This paper investigates the role of quadrature exactness in approximation scheme hyperinterpolation. Constructing a hyperinterpolant degree $n$ requires positive-weight rule with $2n$. We examine behavior such when required $2n$ is relaxed to $n+k$ $0<k\leq n$. Aided by Marcinkiewicz--Zygmund inequality, we affirm that $L^2$ norm exactness-relaxing hyperinterpolation operator bounded constant i...

The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C∗-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting. First, we show that if G is an amenable groupoid acting on an upper-semicontinuous C∗-bundle A with nuclear section algebra A, then the associated g...

The derivation of fast, reliable, and accurate modeling procedures for the solution thermal elastohydrodynamic lubrication problems is a topic significant interest in Tribology community. In this paper, novel model order reduction technique introduced analysis problems. method uses static condensation to reduce size linear elasticity part within overall matrix system, followed by splitting algo...

We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left...

We prove exactness of parabolic restriction and induction functors for conjugation equivariant sheaves on a reductive group generalizing well-known result Lusztig who established this property character sheaves. propose conjectural (but known sheaves) $t$-exactness the Harish-Chandra transform provide evidence that conjecture. also present two applications some results Gabber Loeser perverse an...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. S is a measurable homomorphism). We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applie...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applied to random walk-endomorphisms. M...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applied to random walk-endomorphisms. M...