The importance of knowing in what chemical forms the hormone may exist is accentuated by the recent observation that there exists an abnormally long-acting TSH in blood drawn from many thyrotoxic patients ( Adams, 1958 ).

This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed, bounded convex set in Af.

Systematic reviews of the field have found that the number of ATC are growing rapidly, but have focused on memory and planning, that there is emerging evidence for efficacy, that a lot of scope exists to develop new ATC.

In solution there exists an equilibrium between the acid and its conjugate base.

More explicitly, it is stating that for every indexed family of nonempty sets there exists an indexed family of elements such that for every.

: For any set X of nonempty sets, there exists a choice function f defined on X.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence

that is, for any statement that is a logical consequence of there actually exists a deduction of the statement from.

During Darnley ’ s lifetime there was little public knowledge of the urn, and no record of a published photograph exists before 1921.

The theorem says that, among algorithms that decode strings from their descriptions ( codes ), there exists an optimal one.

Exercise as a teaching tool is deliberately omitted because of a common mistaken assumption that there exists a " correct " position.

It was known as Asuristan during this period, and became a main centre of the Church of the East ( now the Assyrian Church of the East ), with a flourishing Syriac ( Assyrian ) Christian culture which exists there to this day.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

; Inverse element: For each a in A, there exists an element b in A such that a • b

there exists a positive integer n such that

All of these problems can be traced back to the idea that, for every property that can be logically defined, there exists a set of all objects that have that property.

Whether or not an object is present in a set ; that is, exists there as a being, is based on universal experience or evidence of it.

Precisely stated, a function is binary if there exists sets such that

Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.

** for all f in X ′ there exists x in X with ǁxǁ ≤ 1, so that f ( x ) = ǁfǁ.

A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits, such that

For his part, Thompson had explained in a previous letter that there would be nothing but an honorable friendship between Katie and himself.

His lawyer had sent him a statement on his overdue alimony, and there was a letter from the Collector of Internal Revenue asking him to stop in his office and explain last year's exemptions.

`` Of course ( George's letter continued ), there are practical problems to be considered.

Alfred lamented in the preface to his translation of Gregory's Pastoral Care that " learning had declined so thoroughly in England that there were very few men on this side of the Humber who could understand their divine services in English, or even translate a single letter from Latin into English: and I suppose that there were not many beyond the Humber either ".

In his last surviving letter from 14 October 1791, Mozart tells his wife that he collected Salieri and Caterina Cavalieri in his carriage and drove them both to the opera ; about Salieri's attendance at his opera The Magic Flute, speaking enthusiastically: " He heard and saw with all his attention, and from the overture to the last choir there was not a piece that didn't elicit a ' Bravo!

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

In addition, there are no pluses or minuses in the letter grading system.

Although there are infinitely many halting probabilities, it is common to use the letter Ω to refer to them as if there were only one.

In 1914, the historian George Lincoln Burr sided with Upham in a note on Thomas Brattle's letter, " The strange suggestion of W. F. Poole that Brattle here means Cotton Mather himself, is adequately answered by Upham ..." Burr also reprinted Calef in full and dug deep into the historical record for information on the man and concludes "... that he had else any grievance against the Mathers or their colleagues there is no reason to think.

( At the time there was only one RCA studio in Nashville, with no letter designation.

Additionally, according to Plutarch's essay on the meaning of the " E at Delphi "-- the only literary source for the inscription --- there was also inscribed at the temple a large letter E. Among other things epsilon signifies the number 5.

Books are catalogued in ascending numerical order ; when two or more books have the same classification number, the system sub-divides the class alphabetically, by the use of a call number ( usually the first letter, or letters, of the author's last name, or the title if there is no identifiable author.

Part of Jude is very similar to 2 Peter ( mainly 2 Peter chapter 2 ), so much so that most scholars agree that there is a dependence between the two ; that either one letter used the other directly, or they both drew on a common source.

* The letter lacks any references to people in Ephesus, or any events Paul experienced there.

If Paul was the author of the letter, then it was probably written from Rome during Paul's first imprisonment (; ; ), and probably soon after his arrival there in the year 62, four years after he had parted with the Ephesian elders at Miletus.

Another indicator that the letter is early is that there is no hint in the letter of a developed organization within the Christian community at large.

Those who are advocates of Pauline authorship defend the differences that there are between elements in this letter and those commonly considered the genuine work of Paul ( e. g. 1 Thessalonians ).

Although the Estonian orthography is generally guided by phonemic principles, with each grapheme corresponding to one phoneme, there are some historical and morphological deviations from this: for example the initial letter ' h ' in words, preservation of the morpheme in declension of the word ( writing b, g, d in places where p, k, t is pronounced )

If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.

Paul then wrote this letter to the Corinthians, urging uniformity of belief (" that ye all speak the same thing and that there be no divisions among you ", 1: 10 ) and expounding Christian doctrine.

In addition, many scholars in support of this theory believe that there is content within 1 Peter that directly mirrors the situation as portrayed in Pliny ’ s letter.