Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs

Ecological and functional optimization of the pretreatment process for plasma based coatings of cutting tools

Increasing demands in machining of high-tech materials and dry machining lead to higher thermal and mechanical loads on cutting tools. In response to these challenges, enhanced coating solutions are applied to increase performance and life of cutting tools. However, during the production process the cemented carbide substrates are contaminated with grinding oils and residues of organic material. For the subsequent physical vapor deposition (PVD) coating process an intensive and high-quality cleaning process is necessary. In this contribution, plasma electrolytic polishing (PEP) is used as a novel alternative to conventional ecologically harmful cleaning baths. Apart from the ecological advantage, the surface of the substrate can be optimized with regard to the coating adhesion. To examine the performance of the different cleaning processes, machining tests were performed at the IWF to evaluate the layer adhesion and tool life of the tools

'Schwinger Model' on the Fuzzy Sphere

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys. Lett.

Cell and molecular transitions during efficient dedifferentiation

Dedifferentiation is a critical response to tissue damage, yet is not well understood, even at a basic phenomenological level. Developing Dictyostelium cells undergo highly efficient dedifferentiation, completed by most cells within 24 hr. We use this rapid response to investigate the control features of dedifferentiation, combining single cell imaging with high temporal resolution transcriptomics. Gene expression during dedifferentiation was predominantly a simple reversal of developmental changes, with expression changes not following this pattern primarily associated with ribosome biogenesis. Mutation of genes induced early in dedifferentiation did not strongly perturb the reversal of development. This apparent robustness may arise from adaptability of cells: the relative temporal ordering of cell and molecular events was not absolute, suggesting cell programmes reach the same end using different mechanisms. In addition, although cells start from different fates, they rapidly converged on a single expression trajectory. These regulatory features may contribute to dedifferentiation responses during regeneration

Dirac operator on the q-deformed Fuzzy sphere and Its spectrum

The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of \uq and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the Dirac operator on the q-deformed fuzzy sphere-$S_{qF}^{2}(N)$ using the spinor modules of \uq. We explicitly obtain the zero modes and also calculate the spectrum for this Dirac operator. Using this Dirac operator, we construct the \uq invariant action for the spinor fields on $S_{qF}^{2}(N)$ which are regularised and have only finite modes. We analyse the spectrum for both $q$ being root of unity and real, showing interesting features like its novel degeneracy. We also study various limits of the parameter space (q, N) and recover the known spectrum in both fuzzy and commutative sphere.Comment: 19 pages, 6 figures, more references adde

Stellar evolution through the ages: period variations in galactic RRab stars as derived from the GEOS database and TAROT telescopes

The theory of stellar evolution can be more closely tested if we have the opportunity to measure new quantities. Nowadays, observations of galactic RR Lyr stars are available on a time baseline exceeding 100 years. Therefore, we can exploit the possibility of investigating period changes, continuing the pioneering work started by V. P. Tsesevich in 1969. We collected the available times of maximum brightness of the galactic RR Lyr stars in the GEOS RR Lyr database. Moreover, we also started new observational projects, including surveys with automated telescopes, to characterise the O-C diagrams better. The database we built has proved to be a very powerful tool for tracing the period variations through the ages. We analyzed 123 stars showing a clear O-C pattern (constant, parabolic or erratic) by means of different least-squares methods. Clear evidence of period increases or decreases at constant rates has been found, suggesting evolutionary effects. The median values are beta=+0.14 day/Myr for the 27 stars showing a period increase and beta=-0.20 day/Myr for the 21 stars showing a period decrease. The large number of RR Lyr stars showing a period decrease (i.e., blueward evolution) is a new and intriguing result. There is an excess of RR Lyr stars showing large, positive $\beta$ values. Moreover, the observed beta values are slightly larger than those predicted by theoretical models.Comment: 15 pages, 9 figures; to be published in Astronomy and Astrophysics; full resolution version available at http://dbrr.ast.obs-mip.fr/tarot/publis/publis.htm

The Index of (White) Noises and their Product Systems

(See detailed abstract in the article.) We single out the correct class of spatial product systems (and the spatial endomorphism semigroups with which the product systems are associated) that allows the most far reaching analogy in their classifiaction when compared with Arveson systems. The main differences are that mere existence of a unit is not it sufficient: The unit must be CENTRAL. And the tensor product under which the index is additive is not available for product systems of Hilbert modules. It must be replaced by a new product that even for Arveson systems need not coincide with the tensor product

Diagonalizing operators over continuous fields of C*-algebras

It is well known that in the commutative case, i.e. for $A=C(X)$ being a commutative C*-algebra, compact selfadjoint operators acting on the Hilbert C*-module $H_A$ (= continuous families of such operators $K(x)$, $x\in X$) can be diagonalized if we pass to a bigger W*-algebra $L^\infty(X)={\bf A} \supset A$ which can be obtained from $A$ by completing it with respect to the weak topology. Unlike the "eigenvectors", which have coordinates from $\bf A$, the "eigenvalues" are continuous, i.e. lie in the C*-algebra $A$. We discuss here the non-commutative analog of this well-known fact. Here the "eigenvalues" are defined not uniquely but in some cases they can also be taken from the initial C*-algebra instead of the bigger W*-algebra. We prove here that such is the case for some continuous fields of real rank zero C*-algebras over a one-dimensional manifold and give an example of a C*-algebra $A$ for which the "eigenvalues" cannot be chosen from $A$, i.e. are discontinuous. The main point of the proof is connected with a problem on almost commuting operators. We prove that for some C*-algebras if $h\in A$ is a selfadjoint, $u\in A$ is a unitary and if the norm of their commutant $[u,h]$ is small enough then one can connect $u$ with the unity by a path $u(t)$ so that the norm of $[u(t),h]$ would be also small along this path.Comment: 21 pages, LaTeX 2.09, no figure