A limit of the diagram F: J → C is a cone ( L, φ ) to F such that for any other cone ( N, ψ ) to F there exists a unique morphism u: N → L such that φ < sub > X </ sub > o u =

One says that the cone ( N, ψ ) factors through the cone ( L, φ ) with

A functor G lifts limits uniquely for a diagram F if there is a unique preimage cone ( L ′, φ ′) such that ( L ′, φ ′) is a limit of F and G ( L ′, φ ′) =

* create limits for F if whenever ( L, φ ) is a limit of GF there exists a unique cone ( L ′, φ ′) to F such that G ( L ′, φ ′)

Formally, in Euclidean space, the wave front set of ƒ is defined as the complement of the set of all pairs ( x < sub > 0 </ sub >, v ) such that there exists a test function with φ ( x < sub > 0 </ sub >) ≠ 0 and an open cone Γ containing v such that the estimate

More precisely, a direction v is in the complement of if there is a compactly supported smooth function φ with φ ( x ) ≠ 0 and an open cone Γ containing v such that the following estimate holds for each positive integer N:

Image: Water tower cropped. jpg | The water tower consists of a cone, a cylinder, and a hemisphere.

A double cone consists of two cones stacked point-to-point and sharing the same axis of rotation ; it may be generated by rotating a line about an axis that passes through a point of the line.

The system consists of a circular annulus in the condenser, which produces a cone of light.

The mountain consists of four overlapping volcanic cones which have built a complex shape, including the main summit and the prominent satellite cone of Shastina, which has a visibly conical form.

Preparation consists of a cone – lined with a coffee filter and filled with ground coffee – sitting atop a coffee cup.

The human eye's detection system in the retina consists primarily of two types of light detectors, rod cells that capture light, dark, and shapes / figures, and the cone cells that detect color.

The semiwadcutter consists of a conical section that comes to a smaller flat, and a thin sharp shoulder at the base of the cone.

Today's modern lining is the most difficult element to measure, since it consists of trapezoid-shaped strips of canvas assembled to form the shape of a truncated cone.

Instead of the woody cone typical of most gymnosperms, the reproductive structure of the yew consists of a single seed that becomes surrounded by a fleshy, cup-like covering.

The test method consists of pushing an instrumented cone, with the tip facing down, into the ground at a controlled rate ( controlled between 1. 5-2. 5 cm / s accepted ).

Bailey consists of a high main cone on top of an old basaltic andesite shield volcano.

A cone valve consists of a shallowly-tapering cone in a tight-fitting socket placed across the flow of the fluid.

A typical Drumstick-brand ice cream cone consists of a waffle cone filled with ice cream topped with a hardened chocolate shell and nuts, and much later, with a chocolate lined cone, a chunk of chocolate at the bottom of the cone.

The caplock mechanism consists of a hammer, similar to the hammer used in a flintlock, and a nipple ( sometimes referred to as a " cone "), which holds a small percussion cap.

For this reason, a modern dog clutch in an automobile has a synchronizer mechanism or synchromesh, which consists of a cone clutch and blocking ring.

The loudspeaker is a cheap home-made variety that consists of a crystal earpiece attached to a cone made from a foam cup or sections of packing material.

According to a an article about the variations in Akha headdress entitled " High Fashion, Hill Style ", the " Ulo Akha headdress consists of a bamboo cone, covered in beads, silver studs and seeds, edged in coins ( silver rupees for the rich, bath for the poor ) topped by several dangling chicken feather tassels and maybe a woolen pom-pom.

The fuel tank, also a welded structure, consists of a forward dome, tank barrel an aft cone, and internal conduit.

The summit consists of a flat grassy top marked only by a small cairn ( artificial cone of stones ).

This apparatus consists of a container, a specially-configured cone and a dial indicator.

* Cone ( category theory ), a family of morphisms resembling a geometric cone

Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ < sub > X </ sub >: N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ < sub > X </ sub >

The limiting cone is given by the family of maps π < sub > X </ sub >: Cone ( N, F ) → Hom ( N, FX ) where π < sub > X </ sub >( ψ ) = ψ < sub > X </ sub >.

Pineapple ( Ananas comosus ), a tropical plant with edible multiple fruit consisting of coalesced berries, named for resemblance to the pine cone, is the most economically important plant in the Bromeliaceae family.

Cedars share a very similar cone structure with the firs ( Abies ) and were traditionally thought to be most closely related to them, but molecular evidence supports a basal position in the family.

Analysis of Pinaceae cones reveals how selective pressure has shaped the evolution of variable cone size and function throughout the family.

Variation in cone size in the family has likely resulted from the variation of seed dispersal mechanisms available in the environment over time.

A more recent classification divided the subfamilies and genera based on the consideration of features of ovulate cone anatomy among extant and fossil members of the family.

The botanical term galbulus ( plural galbuli ; from the Latin for a cypress cone ) is sometimes used instead of strobilus for members of this family.

The phosphodiesterase ( PDE ) isozymes, found in several tissues including the rod and cone photoreceptor cells of the retina, belong to a large family of cyclic nucleotide PDEs that catalyze cAMP and cGMP hydrolysis.

It has a single central stem up to 5 cm tall bearing a spore-producing cone at the apex, and was previously classified variously in the family Lycopodiaceae or in its own family the Phylloglossaceae, but recent genetic evidence demonstrates it is most closely related to the genus Huperzia and is a sister clade to the genus Phlegmariurus, which was formerly included in Huperzia.

Since cone dystrophy is hereditary and can be asymptomatic early on in the disease process, ERG is an invaluable tool in the early diagnosis of patients with positive family histories.

Given a diagram F: J → C ( thought of as an object in C < sup > J </ sup >), a natural transformation ψ: Δ ( N ) → F ( which is just a morphism in the category C < sup > J </ sup >) is the same thing as a cone from N to F. The components of ψ are the morphisms ψ < sub > X </ sub >: N → F ( X ).

If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by

If one is given an object L of C together with a natural isomorphism Φ: Hom (–, L ) → Cone (–, F ), the object L will be a limit of F with the limiting cone given by Φ < sub > L </ sub >( id < sub > L </ sub >).

The half-angle of this cone is called the acceptance angle, θ < sub > max </ sub >.

* S < sub > d </ sub > to the cone area of the sub woofer ( in m < sup > 2 </ sup >).

These ions are removed by injecting a collisional gas ( He ), or a reactive gas ( H < sub > 2 </ sub >), or a mixture of the two, directly into the plasma as it flows through the skimmer cone and / or the sampler cone.

Since cores are often struck on an edge with a suitable angle ( x < 90 °) for flake propagation, the result is that only a portion of the Hertzian cone is created.

The set of elements 0 ≤ x is often denoted with G < sup >+</ sup >, and it is called the positive cone of G. So we have a ≤ b if and only if-a + b ∈ G < sup >+</ sup >.

For the general group G, the existence of a positive cone specifies an order on G. A group G is a partially ordered group if and only if there exists a subset H ( which is G < sup >+</ sup >) of G such that:

A partially ordered group G with positive cone G < sup >+</ sup > is said to be unperforated if n · g ∈ G < sup >+</ sup > for some natural number n implies g ∈ G < sup >+</ sup >.