{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KD4TSDASEA5RHXKLNJBSS2QRKX","short_pith_number":"pith:KD4TSDAS","schema_version":"1.0","canonical_sha256":"50f9390c12203b13dd4b6a43296a1155c237cc651a5fd7a26666b375e9892db2","source":{"kind":"arxiv","id":"1402.2540","version":1},"attestation_state":"computed","paper":{"title":"Existence of periodic solutions in shifts $\\delta_{\\pm}$ for neutral nonlinear dynamic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Can Koyuncuoglu, Murat Adivar, Youssef N. Raffoul","submitted_at":"2014-02-11T16:01:23Z","abstract_excerpt":"In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \\[ x^{\\Delta}(t)=A(t)x(t)+Q^{\\Delta}\\left(t,x\\left(\\delta_{-}(s,t)\\right) \\right) +G\\left(t,x(t),x\\left(\\delta_{-}(s,t)\\right) \\right) . \\] We utilize the new periodicity concept in terms of shifts operators, which allows us to extend the concept of periodicity to time scales where the additivity requirement $t\\pm T\\in\\mathbb{T}$ for all $t\\in\\mathbb{T}$ and for a fixed $T>0,$ may not hold. More, importantly, the new concept will easily handle time scales that are not periodic "},"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":"1402.2540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-02-11T16:01:23Z","cross_cats_sorted":[],"title_canon_sha256":"0cfb17a0f44a5bd27ad66f656cb9cee37499c63c5425656ff04a8f60c5448ea5","abstract_canon_sha256":"9e265f2e7cc949f87d446c714e2e434ca9f87fe3ea0a7f40d341cef7f21dce7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:19.389161Z","signature_b64":"K18fdsh5+blVw0MK5o4U4DgdEHoSXoPAvhpreH9I2HGc9HUT7JbNoGMbS9neIW84Clz5FkxTG6yhuEWK6vsuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50f9390c12203b13dd4b6a43296a1155c237cc651a5fd7a26666b375e9892db2","last_reissued_at":"2026-05-18T02:59:19.388226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:19.388226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of periodic solutions in shifts $\\delta_{\\pm}$ for neutral nonlinear dynamic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Can Koyuncuoglu, Murat Adivar, Youssef N. Raffoul","submitted_at":"2014-02-11T16:01:23Z","abstract_excerpt":"In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \\[ x^{\\Delta}(t)=A(t)x(t)+Q^{\\Delta}\\left(t,x\\left(\\delta_{-}(s,t)\\right) \\right) +G\\left(t,x(t),x\\left(\\delta_{-}(s,t)\\right) \\right) . \\] We utilize the new periodicity concept in terms of shifts operators, which allows us to extend the concept of periodicity to time scales where the additivity requirement $t\\pm T\\in\\mathbb{T}$ for all $t\\in\\mathbb{T}$ and for a fixed $T>0,$ may not hold. More, importantly, the new concept will easily handle time scales that are not periodic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2540","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.2540","created_at":"2026-05-18T02:59:19.388370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.2540v1","created_at":"2026-05-18T02:59:19.388370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2540","created_at":"2026-05-18T02:59:19.388370+00:00"},{"alias_kind":"pith_short_12","alias_value":"KD4TSDASEA5R","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KD4TSDASEA5RHXKL","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KD4TSDAS","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX","json":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX.json","graph_json":"https://pith.science/api/pith-number/KD4TSDASEA5RHXKLNJBSS2QRKX/graph.json","events_json":"https://pith.science/api/pith-number/KD4TSDASEA5RHXKLNJBSS2QRKX/events.json","paper":"https://pith.science/paper/KD4TSDAS"},"agent_actions":{"view_html":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX","download_json":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX.json","view_paper":"https://pith.science/paper/KD4TSDAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.2540&json=true","fetch_graph":"https://pith.science/api/pith-number/KD4TSDASEA5RHXKLNJBSS2QRKX/graph.json","fetch_events":"https://pith.science/api/pith-number/KD4TSDASEA5RHXKLNJBSS2QRKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX/action/storage_attestation","attest_author":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX/action/author_attestation","sign_citation":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX/action/citation_signature","submit_replication":"https://pith.science/pith/KD4TSDASEA5RHXKLNJBSS2QRKX/action/replication_record"}},"created_at":"2026-05-18T02:59:19.388370+00:00","updated_at":"2026-05-18T02:59:19.388370+00:00"}