Multipliers and Uniformly Continuous Functionals Over Fourier Algebras of Ultraspherical Hypergroups

Let H be an ultraspherical hypergroup associated to a locally compact group G and let A(H) be the Fourier algebra of H. For a left Banach A(H)-submodule X of VN(H), define QX to be the norm closure of the linear span of the set {u f : u ∈ A(H), f ∈ X} in BA(H)(A(H), X ∗ ) ∗ . We will show that BA(H)(A(H), X ∗ ) is a dual Banach space with predual QX. Applications obtained on the multiplier algebra M(A(H)) of the Fourier algebra A(H). In particular, we prove that G is amenable if and only if M(A(H)) = Bλ(H). We also study the uniformly continuous functionals associated with the Fourier algebra A(H) and obtain some characterizations for H to be discrete. Finally, we establish a contractive and injective representation from Bλ(H) into B σ A(H) (Bλ(H)). As an application of this result we show that the induced representation Φ : Bλ(H) → B σ A(H) (Bλ(H)) is surjective if and only if G is amenable

On the Algebras VN(H) and VN(H)(*) of an Ultraspherical Hypergroup H

Let H be an ultraspherical hypergroup and let A(H) be the Fourier algebra associated with H. In this paper, we study the dual and the double dual of A(H). We prove among other things that the subspace of all uniformly continuous functionals on A(H) forms a C∗ -algebra. We also prove that the double dual A(H)∗∗ is neither commutative nor semisimple with respect to the Arens product, unless the underlying hypergroup H is finite. Finally, we study the unit elements of A(H)∗∗

Power boundedness in Fourier and Fourier-Stieltjes algebra of an ultraspherical hypergroup

Let $H$ be an ultraspherical hypergroup associated with a locally compact group $G$ and a spherical projector $\pi$ and let $A(H)$ and $B(H)$ denote the Fourier and Fourier-Stieltjes algebras, respectively, associated with $H.$ In this note, we study power boundedness and Ces\`aro boundedness in $B(H)$. We also characterize the power bounded property for both $A(H)$ and $B(H).

Investigating the Relationship between Various Brittleness Indexes with Specific Ampere Draw in Rock Sawing Process

This study aimed to develop new statistical models for evaluating the specific ampere draw (SI) based on rock brittleness index in rock sawing process. A variety of rocks, including carbonate and granite, were cut by a fully instrumented laboratory-sawing rig with two different types of circular diamond saws. Laboratory tests were performed at different depths of cut and feed rates. Multiple curvilinear regression analysis was utilized in order to estimate the SI from rock brittleness index and operational parameters. Validation of the developed models was checked by t and F tests. Results showed that among the different brittleness indexes, B3 has the best accuracy for both granite and carbonate rocks. Finally, it was concluded that the specific ampere draw can be reliably predicted using the proposed models for both hard and soft rocks