Under this approximation, any element with an atomic number of greater than 137 would require 1s electrons to be traveling faster than c, the speed of light.

Under this approximation, ( outlined under Hartree – Fock algorithm ), all of the terms of the exact Hamiltonian except the nuclear-nuclear repulsion term are re-expressed as the sum of one-electron operators outlined below.

Under this approximation, any element with an atomic number of greater than 137 would require 1s electrons to be traveling faster than c, the speed of light.

Under Placzek ’ s polarizability approximation, it is known that the depolarization ratio of a totally symmetric vibrational mode is less than 0. 75, and that of the other modes equals 0. 75.

Under this approximation, any element with an atomic number greater than 137 would require 1s electrons to be traveling faster than c, the speed of light.

Under that order, we have continued referring workers to the ranch.

Under no circumstances could we mistake one for the other ; ;

Another speaker, William H. Draper, Jr., former Under Secretary of the Army and now with the Palo Alto venture capital firm of Draper, Gaither & Anderson, urged the U.S. to `` throw down the gauntlet of battle to communism and tell Moscow bluntly we won't be pushed around any more ''.

Under such conditions every formula of the form, where ( T ) is a string of quantifiers containing all quantifiers in ( S ) and ( S ') interleaved among themselves in any fashion, but maintaining the relative order inside ( S ) and ( S '), will be equivalent to the original formula Φ '( this is yet another basic result in first-order predicate calculus that we rely on ).

Under these constraints, we would like to maximize the rate of information, or the signal, we can communicate over the channel.

* Minerva is featured on the seals of many schools and colleges: on that of Union College in Schenectady, NY, the motto is ( translated from the French ) " Under the laws of Minerva, we are all brothers.

Under total utility maximization we should prefer B to A, and through a regressive process of population increases and happiness decreases ( in each pair of cases the happiness decrease is more than outweighed by the population increase ) we are forced to prefer Z, a world of hundreds of billion people all living lives barely worth living, to A.

Under Constantine we hear of the foundation of a Christian church in Capua.

Under the influence of ignorance, we believe objects and persons to be independently real, existing apart from causes and conditions.

Under such condition, we would not progress, it'd only lead to over-saturation of the subject matter.

Under the circumstances presented by this case, we conclude that the defendants are not liable for contributory and vicarious copyright infringement and affirm the district court's partial grant of summary judgment.

Under a change of basis, represented by a matrix A, we have

Under storekeeping we should have the following departments and stores: Departments of issue and receipt, pattern room, armoury department, ordnance or park, harness, saddlery and accoutrements, camp equipment, tools and instruments, engineer store, timber yard, breaking-up store, unserviceable store.

As we were coming thro ’ the Gulf of Florida on the 29th of August, a large ball of fire fell from the Element and split our mast in Ten Thousand Pieces, if it were possible ; split our Main Beam, also Three Planks of the Side, Under Water, and Three of the Deck ; killed one man, another had his Hand carried of, and had it not been for the violent rains, our Sails would have been of a Blast of Fire.

Under this model we assume that the underlying rate is distributed log-normally with volatility.

: Under the headline " It's a Whole New Ballgame for Obama ," it is stated that, " Barack Obama, we all know by now, is not an ideologue.

Under the open world assumption, if a statement cannot be proven to be true with current knowledge, we cannot draw the conclusion that the statement is false.

It may be significant that in Johann Zoffany's portrait of Robert Baddeley as Moses, we find that " Under his arm Moses holds a rolled parchment of the Surface family tree that is used as an auction hammer, and he seems to be ticking off pictures in the catalogue ," although in the play Careless is the auctioneer in the relevant scene ( IV. 1 ) and Moses has a relatively minor role.

Under our policies and principles we seek to build up the labor movement, instead of injuring it, and we want all the negroes we can possibly get who will join hands with organized labor.

Under the assumptions of the preceding section, we have

This prime element of the truth may be stated as follows: Under prevailing policy, the U.S. can take the initiative against the Right, but cannot take the initiative against the Left.

Under Swiss law, bankruptcy can be a consequence of insolvency.

Under stressful environmental conditions, the cells produce oval endospores that can stay dormant for extended periods.

Under some circumstances, the signal radiated from the electron guns, scanning circuitry, and associated wiring of a CRT can be captured remotely and used to reconstruct what is shown on the CRT using a process called Van Eck phreaking.

Under optimal conditions, celery can be stored for up to seven weeks between.

Under French law, an association can represent the collective interests of consumers ; however, each claimant must be individually named in the lawsuit.

Under some circumstances, some creditors, otherwise the United States Trustee can request for the court converting the case into a demolition under chapter 7, or appointing a trustee to manage the debtor's business.

Under Dylan the programmer can simply place every function call in the " Private " or " Development " interface, and collect up publicly accessible functions in " Public ".

Under Texas law, the death penalty can only be issued if the jury is convinced that the defendant is not only guilty, but will commit further violent crimes in the future if he is not put to death.

Under the most favorable circumstances, a total solar eclipse can last for 7 minutes, 31 seconds, and can be viewed along a track that is up to 250 km wide.

Under Justinian I, reigning in the 6th century, parts of Italy were for a few decades ( re ) conquered from the Ostrogoths: thus, this famous mosaic, featuring the Byzantine emperor in the center, can be admired at Ravenna.

Under the terms of the accord, films produced using these funds can only be screened on television 24 months after their theatrical release.

Under a Uniform Act in force in most jurisdictions of the United States, being an organ donor is a simple process that can often be accomplished when a driver's license is renewed.

Under extremes of pressure and temperature solids may exhibit large structural and physical changes which can lead to polyamorphic phase transitions.

Under a theocracy, perceived divine status translated into earthly authority under divine law This can take the form of supreme divine authority above the state's, granting a tool for political influence to a priesthood.

Under certain conditions, especially during cooking, nitrites in meat can react with degradation products of amino acids, forming nitrosamines, which are known carcinogens.

Under the EU's Alternative Investment Fund Managers directive, offshore hedge funds using prime brokers as depositaries will be required to use EU-registered credit institutions before they can be sold in the EU.

Under the law, a region can be created out of one or more existing governorates or two or more existing regions, and a governorate can also join an existing region to create a new region.

Under United States tax law, for example, most owners of variable annuities and variable life insurance can invest their premium payments in the stock market and defer or eliminate paying any taxes on their investments until withdrawals are made.

Under a HACCP-concept ( Hazard Analysis and Critical Control Point ) radiation processing can serve and contribute as an ultimate critical control point before the food reaches the consumer.

Under this system, every health condition can be assigned to a unique category and given a code, up to six characters long.

Under the 2010 constitution, the defence forces can no longer be deployed for combat operations within Kenya without the approval of Parliament.