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

With this notion of morphism, there is a category of C-valued sheaves on X for any C. The objects are the C-valued sheaves, and the morphisms are morphisms of sheaves.

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 world peace constantly being threatened, most of us regard the future skeptically, and even with fear.

With dealer stocks of new equipment averaging about 25% below a year ago, the affects of the rural recovery are being felt almost immediately by the country's farm equipment manufacturers.

With civil disobedience resulting in coercive and intolerable acts, and armed conflict resulting in dissidents being proclaimed rebels and outside the King's protection, any loyalty remaining shifted toward independence and how to achieve it.

With German being a pluricentric language, Austrian dialects should not be confused with the variety of Standard German spoken by most Austrians, which is distinct from that of Germany or Switzerland.

With Naram-Sin, Sargon's grandson, this went further than with Sargon, with the king not only being called " Lord of the Four Quarters ( of the Earth )", but also elevated to the ranks of the dingir (= gods ), with his own temple establishment.

The Falcons wore the all black combination against the New Orleans Saints for 4 straight seasons starting in 2004, With the last time being in 2007, losing 34 – 14.

With two of his singles Spraakwater and Kaal of Kammen being major hits in the mid-1990s, Extince was the first Dutch rapper making the MegaCharts.

With these innings he became the second player to score two Test triple centuries, the second player to score two career quadruple centuries, the only player to achieve both these milestones, and regained the distinction of being the holder of both the record first-class individual innings and the record Test individual innings.

With the mosque being located in the area, more Muslim immigrants began to move into private lodgings in Balsall Heath.

With the continuing advances being made in the production of synthetic diamonds, future applications are beginning to become feasible.

With this philosophy in mind, many grassroots efforts such as The Project for Public Spaces are being started to create this " Third Place " in communities.

With " Tertiary " being discouraged as a formal time or rock unit by the International Commission on Stratigraphy, the K – T extinction event is now called the Cretaceous – Paleogene ( or K – Pg ) extinction event by many researchers.

With innate talent, passion, diligence, discipline, self-motivation and tenacity, being the core factors of achieving success to becoming a celebrity, fame and fortune sometimes occurs spontaneously with relatively little effort due to sheer luck, being fortunate with connections, or simply being at the right place during the right time.

With prime time competition, Corrie was again seen as being old fashioned, with the introduction of the ' normal ' Clayton family in 1985 being a failure with viewers.

With the first version of VAC, a ban took hold almost instantly after being detected and the cheater had to wait 2 years to have the account unbanned.

With the second version, Valve instituted a policy of ' delayed bans ,' the theory being that if a new hack is developed which circumvents the VAC system, it will spread amongst the ' cheating ' community.

With the development of the internet, by the late 1990s and early 2000, much of that regulation had been replaced where newer industry technologies developed, offering viewers alternate choices for local events and programming leading to what is today, that being Digital Cable, Internet, and Phone being offered to consumers, bundled, by 2010.

With regard to ( 1 ), Hume argues that the uniformity principle cannot be demonstrated, as it is " consistent and conceivable " that nature might stop being regular.

With forest biotopes being irreplaceable source of new drugs ( such as taxol ), deforestation can destroy genetic variations ( such as crop resistance ) irretrievably.

With focus on performance-oriented keyboards and digital computer technology, manufacturers of commercial electronic instruments created some of the earliest digital synthesizers for studio and experimental use with computers being able to handle built-in sound synthesis algorithms.

With data being transferred 64 bits at a time, DDR SDRAM gives a transfer rate of ( memory bus clock rate ) × 2 ( for dual rate ) × 64 ( number of bits transferred ) / 8 ( number of bits / byte ).