• Consideration of the ordered array of atoms or ions is basic to an understanding of the results.
• Complex numbers are necessary to the mathematical treatment.
• Artificial ventilation is required to maintain a normal atmosphere.
• The presence of an inert strand is requisite for these processes.
• Considerations of phase equilibria are essential to ( or necessary for ) an understanding of any mass-transfer process.
• Calcium is also essential in many biological functions of the vertebrates.
• Carbon dioxide is essential to synthesis.
• Minute in amount but indispensable for life are the hormones and vitamins.