We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity I(i1, . . . , i2k : j1, . . . , j2k) = ∫ On ui1j1 . . . ui2kj2k du replaced by the more advanced quantity I(a) = ∫ On Πu aij ij du, depending on a matrix of exponents a ∈ Mn(N). Among consequences, we establish a number of basic facts regarding the integrals I(a): vanishing condition, sign, poss...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

Density is a critical typology in determining sustainable urban built-form patterns. Built-formrefers to the assemblage and arrangement of the building masses in a city reflecting the spatial layout of spaces.The relationship between density and urban character is also based on at certain densities (thresholds). In a widersense, sustainable cities are a matter of density. Recent debates about t...

Throughout the early and mid 1990s, there was widespread faith in the compact city model's ability to provide urban sustainability. However, where compact city policies had been implemented, follow-up studies began to show the predicted benefits did not happen as they should be. The article tries to peruse two opposite approaches of "Urban Sprawl" and "Compact City", with an analytical - cri...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

Consider the semidirect product group H ×? K, where H and K are two arbitrary locally compact groups and K is also abelian. We introduce the continuous wavelet transform associated to some square integrable representations H ×? K. Moreover, we try to obtain a concrete form for admissible vectors of these integrable representations.