Some Mathematical Operations

Modified composite parameter A composite parameter whose composition has been altered by some mathematical operation. 

It is often easy to measure the flux density, e.g., using a flowmeter, and then determine the hydraulic conductivity or diffusion coefficient by dividing the flux by the driving force. One of the most difficult problems is determining how to represent the driving force. The symbol V is called an operator, which signifies that some mathematical operation is to be performed upon whatever function follows. V means to take the gradient with respect to distance. For Darcy s law under saturated... 

We warn the reader that the word isomorphism is used in many different contexts in mathematics. It generally refers to an injective and surjective function that respects some mathematical operations, and whose inverse also respects those operations. Often it is up to the reader to infer from context exactly what the isomorphism in question respects. 

What is the net sample rate and its uncertainty This raises the general question of calculating the uncertainty in the result of some mathematical operations on an uncertain number. If we consider two independently determined numbers and their uncertainties (standard deviations), A + [Pg.572]

Often we must compute values of quantities that are not simple functions of the space coordinates, such as the y component of the momentum, py, where Equation (E.4) is not applicable. To get around this, we say that corresponding to every classical variable, there is a quantum mechanical operator. An operator is a symbol that directs us to do some mathematical operation. For example, the momentum operators are... 

For the respective quantum mechanical description of a molecule in a stationary state, a few additional aspects need to be addressed. First, the system state is characterized by a wavefunction VP, and system properties, such as the total energy or dipole moment, are calculated through integration of VP with the relevant operator in a distinct way. Note that an operator is simply an instruction to do some mathematical operation such as multiplication or differentiation, and generally (but not always) the order in which such calculations are performed affects the final result. Second, the wavefunctions V obey the Schrodinger equation ... 

Now we will put together the things you have learned about significant figures by considering some mathematical operations in the following examples. 

The next postulate of quantum mechanics states that in order to determine the value of an observable, you have to perform some mathematical operation on a wavefunction. This operation is represented by an operator. An operator is a mathematical instruction Do something to this function or these numbers. In other words, an operator acts on a function (or functions) to produce a function. (Constants are special types of functions, ones that do not change value.)... 

Images are simply 2D or 3D arrays. Consequently, all the array manipulations and operations are applicable. Let us say that a file is read via the imread statement and is stored to an image array. We can carry out some mathematical operations on the image array, which will result in alteration or modification to RGB values of the associated image. 

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