With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces ; they may also be generalized further, to oriented matroids.

With the series expansion of higher rank polygamma function a generalized formula can be given as

With this book, which is unfortunately available only in Divehi, the late Mr. Luthfee tried to clear a number of misconceptions that carelessly researched tourist publications have generalized even among Maldivians.

With the introduction of cannons, the term was morphed to a generalized term for field fortifications lying some distance beyond the ends of the bridge that were emplaced to protect both the bridge and any troops crossing it to the far bank, so became in that era a term used when referring to both the fortifications and the small lodgement on the bank that was closest to the enemy.

With rising levels of socialisation and individuation, more and more people, and more and more aspects of the self come into play in the dialectic of self and generalized other.

With the introduction of PLATO IV, Bitzer declared general success, claiming that the goal of generalized computer instruction was now available to all.

With this book, which is unfortunately available only in Divehi, the late Mr. Luthfee tried to clear a number of misconceptions that carelessly researched tourist publications have generalized even among Maldivians.

With the graduation of the last B-25 class at Reese in January 1960, specialized UPT came to an end and generalized training began.

With the emergence of bioinformatics, the focus moved towards developing generalized techniques which could be applied to an arbitrary set of complexes at acceptable computational cost.

With the use of gel electrophoresis, it can be observed that OROV causes DNA fragmentation in HeLa cells.

With the complex sensory reaction to the variety of spices and flavours, a natural high is achieved that causes subsequent cravings, often followed by a desire to move on to hotter curries.

With the resources thus gained he undertook to enable Philip V to carry out an ambitious foreign policy to undo the Treaty of Utrecht, with the aim of countering the Habsburgs and recovering Spanish possessions in Italy, where he was responsible for unwarranted invasions of Sardinia ( November 1717, strongly supported by Sardinian politician Vicente Bacallar ) and Sicily ( July 1718 ), in spite of promises made to the Pope, while pressing Spanish causes in France with the Cellamare Conspiracy.

With the exception of benthic habitats directly beneath marine farms, most mariculture causes minimal destruction to habitats.

With the looming defeat of the PLA in Siberia, which they were about to learn about via live UAV broadcasts from the CIA through the Internet, student demonstrators in Beijing raid the Politburo, which causes a conservative minister to take control and arrest the perpetrators of the war in Siberia and surrender to the US and Russia.

With the end of the Middle Ages however, Aristotle's approach, especially concerning formal and final causes, was criticized by authors such as Niccolò Machiavelli, in the field of political thinking, and Francis Bacon, concerning science more generally.

With regard to the potential for exposure to chemicals in the workplace and MCS, the U. S. Occupational Safety and Health Administration ( OSHA ) has indicated MCS is highly controversial and there is insufficient scientific evidence to explain the relationship between the theorized causes of MCS and its symptoms.

With the prime causes of cardiac arrest being ischemic heart disease, efforts to promote a healthy diet, exercise, and smoking cessation are important.

With public concern about drug addiction, depression and alcoholism among veterans, and " neurasthenia " among " highly-strung " Southern women, his medicinal concoction was advertised as being particularly beneficial for " ladies, and all those whose sedentary employment causes nervous prostration, irregularities of the stomach, bowels and kidneys, who require a nerve tonic and a pure, delightful diffusible stimulant.

This event and FEMA's performance was reviewed by the National Academy of Public Administration in its February 1993 report " Coping With Catastrophe " which identified several basic paradigms in Emergency Management and FEMA administration that were causes of the failed response.

With other causes including burns, environmental exposure and excess urine loss due to diabetic ketoacidosis and diabetes insipidus.

With the shortened ( or truncated ) nozzle, the recirculation of trapped gases at the base of the plug causes a small thrust which offsets the loss due to the non-ideal shape.

With her as an accomplice Drusus was slowly poisoned and died of seemingly natural causes on September 13, 23.

With its head office in Manhattan and the bulk of its members living in the New York-New Jersey area, the Agudah ensures that it monitors and intercedes on behalf of causes important to it in the politics of New York City, its five boroughs, and in the state government of New York State.

With the onset of summer the following year the stifling atmosphere, along with other causes, led to a large number of deaths in the colony.

With the fall of the Soviet Union, he also ceased his support for a variety of international causes.

With little understanding of the causes and mechanisms of illnesses, widely marketed " cures " ( as opposed to locally produced and locally used remedies ), often referred to as patent medicines, first came to prominence during the 17th and 18th centuries in Britain and the British colonies, including those in North America.

With the rise in estrogens, LH receptors are also expressed on the maturing follicle, which causes it to produce more estradiol.

With depletion of muscle glycogen, the loss of ATP causes the muscles to grow stiff, as the actin-myosin bonds cannot be released.

With a background as a community activist and organizer Gutiérrez often uses non-violent civil disobedience when pushing political causes and legislation.

With direct current however, because the electrode only creates the arc and does not provide filler material, a positively charged electrode causes shallow welds, while a negatively charged electrode makes deeper welds.

With his political career eclipsed by that of his wife, Astor turned to greater involvement in charitable causes.

With the battle raging on in space, the alien ship fires on the station and causes serious damage to the forward section of the station.

With the clues obtained during the history and physical examination the healthcare provider can now formulate a differential diagnosis, a list of potential causes of the symptoms.

With Sigismund defeated and sent packing, and as both an alien and a heretic to the majority of the Swedish nation, and his formal deposition by the Riksdag of the Estates in 1599 was, in effect, a natural vindication and ex post facto legitimization of Charles's position all along, for the same session of the Riksens ständer named him as the ruler as regent.

With Michael VI ’ s deposition, Patriarch Michael Keroularios crowned Isaac I emperor on September 1, 1057, taking much of the credit for Isaac's acceptance as monarch.

With Adolphe Thiers he opposed the war against Prussia in 1870, and at the news of the defeat of Napoleon III at Sedan he demanded the deposition of the emperor.

With Ahmed III's deposition, Mahmud I took the throne ( 1730 – 1754 ).

With the development of modern thin film deposition and growth techniques in the latter half of the 20th century, such as chemical vapour deposition, sputter deposition, and cathodic arc deposition, it became possible to fabricate truly amorphous carbon materials.

With his deposition in 1296, Parliament temporarily became less prominent, but it was again held frequently by King Robert Bruce after 1309.

With an area of 146. 63 km < sup > 2 </ sup >, Aalen is ranked 7th in Baden-Württemberg and 2nd within the Government Region of Stuttgart, after Stuttgart.

Other highlights of that decade included the 1942 debut of Fearless Fosdick as Abner's " ideel " ( hero ); the 1946 Lena the Hyena Contest, in which a hideous Lower Slobbovian gal was ultimately revealed in the harrowing winning entry ( as judged by Frank Sinatra, Boris Karloff and Salvador Dalí ) drawn by noted cartoonist Basil Wolverton ; and an ill-fated Sunday parody of Gone With the Wind that aroused anger and legal threats from author Margaret Mitchell, and led to a printed apology within the strip.

Annan said, " With today's agreement on the Bakassi peninsula, a comprehensive resolution of the dispute is within our grasp.

With both Bolsheviks and Mensheviks weakened by splits within their ranks and by Tsarist repression, they were tempted to try to re-unite the party.

With closer Huston Street injured, the Rockies turned to Franklin Morales, but the Giants started the inning with 3 straight hits to pull to within 4 – 1.

With ex nihilo, the potential and the substance of creation springs from within the creator.

With a setting within the realm of science fiction, the series wisely offers a world that seems entirely realistic considering our present time.

With one third of the game ( 9 levels ) distributed as shareware, Doom was played by an estimated 10 million people within two years of its release, popularizing the mode of gameplay and spawning a gaming subculture ; as a sign of its effect on the industry, games from the mid-1990s boom of first-person shooters are often known simply as " Doom clones ".

With the signing of the Geneva Accords, President Najibullah unsuccessfully sought to end the Democratic Republic of Afghanistan's isolation within the Islamic world and in the Non-Aligned Movement.

With Phelps's encouragement, including a list of Phelps ' contacts in Nashville and some of his credit cards, Brooks traveled to Nashville to pursue a recording contract ; he returned to Oklahoma within 24 hours.

With their season on the line, the Astros would nonetheless rally for two runs to come to within 7 – 6.

With much of the fighting concentrated in their areas, they have either migrated to settled communities away from the marshes or have been forced by government decree to relocate within the marshes.

With the exception of the metabolic disorder diabetes mellitus and metabolic syndrome, insulin is provided within the body in a constant proportion to remove excess glucose from the blood, which otherwise would be toxic.

With this established, he invented a process in which liquids such as milk were heated to kill most bacteria and moulds already present within them.

With Haidallah's ambitious political and social reform program undone by continuing instability, regime inefficiency and a plethora of coup attempts and intrigues from within the military establishment, the CMSN chairman turned increasingly autocratic, excluding other junta officers from power, and provoking discontent by frequently reshuffling the power hierarchy to prevent threats to his position.

Indeed, Paul Samuelson, writing within a Keynesian framework, defended mercantilism, writing: " With employment less than full and Net National Product suboptimal, all the debunked mercantilist arguments turn out to be valid.

" With that said, in practice, magical weapons are usually specific, consecrated items used within ceremonial magic.

With the fresh wound in his chest, and the bullet still within it, Mr. Roosevelt still carries out his scheduled public speech.

" With sentiments of this nature in mind, it is little wonder that national interest fell within preventing the infusion of American investment into the project.

With the support of the Athenians, the Argives succeeded in forging a coalition of democratic states within the Peloponnese, including the powerful states of Mantinea and Elis.

With the treasury and emergency reserve fund of 1, 000 talents dwindling away, the Athenians were forced to demand even more tribute from her subject allies, further increasing tensions and the threat of further rebellion within the Empire.

With 2. 8 million residents in, it is also the country's largest and most populated comune and fourth-most populous city in the European Union by population within city limits.

The difference was remarked upon in dialog between characters in " Trials and Tribble-ations ", an episode of Star Trek: Deep Space Nine when modern-era characters travel back in time to the days of Kirk and Spock ( and via then-brand new CGI techniques, appear within the TOS episode " The Trouble With Tribbles ", frequently coming into contact with the Enterprise crew ).

" Nicolosi adds, " With appropriate masculine affirmation and support, however, they can all be developed within the context of normal heterosexual manhood.

With an attacking partnership, the pair took Australia to within sight of the target.