Q: Remove the spaces from the following sentence: Studies of number theory were vital to the foundations of calculus, and special functions and differential equations were essential to rational mechanics, which supplied concrete problems.
A: [Studiesofnumbertheorywerevitaltothefoundationsofcalculus,andspecialfunctionsanddifferentialequationswereessentialtorationalmechanics,whichsuppliedconcreteproblems.]

Q: Remove the spaces from the following sentence: and lay shameful things to her charge, and bring up an evil name on her, and say, I took this woman, and when I came near to her, I didn't find in her the tokens of virginity;
A: [andlayshamefulthingstohercharge,andbringupanevilnameonher,andsay,Itookthiswoman,andwhenIcameneartoher,Ididn'tfindinherthetokensofvirginity;]

Q: Remove the spaces from the following sentence: Morning temperatures will be around 21 °C. During the day they will reach a maximum of 31 °C. Low temperatures at night will be around 21°C. Southwesterly winds are weak.
A: [Morningtemperatureswillbearound21°C.Duringthedaytheywillreachamaximumof31°C.Lowtemperaturesatnightwillbearound21°C.Southwesterlywindsareweak.]

Q: Remove the spaces from the following sentence: In particular, Schauder's formulation of a fixed point theorem originated a new, extremely fruitful method in the theory of differential equations , known as Schauder's method ...
A:
[Inparticular,Schauder'sformulationofafixedpointtheoremoriginatedanew,extremelyfruitfulmethodinthetheoryofdifferentialequations,knownasSchauder'smethod...]