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The phrase "a cursor on a" is correct and usable in written English.
It can be used when referring to the position or presence of a cursor on a screen or interface, typically in the context of computing or digital devices.
Example: "I noticed a cursor on a blank document, indicating that I could start typing."
Alternatives: "a pointer on a" or "a marker on a".
Exact(50)
Twenty-four students were asked to perform tasks that required constant attention, including tracking a cursor on a screen and pushing a button every time one of four letters appeared on the screen.
They performed two-dimensional horizontal reaching movements in which they used a manipulandum to control the movements of a cursor on a visual display from a central location to one of eight peripheral targets equally spaced around a circle of ∼9 cm radius.
Now imagine the dot as a cursor on a screen.
By moving its wrist, the monkey could manipulate a cursor on a computer screen.
He was musing about how to move a cursor on a computer display.
Mr. Davis moves a cursor on a computer-screen grid and clicks on "Go to Jupiter".
Similar(10)
Resulting neural signals from the motor cortex were electronically extracted by the embedded recording devices, transmitted to a computer and translated by Shenoy's algorithms into commands directing a cursor on an onscreen keyboard to participant-specified characters.
In this mode MATLAB creates a surface plot and animates a cursor on the screen that corresponds to the position of the pen in 3-space.
It controls a cursor on the dash-mounted display.
This system involves the animal working in an enclosure that provides visual access to a computer screen, access to a joystick to control a cursor on the screen, and access to a food dish where pellets are delivered for correct responses.
As described in detail below, such devices work with a virtual keyboard to guide a cursor on the keyboard to select a desired character or function.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com