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 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 a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.

With this end in view he expounded to the Berlin Academy in 1849 a mode of determining an elliptic orbit from three observations, and communicated to that body in 1851 a new method of calculating planetary perturbations by means of rectangular coordinates ( republished in W. Ostwald's Klassiker der exacten Wissenschaften, No. 141, 1903 ).

With respect to one of the complex variables ( conventionally called z ), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.

With most IIR transfer functions there are related transfer functions having a frequency response with the same magnitude but a different phase ; in most case the so-called minimum phase transfer function is preferred.

With this expression one can, in principle, determine the enthalpy if C < sub > p </ sub > and V are known as functions of p and T.

With most constitutional functions delegated to Cabinet, the governor acts in a primarily ceremonial fashion.

With the White House still under construction, she advised as to its furnishings and sometimes served as First Lady for ceremonial functions for President Thomas Jefferson, a widower and their friend.

With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.

With this operation, the set of all multiplicative functions turns into an abelian group ; the identity element is.

With its four arms attached with a combination of different active agents, for example, iRNA ( for gene silencing ), microRNA ( for gene expression regulation ), aptamer ( for targeting ) and ribozyme ( as catalyst ), the X-shaped RNA can achieve therapeutic and diagnostic functions by regulating gene expression and cellular function, and binding to cancer cells with precision, enhanced by its polyvalent nature and synergistic effects by design.

With time witnesses began to appear in court they were not so treated despite the fact that their functions were akin to that of modern witnesses.

With the corpse propped up on a throne, a deacon was appointed to answer for the deceased pontiff, who was condemned for performing the functions of a bishop when he had been deposed and for receiving the pontificate while he was the bishop of Porto, among other revived charges that had been leveled against Formosus in the strife during the pontificate of John VIII.

With the Quake engine source code now able to be changed, further features were added to QuakeC in the form of new builtin functions.

With the decreasing number of such matters to be addressed as the trust territories attained independence and the decolonization movement progressed, the functions of the Special Political Committee were merged into the Fourth Committee during the 1990s.

With the development of the pentagrid converter, these functions were combined inside a single tube which applied the RF signal to the control grid, but also implemented the local oscillator using additional grids.

With the growing power of the territorial sovereigns and the gradual improvement of the ordinary process of justice, the functions of the Fehmic courts were superseded.

With these functions, however, but with the old forms long since robbed of their impressiveness, they survived into the 19th century.

In version 5. 0, the functionality of VBScript was increased with new features such as: regular expressions ; classes ; the With statement ; the Eval, Execute, and ExecuteGlobal functions to evaluate and execute script commands built during the execution of another script ; a function-pointer system via GetRef, and Distributed COM ( DCOM ) support.

With most constitutional functions lent to Cabinet, the governor general acts in a primarily ceremonial fashion.

With its description of the electron wave functions in molecules as delocalized molecular orbitals that possess the same symmetry as the molecule, Hund and Mulliken's molecular-orbital method, including contributions by John Lennard-Jones, proved to be more flexible and applicable to a vast variety of types of molecules and molecular fragments, and has totally eclipsed the valence-bond method.

With respect to their functions, the PLMNs may be regarded as independent communications entities, even though different PLMNs may be interconnected through the PSTN / ISDN for the forwarding of calls or network information.

With time, its functions as dormitory, kitchen, parlour and so on were divided off to separate rooms or, in the case of the kitchen, a separate building.

The Class of 1979, the last all-male class, went so far as to unofficially label themselves " LCWB ," or " Last Class With Balls " an abbreviation that appeared on many of their class-specific items and still appears at reunions, sporting events and other Academy alumni functions.

With an Army joint base commander and an Air Force deputy joint base commander, the garrison supports the installation through directorates and agencies that provide a full range of city services and quality-of-life functions ; everything from facilities maintenance, recreation and family programs to training support and emergency services.

With the exception of the incorporated Town of Millwood, Washington, the Spokane Valley was developed as townships with no governmental functions.