A feeling is a simple and undecomposable mental state.    From Wordnet, Princeton University. 

Verb (used with object) : The bacteria decomposed the milk into its solid and liquid elements.    From Dictionary.com. 

Verb (used without object) : The egg began to decompose after a day in the sun.    From Dictionary.com. 

The earliest impressions which the mind can assimilate are the undecomposable sensations produced by resistance, light, sound, etc.    From Wordnik.com.  [Essays on Education and Kindred Subjects Everyman's Library] Reference

Some silicates are completely decomposed by such treatment; but it saves time (unless one is sure that no undecomposable silicate is present) to treat these in the same way as the others.    From Wordnik.com.  [A Text-book of Assaying: For the Use of Those Connected with Mines.] Reference

Where possible, this is of course valuable, but mathematical research is often almost uniquely undecomposable, because the nature of the problem is that it's solution is unknown and hence undecomposable.    From Wordnik.com.  [Machine Learning (Theory)] Reference

The effects which take place when a succession of conducting decomposable and undecomposable substances are placed in the electric circuit, as, for instance, of wires and solutions, or of air and solutions.    From Wordnik.com.  [Experimental Researches in Electricity, Volume 1] Reference

Putting aside the muscular sense, which had not come into view in Hume's time, the questions arise whether these are all the simple undecomposable materials of thought? or whether others exist of which Hume takes no cognizance.    From Wordnik.com.  [Hume (English Men of Letters Series)] Reference

So far as our knowledge extends, there are about sixty-six of these undecomposable bodies, of which about one half occurs in but exceedingly minute quantities, and a considerable number of the others exists in comparatively small amounts.    From Wordnik.com.  [The Stock-Feeder's Manual the chemistry of food in relation to the breeding and feeding of live stock] Reference

Since those early days of the century when the electric battery performed its miracles and seemingly reached its limitations in the hands of Davy, many new elementary substances have been discovered, but no single element has been displaced from its position as an undecomposable body.    From Wordnik.com.  [A History of Science: in Five Volumes. Volume IV: Modern Development of the Chemical and Biological Sciences] Reference

"common acceptation" -- "as meaning any cognition reached by an undecomposable mental act.".    From Wordnik.com.  [Nature Mysticism] Reference

In the electro-tonic state the homogeneous particles of matter appear to have assumed a regular but forced electrical arrangement in the direction of the current, which if the matter be undecomposable, produces, when relieved, a return current; but in decomposable matter this forced state may be sufficient to make an elementary particle leave its companion, with which it is in a constrained condition, and associate with the neighbouring similar particle, in relation to which it is in a more natural condition, the forced electrical arrangement being itself discharged or relieved, at the same time, as effectually as if it had been freed from induction.    From Wordnik.com.  [Experimental Researches in Electricity, Volume 1] Reference