On the Automorphism Groups of some AG-Codes Based on Ca;b Curves

*Partially supported by NATO.

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.

New Binary Extremal Self-Dual Codes of Lengths 50 and 52

* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.

New Binary $[70,35,12]$ Self-Dual and Binary $[72,36,12]$ Self-Dual Doubly-Even Codes

∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99

Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given.

A Method for Classification of Doubly Resolvable Designs and Its Application

This article presents the principal results of the Ph.D. thesis Investigation and classification of doubly resolvable designs by Stela Zhelezova (Institute of Mathematics and Informatics, BAS), successfully defended at the Specialized Academic Council for Informatics and Mathematical Modeling on 22 February 2010.

Involution Matrix Algebras – Identities and Growth

2000 Mathematics Subject Classification: 16R50, 16R10.

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7

Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува.

Presentation

This volume on TAME systems (Tense-aspect-mood-evidentiality) stems from the 10th Chronos conference that took place in Aston University (Birmingham, UK) on 18th-20th April 2011. The papers collated here are therefore a chosen selection from a stringent peer-review process. They also witness to the width and breadth of the interests pursued within the Chronos community. Besides the traditional Western European languages, this volume explores languages from Eastern Europe (Greek, Romanian, Russian) and much further afield such as Brazilian Portuguese, Korean or Mandarin Chinese. Little known languages from the Amazonian forest (Amondawa, Baure) or the Andes (Aymara) also come under scrutiny.

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Mechanistic studies on the degradation of gasoline oxygenates by advanced oxidation technologies and the reaction of 4-methyl-1,2,4-triazoline-3,5-dione with tetracyclopropylethylene

Gasoline oxygenates (MTBE, methyl tert-butyl ether; DIPE, di-isopropyl ether; ETBE, ethyl tert-butyl ether; TAME, tert-amyl ether) are added to gasoline to boost octane and enhance combustion. The combination of large scale use, high water solubility and only minor biodegradability has now resulted in a significant gasoline oxygenate contamination occurring in surface, ground, and drinking water systems. Combination of hydroxyl radical formation and the pyrolytic environment generated by ultrasonic irradiation (665 kHz) leads to the rapid degradation of MTBE and other gasoline oxygenates in aqueous media. ^ The presence of oxygen promotes the degradation processes by rapid reaction with carbon centered radicals indicating radical processes involving O 2 are significant pathways. A number of the oxidation products were identified. The formation of products (alcohols, ketones, aldehydes, esters, peroxides, etc) could be rationalized by mechanisms which involve hydrogen abstraction by OH radical and/or pyrolysis to form carboncentered radicals which react with oxygen and follow standard oxidation chain processes. ^ The reactions of N-substituted R-triazolinediones (RTAD; R = CH 3 or phenyl) have attracted considerable interest because they exhibit a number of unusual mechanistic characteristics that are analogous to the reactions of singlet oxygen (1O2) and offer an easy way to provide C-N bond(s) formation. The reactions of triazolinedione with olefins have been widely studied and aziridinium imides are generally accepted to be the reactive intermediates. ^ We observed the rapid formation of an unusual intermediate upon mixing tetracyclopropylethylene with 4-methyl-1,2,4-triazoline-3,5-dione in CDCl 3. Detailed characterization by NMR (proton, 13C, 2-D NMRs) indicates the intermediate is 5,5,6,6-tetracyclopropyl-3-methyl-5,6-dihydro-oxazolo[3,2- b][1,2,4]-triazolium-2-olate. Such products are extremely rare and have not been studied. Upon warming the intermediate is converted to 2 + 2 diazetidine (major) and ene product (minor). ^ To further explore the kinetics and dynamics of the reaction activation energies were obtained using Arrhenius plots. Activation energies for the formation of the intermediate from reactants, and 2+2 adduct from the intermediate were determined as 7.48 kcal moll and 19.8 kcal mol−1 with their pre-exponential values of 2.24 × 105 dm 3 mol−1 sec−1 and 2.75 × 108 sec−1, respectively, meaning net slow reactions because of low pre-exponential values caused by steric hindrance. ^

Tamed and Compatible Symplectic Forms on Four-Dimensional Almost Complex Lie Algebras

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved and will give some insights on the proof. The key for the proof is translating the problem into a Linear Algebra setting. This is a joint work with Dr. Draghici.

Sistema de contagem com morfologia matemática fuzzy

Mathematical Morphology presents a systematic approach to extract geometric features of binary images, using morphological operators that transform the original image into another by means of a third image called structuring element and came out in 1960 by researchers Jean Serra and George Matheron. Fuzzy mathematical morphology extends the operators towards grayscale and color images and was initially proposed by Goetherian using fuzzy logic. Using this approach it is possible to make a study of fuzzy connectives, which allows some scope for analysis for the construction of morphological operators and their applicability in image processing. In this paper, we propose the development of morphological operators fuzzy using the R-implications for aid and improve image processing, and then to build a system with these operators to count the spores mycorrhizal fungi and red blood cells. It was used as the hypothetical-deductive methodologies for the part formal and incremental-iterative for the experimental part. These operators were applied in digital and microscopic images. The conjunctions and implications of fuzzy morphology mathematical reasoning will be used in order to choose the best adjunction to be applied depending on the problem being approached, i.e., we will use automorphisms on the implications and observe their influence on segmenting images and then on their processing. In order to validate the developed system, it was applied to counting problems in microscopic images, extending to pathological images. It was noted that for the computation of spores the best operator was the erosion of Gödel. It developed three groups of morphological operators fuzzy, Lukasiewicz, And Godel Goguen that can have a variety applications