At the exact midpoint between the two pKa values, the trace amount of net negative and trace of net positive ions exactly balance, so that average net charge of all forms present is zero.

An exact solution to the scalar-Einstein equations which forms a counter example to many formulations of the

::* Quasi self-similarity: approximates the same pattern at different scales ; may contain small copies of the entire fractal in distorted and degenerate forms ; e. g., the Mandelbrot set's satellites are approximations of the entire set, but not exact copies, as shown in Figure 1

The transition itself can only be illustrated and corroborated by transitional fossils, which will never demonstrate an exact half-way point between clearly divergent forms.

As anyone who's ever used a telephone ( mobile or landline ) knows, however, such channels often fail to produce exact reconstruction of a signal ; noise, periods of silence, and other forms of signal corruption often degrade quality.

* 1593 – The Uppsala Synod is summoned to confirm the exact forms of the Lutheran Church of Sweden.

As with any art forms, the exact characteristics of a short story will vary by creator.

The exact mechanism of the pathogenesis of the various forms of ALD is not known.

SMiLE acquired legendary status as one of the great lost works of Sixties pop, and although fragments were subsequently issued in various forms over the years, the form and exact content of the work as Wilson and Parks had conceived it remained hotly debated.

Both of these come in two forms: approximate values for force and acceleration, which result from simplifications, and hypothetical exact values for force and acceleration, which would require the complete answer to calculate.

Though the exact etymology is obscure, the English and Frisian forms probably derive from an earlier Anglo-Frisian * bō-ja (" little brother "), a diminutive of the Germanic root * bō-(" brother, male relation "), from Proto-Indo-European * bhā -, * bhāt-(" father, brother ").

Forms which are the image of other forms under the exterior derivative, plus the constant 0 function in are called exact and forms

whose exterior derivative is 0 are called closed ( see closed and exact differential forms ); the relationship then says that exact forms are closed.

The converse, however, is not in general true ; closed forms need not be exact.

A simple but significant case is the 1-form of angle measure on the unit circle, written conventionally as dθ ( described at closed and exact differential forms ).

One performs this classification by saying that two closed forms α and β in are cohomologous if they differ by an exact form, that is, if is exact.

One then defines the-th de Rham cohomology group to be the set of equivalence classes, that is, the set of closed forms in modulo the exact forms.

A proliferation forms roots when planted and is often an exact clone of its parent plant.

This is an exact description of what Mr. Sansom does.

The exact definition of an automorphism depends on the type of " mathematical object " in question and what, precisely, constitutes an " isomorphism " of that object.

While an exact number has not been determined, thousands of Canadians have purchased and used what they contend to be grey market radio and television services, licensed in the United States but not in Canada.

( Since there is no citation for this exegesis, readers will need to analyse for themselves whether the " exact parallel " is addressed elsewhere and is generally accepted, or might represent a personal point of view, and readers will also need to discern for themselves what exactly is the " illumination ".

Notice that the exact form of the dual will depend on what sphere we reciprocate with respect to ; as we move the sphere around, the dual form distorts.

While the exact definition and what is included as extreme sport is debatable, some attempted to make classification for extreme sports.

His also counteracts Hacekel ’ s sequence of drawings in the Anthropogenie with what he refers to as “ exact ” drawings, highlighting specific differences.

It is not certain what exact changes will happen to ENSO in the future: Different models make different predictions .< ref name =" Merryfield2006 "> It may be that the observed phenomenon of more frequent and stronger El Niño events occurs only in the initial phase of the global warming, and then ( e. g., after the lower layers of the ocean get warmer as well ), El Niño will become weaker than it was.

Since Galen states that he is using observations of monkeys ( human dissection was prohibited ) to give an account of what the body looks like, Vesalius could portray himself as using Galen's approach of description of direct observation to create a record of the exact details of the human body, since he worked in a time when human dissection was allowed.

Where there are disputes about the exact meaning and application of national laws, it is the responsibility of the courts to decide what the law means.

Although the exact nature and extent of the Christian redaction remains unclear there is broad consensus as to what the original text of the Testimonium by Josephus would have looked like.

In fact, it does not have an exact present form, as " Linnaean taxonomy " as such does not really exist: it is a collective ( abstracting ) term for what actually are several separate fields, which use similar approaches.

It is important to note that what exactly constitutes a machine gun, and whether volley guns are a type of machine gun, and to what extent some earlier types of devices are considered to be like machine guns, is a matter of debate in many cases and can vary depending which language and exact definition is used.

There is no clear consensus on exact amounts, as different scholars differ on exactly what elements of American aid during this period were part of the Marshall Plan.

The exact requirements for capture, as well as what is done with captured stones, vary considerably among games.

One can in this formalism state Heisenberg's uncertainty principle and prove it as a theorem, although the exact historical sequence of events, concerning who derived what and under which framework, is the subject of historical investigations outside the scope of this article.

However, the missile failed shortly after launch, so it is unknown what its exact capabilities are or how close North Korea is to perfecting the technology.

It is always possible to point to the exact text and show what it says.

The exact definition of racism is controversial both because there is little scholarly agreement about the meaning of the concept " race ", and because there is also little agreement about what does and doesn't constitute discrimination.

Kes becomes aware of what is happening, and once she has traveled back to the time corresponding to an earlier part of Voyager's conflict with the Krenim, she informs the Doctor in the past what is happening to her and relays the exact temporal frequency of the chronoton torpedo.

The exact reasons are unclear, as no contemporary author recorded what caused the quarrel between the half-brothers.

The first mention of any location more exact than the New Forest comes from John Leland writing in 1530 who stated that the king died at Thorougham a placename which has since fallen into disuse but was probably located at what is now Park Farm on the Beaulieu estates.

His motivation for changing it to something meaning ' the East electrode ' ( other candidates had been " eastode ", " oriode " and " anatolode ") was to make it immune to a possible later change in the direction convention for current, whose exact nature was not known at the time.

was later shown to be exact in the dense limit of pairs.

His motivation for changing it to something meaning ' the West electrode ' ( other candidates had been " westode ", " occiode " and " dysiode ") was to make it immune to a possible later change in the direction convention for current, whose exact nature was not known at the time.

The exact circumstances of the injury remain unclear ; however, he had suffered problems with alcoholism in his later years.

Furthermore, as noted by Bohr, Moseley's law provided a reasonably complete experimental set of data that supported the ( new from 1911 ) conception by Ernest Rutherford and Antonius Van den Broek of the atom, with a positively-charged nucleus surrounded by negatively-charged electrons in which the atomic number is understood to be the exact physical number of positive charges ( later discovered and called protons ) in the central atomic nuclei of the elements.

Rivalries among European powers enabled the Arab-Berber population, the Maures ( Moors ), to maintain their independence and later to exact annual payments from France, whose sovereignty over the Senegal River and the Mauritanian coast was recognized by the Congress of Vienna in 1815.

Whether this occurred immediately after Sæberht's death or later is impossible to determine from Bede's chronology, which has both events in the same chapter but gives neither an exact time frame nor the elapsed time between the two events.

While the exact relationship of the short and apparently primitive text of Q1 to the later published texts is not resolved, Hardin Craig among others has suggested that it may represent an earlier draft of the play and hence would confirm that the play referred to in 1589 is in fact merely an earlier draft of Shakespeare's play.

Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions arose much later.

Most of the modern scripts of South India have evolved from this script, with the exception of Vatteluttu, the exact origins of which are unknown, and Nandinagari, which is a variant of Devanagari that developed due to later Northern influence.

The exact line was to be determined by surveyors later.

Both systems had the ability to store memory images onto disk snapshots could later be used to restore the Spectrum to its exact previous state.

No physical evidence of the Hazār Afsān has survived so its exact relationship with the existing later Arabic versions remains a mystery.

Some sources incorrectly refer to the June 1982 speech before the British House of Commons as the " Evil Empire " speech, but while Reagan referred twice to totalitarianism in his London speech, the exact phrase " evil empire " did not appear in any speech until later in his Presidency.

However, the exact distance of the ride was never verified and the record was later rejected by both the British Surfing Association and Guinness World Records.

She later claimed she had worn the diamond at social gatherings and had an exact replica made for her performances, but he claimed otherwise.

Bach uses close but not exact imitation: the musical pattern in one part reappears a bar later in another ( sometimes inverted ).

( The exact date of the move is unstated, but was probably 1632, certainly no later than 1634.

* Video evidence corroborated by police witnesses was later shown to be invalid, as Norwegian State Television had filmed Longo on his way per bus to Gothenburg at that exact moment, as part of a documentary.

The exact circumstances of the succession upon Fruela's death one year later are unclear, but the son of Fruela, Alfonso Fróilaz, became king in at least part of the kingdom.

His talents as an orator and rhetorician were greatly admired by his contemporaries, a number of whom were later regarded as forming a school called after him Frontoniani ; his object in his teaching was to inculcate the exact use of the Latin language in place of the artificialities of such first-century authors as Seneca, and encourage the use of " unlooked-for and unexpected words ", to be found by diligent reading of pre-Ciceronian authors.

Dream later recreates him with " some changes ", though the exact nature of these changes is not explicit.

The exact dates of when Nefertiti was married to Akhenaten and later promoted to his Queen are uncertain.

It was actually about 18 years later that I stood in that exact spot and sang my own songs to a packed house.