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 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 this definition of distance, geodesics in a Riemannian manifold are then the locally distance-minimizing paths, in the above sense.

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 rapid rate of closure, the approach from below, the side, and ahead, there would be only a moment when damage could be done.

With the metal shutters closed, the dining room was so dark that it seemed still night in there.

With colleges and universities carrying a large part of the program, and with students looking toward Peace Corps service, there will be an impact on educational curriculum and student seriousness.

With no set standards, there is the tendency to promote to the next highest level when the top of a salary band is reached regardless of performance.

With the source of light behind the copy, there is no loss of lumen output, as with conventional boards illuminated by means of reflected light.

With the diversity of religious viewpoints, there are differences of opinion as to the essential features of religion ; ;

With capital largely squandered, there seemed to them no other course to pursue.

With the lower dealer inventories and the stepped-up demand some manufacturers believe there could be shortages of some implements.

With this movie-to-be in London, and new faces about her there, she would soon be a more tranquil, a wiser person, all the better for her stay out here.

With the loss of the study of ancient Greek in the early medieval Latin West, Aristotle was practically unknown there from c. AD 600 to c. 1100 except through the Latin translation of the Organon made by Boethius.

With their often complex reproductive needs and permeable skins, amphibians are often ecological indicators and in recent decades there has been a dramatic decline in amphibian populations of many species around the globe.

The last film is not based on any Christie work but displays a few plot elements from They Do It With Mirrors ( viz., the ship is used as a reform school for wayward boys and one of the teachers uses them as a crime force ), and there is a kind of salute to The Mousetrap.

With a recreational abalone licence, there is a bag limit of 10 per day, and a total possession limit of 20.

With this restriction, there are only finitely many Archimedean solids.

With the axiom of dependent choice ( which is a weakened form of the axiom of choice ), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

With modern shooting techniques, there is very little value to shooting with a weapon in each hand.

With his father's death in 1892, and his appointment as head of the Bahá ’ í faith, there was much opposition against him, including virtually all his family members.

With a reserve ratio of 10 %, the bank can create 400 million USD in additional loans ( there is a time lag, and the bank has to expect to recover the loaned money back into its books ).

Bahamian tastes in consumer products roughly parallel those in the U. S. With approximately 85 % of the population of primarily African descent, there is a large and growing market in the Bahamas for " ethnic " personal care products.

With the internationalism of modern architecture and design, there were many exchanges between the Vkhutemas and the Bauhaus.

With the end of the war in 1945, there was a great expectation that the Soviet people would not only see the end of the devastation of Nazism, but also the end of Stalin's Purges.

With the transition from English law, which had common law crimes, to the new legal system under the U. S. Constitution, which prohibited ex post facto laws at both the federal and state level, the question was raised whether there could be common law crimes in the United States.

With an increase in the number of college-educated readers, there was a shift away from slapstick comedy and towards more cerebral humor.

With a key of length n bits, there are 2 < sup > n </ sup > possible keys.

With the rising popularity of the Internet, there is a current vogue in China for coining English transliterations, for example, 粉丝 ／ 粉絲 fěnsī " fans ", 黑客 hēikè " hacker " ( lit.