Since the discovery of Newton's law of universal gravitation in the 17th century, the stability of the Solar System has preoccupied many mathematicians, starting with Laplace.

Since, we now have an expression for the Laplace transform of in terms of's Laplace transform:

Since the Laplace transform of 1 is, we continue:

Since the time of Laplace ( 1799 ), scientists had been puzzled as to why pressure variations measured at the Earth's surface associated with the semi-diurnal solar tide dominate those of the diurnal tide in amplitude, when intuitively one would expect the diurnal ( daily ) passage of the sun to dominate.

Since a digital computer is a discrete system, the Laplace transform is replaced with the Z-transform.

Since the Laplace equation is linear, the set of harmonic functions defined on a given domain is, in fact, a vector space.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

Since is a compact operator, is infinitely close to and therefore one has also.

Since just after the turn of the century, most longarm machines are now sold with stitch-regulation, which means that the operator no longer has to synchronize hand speed with that of the motor.

Since is a positive semi-definite operator, it has a spectral decomposition such that where are orthonormal vectors.

Since subtraction is not a commutative operator, the two operands are named.

* Since the early year 2010, local ferry operator Color Line ( serves two ferry routes between Hirtshals and Norway ) have had their own radio station, Color Radio, that plays popular songs from mostly the 80's and 90's.

Since the 1990s, rangefinders have been used in virtual reality systems to detect operator movements and locate objects.

Since an everywhere defined self-adjoint operator is necessarily bounded, one needs be more attentive to the domain issue in the unbounded case.

Since 1987, the airport operator kept all landing fees, while the Civil Aviation Administration collects the navigation fees.

Since T is a unitary operator, its spectrum lie on the unit circle.

Since 2006 Euskotren Trena is the commercial brand for the operator of the railway network in the Basque Country, which is Eusko Trenbideak, while the network itself is owned by the public entity Euskal Trenbide Sarea.

Since the forward difference operator Δ equals

Since 2003, he also owns 34 % of DirecTV Group ( formerly Hughes Electronics ), operator of the largest American satellite TV system, DirecTV, and Intermix Media ( creators of myspace. com ) since 2005.

Since Tierco was on its way to becoming a " premier " regional theme park operator, in 1994 it changed its name to Premier Parks, Inc. Kieran E. Burke, chairman and chief executive officer ( CEO ), noted that the new name signified the beginning of a new era for the company.

Since a standard sewing machine has only one needle, the operator must stop and re-thread the machine manually for each subsequent color in a multi-color design.

for all smooth L < sup > 2 </ sup > functions f, g. Since smooth functions are dense in L < sup > 2 </ sup >, this defines the adjoint on a dense subset of L < sup > 2 </ sup >: P < sup >*</ sup > is a densely-defined operator.

Since electric vehicles use whatever electricity is delivered by their electrical utility / grid operator, electric vehicles can be made more or less efficient, polluting and expensive to run, by modifying the electrical generating stations.

Since the objects being manipulated do not exist in a physical sense, the forces are generated using haptic ( force generating ) operator controls.

Since T is a linear operator, we can talk about eigenvalues and eigenfunctions of T.

Since the crystalline system and hence its Hamiltonian is invariant after such translations, the translation operator must be commutative with the Hamiltonian operator, thus they can be simultaneously diagonalized.

Since subtracting 1 before complementing is equivalent to adding 1 afterwards, the operator would thus effectively add the ten's complement of the subtrahend.

Since the rotation does not depend explicitly on time, it commutes with the energy operator.

Since E − H = 0, and because for infinitesimal rotations ( in the xy-plane for this example ; it may be done likewise for any plane ) by an angle dθ the rotation operator is

Since the complicated process of establishing new communes and reviewing the rudimentary plan left by the French did not even begin until the fall of 1957, this goal appears somewhat ambitious.

Since effective area coverage appears fairly remote, the requirement can be borne in mind while considering the elements: air, surface, sub-surface, fixed installations, mines, and intelligence.

Since the 1980s, the baku appears not as a chimera of an elephant and tiger but as a zoologically recognizable tapir.

Since Arafat's death, he is formally head of Fatah's political bureau and chairman, but his actual political following within Fatah appears limited.

Since the winding resistance appears as a resistance in series with the inductor, it is often called the series resistance.

Since most wiki systems use URLs for individual pages where the page's title appears at the end of an otherwise unchanging address, the simplest way of defining such mappings is by substituting the interwiki prefix for the unchanging part of the URL.

Since then, Lucia di Lammermoor has remained a staple of the standard operatic repertoire, and appears as number nineteen on the Operabase list of the most-performed operas worldwide.

Since the earliest days of Esperanto, the colour green has been used as a symbol of mutual recognition and it appears prominently in all Esperanto symbols.

Since our planet rotates, it appears to a stationary observer on Earth that a gyroscope's axis is completing a full rotation once every 24 hours.

Since neither the Congress nor the President appears to have authorized a privateer during the war, the Navy would not have had the authority to do so by itself.

Since this autoimmune disease appears suddenly, often quite late in life, viral or bacterial infection may trigger antibodies that cross-react with the human TSH receptor ( a phenomenon known as antigenic mimicry, also seen in some cases of type 1 diabetes ).

Since the Simpson family frequently appears in court, other characters have represented the Simpsons in legal matters since Hutz's retirement.

Since their introduction, Koopa Troopas have become the iconic enemy of the Mario franchise, often referenced in popular culture relating to the series: in 2007's The Simpsons Game, a Koopa Troopa appears as the apparent bride of the eccentric geek Professor Frink after Bart and Lisa rescue him from Donkey Kong in a parody of the popular arcade game.

Since porphyrins are not otherwise present in skin, and no UV light is employed, it appears to be safe, and has been cleared for marketing by the U. S. FDA.

Since Etruscan literature has not survived, the meaning of the scenes in which he appears can only be interpreted by comparison to Greek and Roman myths, through information about Etruscan myths preserved by Greek and Latin literature, or through conjectural reconstructions based on other Etruscan representations.

In 2008 the club celebrated what was claimed to be the 150th anniversary of the first meeting of its founding members, published " Melbourne FC – Since 1858 – An Illustrated History " and commemorated its formation by naming " 150 Heroes " as well as a birthday logo which appears on its official jersey.

Since the Second Vatican Council ( 1962 – 65 ), the liturgy for the conferral of the pallium as it appears in the liturgical books is to take place at the beginning of the Mass in which the archbishop takes possession of his see ; however, the practice of Pope John Paul II and Pope Benedict XVI has actually been to summon all new metropolitans to Rome to receive the pallium directly from the hands of the pope on the Feast of Saints Peter and Paul.

Since the mid 1990s, Billie Godfrey has worked with the band as a backing vocalist and appears with them at concerts.

Since BFS appears to cause no actual nerve damage ( at least as seen on the EMG ), patients will likely exhibit a completely normal EMG ( or one where the only abnormality seen is fasciculations ).

Since no one intervenes during the incident, such behaviour appears to have been expected of him.

Since Mrs. Voorhees, the killer in the original Friday the 13th, appears onscreen only during the final scenes of the film, Manfredini had the job of creating a score that would represent the killer in her absence.

Since it appears that Shūzō's mother, Hatsu, was already pregnant when she fell in love with Okakura Kakuzō ( 岡倉 覚三 ), otherwise known as Okakura Tenshin ( 岡倉 天心 ), a protégé of her husband's ( a notable patron of the arts ), the rumour that Okakura was Kuki's father would appear to be groundless.

Since Julia appears on the South Frieze, it is more likely that this figure is Octavia Minor.

Since her retirement from politics, she appears infrequently at space-related events, and appears to be content with being out of the limelight.