For instance, for a field of free ( non-interacting ) bosons, the total energy of the field is found by summing the energies of the bosons in each energy eigenstate.

For a non-interacting system, this wave velocity is equal to the Fermi velocity, while it is higher ( lower ) for repulsive ( attractive ) interactions among the fermions.

For non-interacting particles, the potential would be just a mass term, and there would be no Q-ball.

For non-interacting electrons, a highly successful approach was put forward in 1979 by Abrahams et al.

For a system of point particles without any intrinsic angular momentum ( see below ), it turns out to be

For example, if a colloid consists of a solid phase dispersed in a liquid, the solid particles will not diffuse through a membrane, whereas with a true solution the dissolved ions or molecules will diffuse through a membrane.

For example, negatively-charged colloidal silica or clay particles can be flocculated by the addition of a positively-charged polymer.

For an atemporal interpretation that “ makes no attempt to give a ‘ local ’ account on the level of determinate particles ”, the conjugate wavefunction, (" advanced " or time-reversed ) of the relativistic version of the wavefunction, and the so-called " retarded " or time-forward version are both regarded as real and the transactional interpretation results.

For longer-range ( about a centimetre ) particles, they need a very large depletion depth and large area.

For short-range particles, they need any contact or un-depleted semiconductor on at least one surface to be very thin.

For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases.

For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration increases.

For example, a system can emit energy to another by transferring ( radiating ) electromagnetic energy, but this creates forces upon the particles that absorb the radiation.

For contributions to the unification of the weak and electromagnetic interaction between elementary particles, Abdus Salam, Sheldon Glashow and Steven Weinberg were awarded the Nobel Prize in Physics in 1979.

For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.

For alpha particles and low energy beta particles the " end window " type of GM tube is used as these particles have a limited range even in free air and are easily stopped by a solid material.

For efficient detection of alpha particles the GM tube window should ideally be within 10mm of the radiation source due to the attenuation in free air.

For example, in the solar wind together with ionized hydrogen, the particles interact with the Earth's magnetosphere giving rise to Birkeland currents and the aurora.

For this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic.

For example, a simple routine of coating cotton fabric with silica or titania particles by sol-gel technique has been reported, which protects the fabric from UV light and makes it superhydrophobic.

For a four-dimensional spherical uncharged black hole, the deformation of the horizon is similar to the type of deformation which describes the emission and absorption of particles on a string-theory world sheet.

For a given energy in a given volume, there is an upper limit to the density of information ( the Bekenstein bound ) about the whereabouts of all the particles which compose matter in that volume, suggesting that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of fundamental particles.

For different situations and / or number of particles, the Hamiltonian is different since it includes the sum of kinetic energies of the particles, and the potential energy function corresponding to the situation.

For this reason cross terms for kinetic energy may appear in the Hamiltonian ; a mix of the gradients for two particles:

For each i, let Af.

For many Muslims, i ' thar must be practiced as a religious obligation during specific Islamic holidays.

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For the incremental case ( i. e., ), this simplifies to:

For example, where a person has committed harmful actions of body, speech and mind based on greed, hatred and delusion, rebirth in a lower realm, i. e. an animal, a ghost or a hell realm, is to be expected.

For private suits only the victims or their families could prosecute, while for public suits anyone ( ho boulomenos, ' whoever wants to ' i. e. any citizen with full citizen rights ) could bring a case since the issues in these major suits were regarded as affecting the community as a whole.

For example, the giant elliptical galaxy M87 has an absolute magnitude of − 22 ( i. e. as bright as about 60, 000 stars of magnitude − 10 ).

For example, an array of 10 integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, … 2036, so that the element with index i has the address 2000 + 4 × i.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

For example, an " anti-realist " who denies that other minds exist ( i. e., a solipsist ) is quite different from an " anti-realist " who claims that there is no fact of the matter as to whether or not there are unobservable other minds ( i. e., a logical behaviorist ).

For a rigid body rotating around an axis of symmetry ( e. g. the blades of a ceiling fan ), the angular momentum can be expressed as the product of the body's moment of inertia, I, ( i. e. a measure of an object's resistance to changes in its rotation rate ) and its angular velocity ω:

For instance, chapter 6 ( B '), which ought to follow chapter 7 ( A ') chronologically, is put in parallel with chapter 3 ( B ) because they both deal with the persecution of Daniel and his friends i. e. " God's people.

For many years, apocryphal rumors circulated that a jealous lover had poisoned his coffee, but a more likely scenario is that he died of a bad heart attack after becoming disoriented during a snowstorm ( i. e., he froze to death ).

For objectivists, probability objectively measures the plausibility of propositions, i. e. the probability of a proposition corresponds to a reasonable belief everyone ( even a " robot ") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency.

For example, most areas of law in most Anglo-American jurisdictions include " statutory law " enacted by a legislature, " regulatory law " promulgated by executive branch agencies pursuant to delegation of rule-making authority from the legislature, and common law or " case law ", i. e., decisions issued by courts ( or quasi-judicial tribunals within agencies ).

For example, a ( strict ) 2-category is a category together with " morphisms between morphisms ", i. e., processes which allow us to transform one morphism into another.

For example, if function div stands for the division operation x / y, then div with the parameter x fixed at 1 ( i. e., div 1 ) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv ( y )

For example, while in a conversion to Judaism a convert must accept basic Jewish principles of faith, and renounce all other religions, the process is more like a form of adoption, or changing national citizenship ( i. e. becoming a formal member of the people, or tribe ), with the convert becoming a " child of Abraham and Sarah.

For real values of, we have and for purely imaginary we have hence has a limit at 0 ( i. e., ƒ is complex differentiable at 0 ) if and only if.

For instance, low-end versions of complex architectures ( i. e. using less hardware ) could lead to situations where it was possible to improve performance by not using a complex instruction ( such as a procedure call or enter instruction ), but instead using a sequence of simpler instructions.