It is proved that in Hilbert spaces a single Hilbert–Schmidt operator radonifies cylindrical semimartingales to strong semimartingales. This improves a result due to Badrikian and¨Ustünel (also L. Schwartz), who needed composition of three Hilbert–Schmidt operators.

We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states.

We consider transport of a passive scalar by an isotropic turbulent velocity field in the presence of a mean scalar gradient. The velocity–scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shell-summed energy and scalar spectra. At high Schmidt number, this bound limits the possible ...

Important operations in numerical computing are vector orthogonalization. One of the well-known algorithms for vector orthogonalisation is Gram–Schmidt algorithm. This is a method for constructing a set of orthogonal vectors in an inner product space, most commonly the Euclidean space Rn. This process takes a finite, linearly independent set S = {b1, b2, ..., bk} vectors for k ≤ n and generates...

In this work, an efficient way to predict the dynamics of a scalar at high Schmidt numbers, advected by a turbulent flow, is presented. For high Schmidt numbers, the spatial resolution required for the scalar field has to be finer than the resolution required for the velocity field, leading to a significant computational cost due to the CourantFriedrichsLewy (CFL) constraint. We propose here a ...

Fluid mixing is a crucial and challenging process for microfluidic systems, which are widely used in biochemical processes. Because of their fast performance, active micromixers that use stirrer blades are considered for biological applications. In the present study, by using a robust and convenient Incompressible Smoothed Particle Hydrodynamics (ISPH) method, miscible mix...

Edeltraud Ziegler, Ingeborg Hölzle: Hollenbach. Ein Dorf mit Geschichte und Geschichten, Mulfingen (Selbstverlag Gerhard Bartz) 2018. 477 + 55 S., zahlr. Abb.
 Willy Grün, Rudi Schmidt, Inge Neubert, Walter Blank: Elpersheimer Heimatbuch. 800 Jahre 1219–2019. Chronik, Weikersheim (Stadt Weikersheim, Ortsteil Elpersheim) 2019. 336 Christine Schmidt: Schönbühl, ein kleiner Weiler feiert Jubi...

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in von Neumann entropy to quantify the amount of the bipartite entanglement. In this paper, we map the Schmidt basis and the associated coefficients to quantum circuits to generate random...

We introduce a novel approach for structure activity relationship analysis based on the use of a special kernel. The kernel eÆciently performs Gram-Schmidt orthogonalisation in a kernel de ned feature space. We show that support vector machines in conjunction with Gram-Schmidt kernel, a recent method to extract features, can be adopted successfully to predict the inhibition of dihydrofolate red...