The Board of Appeals shall fix a reasonable time for the hearing of the appeal. At such hearing, any party may appear in person and may be represented by agent or attorney. Upon filing an application to overrule the action of the Zoning Officer or Building Official, or the filing of an application for a variance upon forms to be provided by the Board of Appeals, a date shall be set for a public hearing, and due notice thereof shall be given to the parties. Notice of the time and place of such hearing shall be published in a newspaper having substantial circulation in the City of Derby at least twice, at intervals of not less than 10 days; the first not more than 15 days, nor less than 10 days, and the last not less than two days before such hearing. Notice shall be sent by the applicant, by certified return receipt mail, to the owners of record of all property within 150 feet of the subject property. Evidence of such mailing shall be submitted to the Board prior to or at the public hearing. Whenever the Zoning Board of Appeals has before it for consideration an application for a variance in the use of property, any portion of which lies within 500 feet of a contiguous municipality, such Board shall, at least one week prior to the hearing thereon, notify the Clerk of such municipality, in writing, of the fact of such application and of the date fixed by it for such hearing.