Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

We use the stronger statement that every odd ( antipode-preserving ) mapping h: S < sup > n-1 </ sup > → S < sup > n-1 </ sup > has odd degree.

* XML Schema, also referred to as XML Schema Definition ( XSD ), has achieved Recommendation status within the W3C, and is popular for " data oriented " ( that is, transactional non-publishing ) XML use because of its stronger typing and easier round-tripping to Java declarations.

But Griffith's first use of cross-cutting in The Fatal Hour, made in July 1908, has a much stronger suspense story served by this construction than those in the earlier Pathé examples.

It concludes with blank pages which the owner is meant to use as a journal, should they endure a zombie outbreak, lending the book a stronger, if satiric, kind of realism.

The use of separate manoeuvre elements to support a stronger central group is also well known in pre-mechanised tribal warfare, as is the use of reserve echelons farther back.

In particular, medieval fortifications became progressively stronger — for example, the advent of the concentric castle from the period of the Crusades — and more dangerous to attackers — witness the increasing use of machicolations and murder-holes, as well the preparation of hot or incendiary substances.

Response strategies typically include the use of different, stronger antibiotics ; however, new strains of MRSA have recently emerged that are resistant even to these drugs.

While this design is mostly obsolete today, supplanted by the stronger yet equally convenient swing-out design, manufacturers have begun making reproductions of late 19th century designs for use in cowboy action shooting.

In particular, medieval fortifications became progressively stronger — for example, the advent of the concentric castle from the period of the Crusades — and more dangerous to attackers — witness the increasing use of machicolations and murder-holes, as well the preparation of hot or incendiary substances.

The use of composite materials, such as carbon-Kevlar, made skis stronger, lighter, and more durable.

Another common tactic is to " force forehand " ( force the thrower to use their forehand throw ) since most players, especially at lower levels of play, have a stronger backhand throw.

Ultrasonic foils under the moving wire in a paper machine will use the shock waves from the imploding bubbles to distribute the cellulose fibres more uniform in the produced paper web, which will make a stronger paper with more even surfaces.

Most theorists today use the concept of working memory to replace or include the older concept of short-term memory, thereby marking a stronger emphasis on the notion of manipulation of information instead of passive maintenance.

In 1969, the court established stronger protections for speech in the landmark case Brandenburg v. Ohio which held that " the constitutional guarantees of free speech and free press do not permit a State to forbid or proscribe advocacy of the use of force or of law violation except where such advocacy is directed to inciting or producing imminent lawless action ".

More recent studies using more sophisticated methodologies have generally refuted these findings: density, land use and public transport accessibility can influence travel behaviour, although social and economic factors, particularly household income, usually exert a stronger influence.

The airfoil sections in use at the time were very thin, and could not have a cantilever structure installed within and so attempts were made to provide a stronger structure by adding an external truss-structurally a biplane, but lacking the lower wing.

* It is recommended that when fishing for trout, that the fisher ( s ) should use line in the 4 – 8 lb test for streamfish, and stronger line with the same diameter for trout from the sea or from a large lake, such as Lake Michigan.

Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors.

Steinway won the case on appeal in 1975, forcing their competitor to use only the name " Grotrian " in the U. S. The case set a precedent and established the concept of " initial interest confusion ", in which consumers might be initially attracted to a similarly named but lesser-known brand because of the stronger brand's good reputation.

Still, some users and privacy activists like the American Civil Liberties Union believe that Internet users deserve stronger pseudonymity so that they can protect themselves against identity theft, illegal government surveillance, stalking, and other unwelcome consequences of Internet use ( including unintentional disclosures of their personal information, as discussed in the next section ).

Although US export regulations historically restricted key lengths to 56-bit symmetric keys ( e. g. Data Encryption Standard ), these restrictions are no longer in place, so modern symmetric algorithms typically use computationally stronger 128-to 256-bit keys.

However, both the side effects and the addictive properties of methcathinone are much stronger than those associated with khat use.

A long flat known as the St. John field seemed to answer their purpose, and since the Winooski bridges were at last passable, they decided to use it.

Throughout his later career, he made use of his close connection to Thomson and Scott as he established businesses that supplied rails and bridges to the railroad, offering the two men a stake in his enterprises.

* To make salt bridges for use in electrochemistry.

A common form of lashing sticks, logs, and deciduous branches together involved the use of long reeds or other harvested fibers woven together to form a connective rope capable of binding and holding together the materials used in early bridges.

Dating to the Greek Bronze Age ( 13th century BC ), it is one of the oldest arch bridges still in existence and use.

Beam bridges are the most common bridge type in use today.

Most cantilever bridges use a pair of continuous spans that extend from opposite sides of the supporting piers to meet at the center of the obstacle the bridge crosses.

Some double-decker bridges only use one level for street traffic ; the Washington Avenue Bridge in Minneapolis reserves its lower level for automobile traffic and its upper level for pedestrian and bicycle traffic ( predominantly students at the University of Minnesota ).

But its long curing time of at least a month made it unpopular after World War One in the construction of highways and bridges and many states and construction firms turned to the use of Portland cement.

This finds expression in the concept of collaborative systems that use technology to build bridges between departments.

Players can adjust the string pitches by moving these bridges before playing, and use three finger picks ( on thumb, index finger, and middle finger ) to pluck the strings.

Bridges have been known to break during playing, and with some older instruments which have the surface where the bridges rest being worn due to much use, the bridges may fall during playing, especially when pressing strings.

For purposes of international statistical comparison, the Organisation for Economic Co-operation and Development ( OECD ) defines a road as " a line of communication ( travelled way ) using a stabilized base other than rails or air strips open to public traffic, primarily for the use of road motor vehicles running on their own wheels ," which includes " bridges, tunnels, supporting structures, junctions, crossings, interchanges, and toll roads, but not cycle paths.

Most also used concrete, which the Romans were the first to use for bridges.

Roman bridges were so well constructed that many are in use today.

For example, a fuel excise ( use tax ) is often used to pay for public transportation, especially roads and bridges and for the protection of the environment.

US forces do not have the ability to destroy the silos, as they could only use deep penetrating bombs, which had all been used to destroy Chinese bridges to disrupt the PLA's logistical support.

The maze of canals threaded through the city requires the use of more than 400 bridges to permit the flow of foot traffic.

The only gondole still in common use by Venetians are the traghetti, foot passenger ferries crossing the Grand Canal at certain points without bridges.

For example, an area that is still much too complex for the use of CFD is determining the effects of flow on and around structures, bridges, terrain, etc.

At Folly Bridge in Oxford the remains of an original Saxon structure can be seen, and medieval stone bridges such as Newbridge and Abingdon Bridge are still in use.

Also, because human societies have always made use of water, sometimes the remains of structures that these societies built underwater still exist ( such as the foundations of crannogs, bridges and harbours ) when traces on dry land have been lost.

In wet and cold climates, reinforced concrete for roads, bridges, parking structures and other structures that may be exposed to deicing salt may benefit from use of epoxy-coated, hot dip galvanised or stainless steel rebar, although good design and a well-chosen cement mix may provide sufficient protection for many applications.