Problem: Add spaces: IfrelativemaximumweretakentomeanthatthevalueofthefunctionatthecriticalpointisgreaterthanorequaltothenearbyvaluesthentheconditiononthematrixSisthatitisnegativesemidefinite.

Spaces added: If relative maximum were taken to mean that the value of the function at the critical point is greater than or equal to the nearby values then the condition on the matrix S is that it is negative semidefinite.

Problem: Add spaces: Thefertilisedeggsbecomeembryos,andoneortwoofthemarereplacedbackintotheuterusoftheeggrecipienttocreateapregnancy.

Spaces added: The fertilised eggs become embryos, and one or two of them are replaced back into the uterus of the egg recipient to create a pregnancy.

Problem: Add spaces: Youmadethewordsbelievableandtheceremonyflowedbeautifully

Spaces added: You made the words believable and the ceremony flowed beautifully

Problem: Add spaces: AsinVillaAubertinthewindowsarepositionedsothatthelightisutilizedinthebestpossibleway,bothintheformoflargewindowsfacingeast,aswellashigh-level,smallwindowsfacingnorth.

Spaces added:
As in Villa Aubertin the windows are positioned so that the light is utilized in the best possible way, both in the form of large windows facing east, as well as high-level, small windows facing north.