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[4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_\\beta = h_\\beta + \\bar{g}_\\beta, where f_\\beta is obtained by shearing of analytic vertical strip mapping, with dilatation e^{i\\theta}z^n; n = 1,2,\\theta \\in R, is in S_H^0 and is convex in the direction of the real axis. In this paper, by using Cohn's rule, we generalize this result by considering dilatations (a-z)/(1-az), a\\in (-1,1) and e^{i\\theta} z^n (n\\in N;\\theta\\in R) of right half-plane mapping and f_\\beta, respectively."},"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":"1306.5375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-06-23T06:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"ec4302c96fbd0d64602ae7faa5d12bed26ec75ca1d5e3dda80c20fb0bc289735","abstract_canon_sha256":"14e16a5aedc4588eb3f452eed6790f375379406f492d25becc020e04b5bfbb0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:08.353570Z","signature_b64":"S4D/icWgIEf6RLEqBkJmcW9u2iON5tsWJuJHvVHibkFASmNBnVkeLnHY0ywk7kigJBphdttRpuIXRfXYWx9ACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b6100d0e29642b1970e72a446f3d7ddc45607b67d4b950561bbc65f74e1cef8","last_reissued_at":"2026-05-18T03:20:08.352790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:08.352790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An application of Cohn's rule to convolutions of univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Michael Dorff, Raj Kumar, Sukhjit Singh, Sushma Gupta","submitted_at":"2013-06-23T06:05:10Z","abstract_excerpt":"Dorff et al. 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