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Assuming that $g$ is unimodal and has negative Schwarzian, we indicate explicitly a closed interval $\\mathcal{C} = \\mathcal{C}(h,g'(0),g'(\\kappa)) = [c_*,c^*]$ such that $(*)$ has at least one (possibly, nonmonotone) travelling front propagating at velocity $c$ for every $c \\in \\mathcal{C}$. Here $c_*>0$ is finite and $c^* \\in \\R_+ \\cup \\{+\\infty\\}$. Every time when $\\mathcal{C}$ is not empty, the minimal bound $c_*$ is sharp so that there"},"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":"math/0610025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2006-09-30T16:39:59Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9c4d8840861c4267a05e5b47c3021e7ce9da867596aa9bdb64be7ecfc364f928","abstract_canon_sha256":"b046277ab6b2c751b372a31adb200cfbdc61e2bb0b80bf35b9b0d6833ffbaf31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:18.302254Z","signature_b64":"BHraeJnyb3LugwNkwZYkDgLYeNortK2CLb/7CUAxlZaAFfvnZd2yF+IWe66pcmpWZZRay+81eaZvHOC8oEByCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"939a29e5881944a3254898e491516cdc78a9ebf0f74ad790edb5a0e3dc0c6d0c","last_reissued_at":"2026-05-18T04:11:18.301793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:18.301793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Admissible wavefront speeds for a single species reaction-diffusion equation with delay","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Elena Trofimchuk, Sergei Trofimchuk","submitted_at":"2006-09-30T16:39:59Z","abstract_excerpt":"We consider equation $u_t(t,x) = \\Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*) $, when $g:\\R_+\\to \\R_+$ has exactly two fixed points: $x_1= 0$ and $x_2=\\kappa>0$. Assuming that $g$ is unimodal and has negative Schwarzian, we indicate explicitly a closed interval $\\mathcal{C} = \\mathcal{C}(h,g'(0),g'(\\kappa)) = [c_*,c^*]$ such that $(*)$ has at least one (possibly, nonmonotone) travelling front propagating at velocity $c$ for every $c \\in \\mathcal{C}$. Here $c_*>0$ is finite and $c^* \\in \\R_+ \\cup \\{+\\infty\\}$. 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