Generalized Fourier-Feynman Transforms, Convolution Products, And First Variations On Function Space

In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f((α1, x), . . . , (αn, x)) with x in a very general function space Ca,b[0,T]

Generalized Analytic Fourier-Feynman Transform of Functionals in a Banach Algebra \u3ci\u3eF\u3c/i\u3e_(\u3ci\u3eA\u3c/i\u3e1,\u3ci\u3eA\u3c/i\u3e2)^(\u3ci\u3ea\u3c/i\u3e,\u3ci\u3eb\u3c/i\u3e)

We introduce the Fresnel type class F_(A1,A2)^(a,b).We also establish the existence of the generalized analytic Fourier-Feynman transform for functionals in the Banach algebra F_(A1,A2)^(a,b)

Translation Theorems for the Fourier-Feynman Transform on the Product Function Space C2 a,b, [0,T]

In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then proceed to establish the translation theorems for the functionals in Fa;b A1;A2

Flow Characteristics Around Step-Up Street Canyons with Various Building Aspect Ratios

We investigate the flow characteristics around step-up street canyons with various building aspect ratios (ratio of along-canyon building length to street-canyon width, and upwind building height to downwind building height) using a computational fluid dynamics (CFD) model. Simulated results are validated against experimental wind-tunnel results, with the CFD simulations conducted under the same building configurations as those in the wind-tunnel experiments. The CFD model reproduces the measured in-canyon vortex, rooftop recirculation zone above the downwind building, and stagnation point position reasonably well. We analyze the flow characteristics, focusing on the structural change of the in-canyon flows and the interaction between the in- and around-canyon flows with the increase of building-length ratio. The in-canyon flows undergo development and mature stages as the building-length ratio increases. In the development stage (i.e., small building-length ratios), the position of the primary vortex wanders, and the incoming flow closely follows both the upstream and downstream building sidewalls. As a result, increasing momentum transfer from the upper layer contributes to a momentum increase in the in-canyon region, and the vorticity in the in-canyon region also increases. In the mature stage (i.e., large building-length ratios), the primary vortex stabilizes in position, and the incoming flow no longer follows the building sidewalls. This causes momentum loss through the street-canyon lateral boundaries. As the building-length ratio increases, momentum transfer from the upper layer slightly decreases, and the reverse flow, updraft, and streamwise flow in the in-canyon region also slightly decrease, resulting in vorticity reduction