In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inerti...

We consider semi-group BMO spaces associated with an arbitrary $\sigma$-finite von Neumann algebra $(\mathcal{M}, \varphi)$. prove that the row and column always admit a predual, extending results from finite case. Consequently, we can considered are Banach they interpolate $L_p$ as in commutative situation, namely $[\mathrm{BMO}(\mathcal{M}), L_p^\circ(\mathcal{M})]_{1/q} \approx L_{pq}^\circ(...

We discuss the work of Birman and Solomyak on singular numbers integral operators from point view modern approximation theory, in particular, with use wavelet techniques. are able to provide a simple proof norm estimates for kernel $$B^{1/p-1/2}_{p,p}(\mathbb R,L_2(\mathbb R))$$ . This recovers, extends, sheds new light theorem Solomyak. also these techniques Schur multiplier bounds double ope...

Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In pa...

The paper concerns nilpotent diassociative algebras (also known as associative dialgebras) and their corresponding Schur multipliers. Using Lie (and group) theory a guide, we first extend classic five-term cohomological sequence under alternative conditions in the setting. This main result is then applied to obtain new proof for previous extension of same sequence. It also yields different that...

Let G be a finite group and D division algebra faithfully -graded, dimensional over its center K , where c h r ( ) = 0 . e ∈ denote the identity element suppose ∩ -center of contains ζ n primitive -th root unity, is exponent To such -grading on we associate normal abelian subgroup H positive integer d an o m M μ / Here denotes roots x p Schur multiplier The action trivial induced by Our main th...

Abstract We propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic cholesteric liquid crystals. By applying Lagrangian method, Schur complement director block can be better approximated by weighted mass matrix Lagrange multiplier, at cost making harder to solve. In order solve block, we develop multigrid alg...

Understood in a wide sense, square functions play a central role in classical Littlewood-Paley theory. This entails for instance dyadic type decompositions of Fourier series, Stein’s theory for symmetric diffusion semigroups or Burkholder’s martingale square function. All these topics provide a deep technique when dealing with quasi-orthogonalitymethods, sums of independent variables, Fourier m...