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Lecture

Linear Combinations: Differenced Observations

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Ghost note

In music, notably in jazz, a ghost note (or a dead, muted, silenced or false note) is a musical note with a rhythmic value, but no discernible pitch when played. In musical notation, this is represented by an "X" for a note head instead of an oval, or parentheses around the note head. It should not be confused with the X-shaped notation () that raises a note to a double sharp. On stringed instruments, this is played by sounding a muted string. "Muted to the point where it is more percussive sounding than obvious and clear in pitch.

Eisenstein integer

In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form where a and b are integers and is a primitive (hence non-real) cube root of unity. The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex plane. The Eisenstein integers are a countably infinite set.

Quadratic integer

In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0 with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as , and the complex number i = , which generates the Gaussian integers.

Epoch

In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by congruity, or by following conventions understood from the epoch in question. The epoch moment or date is usually defined from a specific, clear event of change, an epoch event. In a more gradual change, a deciding moment is chosen when the epoch criterion was reached.

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