Since family names are normally written last in European societies ( except in Hungary ), the term last name is commonly used for family name, while in East Asia ( with vertical writing ) the family name may be referred to as upper name ( as in Japanese ).

Since, by the second law of thermodynamics, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any process.

Since the late Middle Ages the Kingdoms of England and Scotland had been evolving towards a quasi-oligarchical or collegiate form of government in which the monarch was held to rule with the consensus of the land-owning upper classes.

Since the lifetime of the laser transition L is long compared to that of Ra ( τ < sub > 32 </ sub > ≫ τ < sub > 43 </ sub >), a population accumulates in level 3 ( the upper laser level ), which may relax by spontaneous or stimulated emission into level 2 ( the lower laser level ).

Since only a few atoms must be excited into the upper laser level to form a population inversion, a four-level laser is much more efficient than a three-level one, and most practical lasers are of this type.

Since operations such as inserting, deleting, and finding values require worst-case time proportional to the height of the tree, this theoretical upper bound on the height allows red – black trees to be efficient in the worst case, unlike ordinary binary search trees.

Since the Second Polish Republic ( 1918 – 1939 ) Sejm has referred only to the lower house of the parliament ; the upper house is called the Senat.

Since 1995 Marine Recruits from the nearby Marine Corps Recruit Depot often visit the games en masse, in uniform, often filling entire sections in the upper deck.

Since the pitch of each note is largely affected by the temperature of the steam, accurate tuning is nearly impossible ; however, the off-pitch notes ( particularly in the upper register ) have become somewhat of a trademark of the steam calliope.

Since the Crown was itself a hereditary dignity, it seemed natural for seats in the upper House of Parliament to be so as well.

Since the early twentieth century, the topsails and topgallants are often split into a lower and an upper sail to allow them to be more easily handled.

Since then the château has continued to welcome the parlement when called upon to sit in a congressional sitting, jointly with the upper house in order to enact constitutional changes or, as happened most recently in June 2009, to listen to a formal declaration by the president.

Since Russell-and 1994-Group universities tend to contain research departments which are above upper critical mass, their qualities are similar.

Since is non-empty and by assumption, it is bounded above, then, by the Least upper bound property of real numbers, exists and is finite.

Since the death of Capability Brown in 1783, no one figure dominated English garden design ; Repton was ambitious to fill this gap and sent circulars round his contacts in the upper classes advertising his services.

Since the late 2000s ( decade ) the southeastern district of Surco has experienced a significant increase in upscale corporate developments in the area comprised by avenues Manuel Holguín, El Derby, El Polo and La Encalada due to lower restrictions to grant construction licences and proximity to residential middle and upper class districts and is set to become, after traditional San Isidro and Miraflores, the new corporate center of Lima.

Since an endoscopy allows a doctor to visually inspect the upper digestive tract the procedure may help identify any additional damage to the tract that may not have been detected otherwise.

Since the upper atmosphere is not homogeneous and contains significant magnetic structure, the solar ultraviolet ( UV ), EUV and X-ray flux varies markedly in the course of the solar cycle.

Since it is a muscle of the upper limb, the trapezius is not innervated by dorsal rami despite being placed superficially in the back.

Since tropical cyclones strengthen these ridges, a positive feedback loop develops between the convective tropical cyclone and the upper level high, where the strength of both systems intensifies.

Since an instrument must match the singer's range, much Cajun singing is sung in the singer's upper range.

Since this occurs on curved areas, they are normally associated with the upper surfaces of the wing, the cockpit canopy, and the nose cone of the aircraft, areas with the highest local curvature.

Now suppose b < u = l is a smaller upper bound for S. Since ( l < sub > n </ sub >) is monotonic increasing it is easy to see that b < l < sub > n </ sub > for some n. But l < sub > n </ sub > is not an upper bound for S and so neither is b. Hence u is a least upper bound for S and ≤ is complete.

Since at this stress the slope of the material's stress-strain curve, E < sub > t </ sub > ( called the tangent modulus ), is smaller than that below the proportional limit, the critical load at inelastic buckling is reduced.

Since the light is turned through 90 degrees by the reflection, the slope of the parabola at P must be 1.

Since both axes use logarithmic units, the slope of the linear section of the curve is called the gamma of the film.

Since the slope shown here reaches the horizontal limit of 0 as T → 0 then the implication is that ΔS → 0, which is the Nernst heat theorem.

Since the green arrow is perpendicular to the surface of the liquid, the slope of the surface must equal the quotient of these forces:

Since the reign of Roman Emperor Augustus ( end of first century BCE ), the northern border of the peninsula has been set on the Alps watershed, but geographically it coincides with a line extending from the Magra to the Rubicone rivers, north of the Tuscan-Emilian Apennines, which excludes the Po Valley and the southern slope of the Alps.

Since the indifference curve is convex with respect to the origin and we have defined the MRS as the negative slope of the indifference curve,

Since the system relies upon being able to drain properly, all piping above the drainback tank, including the collectors, must slope downward in the direction of the drainback tank.

Since the camp was placed to best advantage on a hill or slope near the river, the naval base was usually outside its walls.

Since it is considered that the planar range extends through negative and positive infinity, close observation shows the appearance of two parallel or mirror planes in the sense that if the slope of one plane is traced, the co-plane can be seen to be bypassed or skipped, though in actuality the co-plane is also traced from the opposite perspective.

Since the eastern side of the Front is drained by Chesapeake Bay rivers that drop fairly rapidly through the Ridge and Valley Province to the low-elevation waters of the Great Appalachian Valley, erosion on the eastern slope of this caprock layer has been much more intense than on the western slope, where drainage to low elevations is spread over a greater distance ( particularly considering stream meanders ) through the Appalachian Plateau to the Ohio River.

Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings.

Since the ratio of the daughter and non-radiogenic isotopes is proportional to the ratio of the parent and non-radiogenic isotopes, the slope of the isochron gets steeper with time.

Since this is a different species with different diffusion characteristics ( and different half-reaction ), the slope of current versus added titrant will have a different slope after the equivalence point.

Since many of the outlying southern sites for Linnaea borealis are in habitats that are at high elevations or otherwise in cooler microclimates than the surrounding general landscapes, ongoing and prospective climate change has become a significant concern for the conservation of this species in such places, such as Ice Mountain in West Virginia, a low-elevation algific talus slope with persisting buried ice.

Since the vineyard is large and situated in a slope, it is not homogeneous from a geological point of view.

Since friction is strongly dependent on macrotexture and texture, cross slope as well as curvature can be measured with a road profiler, so road profilers are very useful to identify improperly banked curves that may pose a risk to motor vehicles.

Since the invention of calculus, the slope of the tangent line can be found easily using implicit differentiation.