Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, we might provide limited assistance in such fields as education, essential transport, communications, and agricultural improvement despite the absence of acceptable country programs.

Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus the Ittō-ryū ( Single sword school ) indicates the founder's illumination that all possible cuts with the sword emanate from and are contained in one original essential cut.

Thus, it is essential that partners in PGP communication understand each other's capabilities or at least agree on PGP settings.

Thus, when essential sacred mysteries and teachings are described as myth, in modern English, the word often still implies that it is " idle fancy, fiction, or falsehood ".

Thus for analyzing historical or criminal economic activities, or even professional sports, the instructional capital vs. individual capital vs. social capital distinction is essential.

Thus, whether the symmetry of the pairing wave function is the d symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation.

Thus, the essential first step in any successful assertion of Southern rights had to be the jettisoning of all party ties.

Thus, these programs encouraged the development of alternative sources of supply of these essential materials.

Thus, it is essential to engrave this business of the warrior into one's mind well.

Thus the confinement of PS in the inner monolayer is essential if the cell is to survive its frequent encounters with macrophages of the reticuloendothelial system, especially in the spleen.

Thus, the essential description of a component actually comprises only in-and output that are described fully in terms of data types and their meaning ( semantics ).

Thus a consensus definition of what constitutes the presence of a phenotype is essential for determining the penetrance of an allele.

Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the 30 km / s speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane — tasks that are impossible with current spacecraft propulsion systems alone, making gravity assist maneuvers essential.

Thus, plural marriage is viewed as an essential and fundamental part of the religion.

Thus, out of the depths rises unvanquished the essential idealism of Renan.

Thus, unlike standard versions of functionalism ( often called Functional State Identity Theories ), FSTs do not allow for the multiple realizability of mental states, because the fact that mental states are realized by brain states is essential.

Thus a word such as gowhar which could mean both " essence, truth " and " pearl " would take on both meanings at once as in a phrase such as " a pearl / essential truth which was outside the shell of superficial existence ".

Thus concurrency control is an essential element for correctness in any system where two database transactions or more, executed with time overlap, can access the same data, e. g., virtually in any general-purpose database system.

Thus, a culture that learns and adapts as part of everyday working practices is essential.

Thus, critical thinking without essential intellectual traits often results in clever, but manipulative and often unethical or subjective thought.

Thus, this is the most important and essential function of money.

Thus there are alignments in all directions which would suggest there is little of astronomical significance, However, ethnohistorical records show that the various directions do have cosmological and astronomical significance with various points in the landscape being significant at different times of the year.

Thus, the material body will occupy different configurations at different times so that a particle occupies a series of points in space which describe a pathline.

Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.

Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y =− 1.

Thus, the gamma function must be undefined at those points ; it is a meromorphic function with simple poles at the nonpositive integers.

Thus, there is a direct mathematical relationship between the pressure and the speed, so if one knows the speed at all points within the airflow one can calculate the pressure, and vice versa.

Thus, personal involvement is linked with public opinion Proverbs that speak to the political disgruntlement include: “ When the Czar spits into the soup dish, it fairly bursts with pride ”; “ If the Czar be a rhymester, woe be to the poets ”; and “ The hen of the Czarina herself does not lay swan ’ s eggs .” While none of these proverbs state directly, “ I hate the Czar and detest my situation ” ( which would have been incredibly dangerous ), they do get their points across.

Thus bidding involves anticipating the points that will be accumulated from melds and from the points accumulated from winning tricks.

Thus we can envision a cloud of related genotypes that is rapidly mutating, with sequences going back and forth among different points in the cloud.

Thus, the need to use stars close to the ecliptic (± 9º of latitude ) as a set of observational reference points to help positioning a planet within this ecliptic coordinate system.

Thus if x and y are two points on the real line, then the distance between them is given by:

Thus, in Euclidean geometry, the shortest distance between two points is a straight line.

Thus, unlike, for example, Dungeons and Dragons, Rolemaster describes wounds not only in the number of points of damage dealt ( which are then subtracted from an abstract pool of ' Hit Points '), but with specific details of the injury inflicted.

Thus the IS curve is a locus of points of equilibrium in the " real " ( non-financial ) economy.

Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous.

Thus, in ten days of fighting, on nearly a front, the French 6th Army had progressed as far as six miles ( 10 km ) at points.

Thus, for an application like routing, might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points or nodes.

Thus we want points where and

Thus there are six critical points:

Thus, the weights are and, which are normalized distances between the unknown point and each of the end points.