In mathematics, the infimum ( plural infima ) of a subset S of some partially ordered set T is the greatest element of T that is less than or equal to all elements of S. Consequently the term greatest lower bound ( also abbreviated as glb or GLB ) is also commonly used.

In mathematics, given a subset S of a totally or partially ordered set T, the supremum ( sup ) of S, if it exists, is the least element of T that is greater than or equal to every element of S. Consequently, the supremum is also referred to as the least upper bound ( lub or LUB ).

A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in T. Note that u is an element of P but need not be an element of T. An element m of P is called a maximal element ( or non-dominated ) if there is no element x in P for which m < x.

* Although a woman ( who is exempt from this mitzvah because it is time bound ) may not blow the shofar for men ( whose duty it is to perform the mitzvah ), a female Ba ' alat T ' qiah may intone the shofar for herself and other women.

Hence, at low amounts of bound ligand, the protein prefers the low-affinity T state ; however, as the amount of bound ligand increases, the protein comes to prefer the high-affinity state.

T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm λ x.

In terms of total current, which includes both free and bound current, the line integral of the magnetic B-field ( in tesla, T ) around closed curve C is proportional to the total current I < sub > enc </ sub > passing through a surface S ( enclosed by C ):

Antigens inside a cell are bound to Class I MHC molecules, and brought to the surface of the cell by the Class I MHC molecule, where they can be recognized by the T cell.

The affinity between CD8 and the MHC molecule keeps the T < sub > C </ sub > cell and the target cell bound closely together during antigen-specific activation.

Once at the lymph nodes, the APC begin to present antigen peptides that are bound to Class II MHC, allowing CD4 < sup >+</ sup > T cells that express the specific TCRs against the peptide / MHC complex to activate.

* Aggregate analysis determines the upper bound T ( n ) on the total cost of a sequence of n operations, then calculates the average cost to be T ( n ) / n.

In January 1937, George T. Simon closed a review of the band with the words: " This Herman outfit bears watching ; not only because it's fun listening to in its present stages, but also because its bound to reach even greater stages.

When the barrier field F is high enough for the CFE regime to be operating for metal emission at 0 K, then the condition k < sub > B </ sub > T < d < sub > F </ sub > provides a formal upper bound ( in temperature ) to the CFE emission regime.

There's bound to be someone on guard, but the hat might fool them long enough for me to get close ''.

Mark row on which first stitches have been bound off for armhole by drawing a contrasting colored thread through it.

she sprinkled common sugar directly on the injury and then bound it loosely with cotton cloth, over which she poured turpentine.

As the robbers leave the looted train, the film suddenly cuts back to the station, where the telegrapher's little daughter arrives with her father's dinner pail only to find him bound on the floor.

And this would mean that we live in a mechanistic universe, governed by the laws of cause and effect, bound in chains of determinism that hold the universe on a completely predetermined course in which there is not room for soul or spirit or human freedom.

Part of the time saved was spent on a preliminary estimate for a long-distance plan to free bound oxygen in the sands of Mars to make the planet more friendly to future human generations.

In an appeal on the record from a decision in a judicial proceeding, both appellant and respondent are bound to base their arguments wholly on the proceedings and body of evidence as they were presented in the lower tribunal.

The Aegean Islands are within the sea and some bound it on its southern periphery, including Crete and Rhodes.

* 2006 – Comair Flight 5191 crashes on takeoff from Blue Grass Airport in Lexington, Kentucky bound for Hartsfield-Jackson International Airport in Atlanta, Georgia.

:: Landing on tall ships with a sudden, great bound,

* 1990 – Customs officers in Middlesbrough, England, United Kingdom, say they have seized what they believe to be the barrel of a massive gun on a ship bound for Iraq.

They were bound to be in attendance on certain days under penalty of fine, and sign letters and diplomas.

) However, when m decreases there is no upper bound on how much n can increase — and it will often increase greatly.

Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our Universe only on large scales — local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.

Eventually in 1965, John Bardeen, Leon Cooper and John Schrieffer developed the so-called BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons can give rise to a bound state called a Cooper pair.

In nearly all cases, the monarch is still the nominal chief executive, but is bound by constitutional convention to act on the advice of the Cabinet.

Any attempt to impose an organization on them is bound to be somewhat arbitrary.

Surface forces or contact forces, expressed as force per unit area, can act either on the bounding surface of the body, as a result of mechanical contact with other bodies, or on imaginary internal surfaces that bound portions of the body, as a result of the mechanical interaction between the parts of the body to either side of the surface ( Euler-Cauchy's stress principle ).

Note the position of the hydroxyl group ( red or green ) on the anomeric carbon relative to the CH < sub > 2 </ sub > OH group bound to carbon 5: they are either on the opposite sides ( α ), or the same side ( β ).

In inflicting it, they were guided only by their conscientious convictions of duty ; they had to take an oath that they would act biased by neither partiality nor favour ; and, in addition to this, they were bound in every case to state in their lists, opposite the name of the guilty citizen, the cause of the punishment inflicted on him, Subscriptio censoria.

The whole, however, may be judged from this fragment: " We Irish, though dwelling at the far ends of the earth, are all disciples of St. Peter and St. Paul ... we are bound to the Chair of Peter, and although Rome is great and renowned, through that Chair alone is she looked on as great and illustrious among us ... On account of the two Apostles of Christ, you pope are almost celestial, and Rome is the head of the whole world, and of the Churches ".

" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

If n > 1, then the conditions result in what is sometimes referred to as undersampling, bandpass sampling, or using a sampling rate less than the Nyquist rate 2f < sub > H </ sub > obtained from the upper bound of the spectrum.

They can bring together the ' bound state ' ( eigenvector ) and ' continuous spectrum ', in one place.

The energy spectrum of a bound state is discrete, unlike the continuous spectrum of isolated particles.

Absorption peaks in the visible light spectrum are measured at 495 and 545 / 566 nm, depending on the chromophores bound and the considered organism.

Since there are an infinite number of modes this implies infinite heat capacity ( infinite energy at any non-zero temperature ), as well as an unphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the ultraviolet catastrophe.

The ( bound ) form of the dye has an absorption spectrum maximum historically held to be at 595 nm.

Once again ignoring complications involved with a continuous spectrum of H, suppose it is bounded from below and that its greatest lower bound is E < sub > 0 </ sub >.

This quantum interference in many body system has been described using quantum mechanics by Gregor Wentzel, for the interpretation of the Auger effect, by Ettore Majorana for the dissociation processes and quasi bound states, by Ugo Fano for the atomic auto-ionization states in the continuum of helium atomic spectrum and by Victor Frederick Weisskopf.

Spaces with a discrete spectrum correspond to bound states in quantum mechanics, while a continuous spectrum is associated with scattering states.

In mathematics, the Gershgorin circle theorem may be used to bound the spectrum of a square matrix.

These operators describe conformal bound states with a continuous mass spectrum.

The other " particles "/ bound states have a continuous mass spectrum which can take on any arbitrarily small nonzero mass.