These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

These are now seen as elementary concepts.

These forms were taught to children at the elementary school level.

These assumptions are the elementary theorems of the particular theory, and can be thought of as the axioms of that field.

These include the Oak Park Township, the high school district, the elementary school district, a library district, and a park district.

These schools are part of elementary school District 97, which regularly adopts medium-term strategic plans.

These grades will move out of the two existing elementary schools.

These include one elementary school – St. Christine's – and two secondary schools, Ursuline and Cardinal Mooney.

These blocks of code consist of elementary actions which can perform operations such as changing the text displayed by a text object, or starting a video clip playing.

These tables, which contain mainly integrals of elementary functions, remained in use until the middle of the 20th century.

Armstrong on the fundamental groups of orbit spaces wrote: " These two papers show which parts of elementary covering space theory carry over from the free to the nonfree case.

These include 22 elementary schools with a student population of 7, 700 and nine high schools with a population of 3, 800.

These include 6 elementary schools ( 1, 695 students ), and 3 high schools ( 1, 512 students ).

These bosons are among the heavyweights of the elementary particles.

These include Kawaharagou, Kasamatsu, and Sougawa ; each hamlet has an elementary school, with Kawaharagou home to the village's only Junior High School.

These visual routines are composed of a sequence of elementary visual operators specific to the task at hand.

These programs include an annual science carnival, teaching Spanish to elementary students throughout the state, and the CHAMPS Project.

These studies include The Little Ševčík, an elementary violin tutor, which teaches the semitone system in 149 exercises, the School of Violin Technics ( Schule der Violintechnik, four parts, 1880 ), First Position, vol.

These elementary steps also increase motivation because improved physical status may enhance functional capacity, drive, and energy and thereby increase the patient's expectation that initiative and effort will be successful.

These elementary schools serve the incorporated Sawtelle area:

These attributes motivate many of the stories, which range from an incident with the Christmas turkey, to accidentally destroying Mary Turlington's treasured candles, to filling the elementary school playground with frogs.

These good distributions are called ( t, m, s )- nets and ( t, s )- sequences in base b. To introduce them, define first an elementary s-interval in base b a subset of I < sup > s </ sup > of the form

These include " In-School Operas " performed for and by elementary school students ; full-scale student matinées and a summer " Opera Camp " for secondary school students ; accredited teacher training programs ; large-scale, free community performances for families ; a popular lecture series for ticket holders before every mainstage performance ; and open dress rehearsals for senior centers.

These persons helped in the establishment of emergency hospitals, the North Provincial High School and the re-opening of elementary schools.

These balls are moving in great circles and ellipses, and are of course, the electrons, the particles of negative electricity which by their action create the forces that tie this atom of calcium to the neighboring atoms of oxygen and make up the solid structure of my finger bone.

These particles continue to decay, emitting alpha particles which can damage cells in the lung tissue.

These spherical particles precipitate in highly siliceous pools in Australia and elsewhere, and form these highly ordered arrays after years of sedimentation and compression under hydrostatic and gravitational forces.

These airborne soil particles are often contaminated with toxic chemicals such as pesticides or petroleum fuels, posing ecological and public health hazards when they later land, or are inhaled / ingested.

These are coherent states ( or solitons ) which behave like a particle, and they can be fermionic even if all the constituent particles are bosons.

These measurements helped determine how the particles got their energy and how they were transported through Jupiter's magnetosphere.

These philosophers believed that other elements ( except ether ) were physically palpable and hence comprised minuscule particles of matter.

These particles pose not only numerous scientific problems, but also a terminological problem.

These particles can hit the Earth within 15 minutes to 2 hours of the solar flare.

These so-called " whistler " mode waves can interact with radiation belt particles and cause them to precipitate onto the ionosphere, adding ionization to the D-region.

These exotic particles are known as anyons, and they obey fractional statistics.

These charged particles ( ions ) are found in the fluid that surrounds the entire nervous system.

These folds are studded with small round bodies known as F < sub > 1 </ sub > particles or oxysomes.

These clouds would have a typical density of 30 particles per cubic centimeter.

These particles, or chondrules, are composed mostly of silicate minerals that appear to have been melted while they were free-floating objects in space.

These force carrier particles are strings with endpoints that confine them to their p-branes.

These particles cannot be filtered out before injection, and will accumulate in the body over time, especially in the lungs and eyes, producing various complications such as pulmonary hypertension, an irreversible and progressive disease.

These small particles or organisms gain entry when the shell valves are open for feeding or respiration.

These α subunits are controlled by binding to " cap " structures or regulatory particles that recognize polyubiquitin tags attached to protein substrates and initiate the degradation process.

These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried.

These decay events obey the various conservation laws, and as a result, pairs of particles can be generated so that they are in some specific quantum states.

These reactions occur at far higher energies than with non-ionization radiation, which requires only single particles to ionize.

These strings can oscillate, giving the observed particles their flavor, charge, mass and spin.