On the Derived Categories and Quasitilted Algebras

In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable objects in these categories, using homological properties. Given a complex X*, we consider the set J(X*) = {i is an element of Z vertical bar H(i)(X*) not equal 0} and we define the application l(X*) = maxJ(X*) - minJ(X*) + 1. We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

Algebras determined by their supports

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander-Reiten components of an ada algebra which is not quasi-tilted, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes. (C) 2011 Elsevier B.V. All rights reserved.

A note on tilting sequences

We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.

The bound quiver of a split extension

In this paper, we give a sufficient (which is also necessary under a compatibility hypothesis) condition on a set of arrows in the quiver of an algebra A so that A is a split extension of A/M, where M is the ideal of A generated by the classes of these arrows. We also compare the notion of split extension with that of semiconvex extension of algebras.

FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander-Reiten components.

Macular function in tilted disc syndrome

Tilted disc syndrome can cause visual field defects due to an optic disc anomaly. Recent electrophysiological findings demonstrate reduced central outer retinal function with ophthalmoscopically normal maculae. We measured macular sensitivity with the microperimeter and performed psychophysical assessment of mesopic rod and cone luminance temporal sensitivity (critical fusion frequency)in a 52-year-old male patient with tilted disc syndrome and ophthalmoscopically normal maculae. We found a marked reduction of sensitivity in the central 20 degrees and reduced rod- and cone-mediated mesopic visual function. Our findings extend previous electrophysiological data that suggest an outer retinal involvement of cone pathways and present a case with rod and cone impairment mediated via the magnocellular pathway in uncomplicated tilted disc syndrome.

Ocular refractive and biometric characteristics in patients with tilted disc syndrome

BACKGROUND Tilted disc syndrome (TDS) is associated with characteristic ocular findings. The purpose of this study was to evaluate the ocular, refractive, and biometric characteristics in patients with TDS. METHODS This case-control study included 41 eyes of 25 patients who had established TDS and 40 eyes of 20 healthy control subjects. All participants underwent a complete ocular examination, including refraction and analysis using Fourier transformation, slit lamp biomicroscopy, pachymetry, keratometry, and ocular biometry. Corneal topography examinations were performed in the syndrome group only. RESULTS There were no significant differences in spherical equivalent (P = 0.13) and total astigmatism (P = 0.37) between groups. However, mean best spectacle-corrected visual acuity (Log Mar) was significantly worse in TDS patients (P = 0.003). The lenticular astigmatism was greater in the syndrome group, whereas the corneal component was greater in controls (P = 0.059 and P = 0.028, respectively). The measured biometric features were the same in both groups, except for the lens thickness and lens-axial length factor, which were greater in the TDS group (P = 0.007 and P = 0.055, respectively). CONCLUSIONS Clinically significant lenticular astigmatism, more oblique corneal astigmatism, and thicker lenses were characteristic findings in patients with TDS.

Ocular refractive and biometric characteristics in patients with tilted disc syndrome

Purpose: To evaluate the ocular refractive and biometric characteristics in patients with tilted disc syndrome (TDS). Methods: This case-control study comprised 41 eyes of 25 patients with established TDS and forty eyes of 20 age- and sex-matched healthy control subjects. All had a complete ocular examination including refraction and analysis using Fourier transformation, slit lamp biomicroscopy, pachymetry keratometry, and ocular biometry. Corneal topography examinations were performed in the syndrome group only. Results: There were no significant differences in spherical equivalent (p = 0.334) and total astigmatism (p= 0.246) between groups. However, mean best spectacular corrected visual acuity was significantly worse in TDS patients (P < 0.001). The lenticular astigmatism was significantly greater in the syndrome group, while the corneal component was greater in the controls (p = 0.004 and p = 0.002, respectively). The measured biometric features were the same in both groups, except for the lens thickness, relative lens position, and lens-axial length factor which were greater in the TDS group (p = 0.002, p = 0.015, and p = 0.025, respectively). Conclusions: Clinically significant lenticular astigmatism, more oblique corneal astigmatism, and thicker lens were characteristic findings in patients with TDS.

Room-temperature tilted-target sputtering deposition of highly transparent and low sheet resistance Al doped ZnO electrodes

Target-tilted room temperature sputtering of aluminium doped zinc oxide (AZO) provides transparent conducting electrodes with sheet resistances of <10 Ω □-1 and average transmittance in the visible region of up to 84%. The properties of the AZO electrode are found to be strongly dependent on the target-tilting angle and film thickness. The AZO electrodes showed comparable performance to commercial indium tin oxide (ITO) electrodes in organic photovoltaic (OPV) devices. OPV devices containing a bulk heterojunction active layer comprised of poly(3-n-hexylthiophene) (P3HT):phenyl-C61-butyric acid methyl ester (PCBM) and an AZO transparent conducting electrode had a power conversion efficiency (PCE) of up to 2.5% with those containing ITO giving a PCE of 2.6%. These results demonstrate that AZO films are a good alternative to ITO for transparent conducting electrodes.

High-Rate, Multisymbol-Decodable STBCs From Clifford Algebras

It is well known that space-time block codes (STBCs) obtained from orthogonal designs (ODs) are single-symbol decodable (SSD) and from quasi-orthogonal designs (QODs) are double-symbol decodable (DSD). However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper, a method of constructing g-symbol decodable (g-SD) STBCs using representations of Clifford algebras are presented which when specialized to g = 1, 2 gives SSD and DSD codes, respectively. For the number of transmit antennas 2(a) the rate (in complex symbols per channel use) of the g-SD codes presented in this paper is a+1-g/2(a-9). The maximum rate of the DSD STBCs from QODs reported in the literature is a/2(a-1) which is smaller than the rate a-1/2(a-2) of the DSD codes of this paper, for 2(a) transmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates 1 and 3/4, respectively, whereas the known STBCs from QODs offer only 3/4 and 1/2, respectively. The construction of this paper is applicable for any number of transmit antennas. The diversity sum and diversity product of the new DSD codes are studied. It is shown that the diversity sum is larger than that of all known QODs and hence the new codes perform better than the comparable QODs at low signal-to-noise ratios (SNRs) for identical spectral efficiency. Simulation results for DSD codes at variousspectral efficiencies are provided.

Phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers

We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, tilted with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time-averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first-order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, there are important and observable quantitative differences, which we discuss.

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.