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...

The paper considers the basis and frame properties of the system of weighted exponentials E(g,Z\F ) = {eg(x)}n∈Z\F in L(T), where g ∈ L2(T)\{0} and F ⊂ Z. It is shown that many of the frame properties of E(g,Z\F ) are affected by the cardinalities of F and the behavior of the zeros of g.

In this article the frame-theoretic account of what is archimedean for order-algebraists, and semisimple for people who study commutative rings, deepens with the introduction of J -frames: compact normal frames that are join-generated by their saturated elements. Yosida frames are examples of these. In the category of J -frames with suitable skeletal morphisms, the strongly projectable frames a...

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...

A σ-frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. Aim of this paper is to present σ-frames, actually σ-locales, as a branch of Formal Topology, that is, intuitionistic and predicative pointfree topology. We show that every σframe L can be presented as the lattice of Lindelöf elements (those whose covers admit countable subcovers) o...

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal N = 4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or γ/L) behavior at small quarkantiquark separations,...

This paper describes a Japanese language semantic analyzer based on an extended case frame model, which consists of a re la t ive ly large col lect ion of case re lat ions, modalities and conjunctive re la t ions. The analyzer performs four stage analysis using a frame type knowledge base. It also u t i l i zes p laus ib i l i t y scores for dealing with ambiguities and local scene frames for t...

The longstanding research line investigating free algebra constructions in modal logic from an algebraic and coalgebraic point of view recently lead to the notion of a one-step frame [18], [8]. A one-step frame is a two-sorted structure which admits interpretations of modal formulae without nested modal operators. In this paper, we exploit the potential of one-step frames for investigating proo...

The simplest bimodal combination of unimodal logics L1 and L2 is their fusion, L1 ⊗ L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1 × L2, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezha...