However, because of the relatively small diffusion rates in solids, the corresponding chemical reactions are very slow in comparison to liquid and gas phase reactions.

However, the Theorema Egregium of Carl Friedrich Gauss showed that already for surfaces, the existence of a local isometry imposes strong compatibility conditions on their metrics: the Gaussian curvatures at the corresponding points must be the same.

However she had been corresponding with her uncle Raymond, King and holder of family properties in Antioch where he was seeking further protection from the French crown.

However, other British government officials were beginning to worry more about the rising political dominance of the Russian Empire in eastern Europe and the corresponding decline of the Ottoman Empire.

However, it was never argued by the " Joint Seven-Powers " that put forward the draft resolution, during the corresponding discussions, that it in any way afforded the Assembly new powers.

However, full cutoff fixtures may also trap more light in the fixture than other types of luminaires, corresponding to lower luminaire efficiency, suggesting a re-design of some luminaires may be necessary.

However, in the 11th century, the Pirqe de-Rabbi Eliezer, drawing on ancient legends of the fallen angel or angels, brought back to the mainstream of rabbinic thought the personification of evil and the corresponding myth.

However, appropriate symbols are easy to make by adding a lateral-fricative belt to the symbol for the corresponding lateral approximant ( see below ).

However no corresponding political liberalization has occurred as happened in eastern European countries.

However, creating more data to input to machine-learning systems simply requires a corresponding increase in the number of man-hours worked, generally without significant increases in the complexity of the annotation process.

The year is stated as the ninth year of Ptolemy V's reign ( equated with 197 / 196 BC ), and it is confirmed by naming four priests who officiated in that same year: Aëtus son of Aëtus was priest of the divine cults of Alexander the Great and the five Ptolemies down to Ptolemy V himself ; his three colleagues, named in turn in the inscription, led the worship of Berenice Euergetis ( wife of Ptolemy III ), Arsinoe Philadelpha ( wife and sister of Ptolemy II ) and Arsinoe Philopator, mother of Ptolemy V. However, a second date is also given in the Greek and hieroglyphic texts, corresponding to, the official anniversary of Ptolemy's coronation.

However, the downside of the real estate boom was a corresponding rise in the levels of personal debt ; as prospective homeowners had struggled to meet asking prices, the average level of household debt tripled in less than a decade.

However, this five races under one union principle and the corresponding flag were abandoned in 1927.

However, Hutchison also introduced interchange symbols ( circles for Underground-only, squares for connections with British Rail ) that were black and allowed multiple lines through them, as opposed to Beck who used one circle for each line at an interchange, coloured according to the corresponding line.

However, proportionality of corresponding sides is not by itself sufficient to prove similarity for polygons beyond triangles ( otherwise, for example, all rhombi would be similar ).

However, antennae, mandibles and oral papillae are probably not homologous to the corresponding features in arthropods, i. e., they probably developed independently.

However, because of the reduced mass, the frequencies associated with the spectral lines are less than half of those of the corresponding hydrogen lines.

However, no bio-defense solution seems to be able to compete with a simple reduction of import volumes, and its corresponding reduction in risk of any accidents.

However, if the random variable has an infinite but countable probability space ( i. e. corresponding to a die with infinite many faces ) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable.

However, when we set corresponding coefficients equal in this case, the equation for x < sup > 3 </ sup > is

However, they are still far less compact than the corresponding representations in bases such as decimal — see below for a compact way to codify ternary using nonary and septemvigesimal.

However, since 7s shell completely does not participate, the VSEPR-predicted structure would be trigonal pyramidal ( AX < sub > 3 </ sub > E < sub > 1 </ sub >); UusF < sub > 3 </ sub > has, however, this structure not energetically favored, picking instead the trigonal planar structure ( corresponding to a formula of AX < sub > 3 </ sub >) up.

However, there are no built-in tamper protection mechanisms ( that is, users who can use the RCS tools to version a file also, by design, are able to directly manipulate the corresponding version control file ) and this is leading some security conscious administrators to consider client / server version control systems that restrict users ' ability to alter the version control files.

However, upon change of geometry, i. e., change of, the LCAO coefficients obtain different values and we see corresponding changes in the functional form of the MO.

In a long commentary which he has inserted in the published text of the first act of the play, he says at one point: `` However, that experience never raised a doubt in his mind as to the reality of the underworld or the existence of Lucifer's many-faced lieutenants.

However, Sargon took this process further, conquering many of the surrounding regions to create an empire that reached westward as far as the Mediterranean Sea and perhaps Cyprus ( Kaptara ); northward as far as the mountains ( a later Hittite text asserts he fought the Hattite king Nurdaggal of Burushanda, well into Anatolia ); eastward over Elam ; and as far south as Magan ( Oman ) — a region over which he reigned for purportedly 56 years, though only four " year-names " survive.

However, unlike contemporaries such as Aldhelm, whose Latin is full of difficulties, Bede's own text is easy to read.

However, according to Coogan, considerable historical inaccuracies remain throughout the text, supporting the view that the book of Esther is to be read as a historical novella which tells a story describing historical events but is not necessarily historical fact.

However, every atom of the world contains the whole text within it.

However, the Greek text of the explains the name as, hyios paraklēseōs, meaning " son of consolation " or " son of encouragement ".

However, the illegal copying of books and other text works remains common, especially for educational reasons.

However, no such text exists, apart from some informal popular lectures by Bohr and Heisenberg, which contradict each other on several important issues.

However, because of the Reid v. Covert decision, the U. S. adds a reservation to the text of every treaty that says, in effect, that the U. S. intends to abide by the treaty, but if the treaty is found to be in violation of the Constitution, then the U. S. legally can't abide by the treaty since the U. S. signature would be ultra vires.

However, cable often lacks " interactive " features ( e. g. text services, and extra video-screens ), especially on BSkyB owned channels, and the satellite platform lacks services requiring high degrees of two-way communication, such as true video on demand.

However, some editions of the Bible include text from both deuterocanonical and non-canonical scriptures in a single section designated " Apocrypha ".

However, the " title " attribute of the " img " element specifies the internal entity " example1SVGTitle " whose declaration that does not define an annotation, so it will be parsed by validating parsers and the entity replacement text will be " Title of example1. svg ".

However, through careful research relating to paper construction, handwriting development, and the established principles of textual criticism, scholars can be rather certain about where these errors and changes appeared and what the original text probably said.

However, the text could also be interpreted as indicating that Paul was demanding the legal freedom of Onesimus and, as an act of both trust and reconciliation, holding Philemon accountable in the higher court of God to accomplish this change himself.

However this epistle is not without controversy because there is no evidence of a Greek text.

However, this translation of the letter was apparently based on grave paleographical errors, and the text, in fact, has nothing to do with Christianity, and in fact relates to pagan rituals.

However, some scholars suspect the presence of large-scale changes in the text and attribute this to oral transmission.

However, Jacob had little taste for text editing, and, as he himself confessed, working on a critical text gave him little pleasure.

However, the Huolongjing also describes land mines that were set off by enemy movement, called the ' ground-thunder explosive camp ', one of the ' self-trespassing ' ( zifan ) types, as the text says:

However, further description of how this flint device operated was not made until a Chinese text of 1606 AD revealed that a weight drive ( common in medieval clockworks ) had been used to work the ' steel wheel '.

However, transmission of the text was imperfect, and by the Middle Ages, only the commentary on Numbers and Deuteronomy remained.

However, some scholars such as John Brockington, argue that Jaya and Bharata refer to the same text, and ascribe the theory of Jaya with 8, 800 verses to a misreading of a verse in Adiparvan ( 1. 1. 81 ).

However, it is important to note that nothing in the text of the Constitution explicitly authorized the power of judicial review, despite persistent fears voiced by Anti-federalists over the power of the new Federal court system.

However, in Porphyry's Greek text De Abstinentia (« Περὶ ἀποχῆς ἐμψύχων »), there is a reference to the now-lost histories of the Mithraic mysteries by Euboulus and Pallas, the wording of which suggests that these authors treated the name " Mithra " as an indeclinable foreign word.