If substance is the highest category and there is no substance, being, then the unity perceived in all beings by virtue of their existing must be viewed in another way.

If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.

If a and b are coprime and a divides the product bc, then a divides c. This can be viewed as a generalization of Euclid's lemma.

If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.

If the example with the colored bricks above is viewed as an unbounded knapsack problem, then the solution is to take three yellow boxes and three grey boxes.

Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.

If Mary says she has no pair, but in fact she has a flush, her cards speak and her hand is viewed for its genuine value, that of a flush.

If viewed from a distance of 1 astronomical unit, it would span an angular diameter of 35 ° and shine at magnitude − 38.

If the file is stored on a server for on-demand streaming and this stream is viewed by 1, 000 people at the same time using a Unicast protocol, the requirement is:

If the Americas are viewed as a single continent ( named America ), then it is composed of the subcontinents of North America and South America, the land bridge of Central America, and the islands of the Antillas.

If, on the way to the shrine, these children cried their tears were viewed as signs of imminent and abundant rains.

* If is a topological space ( viewed as a category as above ) and is some small category, we can form the category of all contravariant functors from to, using natural transformations as morphisms.

( If inversion on the unit group is continuous in the subspace topology of R then the topology on the unit group viewed in R or in R × R as above are the same.

If he hoped for such a marriage as a route to power, he was unsuccessful, though his secret marriage to Katherine Parr, Elizabeth's guardian, in late April 1547 was viewed by some as an attempt to become close to the young princess.

If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space ( 1 axis per variable ), PCA can supply the user with a lower-dimensional picture, a " shadow " of this object when viewed from its ( in some sense ) most informative viewpoint.

When Smith viewed the edition, she asked her mother, " If people are so afraid of him, why doesn't someone write a letter asking whether he wants to have a war or not ?".

If the world is reflected in a mirror which switches the left and right side of the car, the " reflection " of this angular momentum " vector " ( viewed as an ordinary vector ) points to the right, but the actual angular momentum vector of the wheel still points to the left, corresponding to the extra minus sign in the reflection of a pseudovector.

If the magnitude of v < sub > 3 </ sub > were to describe a measurable physical quantity, that would mean that the laws of physics would not appear the same if the universe was viewed in a mirror.

If the final image is viewed at approximately

If the original image will be given greater enlargement, or viewed at

If an image is viewed on a low-resolution display medium such as a computer monitor,

If the image is to be viewed only on a low-resolution device, a larger CoC may be appropriate ;

If both input and output are real numbers, this ordered pair can be viewed as the Cartesian coordinates of a point on the graph of the function.

If she did, he could stand it better in the light.

If the input light distribution falls beyond the visible range, Af as expected, since Af.

If it pleases symphony audiences as a light, jolly piece, a series of impressions musically expressed, it succeeds.

If light moves instantaneously, the telescope does not move, and the true direction of the star relative to the observer can be found by following the line ES.

If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.

If appropriate proportions of three primary pigments are mixed, the result reflects so little light as to be called " black ".

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12. 6 lumens.

If it is removed, the light ceases.

If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards ( i. e. the silver sides trail ).

If light pressure were the cause of the rotation, then the better the vacuum in the bulb, the less air resistance to movement, and the faster the vanes should spin.

If the incident light is monochromatic, these sources all have the same phase.

If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit.

If the width of the slits is small enough ( less than the wavelength of the laser light ), the slits diffract the light into cylindrical waves.

If the width of the slits is greater than the wavelength, the Fraunhofer diffraction equation gives the intensity of the diffracted light as:

If a ray tracing is then made as if a light wave ( as understood in classical physics ) is wide enough to take both paths, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually " paint " the expected interference pattern.

If the emulsion is dilute enough, higher-frequency and low-wavelength light will be scattered more, and the emulsion will appear bluer-this is called the " Tyndall effect ".

If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the light spectrum.

If the incident light is unpolarised ( containing an equal mix of s-and p-polarisations ), the reflection coefficient is

If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than c. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does the light travel from the source to the object faster than c, nor does any information travel faster than light.

If Lorentz symmetry can cease to be a fundamental symmetry at Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.