We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

When rails are laid in a railway track, small gaps are left between the ends of adjoining rails to allow for the expansion of the rails when the temperature rises. Rail joints are provided to form a continuous rail path which are normally laid in standard lengths bolted together by fishplates. When two rail joints are exactly opposing each other, they are called square (side by side) joints...

Glossary Ecological validity The degree to which the thoughts recorded in a study reflect the thoughts that actually occur in natural settings. Inner speech The activity of talking to oneself in silence. Left inferior frontal gyrus Also known as Broca’s area, the brain region that gets reliably activated during inner speech production. Predicativeness The syntactically compressed, condensed, ab...

This chapter considers whether any of the inner-sense mechanisms that have been postulated to detect and represent some of our own mental states should qualify as sense modalities. We first review and reject the four standard views of the senses, and then propose a set of properties that would be possessed by a prototypical sensory system. Thereafter we consider how closely the existing models ...

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with homomorphisms G→ H. (Precise statement in §1.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of G itself, is...

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

One of the results of urban renovation is population displacement. If these renovations lead to live prosperous social classes, it is called gentrification. In this regard one of the urban renovation strategies is gentrification that is equal in "the acceptability of texture in public opinion" and is known as a synonym of "improving the quality of living environment for residents and citizens"....

A colored line flanking a darker contour will appear to spread its color onto an area enclosed by the line (watercolor effect). The watercolor effect has been characterized as an assimilative effect, but non-assimilative color spreading has also been demonstrated in the same spatial configuration; e.g., when a black inner contour (IC) is paired with a blue outer contour (OC), yellow color sprea...