Derived categories of graded gentle one-cycle algebras

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules. This is applied to study derived categories of graded gentle one-cycle algebras.Comment: To appear in JPA

Singularity categories of gentle algebras

We determine the singularity category of an arbitrary finite dimensional gentle algebra $\Lambda$. It is a finite product of $n$-cluster categories of type $\mathbb{A}_{1}$. Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If $\Lambda$ is a Jacobian algebra arising from a triangulation \ct of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of \ct.Comment: 11 pages; minor changes, final version, to appear Bulletin of the LM

Spherical subcategories in algebraic geometry

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general result is then applied to algebraic geometry.Comment: 21 pages. Identical to published version. There is a separate article with examples from representation theory, see arXiv:1502.0683

Spherical subcategories in representation theory

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.Comment: 36 pages, many changes to improve presentation, same content as published versio

Frobenius categories, Gorenstein algebras and rational surface singularities

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result to the Frobenius category of special Cohen-Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga-Gorenstein rings of finite GP type. We also apply our method to representation theory, obtaining Auslander-Solberg and Kong type results.Comment: 27 pages, to appear in Comp. Mat

Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities

We construct Kn\"orrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensional local algebras. This generalises Kn\"orrer's equivalence for singularities of Dynkin type A (between Krull dimensions $2$ and $0$) and yields many new equivalences between singularity categories of finite dimensional algebras. Our construction uses noncommutative resolutions of singularities, relative singularity categories, and an idea of Hille & Ploog yielding strongly quasi-hereditary algebras which we describe explicitly by building on Wemyss's work on reconstruction algebras. Moreover, K-theory gives obstructions to generalisations of our main result

Ringel duality for certain strongly quasi-hereditary algebras

We study quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary algebras. As special cases, we obtain a Ringel duality formula for a family of strongly quasi-hereditary algebras arising from a type A configuration of projective lines in a rational, projective surface as recently introduced by Hille and Ploog, for certain Auslander–Dlab–Ringel algebras, and for Eiriksson and Sauter’s nilpotent quiver algebras when the quiver has no sinks and no sources. We also recover Tan’s result that the Auslander algebras of self-injective Nakayama algebras are Ringel self-dual

Large scale production of multi-walled carbon nanotubes by fluidized bed catalytic chemical vapor deposition : a parametric study

A parametric study investigating the impact of temperature, run duration, total pressure, and composition of the gaseous phase on the catalytic growth of multi-walled carbon nanotubes (MWNT) has been performed. MWNT have been produced very selectively on the multi gram scale by catalytic chemical vapor deposition from ethylene in a fluidized bed reactor. The kinetics of MWNT growth is fast and, with the catalyst used, no induction period has been observed. The kinetic law is positive order in ethylene concentration and the process is limited by internal diffusion in the porosity of the catalyst. The formation of MWNT in the macroporosity of the catalyst induces an explosion of the catalyst grains. Such a process, thanks to the absence of temperature gradient and to the efficient mixing of the grains allows a uniform and selective treatment of the catalyst powder leading to very high selectivity towards MWNT formation. High purity MWNT have been obtained after catalyst dissolution. Depending on the temperature of production, the specific surface area of this material ranged between 95 and 455 m2/g

CENTRIN2 Interacts with the Arabidopsis Homolog of the Human XPC Protein (AtRAD4) and Contributes to Efficient Synthesis-dependent Repair of Bulky DNA Lesions

Arabidopsis thaliana CENTRIN2 (AtCEN2) has been shown to modulate Nucleotide Excision Repair (NER) and Homologous Recombination (HR). The present study provides evidence that AtCEN2 interacts with the Arabidopsis homolog of human XPC, AtRAD4 and that the distal EF-hand Ca2+ binding domain is essential for this interaction. In addition, the synthesis-dependent repair efficiency of bulky DNA lesions was enhanced in cell extracts prepared from Arabidopsis plants overexpressing the full length AtCEN2 but not in those overexpressing a truncated AtCEN2 form, suggesting a role for the distal EF-hand Ca2+ binding domain in the early step of the NER process. Upon UV-C treatment the AtCEN2 protein was shown to be increased in concentration and to be localised in the nucleus rapidly. Taken together these data suggest that AtCEN2 is a part of the AtRAD4 recognition complex and that this interaction is required for efficient NER. In addition, NER and HR appear to be differentially modulated upon exposure of plants to DNA damaging agents. This suggests in plants, that processing of bulky DNA lesions highly depends on the excision repair efficiency, especially the recognition step, thus influencing the recombinational repair pathwa