Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

Rough Maximal Oscillatory Singular Integral Operators

2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Variational Principles for Monotone and Maximal Bifunctions

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

Sequences of Maximal Degree Vertices in Graphs

2000 Mathematics Subject Classification: 05C35.

Minimal Subspaces with Maximal Dimensioanal Diameters

Владимир Тодоров - Нека X е компактно метрично пространство с dim X = n. Тогава за n − 1 - мерния диаметър dn−1(X) на X е изпълнено неравенството dn−1(X) > 0, докато dn(X) = 0 (да отбележим, че това е една от характеристиките на размерността на Лебег). От тук се получава, че X съдържа минимално по включване затворено подмножество Y , за което dn−1(Y ) = dn−1(X). Известен резултат е, че от това следва, че Y е Канторово Многообразие. В тази бележка доказваме, че всяко такова (минимално) подпространство Y е даже континуум V^n. Получени са също така някои следствия.

Classification of the Maximal Subsemigroups of the Semigroup of all Partial Order-Preserving Transformations

Илинка А. Димитрова, Цветелина Н. Младенова - Моноида P Tn от всички частични преобразования върху едно n-елементно множество относно операцията композиция на преобразования е изучаван в различни аспекти от редица автори. Едно частично преобразование α се нарича запазващо наредбата, ако от x ≤ y следва, че xα ≤ yα за всяко x, y от дефиниционното множество на α. Обект на разглеждане в настоящата работа е моноида P On състоящ се от всички частични запазващи наредбата преобразования. Очевидно P On е под-моноид на P Tn. Направена е пълна класификация на максималните подполугрупи на моноида P On. Доказано е, че съществуват пет различни вида максимални подполугрупи на разглеждания моноид. Броят на всички максимални подполугрупи на POn е точно 2^n + 2n − 2.

The Maximal Number of Particles in a Branching Process with State-Dependent Immigration

AMS subject classification: 60J80, 60J15.

Maximal Number of Successors in a Nginar(1) Process

2000 Mathematics Subject Classification: 60J80, 60J20, 60J10, 60G10, 60G70, 60F99.

English in a global voluntary work context:a case study of spoken interaction and its implications for language pedagogy

This study analyses a sample of spoken interaction between a Japanese volunteer working for JICA (Japan International Co-operation Agency) and one of her co-workers in Jamaica. Details of the research context are provided, followed by a theoretical grounding of the project, which relates to publications in English as a Lingua Franca and related fields. In terms of methodology and epistemology, the research aligns with discourse analysis, specifically linguistic ethnography and interactional sociolinguistics. After presenting an an analysis of the spoken interaction based on these approaches, the resulting implications for language pedagogy are considered. This includes recommendations for specific aspects of language teaching and testing practice based on the research findings, which could be incorporated into a needs-driven localized pedagogy for future Japanese volunteers. These findings also carry significant implications for other contexts of language education, not only in terms of specific pedagogical practices but also regarding broader conceptions of language and communication.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

Where did we come from? The emergence and early development of voluntary sector studies in the UK

This article considers how the field of voluntary sector studies (VSS) in the UK emerged. Drawing on published and unpublished documents as well as on semi-structured interviews with people involved in the early development of VSS, a timeline of key events is suggested. The analysis reveals both social and cognitive elements in the field's development and considers the broader policy and institutional context within which key events of the VSS field occurred.

Thermal detemplation of SBA-15 mesophases. Effect of the activation protocol on the framework contraction

The potential use of the solvothermal extraction (SE) as a preliminary step to calcination for detemplating SBA-15 mesophases is investigated; aiming to reduce the amount of organics to be burnt and thereby the corresponding structural shrinkage. A systematic study was carried out by soxhlet extraction on mesophases hydrothermally aged between 90 and 130 C. The mesophases containing variable amounts of template were then treated by calcination or pyrolysis/calcination. TGA was applied to quantify the template amount after the various treatments. The as obtained materials were characterized by SAXS and Ar ad/desorption for structural and textural information while 1H NMR gave information about the integrity of the as-recycled template. The study shows that solvothermal conditions remove considerably the template, typically from 50 to 10-20 wt.%, mainly extracted from the primary mesopores. Possible reuse of the extracted template is questionable as it is poor in polyethyleneoxide compared to the synthesis block-copolymer, Pluronic P123. For all thermal protocols applied (direct calcination, calcination after solvent-extraction or pyrolysis/calcination after solvent extraction), the thermal shrinkage decreases with the aging temperature; that is consistent with the condensation degree of the silica. For each mesophase, it was found that the thermal shrinkage becomes less pronounced when the material is fully templated; thus the template can serve as structural support or can control the mass transfer of O2 and thereby the oxidation rate of the template burning. © 2013 Elsevier Inc. All rights reserved.