Sentence examples for calculus expression from inspiring English sources

The 'implicit' suggests that the explicit calculus expression of this governing equation is difficult to derive and not required.

These behaviors are due to the power law behavior of the spectral density and lead, for arbitrary pulling forces, based on causality and the linear superposition principle, to fractional calculus expressions, in accordance to former phenomenological fractional laws in polymer physics.

We then elaborate (in detailed calculus) the expression of the EEP ε, related to J-am model.

Consider that Carnap (1939, 1956b) admitted as legitimate theoretical terms that may be merely implicitly defined in calculi that are themselves only partially interpreted by correspondence rules between some select calculus terms and expressions belonging to an observational language (via non-eliminative reductions).

We use variational calculus to obtain analytical expression for the optimal charging profile.

(8) Using the second fundamental theorem of calculus we obtain an expression for the interfacial velocities dot{x}_{i}(t) =frac{ kappa-u_{text{BC}}) - psi(x_{i}(t),t)+ psi(-L,t)}{z(x_{i}(t),t)},quad i=frac{ kappa-u_{text{BC}}= int_{-L}^{L},mathrm{d} y w bigl( vert x-y vert bigr)H bigl[u(y,t)-kapsi bigr] = int _{x_{i}(t)}^{x_{2}(t)},tathrm{d} y w bigl( vert x-y vert bigr).

Z is an International Standards Organization standard that specifies computations using set theory and predicate calculus operating on typed expressions (Spivey 1992).

Similarly to domain relational calculus, we can simplify this expression by omitting some existential quantifiers and associated variables.

A key component of the query module is the planner agent, which takes a query and transforms it first to a calculus, then to an algebraic expression in order to break it into subqueries which an executor agent can send to the DSAs.

So, we have that the expression for the calculus of Pb under π/4-DQPSK is P b = 1 lo g 2 M ⋅ sin π M 2 π ∫ π 2 - π 2 exp ( γ b ⋅ lo g 2 M ) ⋅ 1 - cos π M ⋅ cos θ 1 - cos π M ⋅ cos θ d θ (14).

Furthermore, the FHAM takes full advantage of the formalism of fractional-order calculus to yield semi-analytic expressions in terms of material parameters.