With this alternate notion of choice function, the axiom of choice can be compactly stated as

With a sufficiently sophisticated switch, it is possible to create a network in which the normal notion of a broadcast domain is strictly controlled.

With the well-publicized notion that sexual acts were a part of lesbianism and their relationships, sexual experimentation was widespread.

With the fall of the Iron Curtain, the demise of the notion of a Pax Sovietica, and the end of the Cold War, the U. S. maintained significant contingents of armed forces in Europe and East Asia.

With CP-67 on the IBM System / 360 Model 67 and Virtual Machine Facility / 370 ( VM / 370 ) on System / 370, IBM introduced the notion of virtual machine, where the operating system itself runs under the control of a hypervisor, instead of being in direct control of the hardware.

With art by Adam Kubert, the design of Kryptonian society is distinct yet again from Birthright, incorporating elements of both pre-Crisis on Infinite Earths continuity and Donner's work on the first two Christopher Reeve films, in particular the notion of Krypton's Council threatening Jor-El with harsh punishment were he to make public his predictions of their planet's imminent doom.

With the innovation of the transaxle, the notion of a yo-yo's response has become important to players.

With the notion being that Spanish words such as La Chingada carry more context then aggressively, or intensely.

With William Empson's notion of placing the complex into the simple, Alpers thus critically defines pastoral as a means of allegory.

With the eastern frontier under less pressure, in 658 Constans defeated the Slavs in the Balkans, temporarily reasserting some notion of Byzantine rule over them and resettled some of them in Anatolia ( ca.

With its manuscript date of 1946, the book has been recognized as including the first formulation of the notion of a generative grammar.

With the advent of the positivists by the early 20th century, however, most western philosophers had rejected the notion of an objective esthetic standard for any form of art, including landscaping.

With the failure of the worldwide revolution envisaged by Lenin and Trotsky, the Civil War, and finally Lenin's death, war measures that were deemed to be temporary, such as forced requisition of food and the lack of democratic control, became permanent and a tool to boost Stalin's power, leading to the emergence of Marxism – Leninism and Stalinism, as well as the notion that socialism can be created and exist in a single state.

With art by Adam Kubert, Jor-El is depicted for the first time with a beard and the design of Kryptonian society is distinct yet again from Birthright and Man of Steel, incorporating elements of Donner's work on the first two Christopher Reeve films, in particular the notion of Krypton's Council threatening Jor-El with harsh penalty of exile to the very Phantom Zone he himself had discovered if he were to make public his predictions of their planet's imminent doom or otherwise attempt to " create a climate of panic.

With this chord, Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion which was soon explored by Debussy and others.

With regards to man-management and motivation, Rijkaard rejects the notion of a " star system " and promotes the idea that every one of his players is a valuable member of the team.

With the modified notion of symmetry for vector fields the symmetry group can also be E < sup >+</ sup >( m ).

With respect to the testing of the claims in court, Windschuttle writes: ".... when they tested specific policies before the Federal Court, and when they argued the general intentions of the parliaments and legislators before the High Court, the historians and political activists who invented the notion of the Stolen Generations proved incapable of substantiating their case.

With the coming of DVD technology, the notion of colorization was once again gaining press.

With the move to Sunnydale, she believes she is starting fresh, a notion her mother also believes and encourages.

The court martial was presided by Tromp and though he was acquitted, De With had the compulsive notion that Tromp had tried to influence witnesses against him.

With the fall of Constantinople and the end of the Byzantine Empire in 1453, the Grand Dukes of Muscovy came to see themselves as the successors of the Byzantine heritage, a notion reinforced by the marriage of Ivan III to Sophia Paleologue ( hence the expression " Third Rome " for Moscow and, by extension, for the whole of Imperial Russia ).

There is no evidence to support the notion that tarot has an Egyptian lineage, but in the credulous stir that followed, Etteilla responded with another book, Manière de se récréer avec le jeu de cartes nommées Tarots (" How to Entertain Yourself With the Deck of Cards Called Tarot ") in 1785.

With the prevalence of environmental problems, many economists embraced the notion that “ if environmental sustainability must coexist for economic sustainability, then the overall system must be one which permits the identification of an equilibrium between the environment and the economy ”.

With the rapid rate of closure, the approach from below, the side, and ahead, there would be only a moment when damage could be done.

With the metal shutters closed, the dining room was so dark that it seemed still night in there.

With colleges and universities carrying a large part of the program, and with students looking toward Peace Corps service, there will be an impact on educational curriculum and student seriousness.

With no set standards, there is the tendency to promote to the next highest level when the top of a salary band is reached regardless of performance.

With the source of light behind the copy, there is no loss of lumen output, as with conventional boards illuminated by means of reflected light.

With the diversity of religious viewpoints, there are differences of opinion as to the essential features of religion ; ;

With capital largely squandered, there seemed to them no other course to pursue.

With the lower dealer inventories and the stepped-up demand some manufacturers believe there could be shortages of some implements.

With this movie-to-be in London, and new faces about her there, she would soon be a more tranquil, a wiser person, all the better for her stay out here.

With the loss of the study of ancient Greek in the early medieval Latin West, Aristotle was practically unknown there from c. AD 600 to c. 1100 except through the Latin translation of the Organon made by Boethius.

With their often complex reproductive needs and permeable skins, amphibians are often ecological indicators and in recent decades there has been a dramatic decline in amphibian populations of many species around the globe.

The last film is not based on any Christie work but displays a few plot elements from They Do It With Mirrors ( viz., the ship is used as a reform school for wayward boys and one of the teachers uses them as a crime force ), and there is a kind of salute to The Mousetrap.

With a recreational abalone licence, there is a bag limit of 10 per day, and a total possession limit of 20.

With this restriction, there are only finitely many Archimedean solids.

With the axiom of dependent choice ( which is a weakened form of the axiom of choice ), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

With modern shooting techniques, there is very little value to shooting with a weapon in each hand.

With his father's death in 1892, and his appointment as head of the Bahá ’ í faith, there was much opposition against him, including virtually all his family members.

With a reserve ratio of 10 %, the bank can create 400 million USD in additional loans ( there is a time lag, and the bank has to expect to recover the loaned money back into its books ).

Bahamian tastes in consumer products roughly parallel those in the U. S. With approximately 85 % of the population of primarily African descent, there is a large and growing market in the Bahamas for " ethnic " personal care products.

With the internationalism of modern architecture and design, there were many exchanges between the Vkhutemas and the Bauhaus.

With the end of the war in 1945, there was a great expectation that the Soviet people would not only see the end of the devastation of Nazism, but also the end of Stalin's Purges.

With the transition from English law, which had common law crimes, to the new legal system under the U. S. Constitution, which prohibited ex post facto laws at both the federal and state level, the question was raised whether there could be common law crimes in the United States.

With an increase in the number of college-educated readers, there was a shift away from slapstick comedy and towards more cerebral humor.

With a key of length n bits, there are 2 < sup > n </ sup > possible keys.

With the rising popularity of the Internet, there is a current vogue in China for coining English transliterations, for example, 粉丝 ／ 粉絲 fěnsī " fans ", 黑客 hēikè " hacker " ( lit.