Here, for the case of squares inscribed in plane curves, we remove the restriction to convexity and give certain other results.

In the first case the fixed elements within each pencil are the multiple secant and the line joining the vertex, P, to the intersection of **zg and the plane of the pencil which does not lie on the multiple secant.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

In at least one case, a plane was hijacked by the official pilot.

# International common strike in case of the impunity of the hijackers or in case of not letting the crew of the hijacked plane out within 48 hours ;

This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 0 specifies only the single point ( 0, 0 ).

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

Centrifugal force arises in the analysis of orbital motion and, more generally, of motion in a central-force field: in the case of a two-body problem, it is easy to convert to an equivalent one-body problem with force directed to or from an origin, and motion in a plane, so we consider only that.

In such a case, the adjacent planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side.

Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex ; the other two ( open and unbounded ) cases are parabolas and hyperbolas.

Rectangular coordinates in the plane can be used intuitively with respect to one's current location, in which case the axis will point to the local North.

In case of plane or spatial coordinates, we typically need several datum points.

In the case of plane geometry ( valid for small areas on the Earth's surface ) the solutions to both problems reduce to simple trigonometry.

This corresponds to the area of the plane covered by the polygon, or to the area of a simple polygon having the same outline as the self-intersecting one ( or, in the case of the cross-quadrilateral, the two simple triangles ).

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

An empty flight case apparently belonging to Clemente was the only personal item recovered from the plane.

The plane of the Moon's orbit around the Earth lies close to the plane of the Earth's orbit around the Sun ( the ecliptic ), rather than in the plane perpendicular to the axis of rotation of the Earth ( the equator ) as is usually the case with planetary satellites.

The Euclidean TSP is a particular case of the metric TSP, since distances in a plane obey the triangle inequality.

In this case, the polarization along one plane is intrinsically tied to the polarization along the other, and by Heisenberg ’ s principle, there is a limit to the certainty with which both states can be known.

In the case of the single-moded plane wave, is a uniform distribution.

This circumstance in the patient's case plus the fact that his tactual capacity remained basically in sound working order constitutes its exceptional value for the problem at hand since the evidence presented by the authors is overwhelming that, when the patient closed his eyes, he had absolutely no spatial ( that is, third-dimensional ) awareness whatsoever.

In this case the description of motion is made in terms of the spatial coordinates, in which case is called the spatial description or Eulerian description, i. e. the current configuration is taken as the reference configuration.

In the case of particles like electrons, neutrons and atoms, the coherence length is related to the spatial extent of the wave function that describes the particle.

Although some spatial indices can have issues as regards to routing load-balance in case of a skewed data set, all the spatial indices are more scalable in terms of the number of hops traversed and messages generated while searching and routing Grid resource queries.

The " solution " to higher sampling in the spatial domain for this case would be to move closer to the shirt, use a higher resolution sensor, or to optically blur the image before acquiring it with the sensor.

The spatial continuity of the random variables is described by a model of spatial continuity that can be either a parametric function in the case of variogram-based geostatistics, or have a non-parametric form when using other methods such as multiple-point simulation or pseudo-genetic techniques.

Notice in the case of one spatial dimension, for one particle, the partial derivative reduces to an ordinary derivative.

Sequential locality, a special case of spatial locality, occurs when data elements are arranged and accessed linearly, e. g., traversing the elements in a one-dimensional array.

Temporal locality is a very special case of the spatial locality, namely when the prospective location is identical to the present location.

Sequential locality, a special case of spatial locality, occurs when relevant data elements are arranged and accessed linearly.

The latter possibility finds an application in the theory of special relativity in the simplified case where there are two spatial dimensions and one time dimension.

For now, consider the simple case of a single particle, without spin, in one spatial dimension.

But objective semblance corresponds with reality ; the spatial or external relations of the reals in this case must, therefore, tally with their inner or actual states.

In this case, inter-layer prediction ( i. e., the prediction of the higher spatial resolution / quality signal from the data of the lower spatial resolution / quality signal ) is typically used for efficient coding.

** A secondary Hadamard transform performed on " DC " coefficients of the primary spatial transform applied to chroma DC coefficients ( and also luma in one special case ) to obtain even more compression in smooth regions.

Hence, the spatial distribution of landforms is often scale-dependent as is the case for soils and geological strata.

Tests can be as simple as dipping a manufactured test strip, as in the case of pH testing, or be more complex, as in the case one study examining the spatial and temporal variation of heavy metal contamination due to industrial runoff.

The coordinates of the vector are equal to the projections of the vector ( yellow ) onto the x-component basis vector ( green )-using the dot product ( a special case of an inner product, see below ).

As in the continuous case, the change of coordinates x → x + ( 1 − A )< sup > – 1 </ sup > b removes the term b from the equation.

The field is defined by p in the prime case and the pair of m and f An additional speed-up is possible if mixed coordinates are used.

In algebraic geometry, the parabola is generalized by the rational normal curves, which have coordinates the standard parabola is the case and the case is known as the twisted cubic.

If you change units ( a special case of a change of coordinates ) from meters to milimeters, a scale factor of 1 / 1000, a displacement of 1 m becomes 1000 mm – a contravariant change in numerical value.

So, in this common case, the Miller indices ( ℓmn ) and both simply denote normals / directions in Cartesian coordinates.

In this case, the column space is precisely the set of vectors ( x, y, z ) ∈ R < sup > 3 </ sup > satisfying the equation z = 2x ( using Cartesian coordinates, this set is a plane through the origin in three-dimensional space ).

In the case of a real affine space, in other words when the coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities

This statement must be qualified in several important ways, by considering points at infinity, allowing complex coordinates ( or more generally, coordinates from the algebraic closure of the ground field ), assigning an appropriate multiplicity to each intersection point, and excluding a degenerate case when X and Y have a common component.

The concept of an absolute velocity, including being " at rest " as a particular case, is ruled out by the principle of relativity, also eliminating any obvious " center " of the universe as a natural origin of coordinates.

For multi-loop integrals that will depend on several variables we can make a change of variables to polar coordinates and then replace the integral over the angles by a sum so we have only a divergent integral, that will depend on the modulus and then we can apply the zeta regularization algorithm, the main idea for multi-loop integrals is to replace the factor after a change to hyperspherical coordinates so the UV overlapping divergences are encoded in variable r. In order to regularize these integrals one needs a regulator, for the case of multi-loop integrals, these regulator can be taken as so the multi-loop integral will converge for big enough's ' using the Zeta regularization we can analytic continue the variable's ' to the physical limit where s = 0 and then regularize any UV integral.

In the simple case of a nonrelativistic particle moving in Euclidean space under a force field with coordinates and momenta, Liouville's theorem can be written

In the case of the conical intersection, the adiabatic parameters are the molecular coordinates.

Shell integration can be considered a special case of evaluating a double integral in polar coordinates.

In the active transformation ( left ), point P moves relative to the coordinate frame to location P ', while the coordinate frame remains unchanged ( in this case, the position of P has rotated clockwise by angle θ ), while in a passive transformation ( right ), point P is observed in two different coordinate frames ( pictured rotated relative to one another by angle θ ) The coordinates of P ' in the active case are the same as the coordinates of P in the rotated frame in the passive case if the rotation of P is clockwise and the rotation of the axes is counterclockwise.