There were numberous Dumoulin firms. There were several Jannsen firms. None of these names was "used" by Pieper.

Henri Pieper, born 1840, ran the company until his death in 1898. He personally held dozens of patents. He was also one of the principles in the founding of Fabrique National. His son Nicolas Pieper ran the company until his death in 1933. The company was in business until 1957.

While there were several Bayards involved in the firearms business. Pieper registered Bayard as a trade mark at least by 1898 and held that trade mark until the company folded.

The records do show association with numberous firms including Jean Warnant, Hippolyte Thonon, Remington, Colt, Smith & Wesson and many others.

Les Hommes, Les armes et les machines du Chevalier Pieper & Cir 1889-1957 par Michel Druart.
Histoire de l'usine Pieper-Imperia par Michel Bedeur
Cinq siècles d'armurerie liégeoise par Claude Gaier
Les Armuries de Liege en catalogues (1892-1930) par Guy Gadisseur
Le qui est qui de l'armurerie Liegeogise 1800-1950 par Gadisseur et Druart

None of these sources gives any indication that Pieper used any trade names but the following:

AEP
Adler under an on the left looking at eagle
Anciens Etablisments Pieper
Automatic Files Pieper
Automatic Gun Pieper
Automatic Pistol Pieper
Automatic Rifle Pieper
Bayard
Bayard Arms S.A.
Bayard drawing stylized of the knight with right "Bayard"
Centaur
centaur drawing with the arc
centaur with Nicolas Pieper
child (one) with before landscape shooting at crocodiles with a gun
Damascus Compound
Diane
E Leroy
Eagle (one) looking at on the left with the word Adler
Eagle Gun Works
Eclipse Compagny
EK
EK in the wood of a stag
Encircled Half-block and not encircled
ES initial interlaced into English crossings of a sword
First Arms Company
H Piepper
Henri Arms Company
Légia Pistol
Lloyd-Pistol
Modified Diana
Monarch Arms Company
N Pieper
National Arms Companay
NP
Old Establishments Pieper
Optimus
Pieper Arms Company
Pieper Gun
Pieper Rifle
Pieper Signal Bolt
Pieper Automatic Files
Pieper Compresssed Steel
Pieper Files
Pieper Pistol
Pistol Pieper Obvious
PN interlaced in an oval
Rifle Pieper's Patent
Royal Gun Works
Schutz model
Snipe in a circle
The Leader
The Rational One
The Rational one with the drawing of Venus
Yser

You continually make the claim that T. Barker, etc were produced by Pieper. Please reference the source for this. Were are the Pieper trade marks on these firearms?

Pete