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The first algorithm was applied over a gradually decreasing value of X to obtain the norm solution Over is a good word to use when talking about ranges.


One should try to not mix the various 1st/2nd/3rd-person voices when writing. An effective form of writing (and exercise in the art of writing) is to try to never use 1st person (e.g. I, we), or 2nd person (You singular or You plural). Instead, using the 3rd person active voice when necessary, but try to use the passive voice when possible. For example, ...


I don't find anything strange in it simply because, from a very general "our", you're turning to address the readers, which is quite effective, as they begin to apply the suggestions internally as they read. By the way, "fulfilling" is one word.


In psychology, these are known as intrusive thoughts(1). The term is chosen because these thoughts seem to enter your mind from outside, without your control. Intrusive thoughts can occur across a wide spectrum of subjects, from uncontrollable fears, to the urges toward mischief or violence which you experience, to the urge to harm oneself without reason, to ...


Sipping is a particular way of drinking. It means to drink little by little over a period of time while to drink is general.


"To sip" implies smaller amounts, whereas "To drink" implies average. (Something like "To gulp" would imply larger amounts)


The two phrases "kinda figured it out" and "kinda figured out" can both be grammatically correct (assuming you use colloquial language instead of "kind of"), but they must be used in different contexts. "Kinda figured it out" can be used like a verb: I kinda figured it out. while "kinda figured out" can be used like an adjective: I got it kinda ...


This is not an ungrammatical expression. The sentence is a combination of the phrases "It was cute" and "It was like a shy teenager". One could consider this a case of unclear pronoun reference, which would generally be considered more of a stylistic than grammatical error.

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