In themathematical theoryof tensegrity, a third kind of element (or “member”) is sometimes allowed that acts in the opposite manner to the cable. This element, called a strut, is straight when compressed and floppy when stretched. In simple mathematical terms, then, the three kinds of elem...
The terms are meant to contrast with computer programming which solves such problems by implementing algorithms which may be designed specifically for a given problem. By mathematical programming, we consider declarative approaches. This means that a separation is considered between the representation of ...
There are two options for delimiting a math expression inline with your text. You can either surround the expression with dollar symbols ($), or start the expression with$`and end it with`$. The latter syntax is useful when the expression you are writing contains characters that overlap with...
getVariableTerms()); exp = Subtract(Multiply(Literal(1), x), Literal(-5)); print(exp); print(exp.simplify()); print(Pow(Add(x, y), Literal(2))); print(Pow(Pow(Literal(3), Literal(3)), Literal(2)).evaluate()); print(Pow(Literal(3), Pow(Literal(3), Literal(2)))....
"Below is an instruction that describes a task. Write a response that appropriately completes the request.\n\n### Instruction:\n{instruction}\n\n### Response: Let's think step by step." Thanks for the open source code ofWizardMathandRFT. Some of our codes are based on them. ...
For instance, the infix identity-forming operation maps two terms s and t to the formula (s = t), while the Polish identity-forming operation transforms s and t into =st, and so on for the other symbols of L. Together, these constructor operations permit the successive construction of ...
Open AccessThis chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to...
dx/dt=f(x)+Z(x)I(t), where the impact of the input currentI(t)is modulated by the phase sensitivity functionZ(x). Similarly, earlier work analyzed optimal weak inputs to start or stop repetitive spiking in a general biological oscillator, with dynamics expressed in polar coordinates as ...
But even in his own terms, there is a failure to test his analysis of purpose against reality. Is it a “spontaneous judgement” without any“conscious train of reasoning” that leads one to recognise a complicated though computable ordering as being a well-ordering? Can one truly say that ...
(In metaphorical terms, the Platonic theory claims that numbers exist ‘in another world’, and the Aristotelian theory claims that they exist ‘in this world’.) By contrast with each of these positions, the central claim of conceptualism is that mathematics concerns objects (e.g. numbers) ...