# While ideal gas molecules do not interact, we consider molecules attracting others within a distance of several molecules ' radii.

# Inertial reference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal gyroscopes ; the axis points to the vernal equinox

AA # 9, however, will fill the case much better, and the slow burn rate of AA # 9 is ideal for magnum handgun rounds, producing 20 % higher velocities ( at maximum levels ) while still producing less pressure than the fast burning AA # 2.

# Every principal ideal domain is Noetherian.

# All principal ideal domains are integrally closed.

# Every prime ideal of A is principal.

# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.

# If n = 2k + 1, then the action of the unit vector u on the left ideal decomposes the space into a pair of isomorphic irreducible eigenspaces ( both denoted by Δ ), corresponding to the respective eigenvalues + 1 and − 1.

# Harmonic distortion: defined as a departure from the ideal sinusoidal waveform expected on the line.

# It is an ideal emitter: it emits as much or more energy at every frequency than any other body at the same temperature.

This is similar ( but more categorical ) to concepts in group theory or module theory, where a given decomposition of an object into a direct sum is " not natural ", or rather " not unique ", as automorphisms exist that do not preserve the direct sum decomposition – see Structure theorem for finitely generated modules over a principal ideal domain # Uniqueness for example.

# REDIRECT ideal ( ring theory )

# redirect Boolean prime ideal theorem

# REDIRECT ideal ( ring theory )

# Methods: the most appropriate ways to achieve the ideal arrangement.

# In the Aeneid by Virgil, Nisus and Euryalus are ideal friends and lovers, who died during a raid on the Rutulians.

# those who, like Plato, distinguished ideal and mathematical numbers ;

# those who, like Xenocrates, identified ideal numbers with mathematical numbers

# SGI, based on the ideal of world citizenship, shall safeguard fundamental human rights and not discriminate against any individual on any grounds.

# SGI shall promote, based on the Buddhist ideal of symbiosis, the protection of nature and the environment.

# Determine the target market's preferred combination of attributes ( referred to as an ideal vector )

# The radical of the ideal 4Z of integer multiples of 4 is 2Z.

# Socialism Social-Democratic Style

# The Absolutist View rejects all compromise and believes that, if obeying the scripture costs the welfare of the believer, then that is a reasonable sacrifice for salvation.

# Human welfare is best served by improving the quality and flow of desired services delivered, rather than by merely increasing the total dollar flow.

# reserves managed for the welfare of a particular village, town or tribe ( see also ḥaram, although that term usually refers more to water protection measures )

# Refinement refers to methods that alleviate or minimize potential pain, suffering or distress, and enhance animal welfare for the animals still used.

# SGI shall contribute to peace, culture and education for the happiness and welfare of all humanity based on Buddhist respect for the sanctity of life.

# Emunah of America: Chapters and divisions around the United States support Israel ’ s largest Religious Zionist educational and social welfare organizations.

# there was to be global economic cooperation and advancement of social welfare ;

# REDIRECT Corporate welfare

# Christian-democratic welfare states are based on the principle of subsidiarity and the dominance of social insurance schemes, offering a medium level of decommodification and a high degree of social stratification.

# Change in social welfare policies and focus on economic development and job creation at the macro level.

# Developing social services: health, education, housing, welfare, culture, and sports

# Preference for the welfare and collective well-being of the community over individual rights

# Our common welfare should come first ; personal recovery depends upon A. A. unity.

# Decreasing dependency on welfare

# institutions organised to protect the community against what are felt to be intentional dangers to it, with the welfare of the people thus sequestered not the immediate issue: concentration camps, P. O. W.

# Promote the welfare of my profession ;

# that the ultimate test of an action is its tendency to promote the general harmony or welfare ;

# Animal welfare is generally improved because animals are not kept in stifling conditions.

# We demand an expansion on a large scale of old age welfare.

# Everyone contributes to the upkeep and welfare of the village and works to become a productive member of the community.

# No disruptive behavior of any kind that disturbs the general peace and welfare of the village.

# the divine revelation as well as the moral and social welfare of all the nations.

# Kesejahteraan Sosial ( Social Welfare ), influenced by the idea of the welfare state, an emphasis on populist Socialism

# To make Pakistan a true Islamic welfare state to ensure justice to people and eradicate corruption whatsoever.