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An additive mapping $\\delta$ from $\\mathcal R$ into $\\mathcal{M}$ is called an \\emph{$(m,n)$-Jordan derivation} if $(m+n)\\delta(A^{2})=2mA\\delta(A)+2n\\delta(A)A$ for every $A$ in $\\mathcal R$. In this paper, we prove that every $(m,n)$-Jordan derivation from a $C^{*}$-algebra into its Banach bimodule is zero. An additive mapping $\\delta$ from $\\mathcal R$ into $\\mathcal{M}$ is called a $(m,n)$-Jordan derivable mapping at $W$ in $\\mathcal R$ if $(m+n)\\delta(AB+BA)=2m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.02046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-03-06T07:43:07Z","cross_cats_sorted":[],"title_canon_sha256":"cf136010add1fb3f3bdf7fbf2469c5c944eb293ceb140428bbf70f1d103f16a6","abstract_canon_sha256":"be49491d2cf5465ffc9d3dc11a932c5475b79c30d55c62e40862e3f518941e1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:55.967152Z","signature_b64":"eqiz/pfkR0cnAowz8ImLjfgL2vbOSoSyImqk+zzGVKJnX7Vgy9YaeK27JdDPeyMkL0gxd3qiSwEEIYgZQ3OMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfa4953754d3d98aab39a82ab21ebfa1a9ee914a80156dba313f4c7e681a1256","last_reissued_at":"2026-05-18T00:21:55.966565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:55.966565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of $(m,n)$-Jordan derivations on some algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guangyu An, Jun He","submitted_at":"2018-03-06T07:43:07Z","abstract_excerpt":"Let $\\mathcal R$ be a ring, $\\mathcal{M}$ be a $\\mathcal R$-bimodule and $m,n$ be two fixed nonnegative integers with $m+n\\neq0$. 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