# Notation issue: Grad with a vector subscript

• Hoplite
In summary, the conversation discusses a journal article that uses a notation involving the symbol \nabla_{\vec Q}, which is not explicitly defined. It is mentioned that \vec Q represents the orientation of a polymer. The speaker has not seen a vector subscript on the gradient symbol \nabla before and asks for clarification on its meaning. One possible interpretation is that it represents the derivative in the direction of the vector \vec Q.

#### Hoplite

I'm reading a journal article at the moment which uses a piece of notation which they don't actually define. It looks like this:

$$\nabla_{\vec Q}$$

(As it happens, $$\vec Q$$ is an ordinary vector indicating the orientation of a polymer.)

I've never seen vector subscript on the gradient symbol "$$\nabla$$" before.

Could anyone please tell me what $$\nabla$$ with a vector subscript usually means?

First, since you mention polymers, I am inclined to think the symbol has more to do with chemistry than mathematics. If it really is purely mathematics then I would be inclined to think "the derivative in the direction of $\vec{Q}$".

Thanks, the derivative in the direction of the vector makes sense in context.

## 1. What is a notation issue?

A notation issue refers to a problem or confusion that arises when using symbols or notations to represent mathematical or scientific concepts. It can occur when the notation is ambiguous, inconsistent, or not well-defined.

## 2. What does "grad" refer to in this notation issue?

In this context, "grad" refers to the gradient operator, which is used to calculate the rate of change of a function with respect to its variables.

## 3. What does the vector subscript indicate?

The vector subscript indicates that the gradient operator is applied to a vector quantity, rather than a scalar quantity. This means that the resulting gradient will also be a vector, with each component representing the rate of change of the corresponding component of the original vector.

## 4. Why is this notation issue important?

This notation issue is important because it can lead to confusion or errors in calculations if not properly understood. It is also important to use consistent and clear notation in scientific and mathematical communication.

## 5. How can this notation issue be resolved?

To resolve this notation issue, it is important to clearly define and explain the meaning of the notation being used. It may also be helpful to use additional notation or symbols to clarify the meaning, or to use different notation altogether if the current one is too ambiguous or confusing.