equation of the envelope of a plane family of curves defined by the equation f(x, y, C) = 0, which contains a parameter C, can be obtained by eliminating C from the system of equations

Here it is assumed that f(x, y, C) has continuous partial derivatives of the first order with respect to all three arguments. In general, this elimination yields not only the envelope but also the locus of the singular points of the curves of the family, that is, the points for which f″x and f″y, vanish simultaneously.

Figure 1

The following are examples in the plane. (1) The family of circles of radius R whose centers lie on a line has as an envelope a pair of lines parallel to the line of the centers and located at a distance R from that line (see Figure 1). (2) Any curve is the envelope of the family of its tangents and of the family of its circles of curvature. (3) The envelope of the family of normals to a given curve is its evolute (the evolute of an ellipse is shown in Figure 2).

Figure 2

The envelope of a family of surfaces in space may touch each member of the family at a point or along a curve.

For example, (1) the envelope of a family of spheres of radius R with centers lying on a single line is a circular cylinder of radius R whose axis is that line (the cylinder touches each sphere along a circle); (2) the envelope of a family of spheres of radius R whose centers lie in a single plane is a pair of planes parallel to the plane of the centers and located at a distance R from that plane (the planes forming the envelope touch each sphere in a point).

The concept of an envelope has significance not only in geometry but also in certain problems in mathematical analysis (singular solutions in the theory of differential equations) and theoretical physics (the caustic and the wave front in optics).

REFERENCES

Tolstov, G. P. “K otyskaniiu ogibaiushchei semeistva ploskikh krivykh.” Uspekhi matematicheskikh nauk, 1952, vol. 7, no. 4.
La Vallée Poussin, C. J. de. Kurs analiza beskonechno malykh, vol. 2. Leningrad-Moscow, 1933. (Translated from French.)
Il’in, V. A., and E. G. Pozniak. Osnovy matematicheskogo analiza, 3rd ed., part 1. Moscow, 1971.

envelope

[′en·və‚lōp]
(communications)
A curve drawn to pass through the peaks of a graph, such as that of a moduated radio-frequency carrier signal.
(cell and molecular biology)
The sum of all cell-surface elements that are located outside the plasma membrane.
(engineering)
The glass or metal housing of an electron tube or the glass housing of an incandescent lamp.
(mathematics)
The envelope of a one-parameter family of curves is a curve which has a common tangent with each member of the family.
The envelope of a one-parameter family of surfaces is the surface swept out by the characteristic curves of the family.
(virology)
The outer membranous lipoprotein coat of certain viruses. Also known as bulb.

envelope

1. The imaginary shape of a building indicating its maximum volume; used to check the plan and setback (and similar restrictions) with respect to zoning regulations.
2. The folded-over, continuous edge formed by turning the lowest ply of a built-up roofing membrane over the top surface layer; prevents bitumen from dripping through the exposed edge joints and seepage of water into the insulation.

envelope

(1) A range of frequencies for a particular operation.

(2) A group of bits or items that is packaged and treated as a single unit.

Envelope

(dreams)
Mail or letters usually come in envelopes. When we see envelopes in our dreams, we are typically dreaming about receiving news, information, or messages from someone specific or from the world at large. If you are the individual that looks forward to mail, this dream may be positive. However, if you dread the envelopes that typically hold the monthly bills, then this dream may have negative and anxiety provoking symbolism. Typically, however, dreaming about receiving letters has positive and at times spiritual connotations. You may be coming into awareness about some aspect of your life where you make new realizations and get to the “truth” of things. Some believe that seeing many unopened envelopes in your dreams may represent missed opportunities.
References in periodicals archive ?
To be in with a chance of winning your cash back in the first week of the game, you need to post your Cashback Envelope at your local ASDA store by the evening of Wednesday May 19 OR make sure your Cashback Envelope arrives at the address in Step Two by the morning of Friday May 21.
Many small, inexpensive items can be added to a camp envelope to spark curiosity even before that envelope is opened.
Thus, corporate artwork tends to be smaller and concentrated in the upper left quadrant of the envelope.
Alert marketers take a more logical course: What to do and what not to do on the envelope depends on the Cardinal Rule of Envelope Copy:
Postal Service bar code and print the code in the proper place on the envelope.
The envelope company then brought an action for specific performance of the contract, to compel the owner to close on the property.
Ken Winterhalter, National Envelope president and CEO, said, "As an industry leader in environmentally responsible products, National Envelope is pleased to add "TreeFrog by National" to its full line of eco-friendly, sustainable envelope options.
com features detailed online information regarding the measurements of its business envelope window placements, enabling shoppers to begin printing relevant checks, forms, and invoices in advance, or to order corresponding documents from the company's inventory of customizable forms and checks.
When you bring out the envelope and bird, keep the back of the envelope toward you.
The "Current Issue Enclosed" teaser moved me to open the envelope immediately--only to be disappointed to find that the "current issue" is, in fact, a 16-page promotional magalog.
This paper style looks best with calligraphy and a matching envelope, possibly tied like a package with a raffia bow.

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