Bohr showed that quasiperiodic functions arise as restrictions of high-dimensional periodic functions to an irrational slice ( an intersection with one or more hyperplanes ), and discussed their Fourier point spectrum.

: is the intersection of the ecliptic of " date " ( that is, the ecliptic in its position at " date ") with the mean equator ( that is, the equator rotated by precession to its position at " date ", but free from the small periodic oscillations of nutation ).

The intersection of the disk with the given periodic orbit comes back to itself every period of the orbit and so do points in its neighborhood.

In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to the flow of the system.

From its northern terminus in Maryland headed south, the range is composed mainly of a single north-south running ridge with periodic low-lying gaps, though it does contain several spur ridges, most notably near its intersection with South Mountain at its northern terminus.

Although an eclipse can only occur when the Moon is either new or full, it must also be positioned very near the intersection of Earth's orbit plane about the Sun and the Moon's orbit plane about the Earth ( that is, at one of its nodes ).

Since the ascending node is the point of intersection between the ecliptic and the plane of the lunar orbit where the Moon is ascending from the South to the North, it is sometimes called the North node.

Each point with abscissa T on the graph represents an intersection between C and Af.

In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line.

Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection ; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

# Yoga of the Grothendieck – Riemann – Roch theorem ( K-theory, relation with intersection theory ).

At the intersection with 72nd street, the triangle of tiny Verdi Square is surrounded by several notable apartment buildings, including The Ansonia, and the Florentine palazzo occupied by Apple Bank for Savings.

At its intersection with 78th Street, Broadway shifts direction, to continue directly uptown aligned approximately with the Commissioners ' grid.

The intersection with Saint Nicholas Avenue at 167th Street forms Mitchell Square Park.

Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties.

The northern rail line out of Santiago is now disused past the intersection with the Valparaíso line.

At the intersection between community development and community building are a number of programs and organizations with community development tools.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Gauss's method involved determining a conic section in space, given one focus ( the Sun ) and the conic's intersection with three given lines ( lines of sight from the Earth, which is itself moving on an ellipse, to the planet ) and given the time it takes the planet to traverse the arcs determined by these lines ( from which the lengths of the arcs can be calculated by Kepler's Second Law ).

In a final, production quality rendering of a ray traced work, multiple rays are generally shot for each pixel, and traced not just to the first object of intersection, but rather, through a number of sequential ' bounces ', using the known laws of optics such as " angle of incidence equals angle of reflection " and more advanced laws that deal with refraction and surface roughness.

A metric space X is complete if and only if every decreasing sequence of non-empty closed subsets of X, with diameters tending to 0, has a non-empty intersection: if F < sub > n </ sub > is closed and non-empty, for every n, and diam ( F < sub > n </ sub >) → 0, then there is a point x ∈ X common to all sets F < sub > n </ sub >.

The remaining western border runs slightly east of due south from its intersection with the arc.

Receivers identified which hyperbola they were on and a position could be plotted at the intersection of the hyperbola from different patterns, usually by using the pair with the angle of cut closest to orthogonal as possible.

An ellipse obtained as the intersection of a cone ( geometry ) | cone with an inclined plane.

Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry.

Because the orbital plane of the Moon is tilted with respect to the orbital plane of the Earth ( the ecliptic ), eclipses can occur only when the Moon is close to the intersection of these two planes ( the nodes ).

This continues until an intersection is found ( with three or more open boundary pixels ).

In algebraic topology, the intersection number appears as the Poincaré dual of the cup product.

Specifically, if two manifolds, X and Y, intersect transversely in a manifold M, the homology class of the intersection is the Poincaré dual of the cup product of the Poincaré duals of X and Y.

In his 1895 paper Analysis Situs, Poincaré tried to prove the theorem using topological intersection theory, which he had invented.

Verdier duality is the appropriate generalization to ( possibly singular ) geometric objects, such as analytic spaces or schemes, while intersection homology was developed R. MacPherson and M. Goresky for stratified spaces, such as real or complex algebraic varieties, precisely so as to generalise Poincaré duality to such stratified spaces.

For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold.

Classically — going back, for instance, to Henri Poincaré — this duality was understood in terms of intersection theory.

This product is dual to the cup product, i. e. the homology class of the intersection of two submanifolds is the Poincaré dual of the cup product of their Poincaré duals.

Geometrically, in singular cohomology of a manifold, one can interpret the product dually in terms of bounding manifolds and intersections, following Poincaré duality: dual to cocycles are cycles, often representable as closed manifolds ( without boundary ), dual to product is intersection, and dual to the subtraction of the bounding products is gluing the two bounding manifolds together along the boundary, obtaining a closed manifold which represents the homology class dual of the Massey product.

The hyperbola is one of the four kinds of conic section, formed by the intersection of a plane and a cone.

The lines traced out by orbits dominated by the gravity of a central source are conic section s: the shapes of the curves of intersection between a plane and a cone.

In mathematics, a parabola (; plural parabolae or parabolas, from the Greek παραβολή ) is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.

If the planes don't pass through the sphere's center, then the intersection is called spheric section.

The intersection of a plane containing the normal with the surface will form a curve called a normal section and the curvature of this curve is the normal curvature.

The first section of Route 7 begins at an intersection with U. S. Route 1-9 Truck and County Route 645 ( Charlotte Avenue ) in Jersey City, Hudson County, heading to the west on a four-lane highway that is signed east – west.

Past this intersection, County Route 507 splits from Route 7 by heading north on River Road, County Route 699 heads to the south on Passaic Avenue, and Route 7 continues west, crossing the Passaic River on a lift bridge, known as the Bellrville Turnpike Bridge or Rutgers Street Bridge, into Belleville, Essex County, where the first section of Route 7 ends at an intersection with Route 21.

This complex of racetracks and entertainment venues is planned to be on nearly of land near the intersection of Industrial Parkway ( Alabama State Route 158 ) and US Highway 45 in the northern section of Prichard.

Route 50 northbound at Cape May CR 610 in Upper Township, New Jersey | Upper TownshipRoute 50 begins at an intersection with US 9 in the Seaville section of Upper Township, Cape May County, heading to the north on a two-lane undivided road.

Route 55 begins at a signalized intersection with Route 47 in the Port Elizabeth section of Maurice River Township, Cumberland County, heading to the north as a two-lane undivided road through wooded areas.

* The center of North Coventry is at the intersection of Main Street ( CT Route 31 ) and U. S. Route 44 ( section officially known as the Boston Turnpike, but usually referred to simply as " Route 44 ").

In one section of the new resurvey Sulivane changed the course of the road that constitutes the southern portion of the main street from its current intersection ( Md.

Principal numbered state highways traveling within Quincy include: Route 3A south to north from Weymouth via Washington Street, Southern Artery, Merrymount Parkway and Hancock Street to the Neponset River Bridge and the Dorchester section of Boston ; Route 28, which travels south to north from Randolph to Milton along Randolph Avenue in Quincy through a remote section of the Blue Hills Reservation ; and Route 53, which enters traveling south to north from Braintree as Quincy Avenue, turning right to form the beginning of Southern Artery in Quincy Point before ending at the intersection with Washington Street / Route 3A.

While at the southeast corner, exit 326 to Levering Road ( C-66 ) lies almost exactly on the boundary with Munro Township, with half of the intersection in section 36 of Hebron and the other half in section 1 of Munro.

After the death of postmaster Chauncey D. Walcott in 1865, the office moved to the township line in the northeast quarter of section 4 ( near the intersection of 14 Mile Road and Farmington Road ).

Solomon Whitaker, Charles and Joseph Pulcifer located in the area in 1830, and in 1833, Jenks Pullen and his six sons settled at what became known as " Pullen's Corners " ( located in section 19 at the intersection that is now commonly called " Five Points ").

The oldest developed section of Plainsboro is at the intersection of Dey and Plainsboro Roads.

The opening of the exit and redesign of the interchange fueled growth of the Barnegat section starting in the 2010s, with the opening of a CVS Pharmacy and Wawa, as well as a major shopping center under construction at the intersection.

* Long Lake – The hamlet of Long Lake, near the intersection of Routes NY-28N and NY-30 and near the middle section of the lake also called Long Lake.

The Swetland Shaft was located on the northwest corner of the intersection of Vine and State streets in the Poke Hollow section of what is now Larksville Borough.