However, in this approach the question of the change in radius of curvature with s is handled completely formally, consistent with a geometric interpretation, but not relying upon it, thereby avoiding any questions the image above might suggest about neglecting the variation in ρ.

However, as we will see below, they are distinct from the geometric microliths because of the strokes used in the manufacture of geometric microliths, which mainly involved the microburin technique.

However, the spoken language uses both arithmetic and geometric numerals.

However, the most important contribution of Minkowski's geometric viewpoint of spacetime turned out to be in Einstein's later development of general relativity, since the correct description of the effect of gravitation on space and time was found to be most easily visualized as a " warp " or stretching in the geometrical fabric of space and time, in a smooth and continuous way that changed smoothly from point-to-point along the spacetime fabric.

However, the linking of basic geometric forms with inherent beauty and ease of industrial application — which had been prefigured by Marcel Duchamp from 1914 — was left to the founders of Purism, Amédée Ozenfant and Charles-Édouard Jeanneret ( better known as Le Corbusier ,) who exhibited paintings together in Paris and published Après le cubisme in 1918.

However, the stability analyses of the bubble show that the bubble itself undergoes significant geometric instabilities, due to, for example, the Bjerknes forces and Rayleigh – Taylor instabilities.

However, the most successful system of this type was the one introduced by John Robert Gregg in 1888, who had studied not only the geometric English systems, but also the German Stolze stenography, a script shorthand.

However some of the puzzles require lateral thinking and are not just about making geometric shapes.

However, the crescent was not a symbol used for Islam by Muhammad or any other early Muslim rulers, as the Islamic religion is, in fact, against appointing " holy symbols " ( so that during the early centuries of Islam, Muslim authorities simply didn't want any geometric symbols to be used to symbolize Islam, in the way that the cross symbolizes Christianity, the menorah was a commonly occurring symbol of Judaism, etc .).

( However a manifold can have many different geometric structures of the same type ; for example, a surface of genus at least 2 has a continuum of different hyperbolic metrics.

However this minimal decomposition is not necessarily the one produced by Ricci flow ; if fact, the Ricci flow can cut up a manifold into geometric pieces in many inequivalent ways, depending on the choice of initial metric.

However it is famous for its central pillar, which has a square base and an octagonal shaft, both carved with bands of geometric and floral designs, further its thirty-six serpentine brackets support a circular platform for Akbar, which is connected to each corner of the building on the first floor, by four stone walkways.

However, what makes Mitla unique among Mesoamerican sites is the elaborate and intricate mosaic fretwork and geometric designs that cover tombs, panels, friezes and even entire walls.

However for graphical and image applications geometric fitting seeks to provide the best visual fit ; which usually means trying to minimize the orthogonal distance to the curve ( e. g., total least squares ), or to otherwise include both axes of displacement of a point from the curve.

However, the explicit formula for the sinc function for the hexagonal, body centered cubic, face centered cubic and other higher dimensional lattices can be explicitly derived using the geometric properties of Brillouin zones and their connection to zonotopes.

However the axioms of determinacy and dependent choice, together, are sufficient for most geometric measure theory, potential theory, Fourier series and Fourier transforms, while making all subsets of the real line Lebesgue measurable.

However, sound radiated from an infinite plane source is not attenuated due to geometric spreading, but is affected by other sound propagation effects.

However, for an aircraft flying through the never-uniform and never-quiescent atmosphere, the relating of pulse transmission and reception times to successive geometric positions of the antenna must be accompanied by constant adjusting of the return phases to account for sensed irregularities in the flight path.

However, there is a spiral which has exactly the geometric property of constant distance between successive coils in the sense of parallel curves, the involute of a circle.

However, ordinary Riemannian geometry is unable to describe the properties of the electromagnetic field as a purely geometric phenomenon.

However, " geometric coefficient of variation " has also been defined as:

However, these tests generally include a control ( negative and / or positive ), a geometric dilution series or other appropriate logarithmic dilution series, test chambers and equal numbers of replicates, and a test organism.

However the primary submodules associated to the non-minimal associated primes ( called embedded primes for geometric reasons ) need not be unique.

However, despite the insight of many of his observations, his own conclusions are open to suspicion because of his failure to employ at all times the correct research methods.

However, he turned out to be a complete failure in his new position.

However, as Erickson has noted, the individual's failure to develop preliminary identities during infancy and childhood need not be irreversibly deterministic with respect to a given area of identity diffusion in his ( or her ) adolescence.

Experiments have been conducted to attempt the synthesis of ununennium ( Uue ), which is likely to be the next member of the group, but they have all met with failure .< ref name =" link "> However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements.

However, poor marketing and failure to repeat the technological advances of the first systems meant that the Amiga quickly lost its market share to competing platforms, such as the fourth generation game consoles, Apple Macintosh and IBM PC compatibles.

However the failure of this work was more than made up for with his next Parisian opera Tarare with a libretto by Beaumarchais.

However the French ships were hampered by their inadequate deployment, reduced crews and the failure of the rear division under Villeneuve to meaningfully participate, all of which contributed to their defeat.

However, the 1964 rebellion ended in failure.

However, failure of both eyes to move to one side, can indicate damage or destruction of the affected side.

However, in the ensuing decades there have been numerous secret attempts to recreate Erskine's treatment, only to have them end in failure.

However, if a second failure occurs before the RAID group is completely repaired from the first failure, then data can be lost.

However, if a second failure occurs before the RAID group is completely repaired from the first failure, then data can be lost.

However, General Niazi proved to be a failure and ineffective ruler.

However, this experiment was a dismal failure.

However, in a small minority of patients with renal failure, at least four such agents have been associated with development of the rare nodular inflammatory disease nephrogenic systemic fibrosis.

However, the EU's desire to work on foreign policy was undermined due to its failure to act during the Yugoslav wars, and its division over whether to support the United States lead Iraq War.

However several of the examples below rely on the fact that many expressions do not immediately return success or failure, returning values in the meantime.

However, some locomotive hauled passenger trains may utilize more than one locomotive, as do many locomotive hauled freight trains, and so are able to continue at reduced speed after the failure of one locomotive.

However, during the Battle of Dunkirk it experienced its first failure.

However, persuaded by popular demand, letters from children, and the failure of his new books, he returned to the series each time.

However the same metal can also be vulnerable to fatigue damage through repeated use or from sudden stress failure when a load capacity is exceeded.

However, part of the system state is lost with the failing server, hence this approach requires applications to cope with failure.

However, this study Azithromycin Failure in Mycoplasma genitalium Urethritis says that "... doxycycline and levofloxacin have substantial failure rates ..." and "... Recurrent urethral symptoms following azithromycin therapy only occurred in persons with persistent M. genitalium infection and resolved with moxifloxacin.