This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

PVC frame cutting process by guillotine is a common method that attracted attention of car parts and PVC decorating furniture producers. In this paper, the effects of main parameters such as cutting speed, lubricants and cutting frame holder pressure force on PVC frame section surface smoothness is investigated by experimental methods on a specified PVC frame sample and then by FEM simulation u...

Abstract It is often useful to be able deal with locales in terms of presentations their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for locale, its sublocales can obtained by simply appending additional relations, but case quotient more subtle. We provide simple procedures obtaining open quotients, proper quotients general triquotients f...

Solving constraints over floating-point numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms over the floating-point numbers have been so far limited to 2b-consistency and its derivatives. Though safe, such filtering techniques suffer from the well known pathological problems of local consistencies, e.g., inability to efficie...