Instead of a single closed path we can consider a linear combination of closed path where the scalars are integers.

Instead the ideles are identified with the closed subset of all pairs ( x, y ) of A × A with xy = 1, with the subset topology.

Instead, it was developed as an industrial center, with footwear and white goods factories ( which eventually closed down with the collapse of the socialist economy ).

Instead of each cylinder having a single piston and being closed at one end with a cylinder head, the Jumo-based design used an elongated cylinder containing two pistons moving in opposite directions towards the centre.

Instead, Fort King was closed in 1828.

Instead, a " great crown " comprising a circlet of gold with crosses and fleurs-de-lys atop its rim, but without arches ( an open crown ), was a king's usual headgear on state occasions until the time of Henry V, who is depicted in statuary and illustrations with an " imperial crown ", i. e., the great crown with gold arches added ( also called a closed crown ).

Instead of being made from a ball of dough, the dough is rolled flat, cut into a shape, filled with other ingredients, and then the dough is closed around the filling.

Instead of keeping the glottis tightly closed, it is tensed but left slightly open to allow a thin stream of air through.

Instead, he remained at Marly and ordered the hall closed, expecting to prevent the Assembly from meeting for several days while he prepared.

Instead of a plate being brought down to put pressure on the grapes, plates from either side of a closed cylinder are brought together to squeeze the grapes.

Instead, the mattress usually lies on a wood platform or wire mesh and is held in place so as not to sag when in a closed position.

Instead, the larger Kwik Save stores were converted, some were sold or closed and the chain became a trading division of Somerfield Stores Ltd, sharing its supply chain and back office systems with Somerfield.

Instead, five years later in 1997, Sunderland moved to the Stadium of Light, in nearby Monkwearmouth, on the site of the closed Monkwearmouth Colliery.

Instead the so-called closed magnetic circuit type transformer having a small leakage inductance was used as a step-up transformer.

Instead, they organized themselves into closed societies ( i. e., Gesellschaften ) and would point to their belonging to certain families or " houses " ( i. e., Geschlechter ), as documented for Imperial Free Cities of Cologne, Frankfurt am Main, Nuremberg.

Instead, the south tube was closed at 8 p. m. each night, after which hundreds of feet of mobile scaffold and other equipment was hauled in.

Instead, if actively observed for a few minutes, one becomes aware of an apparent disorganized motion, a random field of lightness / darkness that overlays the redness / blackness of your closed eyelids.

Instead, you closed on the target and blatantly disobeyed the direction to " hold fire.

Instead many lines with little traffic were closed down.

Instead, the oxygen in the forced air ignited silicon and carbon impurities in the iron, starting a positive feedback loop.

Instead they fall back to an error condition displaying messages to the operator, and enter an infinite loop waiting for the user to either respond to a prompt to continue, or to reset the device.

Instead the papacy confined itself ( see Prisoner in the Vatican ) to the Apostolic Palace and adjacent buildings in the loop of the ancient fortifications known as the Leonine City, on Vatican Hill.

Instead of by traditional trunnions, the guns were attached to the carriage by a loop under the barrel.

Instead of the typical pretzel loop, they were made in the similar shape of a peace symbol.

Instead of stretching the sample, which would change the sample's timbre and pitch, ReCycle slices the loop into little pieces so that each beat gets its own sample.

Instead academics focus on the multiplicity of processes by which technology is funded, researched and produced, forming a feedback loop when the technologies are used and often transformed by their users, which then feeds into the process of guiding their future development.

Instead, using a gaseous helium coolant loop, SABRE dramatically cools the air from 1000 ° C down to-140 ° C in a heat exchanger while avoiding liquefaction of the air or blockage from freezing water vapour.

Instead of creating a magnetization distribution in analog recording, digital recording only needs two stable magnetic states, which are the + Ms and-Ms on the hysteresis loop.

Instead, it can be thought of in terms of smooth map from S < sup > 1 </ sup > to ; a smooth parameterized loop in, in other words.

Instead of being a continuous loop, these tracks have checkpoints at either end of the course, and the starting grid in the center.

) Instead of changing formats when the countdown ended, it stunted for another week with a six hour loop of novelty songs they called " goofy loops " played repeatedly.

Instead, the radiation pattern peaks in directions along the plane of the loop.

Instead of terminating before I-75 as it did, it now continues west across a former go-kart track to the other side, crossing Barrett Lakes Boulevard and a bridge over an unnamed tributary of Noonday Creek, to meet the southern tip of a loop road south of Chastain Road.

Instead of pulling the new loop forward, the right needle is now situated to pull the new loop backward through the old loop.

Instead of seeing it as a fair system under which ' everyone ' has equal rights, they saw it as the numerically preponderant poor tyrannizing over the rich.

Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of the operating system.

Instead, it is important that support for the CRM system is companywide.

Instead the distinction went to the 1884 route from Archway to Highgate, north London, which used a continuous cable and grip system on the 1 in 11 ( 9 %) climb of Highgate Hill.

Instead, this effort evolved into the SAGE system for the US Air Force, which used large screens and light guns to allow operators to interact with radar data stored in the computer.

Instead of enabling the guest operating system to dialog with hardware, virtual device drivers take the opposite role and emulate a piece of hardware, so that the guest operating system and its drivers running inside a virtual machine can have the illusion of accessing real hardware.

Instead, assuming that a civilization is still on an increasing curve of propulsion system velocity, not yet having reached the limit, the resources should be invested in designing a better propulsion system.

Instead of an internal power supply like the original system had, the Intellivision II would use an external AC adapter.

Instead of three categories ( heterosexual, bisexual and homosexual ), a seven-category Kinsey Scale system was used ( an 8th category for asexuals was added by Kinsey's associates ).

Instead, it is thought that most of them probably originate when dynamical interactions with other stars cause a binary system to coalesce into one star.

Instead of the standard American system of primary elections to choose each party's candidate, followed by a general election contest between the winners of the primaries, the Louisiana primary allows voters to select any candidate, regardless of party affiliation.

Instead, it maintained a system of taxation on the production that took place in the territories that they controlled, in exchange for protecting the growers and establishing law and order in these regions by implementing its own rules and regulations.

Instead, the system produced a large class of wage labourers generally resentful of foreign influence.

Instead of a thermal protection system, its surface was primarily covered with simulated tiles made from polyurethane foam.

Instead, approximation techniques, such as mean field approximations from statistical physics, or computer simulations are used to understand the behaviors of the system.

Instead, it is a set of wishful characteristics of a future system.

Instead, Coherentists might say that it is very unlikely that the whole system would be both untrue and consistent, and that if some part of the system was untrue, it would almost certainly be inconsistent with some other part of the system.

Instead, Jackson started work on a new " third generation " role-playing system.

Instead of the conservative motto, " A fair day's wage for a fair day's work ," we must inscribe on our banner the revolutionary watchword, " Abolition of the wage system.

Instead, he proposed a government sponsored system in which the price of farm land was set at a high enough level to prevent urban workers from easily purchasing it and thus leaving the labour market.

Instead, the court laid out a set of directives requiring the State to implement some system whereby same-sex couples would be granted equivalent statutory rights and privileges to male-female couples.