Sentence examples for differential notation from inspiring English sources

The small "d"s are differential notation, another Newtonian invention that appears in countless physical equations and that allows you to mathematically predict how something will change as another related parameter is incrementally altered – in this case, time.

That is, we obtain a stochastic partial differential equation with multiplicative noise given by V t = V 0 + ∫ 0 t τ − 1 ( V s + F ( V s, s ) ) d s + ϵ n ∫ 0 t G ( V s, s ) ∘ ι − 1 d W s, or in differential notation d V t = τ − 1 ( V t + F ( V t, t ) ) d t + ϵ n G ( V t, t ) ∘ ι − 1 d W t. (2.22).

(7) 1 Ep dp dt + p − p b R = I (t ) + σ ε (t ) Next we exploited the fundamental relationship between a white noise process ε(t) and a Brownian motion process W t): W (t ) = ∫ s = 0 s = t ε (s ) ds a, which, when written in differential notation, yields dW = ε(t) dt.

Vectors are written using the usual differential geometry notation [13], namely (boldsymbol{X}=(X^{t}, X^{r}, X^{theta}, X^{phi}) = X^{t} partial_{t} + X^{r} partial_{r} + X^{theta} partial_{theta} + X^{phi} partial_{phi}).

(22 25) populations are denoted in differential equations notation from the right-hand column of Table 1): m· T = m·(S + X + C + XC) = m· S + m· X + m· C + m· XC.     (22) The total ("all cause" or "crude") death hazard for the population is written mtot.

Recall that, in terms of the differential equations notation from the right-hand column of Table 1, π~X = πC + πS, π~X~C = πS and π~XC = πC, the values of which are determined according to one of the six cases defined above in interaction (1).

The fractional differential equations related notations adopted in this paper can be found, if not explained specifically, in almost all literature related to fractional differential equations.

Section 2 contains some preliminary material on differential inclusions and the notation to be followed in the sequel, while Section 3 presents the concept of mild solutions for fractional neutral stochastic inclusions.

(Leibniz's notation and "differential Method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians).

A consequence of the direct meaning of kinetic orders in BST is that it is possible to set up differential equations in symbolic notation, solely based on the structure of a metabolic pathway and its regulatory structure, whereas deep knowledge of their regulatory mechanisms is not needed.

The dynamical system is then cast in the form of a first-order differential equation by using matrix notation.