In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if

Additional fresh water comes from the difference of precipitation less evaporation, which is positive.

An " elementary " proof can be given using the fact that geometric mean of positive numbers is less than arithmetic mean

More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.

An example of a problem which is known to be in NP and in co-NP is integer factorization: given positive integers m and n determine if m has a factor less than n and greater than one.

However, the combined effects of ethnic and religious fractionalization, i. e. the more chance that any two randomly chosen people will be from separate ethnic or religious groups the less chance of a civil war, were also significant and positive, as long as the country avoided ethnic dominance.

These digits are often used with a decimal separator which indicates the start of a fractional part, and with a symbol such as the plus sign + ( for positive ) or minus sign − ( for negative ) adjacent to the numeral to indicate whether it is greater or less than zero, respectively.

For example, air pollution may generate a negative externality, and education may generate a positive externality ( less crime, etc .).

The ellipse can also be defined as the set of points such that the distance from any point in that set to a given point in the plane ( a focus ) is a constant positive fraction less than 1 ( the eccentricity ) of the perpendicular distance of the point in the set to a given line ( called the directrix ).

On the most basic level, electronegativity is determined by factors like the nuclear charge ( the more protons an atom has, the more " pull " it will have on negative electrons ) and the number / location of other electrons present in the atomic shells ( the more electrons an atom has, the farther from the nucleus the valence electrons will be, and as a result the less positive charge they will experience — both because of their increased distance from the nucleus, and because the other electrons in the lower energy core orbitals will act to shield the valence electrons from the positively charged nucleus ).

Also, macroscopic objects made of conductive elements, can more or less easily ( depending on the element ) take on or give off electrons, and then maintain a net negative or positive charge indefinitely.

The molecule is said to have a positive oxygen balance if it contains more oxygen than is needed and a negative oxygen balance if it contains less oxygen than is needed.

Subtracting a small positive number from a big number enough times until what is left is less than the original smaller number can be replaced by finding the remainder in long division.

Alkaline earth ions, with their two positive charges and requirement for two non-bridging oxygen ions to compensate for their charge, are much less mobile themselves and also hinder diffusion of other ions, especially the alkalis.

While the immediate response from the West German population was positive, the Soviet authorities were less pleased with the combative Lass sie nach Berlin kommen.

As a general expression of positive sentiment ( a stronger form of like ), love is commonly contrasted with hate ( or neutral apathy ); as a less sexual and more emotionally intimate form of romantic attachment, love is commonly contrasted with lust ; and as an interpersonal relationship with romantic overtones, love is sometimes contrasted with friendship, although the word love is often applied to close friendships.

In mathematics, a Mersenne number, named after Marin Mersenne ( a French monk who began the study of these numbers in the early 17th century ), is a positive integer that is one less than a power of two:

While this is four times less than the number of Mauritians travelling to Singapore, the trend remains highly positive.

Media coverage of mental illness comprises predominantly negative and pejorative depictions, for example, of incompetence, violence or criminality, with far less coverage of positive issues such as accomplishments or human rights issues .< ref > Such negative depictions, including in children's cartoons, are thought to contribute to stigma and negative attitudes in the public and in those with mental health problems themselves, although more sensitive or serious cinematic portrayals have increased in prevalence.

During the negotiation, negotiators who are in a positive mood tend to enjoy the interaction more, show less contentious behavior, use less aggressive tactics and more cooperative strategies.

One of the most important values of Poznań is the positive attitude of public administration towards investments, and less bureaucracy than elsewhere in Poland.

On the positive side, the external debt burden has declined markedly over the last 20 years, and domestic debt is almost negligible ; external debt as a percent of GDP was less than 20 percent in 2006

The recently concluded Investment Climate Assessment provides some positive findings in this regard, namely that Swaziland firms are among the most productive in Sub-Saharan Africa, although they are less productive than firms in the most productive middle-income countries in other regions.

Depending on the client's needs and the jurisdiction's requirements, the spectrum of the architect's services may be extensive ( detailed document preparation and construction review ) or less inclusive ( such as allowing a contractor to exercise considerable design-build functions ).

Nevertheless, a 2009 systematic review and meta-analysis of trials in people diagnosed with schizophrenia found that less than half ( 41 %) showed any therapeutic response to an antipsychotic, compared to 24 % on placebo, and that there was a decline in treatment response over time, and possibly a bias in which trial results were published.

Some authors see a centralized peer – review process as less relevant and publish on their home pages or on unreviewed sites like arXiv.

The Independent review of the 1995 National Theatre revival praised the production, writing " For three hours of gloriously barbed bliss and bewitchment, Sean Mathias's production establishes the show as a minor miracle of astringent worldly wisdom and one that is haunted by less earthy intimations.

Evil Dead II holds a 98 % approval rating on the review aggregator Rotten Tomatoes, slightly less than The Evil Dead, which holds a 100 % rating.

Time magazine writer Richard Corliss was less scathing, but agreed that it was forgettable, saying that people would " forget all about movie by the time they leave the multiplex ," even joking at the end of his review that he had forgotten the film's name.

Impartial review, especially of work in less narrowly defined or inter-disciplinary fields, may be difficult to accomplish ; and the significance ( good or bad ) of an idea may never be widely appreciated among its contemporaries.

In 1996, Social Text did not conduct peer review because its editors believed that an editorial open policy would stimulate more original, less conventional research.

Tax returns are subject to review and adjustment by taxing authorities, though far less than all returns are reviewed.

Boucher and McComas gave The Illustrated Man a mixed review, faulting the framing story as " markedly ineffective " and the story selection for seeming " less than wisely chosen.

However, in spite of its initial short term success and critical reaction, as represented by a review in La Gazzetta privilegiata which stated that " A new masterwork has been added to Italian music ..... Belisario not only pleased and delighted, but also conquered, enflamed and ravished the full auditorium ", in the long run, had " Donizetti poured music of the calibre of his Lucia di Lammermoor into the score of Belisario the shortcomings of its wayward plot and dramatic structure would matter less ".

In his review of Ivry's biography for Library Journal Larry Lipkis is persuaded by Ivry's research that, " There seems to be little question that Ravel was an affected, intensely secretive dandy with gay inclinations ," but also expresses the view that Ivry's work is less persuasive in definitively linking Ravel's sexuality to characteristics of his musical oeuvre.

However, an April 2007 review showed that, in a double-blind test, reviewers generally preferred the output produced using third-party ink over OEM ink .< REF name =" Auto5I-8 "/> In general, OEM inks have undergone significant system reliability testing with the cartridge and print-head materials, whereas R & D efforts on third-party ink material compatibility is likely to be significantly less.

Over the 10 years prior to the review, the overall objection rate was so low as to be practically negligible, at less than 0. 1 percent.

A recent review of CRPS treatment concluded: " Some common treatments ( e. g., local anesthetic blockade of sympathetic ganglia ) are not supported by the aggregate of published studies and should be used less frequently.

" Roger Ebert gave the theatrical version of the film a less than positive review, but later gave a positive review of the director's cut.

A review of the scientific literature on caffeine concluded that moderate caffeine intake ( less than 400 mg per day ) does not adversely affect cardiovascular health.

Kamil Crater, discovered from Google Earth image review in Egypt, 45 meters in diameter, 10 meters deep is thought to have been formed less than 3, 500 years ago in a then-unpopulated region of Western Egypt.

In a review of the Grampa-centric episode " Lady Bouvier's Lover ", Patrick Bromley of DVD Verdict said that he is " never terribly interested " in episodes that revolve around Grampa, because he believes Grampa is " great as a background character, but less so when he takes center stage.

In his review in The New York Times, Vincent Canby called the film " an uproarious display of brilliance, nerve, dance, maudlin confessions, inside jokes and, especially, ego " and " an essentially funny movie that seeks to operate on too many levels at the same time ... some of it makes you wince, but a lot of it is great fun ... A key to the success of the production is the performance of Roy Scheider as Joe Gideon ... With an actor of less weight and intensity, All That Jazz might have evaporated as we watched it.

* Received only one negative review on Rotten Tomatoes and a " 98 %" approval rating, 2 points less than The Godfather ( although it does hold a higher rating average of 9. 2 / 10 compared to the predecessor's 9. 1 / 10 ) but 32 points more than The Godfather Part III.

Upon the release of The Italian, the Los Angeles Times gave the film a positive review which included the following comments :" There are possibilities in the role of Pietro, in ' The Italian ' ... that a less clever character artist than George Beban might overlook ...

Nora Sayre, in a 7 February, 1974 review for The New York Times, called Zardoz a melodrama that is a " good deal less effective than its special visual effects " ... a film " more confusing than exciting even with a frenetic, shoot-em-up climax.

Accordingly, meta-analytic review of 71 studies by Steel ( 2007 ) indicate that typically perfectionists actually procrastinate slightly less than others, with " the exception being perfectionists who were also seeking clinical counseling.