Digit systems over commutative rings

Let epsilon be a commutative ring with identity and P is an element of epsilon[x] be a polynomial. In the present paper we consider digit representations in the residue class ring epsilon[x]/(P). In particular, we are interested in the question whether each A is an element of epsilon[x]/(P) can be represented modulo P in the form e(0)+ e(1)x + ... + e(h)x(h), where the e(i) is an element of epsilon[x]/(P) are taken from a fixed finite set of digits. This general concept generalizes both canonical number systems and digit systems over finite fields. Due to the fact that we do not assume that 0 is an element of the digit set and that P need not be monic, several new phenomena occur in this context.

Construction and decoding of BCH codes over chain of commutative rings

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

A note on units of finite local rings in an ascending chain

In this paper we present matrices over unitary finite commutative local rings connected through an ascending chain of containments, whose elements are units of the corresponding rings in the chain such that the McCoy ranks are the largest ones.

Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

A Note on Linear Codes over Semigroup Rings

In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.

Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A New Fluorinated Polymer Having Two Connected Rings in the Main Chain: Synthesis and Characterization of Fluorinated Poly(1,3-cyclohexadiene)

The high electronegativity and small size of the fluorine atom and the high stability of C-F bonds impart interesting properties and applications to fluorine containing polymers. The unique properties of fluoropolymers include high thermal stability, improved chemical resistance, low surface energies, low coefficients of friction, and low dielectric constants. Applications of fluorinated polymers include use as noncorrosive materials, polymer processing aids, chemically resistant and antifouling coatings, as well as interlayer dielectrics. Fluorine-containing polymers can be directly synthesized via polymerization of fluorine-containing monomers or by post-polymerization modification. The latter method can be used to attach fluorinated species, such as perfluoroalkyl groups, onto conventional polymer chains, thereby imparting properties of fluorine-containing polymers into conventional polymers and widening their range of potential applications.

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.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

In-plane mapping of buried InGaAs quantum rings and hybridization effects on the electronic structure

This work reports the investigation on the structural differences between InAs quantum rings and their precursor quantum dots species as well as on the presence of piezoelectric fields and asymmetries in these nanostructures. The experimental results show significant reduction in the ring dimensions when the sizes of capped and uncapped ring and dot samples are compared. The iso-lattice parameter mapped by grazing-incidence x-ray diffraction has revealed the lateral extent of strained regions in the buried rings. A comparison between strain and composition of dot and ring structures allows inferring on how the ring formation and its final configuration may affect optical response parameters. Based on the experimental observations, a discussion has been introduced on the effective potential profile to emulate theoretically the ring-shape confinement. The effects of confinement and strain field modulation on electron and hole band structures are simulated by a multiband k.p calculation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4733964]

Effects of high-energy astrophysical events on habitable planets

With the possible exception of meteor impacts, high-energy astrophysical events such as supernovae, gamma-ray bursts (GRB) and flares are usually not taken into account for biological and evolutionary studies due to their low rates of occurrence. We show that a class of these events may occur at distances and time scales in which their biological effects are non-negligible, maybe more frequent than the impacts of large asteroids. We review the effects of four transient astrophysical sources of ionizing radiation on biospheres - stellar flares, giant flares from soft gamma repeaters (SGR), supernovae and GRB. The main damaging features of them are briefly discussed and illustrated. We point out some open problems and ongoing work. Received 28 February 2012, accepted 6 July 2012, first published online 10 August 2012

Exercise training improves relaxation response and SOD-1 expression in aortic and mesenteric rings from high caloric diet-fed rats

Abstract Background Obesity has been associated with a variety of disease such as type II diabetes mellitus, arterial hypertension and atherosclerosis. Evidences have shown that exercise training promotes beneficial effects on these disorders, but the underlying mechanisms are not fully understood. The aim of this study was to investigate whether physical preconditioning prevents the deleterious effect of high caloric diet in vascular reactivity of rat aortic and mesenteric rings. Methods Male Wistar rats were divided into sedentary (SD); trained (TR); sedentary diet (SDD) and trained diet (TRD) groups. Run training (RT) was performed in sessions of 60 min, 5 days/week for 12 weeks (70–80% VO2max). Triglycerides, glucose, insulin and nitrite/nitrate concentrations (NOx-) were measured. Concentration-response curves to acetylcholine (ACh) and sodium nitroprusside (SNP) were obtained. Expression of Cu/Zn superoxide dismutase (SOD-1) was assessed by Western blotting. Results High caloric diet increased triglycerides concentration (SDD: 216 ± 25 mg/dl) and exercise training restored to the baseline value (TRD: 89 ± 9 mg/dl). Physical preconditioning significantly reduced insulin levels in both groups (TR: 0.54 ± 0.1 and TRD: 1.24 ± 0.3 ng/ml) as compared to sedentary animals (SD: 0.87 ± 0.1 and SDD: 2.57 ± 0.3 ng/ml). On the other hand, glucose concentration was slightly increased by high caloric diet, and RT did not modify this parameter (SD: 126 ± 6; TR: 140 ± 8; SDD: 156 ± 8 and TRD 153 ± 9 mg/dl). Neither high caloric diet nor RT modified NOx- levels (SD: 27 ± 4; TR: 28 ± 6; SDD: 27 ± 3 and TRD: 30 ± 2 μM). Functional assays showed that high caloric diet impaired the relaxing response to ACh in mesenteric (about 13%), but not in aortic rings. RT improved the relaxing responses to ACh either in aortic (28%, for TR and 16%, to TRD groups) or mesenteric rings (10%, for TR and 17%, to TRD groups) that was accompanied by up-regulation of SOD-1 expression and reduction in triglycerides levels. Conclusion The improvement in endothelial function by physical preconditioning in mesenteric and aortic arteries from high caloric fed-rats was directly related to an increase in NO bioavailability to the smooth muscle mostly due to SOD-1 up regulation.

Stability and dynamics of terrestrial planets in binary star systems: application on Alpha Centauri

Binary stars are frequent in the universe, with about 50% of the known main sequence stars being located at a multiple star system (Abt, 1979). Even though, they are universally thought as second rate sites for the location of exo-planets and the habitable zone, due to the difficulties of detection and high perturbation that could prevent planet formation and long term stability. In this work we show that planets in binary star systems can have regular orbits and remain on the habitable zone. We introduce a stability criterium based on the solution of the restricted three body problem and apply it to describe the short period planar and three-dimentional stability zones of S-type orbits around each star of the Alpha Centauri system. We develop as well a semi-analytical secular model to study the long term dynamics of fictional planets in the habitable zone of those stars and we verify that planets on the habitable zone would be in regular orbits with any eccentricity and with inclination to the binary orbital plane up until 35 degrees. We show as well that the short period oscillations on the semi-major axis is 100 times greater than the Earth's, but at all the time the planet would still be found inside the Habitable zone.

The Gemini planet-finding campaign: the frequency of giant planets aroud debris disk stars

We have completed a high-contrast direct imaging survey for giant planets around 57 debris disk stars as part of the Gemini NICI Planet-Finding Campaign. We achieved median H-band contrasts of 12.4 mag at 0.''5 and 14.1 mag at 1'' separation. Follow-up observations of the 66 candidates with projected separation <500 AU show that all of them are background objects. To establish statistical constraints on the underlying giant planet population based on our imaging data, we have developed a new Bayesian formalism that incorporates (1) non-detections, (2) single-epoch candidates, (3) astrometric and (4) photometric information, and (5) the possibility of multiple planets per star to constrain the planet population. Our formalism allows us to include in our analysis the previously known β Pictoris and the HR 8799 planets. Our results show at 95% confidence that <13% of debris disk stars have a ≥5 M Jup planet beyond 80 AU, and <21% of debris disk stars have a ≥3 M Jup planet outside of 40 AU, based on hot-start evolutionary models. We model the population of directly imaged planets as d 2 N/dMdavpropm α a β, where m is planet mass and a is orbital semi-major axis (with a maximum value of a max). We find that β < –0.8 and/or α > 1.7. Likewise, we find that β < –0.8 and/or a max < 200 AU. For the case where the planet frequency rises sharply with mass (α > 1.7), this occurs because all the planets detected to date have masses above 5 M Jup, but planets of lower mass could easily have been detected by our search. If we ignore the β Pic and HR 8799 planets (should they belong to a rare and distinct group), we find that <20% of debris disk stars have a ≥3 M Jup planet beyond 10 AU, and β < –0.8 and/or α < –1.5. Likewise, β < –0.8 and/or a max < 125 AU. Our Bayesian constraints are not strong enough to reveal any dependence of the planet frequency on stellar host mass. Studies of transition disks have suggested that about 20% of stars are undergoing planet formation; our non-detections at large separations show that planets with orbital separation >40 AU and planet masses >3 M Jup do not carve the central holes in these disks.