While current mouthwash treatments must be used with a degree of frequency to prevent this bacteria from regrowing, future treatments could provide a viable long term solution.

* While the decision problem is NP-complete the optimization problem is NP-hard, its resolution is at least as difficult as the decision problem, and there is no known polynomial algorithm which can tell, given a solution, whether it is optimal ( which would mean that there is no solution with a larger, thus solving the decision problem NP-complete ).

While draining, water and organic acid from the soil slowly ( over thousands or millions of years ) enlarges these cracks, dissolving the calcium carbonate and carrying it away in solution.

While the process is secret, the general method for making yeast extract on a commercial scale is to add salt to a suspension of yeast, making the solution hypertonic, which leads to the cells shrivelling up ; this triggers " autolysis ", in which the yeast self-destructs.

While Aurelian and Probus were prepared to accompany their armies thousands of miles between war regions, this was not an ideal solution.

While he was working in his experimental laboratory in Berlin in 1789, Klaproth was able to precipitate a yellow compound ( likely sodium diuranate ) by dissolving pitchblende in nitric acid and neutralizing the solution with sodium hydroxide.

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

While the crew and experts on the ground try to find a solution, the jet cruises across Europe and Africa.

While there were earlier institutions that housed the " insane " the arrival of institutionalisation as a solution to the problem of madness was very much an event of the nineteenth century.

While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest energy of those generated.

While a number of possible models were considered, including that of a loose federation, the solution finally adopted was that of an integrated institution, Concordia University, operating under the existing Sir George Williams charter.

While material dissolves at places where grains are in contact, material crystallizes from the solution ( as cement ) in open pore spaces.

While several characters have asserted that transporters cannot transport through a ship's shields or planetary defense shields, there are instances of this " rule " being broken through a technobabble solution ( TNG: " The Wounded ", DS9: " Trials and Tribble-ations ") or disregarded by the show's writers ( VOY: " Caretaker ").

" While this was not seen by Israel as a significant moderation of PLO policy, the phrasing was extremely controversial within the PLO itself, where it was widely regarded as a move towards a two-state solution.

While inferences about protein folding can be made through mutation studies ; typically, experimental techniques for studying protein folding rely on the gradual unfolding or folding of a solution of proteins and observing conformational changes using standard non-crystallographic techniques for observing protein structure.

While these considerations may be directed toward any building, achieving an ideal optimized cost / performance solution requires careful, holistic, system integration engineering of these scientific principles.

While Conti was not experienced in film, Rodis believed his background in engineering and design made him well-equipped for Rodis ' planned solution: the creation of independent and self-contained miniature whale models.

While a brute-force search is simple to implement, and will always find a solution if it exists, its cost is proportional to the number of candidate solutions-which in many practical problems tends to grow very quickly as the size of the problem increases.

While it has provided some jobs, this industry has not been the economic solution for which many residents hoped.

While noting costs are falling, and generally positive about the technology for affluent areas in proximity to oceans, a 2004 study argued, " Desalinated water may be a solution for some water-stress regions, but not for places that are poor, deep in the interior of a continent, or at high elevation.

While Sabian tries to come up with a solution, Roman, with the help of Timmons and Maggie, gets into Niebaum's computer and discovers recordings of wiretaps, including his last conversation with Roenick.

Another former prostitute who worked in four different brothels from Nevada attacked the system, saying that " Under this system, prostitutes give up too much autonomy, control and choice over their work and lives " and " While the brothel owners love this profitable solution, it can be exploitative and is unnecessary ".

While James credits Velikovsky with " point the way to a solution by challenging Egyptian chronology ", he severely criticised the contents of Velikovsky's chronology as " disastrously extreme ", producing " a rash of new problems far more severe than those it hoped to solve " and claiming that " Velikovsky understood little of archaeology and nothing of stratigraphy.

( While the use of Hindu-Arabic numerals is occasionally seen, such as in the game Pop-O-Matic Trouble, the ambigrammatic properties of the digits ( for instance, 6 can look like a 9 upside down ) make such dice uncommon.

While interrelations are acknowledged in both directions between the model elements, in the last instance the purpose is to explain variations in the power and reach of organized crime in the sense of an ultimately unified organizational entity.

While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.

While usually trying cases in appeal in third instance ( as is normally the case in the Eastern Catholic Churches ), or even in second instance if appeal is made to it directly from the sentence of a tribunal of first instance, it is also a court of first instance for cases specified in the law and for others committed to the Rota by the Roman Pontiff.

Like the " dimension of image " characterization this can be generalized to a definition of the rank of a linear map: the rank of a linear map f from V → W is the minimal dimension k of an intermediate space X such that f can be written as the composition of a map V → X and a map X → W. While this definition does not suggest an efficient manner to compute the rank ( for which it is better to use one of the alternative definitions ), it does allow to easily understand many of the properties of the rank, for instance that the rank of the transpose of A is the same as that of A.

While the defense could show no specific instance where any part of North's congressional testimony was used in his trial, the Court of Appeals ruled that the trial judge had made an insufficient examination of the issue, and ordered North's convictions reversed.

While this definition is the most abstract, it is also the one most easily transferred to other settings, for instance to the varieties considered in algebraic geometry.

While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

While material substance is not required for electromagnetic waves to propagate, such waves are usually affected by the transmission media they pass through, for instance by absorption or by reflection or refraction at the interfaces between media.

While the name spank skirt suggests that the wearer could be spanked " bare bottom " without removing or repositioning the skirt, this item may be worn for reasons other than spanking ( for instance, exposure ).

While there is no known instance of a male mule siring offspring, female mules have on very rare occasion given birth to viable offspring.

While most drugs are legal to possess, many governments regulate the manufacture, distribution, marketing, and sale of some drugs, for instance through a prescription system.

While binding, it is limited to the single instance of amending the Constitutional provision on the maximum parliamentary term of five years.

While Natya Shastra contains the largest number of the movements, and the most detailed descriptions, Abhinaya Darpanam, for instance, has defined only 9 head movements, 4 neck movement and 8 eye movements ( compared with 36 of Natya Shastra ) which are used extensively throughout the dance.

While many physicians in England at the time had lost faith in the general value of bloodletting, some still considered it beneficial in some circumstances, for instance to " clear out " infected or weakened blood or its ability to " cause hæmorrhages to cease "— as evidenced in a call for a " fair trial for blood-letting as a remedy " in 1871.

" While pondering the generally negative reactions to the book Joyce said: I can't understand some of my critics, like Pound or Miss Weaver, for instance.

While the action of superoxide in the pathogenesis of some conditions is strong, for instance, mice and rats overexpressing CuZnSOD or MnSOD are more resistant to strokes and heart attacks, the role of superoxide in aging must be regarded as unproven for now.

While some ceremonies are open to non-Zuni peoples, others are private ; for instance the Shalako ceremony and feast has been closed to outsiders since 1990.

While usually the Rudras are described to eleven, in one instance in the Mahabharata ; they are said to be eleven thousand and surrounding Shiva.

While letters are in the first instance chosen for phonetic similarity, visual equivalence, and corresponding keyboard keys, are used when phonetically similar letters are exhausted.

While at Berlin in 1824 – 1825 he was thrown into prison, either on some ill-defined political charge at the instance of the French police, or as a result of an indiscreet conversation.

While brigs could not sail into the wind as easily as fore and aft rigged vessels such as schooners, a trait that is common to all square-rigged ships, a skilled brig captain could " manoeuvre it with ease and elegance ; a brig could for instance turn around almost on the spot ".