Reduced-complexity partial-interference-cancellation group decoder for STBCs

In this letter, we propose a reduced-complexity implementation of partial interference cancellation group decoder with successive interference cancellation (PIC-GD-SIC) by employing the theory of displacement structures. The proposed algorithm exploits the block-Toeplitz structure of the effective matrix and chooses an ordering of the groups such that the zero-forcing matrices associated with the various groups are obtained through Schur recursions without any approximations. We show using an example that the proposed implementation offers a significantly reduced computational complexity compared to the direct approach without any loss in performance.

Structural variations in aromatic 2 pi-electron three-membered rings of the main group elements

Structural variations of different Z pi-aromatic three-membered ring systems of main group elements, especially group 14 and 13 elements as compared to the classical description of cyclopropenyl cation has been reviewed in this article. The structures of heavier analogues as well as group 13 analogues of cyclopropenyl cation showed an emergence of dramatic structural patterns which do not conform, to the general norms of carbon chemistry. Isolobal analogies between the main group fragments have been efficiently used to explain the peculiarities observed in these three-membered ring systems.

Partial rotation of the isopropyl group in the solid state: single-crystal-to-single-crystal phase transformation in a carvacrol derivative

A hitherto unseen rotation of the isopropyl group in the solid state, predicted to be forbidden based on theoretical investigations, is reported. This C-C rotation observed during the temperature dependent single-crystal-to-single-crystal transformation is attributed to the concomitant changes in molecular structure and intermolecular packing.

Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Accelerated partial breast irradiation with interstitial brachytherapy as second conservative treatment for ipsilateral breast tumour recurrence: multicentric study of the GEC-ESTRO Breast Cancer Working Group

PURPOSE To analyse the clinical outcome after salvage lumpectomy and multi-catheter brachytherapy (MCB) for ipsilateral breast tumour recurrence (IBTR). MATERIAL AND METHODS Between 09/00 and 09/10, 217 patients presenting an IBTR underwent lumpectomy and MCB (low, pulsed, or high-dose rate). Survival rates without second local recurrence (2nd LR), distant metastasis (DM), and overall survival (OS) were analysed as well as late effects and cosmetic results. Univariate and multivariate analyses (MVA) based on IBTR data were performed to find prognostic factors for 2nd LR, DM, and OS. RESULTS Median follow-up after the IBTR was 3.9 years [range: 1.1-10.3]. Five and 10-year actuarial 2nd LR rates were 5.6% [range: 1.5-9.5] and 7.2% [range: 2.1-12.1], respectively. Five and 10-year actuarial DM rates were 9.6% [range: 5.7-15.2] and 19.1% [range: 7.8-28.3], respectively. Five and 10-year actuarial OS rates were 88.7% [range: 83.1-94.8] and 76.4% [range: 66.9-87.3], respectively. In MVA, histological grade was prognostic factor for 2nd LR (p=0.008) and OS (p=0.02); while tumour size was prognostic factor for DM (p=0.03). G3-4 complication rate was 11%. Excellent/good cosmetic result was achieved in 85%. CONCLUSION This study suggests that in case of IBTR, lumpectomy plus MCB is feasible and effective in preventing 2nd LR with an OS rate at least equivalent to those achieved with salvage mastectomy.

Chemistry of pyrrocorphins: synthesis of isobacteriochlorins and pyrrocorphins bearing a methyl group at the meso position between rings A and D

A sigmatropic methyl shift from the angular position C-1 in ring to the position C-20 between rings and constitutes the crucial step in syntheses leading to a 20-methyl-isobacteriochlorin and to 20-methyl-pyrrocorphins which served as substrates in the investigation presented in the accompanying communication.

Recommendations from GEC ESTRO Breast Cancer Working Group (I): Target definition and target delineation for accelerated or boost Partial Breast Irradiation using multicatheter interstitial brachytherapy after breast conserving closed cavity surgery

OBJECTIVE The aim was to develop a delineation guideline for target definition for APBI or boost by consensus of the Breast Working Group of GEC-ESTRO. PROPOSED RECOMMENDATIONS Appropriate delineation of CTV (PTV) with low inter- and intra-observer variability in clinical practice is complex and needs various steps as: (1) Detailed knowledge of primary surgical procedure, of all details of pathology, as well as of preoperative imaging. (2) Definition of tumour localization before breast conserving surgery inside the breast and translation of this information in the postoperative CT imaging data set. (3) Calculation of the size of total safety margins. The size should be at least 2 cm. (4) Definition of the target. (5) Delineation of the target according to defined rules. CONCLUSION Providing guidelines based on the consensus of a group of experts should make it possible to achieve a reproducible and consistent definition of CTV (PTV) for Accelerated Partial Breast Irradiation (APBI) or boost irradiation after breast conserving closed cavity surgery, and helps to define it after selected cases of oncoplastic surgery.

A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions

2000 Mathematics Subject Classification: 33A65, 33C20.

Social adaptation of children with mild intellectual disability : effects of partial integration within primary school classes

Examined the social adaptation of 32 children in grades 3–6 with mild intellectual disability: 13 Ss were partially integrated into regular primary school classes and 19 Ss were full-time in separate classes. Sociometric status was assessed using best friend and play rating measures. Consistent with previous research, children with intellectual disability were less socially accepted than were a matched group of 32 children with no learning disabilities. Children in partially integrated classes received more play nominations than those in separate classes, but had no greater acceptance as a best friend. On teachers' reports, disabled children had higher levels of inappropriate social behaviours, but there was no significant difference in appropriate behaviours. Self-assessments by integrated children were more negative than those by children in separate classes, and their peer-relationship satisfaction was lower. Ratings by disabled children of their satisfaction with peer relationships were associated with ratings of appropriate social skills by themselves and their teachers, and with self-ratings of negative behaviour. The study confirmed that partial integration can have negative consequences for children with an intellectual disability.

Hydrogen bonding in the water stabilized structure of the modified unsymmetrically substituted viologen chromophore, N-ethyl-N'-(2-phosphonomethyl)-4,4'-bipyridylium dichloride

The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.

Accelerated Partial Breast Irradiation (APBI) : a review of available techniques

Breast conservation therapy (BCT) is the procedure of choice for the management of the early stage breast cancer. However, its utilization has not been maximized because of logistics issues associated with the protracted treatment involved with the radiation treatment. Accelerated Partial Breast Irradiation (APBI) is an approach that treats only the lumpectomy bed plus a 1-2 cm margin, rather than the whole breast. Hence because of the small volume of irradiation a higher dose can be delivered in a shorter period of time. There has been growing interest for APBI and various approaches have been developed under phase I-III clinical studies; these include multicatheter interstitial brachytherapy, balloon catheter brachytherapy, conformal external beam radiation therapy and intra-operative radiation therapy (IORT). Balloon-based brachytherapy approaches include Mammosite, Axxent electronic brachytherapy and Contura, Hybrid brachytherapy devices include SAVI and ClearPath. This paper reviews the different techniques, identifying the weaknesses and strength of each approach and proposes a direction for future research and development. It is evident that APBI will play a role in the management of a selected group of early breast cancer. However, the relative role of the different techniques is yet to be clearly identified.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.