The second part of Kuratowski's thesis was devoted to continua irreducible between two points.

Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory:

Knaster's and Kuratowski's brought a comprehensive and precise study on connected components theory.

* in Graph theory, the characterization of Planar graphs now known as Kuratowski's theorem ;

* K < sub > 5 </ sub >, in graph theory, the complete graph used in Kuratowski's theorem

In particular, Kuratowski's theorem and Wagner's theorem characterize planar graphs by forbidden complete and complete bipartite subdivisions and minors, respectively.

Since Janiszewski was deceased, Kuratowski's supervisor was Wacław Sierpiński.

Two important characterizations of planar graphs, Kuratowski's theorem that the planar graphs are exactly the graphs that contain neither K < sub > 3, 3 </ sub > nor the complete graph K < sub > 5 </ sub > as a subdivision, and Wagner's theorem that the planar graphs are exactly the graphs that contain neither K < sub > 3, 3 </ sub > nor K < sub > 5 </ sub > as a minor, encompass this result.

Hence the dual of i, the topological closure operator c, can be defined in terms of i, and Kuratowski's axioms for c are theorems.

Just as the class P can be thought of as the tractable problems ( Cobham's thesis ), so NC can be thought of as the problems that can be efficiently solved on a parallel computer.

The one-dimensional Ising model has no phase transition and was solved by himself in his 1924 thesis.

Thus, the integrability of the problem of three point vortices on the plane was solved in the 1877 thesis of a young Swiss applied mathematician named Walter Gröbli.

In his PhD thesis project, Paul Dirac discovered that the equation for the operators in the Heisenberg representation, as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson brackets, a procedure now known as canonical quantization.

" Cohen therefore considers it paradoxical " that the rise of early modern science was due at least in part to developments in Christian thought — in particular, to certain aspects of Protestantism " ( a thesis first developed as what is now sometimes called the Merton thesis ).

Clement attributes his source to a " collection of marvels " by a certain " Monimos " of whom nothing is known, and claims, in pursuit of his thesis that daimon-worshipers become as cruel as their gods, that in " Pella of Thessaly human sacrifice is offered to Peleus and Cheiron, the victim being an Achaean ".

This thesis was concocted around Turner's picture of The Golden Bough, a sacred grove where a certain tree grew day and night ; a transfigured landscape in a dream-like vision of the little wood-land lake of Nemi -- " Diana's Mirror " where religious ceremonies and the " fulfillment of vows " of priests and kings were held.

# The metaphysical thesis: Moral propositions are true when actions and other objects of moral assessment have the relevant moral properties ( so that the relevant moral facts obtain ), where these facts and properties are robust: their metaphysical status, whatever it is, is not relevantly different from that of ( certain types of ) ordinary non-moral facts and properties.

Indeed, the question of how to classify certain logically possible ( if eccentric ) views — such as the rejection of the semantic and alethic theses in conjunction with the acceptance of the metaphysical thesis — turns on which model we accept.

She received a Ph. D. in zoology in 1915, with a thesis on regeneration in certain annelid worms.

He continued his studies at Columbia University, where he was awarded his doctorate for a thesis on the magnetic susceptibility of certain crystals.

James Madison made this recommendation in a letter to Thomas Jefferson of 24 October 1787, which summarized the thesis of The Federalist # 10: " Divide et impera, the reprobated axiom of tyranny, is under certain qualifications, the only policy, by which a republic can be administered on just principles.

" The camaraderie amoureuse thesis ", he explained, " entails a free contract of association ( that may be annulled without notice, following prior agreement ) reached between anarchist individualists of different genders, adhering to the necessary standards of sexual hygiene, with a view toward protecting the other parties to the contract from certain risks of the amorous experience, such as rejection, rupture, exclusivism, possessiveness, unicity, coquetry, whims, indifference, flirtatiousness, disregard for others, and prostitution.

It explored the thesis that the health of certain patients would permanently improve if their psychotic process was not interrupted by administration of antipsychotic pharmaceutical drugs.

But a thesis concerning the extent of effective methods — which is to say, concerning the extent of procedures of a certain sort that a human being unaided by machinery is capable of carrying out — carries no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with ' explicitly stated rules.

He later changed his mind and submitted a thesis in 1926, titled Some theorems about integral solutions to certain algebraic equations and inequalities.

Melissus may have argued for this quality due to certain issues arising in Parmenides ’ thesis ( 8. 42-9 ).

These are considered honours programs and require additional co-curricular work such as a thesis or research project, and / or that certain classes be taken.

The pejorative use of the expression " Pauline Christianity " relies in part upon a thesis that Paul's supporters, as a distinct group, had an undue influence on the formation of the canon of scripture, and also that certain bishops, especially the Bishop of Rome, influenced the debates by which the dogmatic formulations known as the Creeds came to be produced, thus ensuring a Pauline interpretation of the gospel.

The Royal College of Surgeons in Ireland along with certain National University of Ireland medical schools offers a BMedSci qualification on completion of a thesis based on 2 – 3 months of summer research ; only students achieving honours in their preclinical courses are eligible to receive the degree.

He had already read Hilberg's master's thesis, and found, as both a deeply patriotic German and a Jew, that certain themes sketched there were unbearably painful.

However, in light of the Church – Turing thesis their intuitive meaning is the same: a recursive function can be described as the least fixed point of a certain functional, mapping functions to functions.

There are similar challenges to substance naturalism that maintain that the substance naturalists ' thesis that all facts of knowledge are natural facts is not only circular but fails to accommodate certain facts.

During the summer vacations of 1890 and 1891, Walden was visiting Ostwald at the University of Leipzig and in September 1891 defended there a master thesis on the affinity values of certain organic acids.

" The camaraderie amoureuse thesis entails a free contract of association ( that may be annulled without notice, following prior agreement ) reached between anarchist individualists of different genders, adhering to the necessary standards of sexual hygiene, with a view toward protecting the other parties to the contract from certain risks of the amorous experience, such as rejection, rupture, exclusivism, possessiveness, unicity, coquetry, whims, indifference, flirtatiousness, disregard for others, and prostitution.

Its central thesis, that a diverse collection of independently deciding individuals is likely to make certain types of decisions and predictions better than individuals or even experts, draws many parallels with statistical sampling, but there is little overt discussion of statistics in the book.

The Bohrs returned to Denmark in 1945, and Aage resumed his university education, graduating with a master's degree in 1946, with a thesis concerned with some aspects of atomic stopping problems.

In 1958 he received a Master of Science in Surgery for a thesis entitled, " The aortic valve – problems in the fabrication and testing of a prosthetic valve ".

Ingo Rechenberg and his group were able to solve complex engineering problems through evolution strategies as documented in his 1971 PhD thesis and the resulting 1973 book.

Meanwhile a committee at Haifa University claimed to have found serious problems with the thesis, including " quotations " that were contradicted by Katz's taped records of interview.

In 1948, a paper put forward by Stone in support of Tawney's thesis was vigorously attacked by Trevor-Roper who, in a rancorous counter-essay, showed that Stone had exaggerated the debt problems of the Tudor nobility.

A notable thesis propagated by Trevor-Roper was the “ general crisis of the 17th century .” He argued that the middle years of the 17th century in Western Europe saw a widespread break-down in politics, economics and society caused by a complex series of demographic, social, religious, economic and political problems.

The “ general crisis ” thesis generated much controversy between those, such as the Marxist historian Eric Hobsbawm, who believed in the thesis, but saw the problems of 17th-century Europe as being more social and economic in origin than Trevor-Roper would allow.

For Overy, a major problem with the Mason thesis was that it rested on the assumption that in a way unrecorded by the records, that information was passed on to Hitler about the Reichs economic problems.

He then returned to the University of Leiden and in 1929 defended his PhD thesis titled " Minimumproblemen in de natuurkunde en de economie " ( Minimisation problems in Physics and Economics ).

The Reform party claimed that this thesis of two founding peoples was flawed and Preston Manning called for a New Canada with a new identity that would solve existing problems, and stated this in his book The New Canada ( 1992 ) and laid out a solution:

Weil was a young Marxist who had written his doctoral thesis on the practical problems of implementing socialism and was published by Karl Korsch.

* 1941: Alexander Hrennikoff submitted his D. Sc thesis in MIT on the discretization of plane elasticity problems using a lattice framework

A committee at Haifa University found problems with the thesis and ruled that it: " failed at the stage of presenting the raw material for the reader's judgment, both in terms of its organization according to strict criteria of classification and criticism, and in terms of the apparent instances of disregard for the interviewees '

While pregnant with her second child, Sheila Macintyre stopped teaching but continued work on a thesis on Some problems in interpolatory function theory and received her PhD from Aberdeen in 1947.

Its thesis was that " the intellectual life of the whole of western society " was split into the titular two cultures — namely the sciences and the humanities — and that this was a major hindrance to solving the world's problems.

Early on, he was interested in social problems, and he went on to get his masters degree in sociology at the University of Kansas, where he wrote a thesis on workers ’ leisure activities.

He completed his PhD thesis titled Zakah and its effect on solving social problems in 1973 with First Merit, and was awarded his PhD degree from Al Azhar.

# Krige, D. G, A statistical approach to some mine valuations and allied problems at the Witwatersrand, Master's thesis of the University of Witwatersrand, 1951

A set of problems formulated in this thesis for a long time attracted attention from mathematicians.

Cobham's thesis holds that P is the class of computational problems which are " efficiently solvable " or " tractable "; in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.