We prove some unique factorization results for tensor products of free quantum group factors. They are type III analogues of factorization results for direct products of bi-exact groups established ...by Ozawa and Popa. In the proof, we first take continuous cores of the tensor products, which satisfy a condition similar to condition (AO), and discuss some factorization properties for the continuous cores. We then deduce factorization properties for the original type III factors. We also prove some unique factorization results for crossed product von Neumann algebras by direct products of bi-exact groups.
We consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a ...corollary, we prove that \(\rm II_1\) factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type \(\rm III_1\) factors with such a condition are semisolid as a \(\rm II_\infty\) factor.
We define Ozawa's notion of bi-exactness to discrete quantum groups, and then prove some structural properties of associated von Neumann algebras. In particular, we prove that any non amenable ...subfactor of free quantum group von Neumann algebras, which is an image of a faithful normal conditional expectation, has no Cartan subalgebras.
Millimeter wave imaging radar is indispensible for collision avoidance of self-driving system, especially in optically blurred visions. The range points migration (RPM) is one of the most promising ...imaging algorithms, which provides a number of advantages from synthetic aperture radar (SAR), in terms of accuracy, computational complexity, and potential for multifunctional imaging. The inherent problem in the RPM is that it suffers from lower angular resolution in narrower frequency band even if higher frequency e.g. millimeter wave, signal is exploited. To address this problem, the k-space decomposition based RPM has been developed. This paper focuses on the experimental validation of this method using the X-band or millimeter wave radar system, and demonstrated that our method significantly enhances the reconstruction accuracy in three-dimensional images for the two simple spheres and realistic vehicle targets,
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras \(M = B \rtimes \Gamma\) arising from arbitrary actions \(\Gamma \curvearrowright B\) of bi-exact ...discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra \(N' \cap M^\omega\) of any nonamenable von Neumann subalgebra with normal expectation \(N \subset M\). We use this result to show that for any strongly ergodic essentially free nonsingular action \(\Gamma \curvearrowright (X, \mu)\) of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor \({\rm L}^\infty(X) \rtimes \Gamma\) has no nontrivial central sequence. Using recent results of Boutonnet-Ioana-Salehi Golsefidy BISG15, we construct, for every \(0 < \lambda \leq 1\), a type III\(_\lambda\) strongly ergodic essentially free nonsingular action \(\mathbf F_\infty \curvearrowright (X_\lambda, \mu_\lambda)\) of the free group \(\mathbf F_\infty\) on a standard probability space so that the corresponding group measure space type III\(_\lambda\) factor \({\rm L}^\infty(X_\lambda, \mu_\lambda) \rtimes \mathbf F_\infty\) has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type III factors with no nontrivial central sequence.
We show that whenever \(m \geq 1\) and \(M_1, \dots, M_m\) are nonamenable factors in a large class of von Neumann algebras that we call \(\mathcal C_{(\text{AO})}\) and which contains all free ...Araki-Woods factors, the tensor product factor \(M_1 \mathbin{\overline{\otimes}} \cdots \mathbin{\overline{\otimes}} M_m\) retains the integer \(m\) and each factor \(M_i\) up to stable isomorphism, after permutation of the indices. Our approach unifies the Unique Prime Factorization (UPF) results from OP03, Is14 and moreover provides new UPF results in the case when \(M_1, \dots, M_m\) are free Araki-Woods factors. In order to obtain the aforementioned UPF results, we show that Connes's bicentralizer problem has a positive solution for all type \({\rm III_1}\) factors in the class \(\mathcal C_{(\text{AO})}\).
We study (quasi-)cohomological properties through an analysis of quantum
Markov semi-groups. We construct higher order Hochschild cocycles using
gradient forms associated with a quantum Markov ...semi-group. By using
Schatten-$\mathcal{S}_p$ estimates we analyze when these cocycles take values
in the coarse bimodule. For the 1-cocycles (the derivations) we show that under
natural conditions they imply the Akemann-Ostrand property (using the Riesz
transform). We apply this to $q$-Gaussian algebras $\Gamma_q(H)$. As a result
$q$-Gaussians satisfy AO$^+$ for $| q | \leqslant \dim(H)^{-1/2}$. This
includes a new range of $q$ in low dimensions compared to Shlyakhtenko.
We generalize Kirchberg's weak exactness to inclusions of C*-algebras in von Neumann algebras and study some characterizations and permanence properties which are similar to those of exact groups. We ...then consider a similar condition to Ozawa's condition (AO) with our weak exactness and generalize Ozawa's theorem for bi-exact groups. As a corollary, we give new examples of prime factors.
The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct \({\rm II_1}\) factors Po95 to the framework of ultraproduct von Neumann algebras ...\((M^\omega, \varphi^\omega)\) where \((M, \varphi)\) is a \(\sigma\)-finite von Neumann algebra endowed with a faithful normal state satisfying \((M^\varphi)' \cap M = \mathbf{C} 1\). More precisely, we show that whenever \(P_1, P_2 \subset M^\omega\) are von Neumann subalgebras with separable predual that are globally invariant under the modular automorphism group \((\sigma_t^{\varphi^\omega})\), there exists a unitary \(v \in \mathcal U((M^\omega)^{\varphi^\omega})\) such that \(P_1\) and \(v P_2 v^*\) are \(\ast\)-free inside \(M^\omega\) with respect to the ultraproduct state \(\varphi^\omega\). Combining our main result with the recent work of Ando-Haagerup-Winsl\o w AHW13, we obtain a new and direct proof, without relying on Connes-Tomita-Takesaki modular theory, that Kirchberg's quotient weak expectation property (QWEP) for von Neumann algebras is stable under free product. Finally, we obtain a new class of inclusions of von Neumann algebras with the relative Dixmier property.
Ag sintering technology is one of the best candidates for SiC die attach because of good mechanical and thermal properties at high temperature. However cracks propagates into SiC dies or DBC ...substrates at thermal fatigue test at more than 200 °C because Ag is too hard for die attach materials and 10ppm/ °C of CTE mismatch between SiC dies and Ag layers is too big. Therefore a development of low CTE sintering materials is dispensable for SiC power device operated at high temperature. In this study, a method to coat Si particles with Ag layer at room and its sintering properties are researched. Si particles with φ30μm and Ag flakes with φ5μm are prepared and Si-20,40and 60 vol%Ag particles are produced by utilizing high-speed 3D motion of a patented 3D Ball Mill producted by Nagao System Inc.. It is revealed that their Si particles after the ball milling are almost covered by Ag layer except for Si-20vol.%Ag particles and furthermore the coated particles are crushed to 5μm by SEM observation. Their Si-Ag particles are mixed with a solvent to formulate into pastes. These Si-Ag pastes are printed onto Ag electroplated Cu plats, and then the bonding experiments are carried out at temperatures of 250°C for 60 min without pressure at air atmosphere. It is revealed that some Ag layers are jointed on the surface of Si particles and others are delaminated by FE-SEM observation. Si particles are connected via Ag layers on their surface. The strength between Ag layer and Si particles must be improved in order to adopt Ag-Si sintering paste to die-attach technology.
