The owner of the jewelry maker Alex and Ani has withdrawn a request for a state energy subsidy for a solar power system on her Newport mansion. The Providence Journal reported that the state’s Economic Development Corp. was notified Monday that the application for renewable energy funding had been withdrawn. The agency’s board had planned to take up the request Thursday. Carolyn Rafaelian, Alex and Ani’s designer and majority stakeholder, told the newspaper that she did not know the company working on the solar energy project was seeking $18,500 in state funding. She said she asked the company to withdraw the application once she learned about it.