Here, the apostle attempted to convey the underlying concepts about Christ to a Greek audience, and the sermon illustrates some key elements of future Christological discourses that were first brought forward by Paul.

Here the underlying meaning of " te pilla " or " prayer " is a conception of petitionary prayer that has a sense of judgment or a " plea " in the court of judgment.

Here composition of morphisms is just ring multiplication and the unique hom-set is the underlying abelian group.

' Here no doubt the underlying notion is not merely symbolical, but in origin the stone is itself the god, an idea which later religion expressed in the cult-title specially used in this connection, Iuppiter Lapis. In Chapter Two: The ' Antecedents ' of Roman Religion.

Here the underlying geometrical incidence relation ( points lying on lines, in Crofton's case ) is seen in a freer light, as the site for an integral transform composed as pullback onto the incidence graph and then push forward.

Here we exploit developmental integration between the brain and its underlying skeletal base to test hypotheses about brain evolution in Homo.

Here for a curve, C, what matters is the point set ( typically in the plane ) underlying C, not a given parametrisation.

Here " simple " indicates that the underlying type theory is simple, not polymorphic or dependent.

Here the underlying theory is of electrons in a metal interacting with lattice vibrations called phonons.

Here a paradigm is not a particular solution, but rather the underlying system of ideas that causes a range of solutions to be ' normal ' or ' obvious '.

Here the price of the underlying instrument is usually modelled such that it follows a geometric Brownian motion with constant drift and volatility.

Here, the underlying asset is the resource itself ; the value of the asset is a function of both quantity of resource available, and the price of the commodity in question.

Here we have evidently a mystical allusion to the King of Kings on His throne in the tabernacle, and this is the theme underlying the whole poem.

Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector.

Here he helped develop the underlying basic medical science and technology for haemodynamic doppler ultrasound vascular assessment in the Non Invasive Angiology Group, and set up the clinical Ultrasonic Angiology Unit.

Here the number of trials is a random variable, not a fixed number.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

Here methods like random self-reducibility can be used for some specific problems to show that the worst case is no harder than the average case, or, equivalently, that the average case is no easier than the worst case.

Here the random vector is the vector r of random returns on the individual assets, and the portfolio return p ( a random scalar ) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets.

Here, the reader removes cards at random and assigns significance to them based in the order they were chosen.

Here are some random walk MCMC methods:

Here, random and uncoordinated thermally activated atomic jumps control formation and the interface is then rebuilt by reconstructive diffusion.

Here the Protestants made an effective stand, rallied by a strong artillery position until a random Spanish countershot exploded the Protestant magazine, costing the Badeners their position.

Here the word ' random ' must be interpreted as subject to correct symmetry considerations.

Here the Drode reveals ( in the form of complaining ) that the Animorphs were, in fact, not a random assortment who had found Elfangor but that they had been picked out by the Ellimist: Elfangor's son Tobias, his brother Aximili, Cassie — a kind of ' nexus point ' who by her very nature would disrupt any attempt to replace the true reality with an alternate one -, and the son of Visser One's host body ( Marco )— as he put it, the Ellimist had " stacked the deck " with them for their specific abilities and positions.

Here, is a specific value drawn from a collection of ( discrete or continuous ) random variables X.

Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision.

Here is a nonempty closed subset of, is a random vector whose probability distribution is supported on a set, and.

Here, the left-hand side is the Malliavin derivative of the random variable in the direction and the integral appearing on the right hand side should be interpreted as an Itô integral.

Here, is a Poisson process with rate, and are independent and identically distributed random variables, with distribution function G, which are also independent of

Here are two code samples that a programmer who is not familiar with the limitations of the random number generators in standard programming libraries might implement:

Here, in order to analyze the characteristics of a project ’ s net present value ( NPV ), the cash flow components that are ( heavily ) impacted by uncertainty are modeled, incorporating any correlation between these, mathematically reflecting their " random characteristics ".

Here the contestant wins a random cash prize or a holiday, and moves on.

Here, is a discrete random variable with possible outcomes and corresponding probabilities for, and the logarithm is base 2.

Here they wear tiny versions of standard miner's garb and commit random mischief, such as stealing miners ' unattended tools and food.

Here variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds.

Here, the " constant " of integration is no longer a constant, but instead a function of all the variables of the original function except x.

Here the X < sub > i </ sub > are the generalized forces corresponding to the external variables x < sub > i </ sub >.

Here the are the external variables and the the corresponding generalized forces.

Here, Marital Status and Geographical Region are the 2 explanatory dummy variables.

Here, beliefs and desires represent the central variables responsible for the folk theories of intention.

Here it is stated that a function F of n variables x < sub > 1 </ sub >, ..., x < sub > n </ sub > that is homogeneous of degree r, satisfies

Here the flux through the inductor and the charge in the capacitor are canonically conjugate variables which obey the commutation relation

Here atoms ( φ ) is the set of propositional variables occurring in φ, and ⊨ is the semantic entailment relation for propositional logic.

Here and in the following it is assumed that primed variables are integrated.