* 1994-Robert J. Sawyer, " Just Like Old Times ", in On Spec, Summer 1993

Just as the subject itself was divided into the study of affine and projective varieties ( see the Algebraic variety definitions ) the Zariski topology is defined slightly differently for these two.

Just as in the classical case, to move from the affine to the projective definition we need only replace " ideal " by " homogeneous ideal ", though there is a complication involving the " irrelevant maximal ideal ," which is discussed in the cited article.

Just as members of a set of vectors are linearly independent if none is a linear combination of the others, so also they are affinely independent if none is an affine combination of the others.

Just as non-degenerate real conics can be classified by the discriminant of their imaginary part, considered as a quadratic form in ( the determinant of the matrix of the associated symmetric form ), a conic is degenerate if and only if the discriminant of the homogeneous quadratic form in is zero, where the affine equation

Just as bicycles come in many varieties, there are different types of pedals to support different types of cycling.

Just like C. annuum, C. chinense has many different varieties.

Just like with the Arc de Triomphe, Napoleon's 1815 defeat at the Battle of Waterloo, halted the construction of the monumental arch, but Emperor Franz Josef I of Austria ordered it to be completed as a celebration of the Vienna Congress and the peace treaties of 1815.

Just down the street from here a new bus station is under construction.

Just prior to the construction of the Central Washington Railroad line in 1889, no towns existed west of Davenport in Lincoln County.

Just before Stamford, the Great North Road, now labelled the A1, crosses the river, and a pumping station on the north bank at Stamford Meadows has pumped large quantities of water to the Rutland Water reservoir since its construction in 1975.

Just 2 % of the construction work is visible from above ground.

Just over 19 % of the population is dedicated to industry, manufacturing, construction and transportation.

Just as the limit is a special case of the universal construction, so is the product.

Just under 80 % are employed in commerce, 17. 5 % are employed in manufacturing and construction and. 1 % in agriculture.

Just south of the tunnel which carries the line under Church Avenue, the construction of the cut wall visibly changes.

Just prior to the start of construction on the Dumbarton Bridge, San Francisco Supervisor Richard J. Welch noted that the Bay Shore Highway would need to be built all the way to San Jose as an escape valve for the additional traffic that the bridge would attract.

Just four days later, Metro, D. C. and Prince George's County officials, and advocates of both the Branch Avenue and Rosecroft routes reached an agreement to begin construction of the Green Line fron L ' Enfant Plaza to Anacostia, pending resolution of the line's final route by December 6, 1984.

Just three months after the Joralemon Tunnel opened, construction began on the third track and the western island platform at Bowling Green.

Just prior to the onset of World War II, James Vernor II presided over the construction of a bottling plant and headquarters, encompassing an entire city block on Woodward Avenue, one block from the Detroit River.

Just before that plaza, US 22 exits the freeway as well, joining the William Penn Highway ( its original routing prior to the construction of the Penn-Lincoln Parkway ).

Just after the Second World War, Gif-sur-Yvette acquired an international scientific reputation, with the construction of the CNRS and of the CEA.

Just six days later, the Mayor presided over groundbreaking ceremonies and construction proceeded rapidly.

Just two years prior to his death, LeTourneau recorded his thoughts about the future of earthmoving equipment: “ Within the next few years construction machinery will grow bigger and bigger, and more and more powerful.

Just before the motorway was Dog Bridge, but this was demolished and the road it carried was realigned as part of the motorway construction.

Just days after the 1933 Nazi takeover, Adolf Hitler enthusiastically embraced an ambitious autobahn construction project and appointed Fritz Todt, the Inspector General of German Road Construction, to lead up the project.

Just north of the Crawford-Washington County line is the Bobby Hopper Tunnel, the only large highway tunnel in Arkansas ; its namesake ( from Springdale ) was the chairman of the Arkansas Highway Commission during its construction.

Just as important as the planning of the construction and location of the transmitter is how its output fits in with existing transmissions.

Just beyond the watered section, the plans showed a tunnel, but construction of this was not started.

Just under fifty percent are employed in industry, construction, and the making of handcrafts.

Just south of the site a single 17-story apartment building was constructed, the only construction of a planned development known as River City ( designed by Bertrand Goldberg who also designed the landmark " Marina City " along the main branch of the Chicago River ), was constructed on the former coach yard and approaches to the terminal.

Just as the orthogonal group has the special orthogonal group SO ( n ) as subgroup and the projective orthogonal group PO ( n ) as quotient, and the projective special orthogonal group PSO ( n ) as subquotient, the unitary group has associated to it the special unitary group SU ( n ), the projective unitary group PU ( n ), and the projective special unitary group PSU ( n ).

Just as in classical algebraic geometry, any spectrum or projective spectrum is compact, and if the ring in question is Noetherian then the space is a Noetherian space.

Just like the real case, the complex projective space is the space of directions through the origin of C < sup > n + 1 </ sup >, where two directions are regarded as the same if they differ by a phase.

Just as modern transportation has outmoded the early Studebaker covered wagon, the demand of today's sportsmen and women has necessitated changes in their equipment.

Just as heavily invested are the endeavors of multitudes of modern men who carry on the quest for the enchanting index.

Just as Hart Crane had little influence on anyone except very reactionary writers -- like Allen Tate, for instance, to whom Valery was the last word in modern poetry and the felicities of an Apollinaire, let alone a Paul Eluard were nonsense -- so Dylan Thomas's influence has been slight indeed.

Just a few of the instructions are, for example ( with some modern interpretation ):

Just as medieval group litigation bound all members of the group regardless of whether they all actually appeared in court, the modern class action binds all members of the class, with the exception of those who appear and object.

Just as modern Mexicans do today, the Aztecs developed a range of chocolate cuisine.

Just as modern military engineers enhance field fortifications with obstacles such as barbed wire, Medieval engineers used a number of obstacle types including abatis, caltrops, cheval de frise, and trou de loup.

Along with Simon Peter and James the Just he was one of the most prominent early Christian leaders .< ref >" The Canon Debate ," McDonald & Sanders editors, 2002, chapter 32, page 577, by James D. G. Dunn: " James, the brother of Jesus, and Paul, the two other most prominent leading figures Peter < nowiki ></ nowiki > in first-century Christianity "</ ref > Fourteen epistles in the New Testament are traditionally attributed to Paul, although his authorship of seven of the fourteen is questioned by modern scholars.

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).

Hārūn al-Rashīd (; Hārūn ar-Rashīd ;, Aaron the Just, or Aaron the Rightly Guided ) ( 17 March 763 or February 766 – 24 March 809 ) was the fifth Arab Abbasid Caliph that encompassed modern Iraq.

Just to the northwest of there, off the modern road, is where Evans chose to have Villa Ariadne built as his home away from home and an administrative center.

Just within the modern boundaries of Streatham Hill, although historically it was in Norwood, there is also a blue plaque on the house in Lanercost Road where Arthur Mee the writer of Arthur Mee's Children's Encyclopedia lived.

Many modern nations ' views on the ethics of civilian casualties align with the Just War theory, which advocates a system of proportionality.

" Just before the outbreak of World War II in 1939, a modern large football stadium had been built where the World University Games were staged at the newly named " Stade Prince Louis II.

Just 100 g of scavenged African ruminant brain matter provide more DHA than is consumed by a typical modern U. S. adult in the course of a week.

Just outside the village lives Jonathan Bell, owner of a " modern mechanical farm ", who has a friendly rivalry with Windy Miller, owner of a clanking old – but nevertheless efficiently functional-windmill and a firm believer in old-fashioned farming methods.

Just like in most modern countries, China has a fast production of different types of new music, while the old music is also kept alive.

Just as in modern literature, it is a complex and rich field of study, from the utterly sacred to the exuberantly profane, touching all points in-between.

Just thirty years earlier, Montacute House, exemplifying the English Renaissance, had been revolutionary ; only a century earlier, the juxtaposing mass of wings that is Compton Wynyates, one of the first houses to be built without complete fortification, had just been completed and was considered modern.

Just like every other player of his time, Start never fielded with a glove, as modern players do, making his fielding contributions more impressive.

Just outside of the eastern gopura there is a modern buddhist temple.

Returning to England in 1905 he had in his head The Four Just Men, the prototype of modern thriller novels, about four young, handsome, immensely wealthy vigilantes ( including a European Prince ) who kill people in the name of Justice.

Just as often however, others argue that Mills more closely identified with the work of Max Weber, whom many sociologists interpret as an exemplar of sophisticated ( and intellectually adequate ) anti-Marxism and modern liberalism.

Just as in modern computer keyboards, the shifted position was used to produce capitals and secondary characters.