With this definition, it is necessary to consider the direction of p ( pointed clockwise or counter-clockwise ) to figure out the sign of L. Equivalently:

" With the latter definition, Confucianism is religious, even if non-theistic, in the sense that it " performs some of the basic psycho-social functions of full-fledged religions ", in the same way that non-theistic ideologies like Communism do.

With digital terrestrial television ( DTV ) broadcasting, the range of formats can be broadly divided into two categories: high definition television ( HDTV ) for the transmission of high-definition video and standard-definition television ( SDTV ).

With second wave feminism and growth of scholarship in women's history and sexuality in the 20th century, the definition of lesbian broadened, sparking a debate about sexual desire as the major component to define what a lesbian is.

With this definition there are 5 regular compounds.

With the above definition in each step always a single symbol ( top of the stack ) is popped, replacing it with as many symbols as necessary.

With the development of the atomic clock in the early 1960s, it was decided to use atomic time as the basis of the definition of the second, rather than the revolution of the Earth around the Sun.

With the generalization of the definition, this naming system is no longer strictly adhered to.

With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces ; they may also be generalized further, to oriented matroids.

With this definition, it is possible to have a SINAD level less than one.

With respect to investment schemes that do not fall within the traditional categories of securities listed in the definition of a security ( Sec.

" With this definition, wisdom can supposedly be measured using the following criteria.

With the requirement of consent, the fourth type of interpretation above would usually not fall under the definition of " victimless crime ".

With the different types of wordplay and definition possibilities, the composer of a cryptic puzzle is presented with many different possible ways to clue a given answer.

With the definition of elliptic functions given above ( which is due to Weierstrass ) the Weierstrass elliptic function is constructed in the most obvious way: given a lattice as above, put

" With fewer than three murders attributed to him, Gein does not meet the traditional definition of a serial killer.

With no clear definition of the type, and few early illustrations or detailed descriptions to go by, the early history of the dory is muddled at best.

With the former definition, an " open universe " may either be an open manifold, i. e. one that is not compact and without boundary, or a closed manifold, while a " closed universe " is necessarily a closed manifold.

With the first equality by the definition of pdf for multiple variables, the second by the remark above, the third by hypothesis, and the fourth because the summation is not over.

With the first equality by definition of conditional probability density, the second by the remark above, the third by the equality proven above, and the fourth by simplification.

With this definition of length, every connected Riemannian manifold M becomes a metric space ( and even a length metric space ) in a natural fashion: the distance d ( x, y ) between the points x and y of M is defined as

With the integration of Jews from around the world in Israel, North America, and other places, the religious definition of an Ashkenazi Jew is blurring, especially outside Orthodox Judaism.

With a definition of effective calculation came the first proofs that there are problems in mathematics that cannot be effectively decided.

The base A0 size of paper is defined to have an area of 1 m. With this definition and the given aspect ratio of square root of two, one can calculate the sides of an A0 sheet as follows: The long side is 1 metre multiplied by the square root of the square root ( that is, the fourth root ) of 2 and the short side is 1 metre divided by the same.

With the Lombard invasion of Italy it was annexed to the Duchy of Benevento, until it was finally destroyed by the Byzantines of Constans II in 663, reducing to a small hamlet known as Quintodecimo ( referring to its distance of 15 miles from Benevento ).

With this work under his belt, Bessel was able to achieve the feat for which he is best remembered today: he is credited with being the first to use parallax in calculating the distance to a star.

With an apparent brightness of 0. 03m, this is the second brightest star of the northern hemisphere ( after Arcturus ) and the fifth brightest star in all ; its spectral class is A0 V and it lies at a distance of only 25. 3 ly.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

With this distance, the set of n-node binary trees becomes a metric space: the distance is symmetric, positive when given two different trees, and satisfies the triangle inequality.

With the addition of a new bullpen in right field of Fenway Park, which reduced the distance from home plate from 400 feet to 380 feet, the bullpen was nicknamed " Williamsburg ", because the new addition was " obviously designed for Williams ".

With the German rulers at a distance, Avignon set up as a republic with a consular form of government, between 1135 and 1146.

With respect to one another, their relative refractive indices are, in order of distance from the core: lowest, highest, lower, higher.

With long distance rates at historic lows, using regular business lines, OUTWATS service became obsolete late in the 20th century.

With the catapult launch, the plane successfully traveled the distance outlined by the competition, but was declined the prize due to the takeoff method.

With a fixed spool, spin cast reels can cast lighter lures than bait cast reels, although friction of the nose cone against the unspooling line slightly reduces casting distance compared to spinning reels.

With maglev a vehicle is levitated a short distance away from a guideway using magnets to create both lift and thrust.

With a total distance of around 1, 850 km ( 1, 150 mi ) it is the longest historic stock route in the world.

With the triangulation method, distances, elevations and directions between objects at great distance from one another can be determined.

With repeaters in the fiber optic cable the distance from the telephone exchange can be extended much farther.

With a course that covers a distance of 829 km, it is the fourth-longest in the Iberian peninsula, and its hydrological basin extends into an area of approximately 68, 000 km² ( the majority of which lies within Spain ).

With an area of 112, 622 square kilometers, roughly the size of Pennsylvania and slightly bigger than Bulgaria, Benin extends from the Niger River in the north to the Atlantic Ocean in the south, a distance of.

With the exception of the longer, distance contests, Quarter Horse races are run flat out, with the horses running at top speed for the duration.

With the typical 5 mil scale ( each mark is 5 mil ), a lighthouse that is 3 marks high that is known to be 120 meters tall is 8000 meters distance.

With his University of Kansas teammates he also anchored a world record in the sprint medley relay ( 3: 15. 2 ) and twice in the distance medley relay ( 9: 33. 8 at the Drake Relays in 1967 and then 9: 33. 0 at the Kansas Relays in 1969, Ryan's 3: 57. 6 anchor leg for the mile being his last collegiate race on his home track ).