On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Finite group lattice gauge theories for quantum simulation

The present manuscript focuses on Lattice Gauge Theories based on finite groups. For the purpose of Quantum Simulation, the Hamiltonian approach is considered, while the finite group serves as a discretization scheme for the degrees of freedom of the gauge fields. Several aspects of these models are studied. First, we investigate dualities in Abelian models with a restricted geometry, using a systematic approach. This leads to a rich phase diagram dependent on the super-selection sectors. Second, we construct a family of lattice Hamiltonians for gauge theories with a finite group, either Abelian or non-Abelian. We show that is possible to express the electric term as a natural graph Laplacian, and that the physical Hilbert space can be explicitly built using spin network states. In both cases we perform numerical simulations in order to establish the correctness of the theoretical results and further investigate the models.

Effect of cyclic load on vertical misfit of prefabricated and cast implant single abutment

OBJECTIVES: The purpose of this in vitro study was to evaluate misfit alterations at the implant/abutment interface of external and internal connection implant systems when subjected to cyclic loading. MATERIAL AND METHODS: Standard metal crowns were fabricated for 5 groups (n=10) of implant/abutment assemblies: Group 1, external hexagon implant and UCLA cast-on premachined abutment; Group 2, internal hexagon implant and premachined abutment; Group 3, internal octagon implant and prefabricated abutment; Group 4, external hexagon implant and UCLA cast-on premachined abutment; and Group 5, external hexagon implant and Ceraone abutment. For groups 1, 2, 3 and 5, the crowns were cemented on the abutments and in group 4 crowns were screwed directly on the implant. The specimens were subjected to 500,000 cycles at 19.1 Hz of frequency and non-axial load of 133 N in a MTS 810 machine. The vertical misfit (μm) at the implant/abutment interface was evaluated before (B) and after (A) application of the cyclic loading. Data were analyzed statistically by using two-away ANOVA and Tukey's post-hoc test (p<0.05). RESULTS: Before loading values showed no difference among groups 2 (4.33±3.13), 3 (4.79±3.43) and 5 (3.86±4.60); between groups 1 (12.88±6.43) and 4 (9.67±3.08), and among groups 2, 3 and 4. However, groups 1 and 4 were significantly different from groups 2, 3 and 5. After loading values of groups 1 (17.28±8.77) and 4 (17.78±10.99) were significantly different from those of groups 2 (4.83±4.50), 3 (8.07±4.31) and 5 (3.81±4.84). There was a significant increase in misfit values of groups 1, 3 and 4 after cyclic loading, but not for groups 2 and 5. CONCLUSIONS: The cyclic loading and type of implant/abutment connection may develop a role on the vertical misfit at the implant/abutment interface.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

Synergistic Effect of Porcine Follicular Fluid and Dibutyryl Cyclic Adenosine Monophosphate on Development of Parthenogenetically Activated Oocytes from Pre-Pubertal Gilts

This study investigated the effect of porcine follicular fluid (PFF) and dibutyryl cyclic adenosine monophosphate (dbcAMP) during in vitro maturation (IVM) of porcine oocytes on meiotic maturation, fertilization and embryo development, and compared the effect of supplementing the embryo culture media with PFF or foetal bovine serum (FBS) on embryo development. Oocytes from pre-pubertal gilts were IVM for 44 h, and parthenogenetically activated or in vitro-fertilized. Embryos were cultured in porcine zygote medium (PZM3) for 7 days. Cleavage and blastocyst rates were evaluated at 48 h and 7 days of culture. The supplementation of the IVM medium with 25% PFF and 1 mm dbcAMP for the first 22 h resulted in more (p < 0.05) embryos developing to the blastocyst stage as compared with the inclusion of dbcAMP alone. The dbcAMP + PFF combination increased (p < 0.05) the average number of nuclei per blastocyst as compared with either of these components alone or in its absence. A synergistic effect of dbcAMP + PFF during IVM was also reflected in the capacity of oocytes to regulate sperm penetration and prevent polyspermy, as twice as many oocytes from the control group were penetrated by more than one sperm as compared with those matured in the presence of both dbcAMP and PFF. The supplementation of PZM3 with 10% FBS from days 5 to 7 of culture significantly improved the total cell quantity in embryos derived either from control or dbcAMP + PFF matured oocytes. There was no effect on the total cell quantity when FBS was replaced by the same concentration of PFF. These studies showed that dbcAMP, PFF and FBS can improve both the quantity (57.3% vs 41.5%) and quality (74.8 vs 33.3 nuclei) of porcine blastocysts derived from oocytes recovered of pre-pubertal gilts.

Cyclic Fatigue Resistance of Rotary Nickel-Titanium Instruments Submitted to Nitrogen Ion Implantation

Introduction: The aim of this study was to assess cyclic fatigue resistance in rotary nickel-titanium instruments submitted to nitrogen ion implantation by using a custom-made cyclic fatigue testing apparatus. Methods: Thirty K3 files, size #25, taper 0.04, were divided into 3 experimental groups as follows: group A, 12 files exposed to nitrogen ion implantation at a dose of 2.5 x 10(17) ions/cm(2), accelerating voltage of 200 kV, currents of 1 mu A/cm(2), 130 degrees C temperature, and vacuum conditions of 10 x 10(-6) torr for 6 hours; group B, 12 nonimplanted files; and group C, 6 files submitted to thermal annealing for 6 hours at 130 degrees C. One extra file was used for process control. All files were submitted to a cyclic fatigue test that was performed with an apparatus that allowed the instruments to rotate freely, simulating rotary instrumentation of a curved canal (40-degree, 5-mm radius curve). An electric motor handpiece was used with a contra-angle of 16:1 at an operating speed of 300 rpm and a torque of 2 N-cm. Time to failure was recorded with a stopwatch in seconds and subsequently converted to number of cycles to fracture. Data were analyzed with the Student t test (P < .05). Results: Ion-implanted instruments reached significantly higher cycle numbers before fracture (mean, 510 cycles) when compared with annealed (mean, 428 cycles) and nonimplanted files (mean, 381 cycles). Conclusions: Our results showed that nitrogen ion implantation improves cyclic fatigue resistance in rotary nickel-titanium instruments. Industrial implementation. of this surface modification technique would produce rotary nickel-titanium instruments with a longer working life. (J Endod 2010;36:1183-1186)

Modelling basin level allocation of water in the Murray-Darling Basin in a world of uncertainty, Murray-Darling Program Working Papers WPM05-1, Risk and Sustainable Management Group, 8 February 2005

Abstract: The Murray-Darling Basin comprises over 1 million km2; it lies within four states and one territory; and over 12, 800 GL of irrigation water is used to produce over 40% of the nation's gross value of agricultural production. This production is used by a diverse collection of some-times mutually exclusive commodities (e.g. pasture; stone fruit; grapes; cotton and field crops). The supply of water for irrigation is subject to climatic and policy uncertainty. Variable inflows mean that water property rights do not provide a guaranteed supply. With increasing public scrutiny and environmental issues facing irrigators, greater pressure is being placed on this finite resource. The uncertainty of the water supply, water quality (salinity), combined with where water is utilised, while attempting to maximising return for investment makes for an interesting research field. The utilisation and comparison of a GAMS and Excel based modelling approach has been used to ask: where should we allocate water?; amongst what commodities?; and how does this affect both the quantity of water and the quality of water along the Murray-Darling river system?

The development and application of a novel safety-catch linker for BOC-based assembly of libraries of cyclic peptides

Cyclic peptides are appealing targets in the drug-discovery process. Unfortunately, there currently exist no robust solid-phase strategies that allow the synthesis of large arrays of discrete cyclic peptides. Existing strategies are complicated, when synthesizing large libraries, by the extensive workup that is required to extract the cyclic product from the deprotection/cleavage mixture. To overcome this, we have developed a new safety-catch linker. The safety-catch concept described here involves the use of a protected catechol derivative in which one of the hydroxyls is masked with a benzyl group during peptide synthesis, thus making the linker deactivated to aminolysis. This masked derivative of the linker allows BOC solid-phase peptide assembly of the linear precursor. Prior to cyclization, the linker is activated and the linear peptide deprotected using conditions commonly employed (TFMSA), resulting in deprotected peptide attached to the activated form of the linker. Scavengers and deprotection adducts are removed by simple washing and filtration. Upon neutralization of the N-terminal amine, cyclization with concomitant cleavage from the resin yields the cyclic peptide in DMF solution. Workup is simple solvent removal. To exemplify this strategy, several cyclic peptides were synthesized targeted toward the somatostatin and integrin receptors. From this initial study and to show the strength of this method, we were able to synthesize a cyclic-peptide library containing over 400 members. This linker technology provides a new solid-phase avenue to access large arrays of cyclic peptides.

Toroid inductor development for a SIC DC-DC converter up to 150kW, based on finite element method

Dissertação para a obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Energia

Deep infiltrating endometriosis of the colon causing cyclic bleeding

[Description] Endometriosis, the presence of functional endometrial tissue outside the uterus, occurs in about 3–10% of women of reproductive age and is a cause of chronic pelvic pain and infertility for some.1 Bowel involvement may be present in about 5–10% of these women, mostly affecting the rectum and distal sigmoid (over 80% of cases), and, more infrequently, the appendix, ileum and caecum. The most common lesions involve only the serosa (endometriotic implants) but they can penetrate the muscular layers of the wall, in which case they are called deep infiltrating endometriosis. (...)

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.