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 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 J. J. Thomson's discovery of the electron in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles.

With the discovery of oil in the later half of the 19th century, even oil stocks entered into the curb market.

With the discovery of the Dead Sea scroll, 4QDan < sup > c </ sup > at Qumran, dating 125 BCE, it does not reassure critics that Daniel was written in the 2nd century BCE.

With modern biotechnology, these genes can be used as targets for the development of effective new therapies, which could significantly shorten the drug discovery process.

With the development of modern microscopes in the 20th century, the discovery was confirmed.

With the discovery of the Orcutt and Lompoc fields, northern Santa Barbara County became a regional center of production ; towns such as Orcutt owe their existence to the quickly growing industry.

With these techniques, he was able to discover the bacterium causing tuberculosis ( Mycobacterium tuberculosis ) in 1882 ( he announced the discovery on 24 March ).

With the continual discovery of " new " Medieval and Renaissance fighting manuals, the practice of Historical European Martial Arts and other Western Martial Arts are growing in popularity across the United States and Europe.

With the discovery of the Mani-Codex, it also became clear that he was raised in a Jewish-Christian baptism sect, the Elcesaites, and was influenced by their writings as well.

With this discovery, came the realization that movement of ice sheets might act to concentrate meteorites in certain areas.

With this discovery, they realized an entire class of gases was missing from the periodic table.

With the discovery of the neutron, scientists at last could calculate what fraction of binding energy each nucleus had, from comparing the nuclear mass with that of the protons and neutrons which composed it.

With the discovery of plate tectonics, it became apparent that land masses move relative to one another over time.

With the discovery of the New World came new spices, including allspice, bell and chili peppers, vanilla, and chocolate.

With the advent of Z39. 50: 1992, the termination of support for the free WAIS from Thinking Machines and the establishment of WAIS Inc as a commercial venture, the U. S. National Science Foundation funded CNIDR to create a clearinghouse of information related to Internet search and discovery systems and to promote open source and standards.

With the 1886 discovery of gold in the Transvaal, the resulting gold rush brought thousands of British and other prospectors and settlers from across the globe and over the border from the Cape Colony ( under British control since 1806 ).

With respect to celestial X-ray sources, X-ray astrophysics tends to focus on the physical reason for X-ray brightness, whereas X-ray astronomy tends to focus on their classification, order of discovery, variability, resolvability, and their relationship with nearby sources in other constellations.

With rigorous external reviews ensuring that only the most innovative research secures funding, the IRP is responsible for many scientific accomplishments, including the discovery of fluoride to prevent tooth decay, the use of lithium to manage bipolar disorder, and the creation of vaccines against hepatitis, Haemophilus influenzae ( HIB ), and human papillomavirus.

With all the important work he accomplished in physics – the enunciation of Boyle's law, the discovery of the part taken by air in the propagation of sound, and investigations on the expansive force of freezing water, on specific gravities and refractive powers, on crystals, on electricity, on colour, on hydrostatics, etc.

With discovery of new lands to the west ( which they thought at the time to be East Asia ), the poor young men were attracted to whispers of glory and wealth.

With reference to science and academic disciplines, discovery is the observation of new phenomena, new actions, or new events and providing new reasoning to explain the knowledge gathered through such observations with previously acquired knowledge from abstract thought and everyday experiences.

With the 1928 discovery of oil within the city limits ( including under the State Capitol ), it became a center of oil production.

" With what Freud called the " disagreeable discovery that on the one hand ( super -) ego and conscious and on the other hand repressed and unconscious are far from coinciding ," Freud took the step in the structural model to " no longer use the term ' unconscious ' in the systematic sense ," and to rename " the mental region that is foreign to the ego ... in future call it the ' id '.

With the discovery of bituminous coal deposits at the end of the 18th century by a local church priest, new industrial sectors developed in the Chorzów area.

With the discovery of gold, the area quickly became a mecca for those trying to make their fortune.