The Weil proof and the geometry of the adèles class space

This paper explores analogies between the Weil proof of the Riemann hypothesis for function fields and the geometry of the adèles class space, which is the noncommutative space underlying Connes' spectral realization of the zeros of the Riemann zeta function. We consider the cyclic homology of the cokernel (in the abelian category of cyclic modules) of the “restriction map” defined by the inclusion of the idèles class group of a global field in the noncommutative adèles class space. Weil's explicit formula can then be formulated as a Lefschetz trace formula for the induced action of the idèles class group on this cohomology. In this formulation the Riemann hypothesis becomes equivalent to the positivity of the relevant trace pairing. This result suggests a possible dictionary between the steps in the Weil proof and corresponding notions involving the noncommutative geometry of the adèles class space, with good working notions of correspondences, degree, and codegree etc. In particular, we construct an analog for number fields of the algebraic points of the curve for function fields, realized here as classical points (low temperature KMS states) of quantum statistical mechanical systems naturally associated to the periodic orbits of the action of the idèles class group, that is, to the noncommutative spaces on which the geometric side of the trace formula is supported

Effect Of Polymerization Cycles On Gloss, Roughness, Hardness And Impact Strength Of Acrylic Resins

The aim of this study was to evaluate the conventional and boiled polymerization cycles on gloss, roughness, hardness and impact strength of acrylic resins. Samples were made for each Classico and QC-20 materials (n=10) in dental stone molds obtained from rectangular metallic matrices embedded in metallic flasks. The powder-liquid ratio and manipulation of the acrylic resins' were accomplished according to manufacturers' instructions and the resins were conventionally packed in metallic flasks. After polymerization by (1) conventional: 74 °C for 9 h (Classico) and (2) boiled: 20 min (QC-20) cycles, the samples were deflasked after cooling at room temperature and conventionally finished and polished. The properties were evaluated after storage in water at 37 °C for 24 h. Gloss was verified with Multi Gloss 268 meter (Konica Minolta), surface roughness was measured with Surfcorder SE 1700 rugosimeter (Kosaka), Knoop hardness number was obtained with HMV-200 microdurometer, and impact strength was measured in an Otto Wolpert-Werke device by Charpy system (40 kpcm). Data were subjected to Student's t-test (at α=0.05). The results were: Gloss: 67.7 and 62.2 for Classico and QC-20 resins, respectively; Surface roughness: 0.874 and 1.469 Ra-µm for Classico and QC-20, respectively; Knoop hardness: 27.4 and 26.9 for Classico and QC-20, respectively; and Impact strength: 37.6 and 33.6 kgf/cm2 for Classico and QC-20, respectively. No statistically significant difference (p>0.05)were found between the resins for the evaluated properties. In conclusion, conventional and boiled polymerization cycles had similar effects on gloss, roughness, hardness and impact strength of both Classico and QC-20 resins.27217618

Effect of polymerization cycles on gloss, roughness, hardness and impact strength of acrylic resins

The aim of this study was to evaluate the conventional and boiled polymerization cycles on gloss, roughness, hardness and impact strength of acrylic resins. Samples were made for each Classico and QC-20 materials (n=10) in dental stone molds obtained from rectangular metallic matrices embedded in metallic flasks. The powder-liquid ratio and manipulation of the acrylic resins' were accomplished according to manufacturers' instructions and the resins were conventionally packed in metallic flasks. After polymerization by (1) conventional: 74 °C for 9 h (Classico) and (2) boiled: 20 min (QC-20) cycles, the samples were deflasked after cooling at room temperature and conventionally finished and polished. The properties were evaluated after storage in water at 37 °C for 24 h. Gloss was verified with Multi Gloss 268 meter (Konica Minolta), surface roughness was measured with Surfcorder SE 1700 rugosimeter (Kosaka), Knoop hardness number was obtained with HMV-200 microdurometer, and impact strength was measured in an Otto Wolpert-Werke device by Charpy system (40 kpcm). Data were subjected to Student's t-test (at α=0.05). The results were: Gloss: 67.7 and 62.2 for Classico and QC-20 resins, respectively; Surface roughness: 0.874 and 1.469 Ra-µm for Classico and QC-20, respectively; Knoop hardness: 27.4 and 26.9 for Classico and QC-20, respectively; and Impact strength: 37.6 and 33.6 kgf/cm2 for Classico and QC-20, respectively. No statistically significant difference (p>0.05)were found between the resins for the evaluated properties. In conclusion, conventional and boiled polymerization cycles had similar effects on gloss, roughness, hardness and impact strength of both Classico and QC-20 resins272176180CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQSem informaçãoO propósito neste estudo foi avaliar os ciclos de polimerização convencional e por fervura sobre o brilho, rugosidade, dureza e resistência ao impacto de resinas acrílicas. Amostras foram confeccionadas para cada resina Clássico ou QC-20 (n=20) em moldes de gesso obtidos de matrizes metálicas retangulares incluídas em muflas metálicas. A proporção monômero/polímero das resinas e manipulação foram de acordo com as recomendações dos fabricantes e a massa convencionalmente incluída em muflas metálicas. Após polimerização nos ciclos (1) convencional: 74 °C por 9 horas (Clássico) e (2) fervura: 20 min (QC-20), as amostras foram demufladas após esfriadas em temperatura ambiente e convencionalmente acabadas e polidas. As propriedades foram avaliadas após armazenagem das amostras em água a 37 °C por 24 h. O brilho foi verificado com medidor Multi Gloss 268 (Konica Minolta), a rugosidade avaliada com rugosímetro Surfcorder SE 1700 (Kosaka), a dureza Knoop foi obtida com microdurômetro HMV-200 (Shimadzu) e a resistência ao impacto determinada pelo sistema Charpy (Otto Wolpert Werke). Os dados submetidos ao teste t de Student (α=0.05) mostraram que Os resultados foram: brilho: 67,7 e 62,2 para Clássico e QC-20, respectivamente; rugosidade: 0,874 e 1,469 Ra-µm para Clássico e QC-20, respectivamente; dureza: 27,4 e 26,9 para Clássico e QC-20, respectivamente; e resistência ao impacto: 37,6 e 33,6 kgf/cm2 para Clássico e QC-20, respectivamente. Não houve diference estatisticamente significante entre as resinas para as propriedades avaliadas. Conclui-se que os ciclos de polimerização convencional e por fervura promoveram similares efeitos sobre o brilho, rugosidade, dureza e resistência ao impacto para ambas as resinas Clássico e QC-2

Polymerization cycles on hardness and surface gloss of denture bases

The aim of this study was to evaluate different polymerization cycles on the hardness and surface gloss of acrylic resins for denture bases. Classico and Vip Cril Plus acrylic resins samples were made in dental stone molds. Powder-liquid ratio and resin manipulation were according to the manufacturers’ instructions, and the resulting mass pressed in metallic fl asks. The polymerization cycles were A - hot water bath at 74°C for 9 hours; B - hot water bath at 74°C for 8 hours + 100°C for 1 hour, and C - hot water bath at 74°C for 2 hours + 100°C for 1 hour. After polymerization, the samples were defl asked and submitted to finishing and polishing procedures, and stored in water at 37°C for 24 hours. A hardness indenter with load of 25 gf for 10 s evaluated the Knoop hardness values. A gloss meter evaluated the surface gloss using a light incidence of 60°. Data were submitted to ANOVA and Tukey’s test (α = 0.05). Hardness: There were signifi cant differences between resins regardless of polymerization cycles (Classico = 22.28 and Vip Cril Plus = 25.83). Significant differences occurred among polymerization cycles regardless of resins (A = 25.83, B = 24.64 and C = 21.73). There was similarity for the resin and cycle interaction (Classico: A = 24.51, B = 22.68 and C = 19.65; Vip Cril Plus: A = 27.15, B = 26.53 and C = 23.81). Surface gloss. Significant differences were shown between resins regardless of polymerization cycle (Classico = 57.26 and Vip Cril Plus = 49.38) and between polymerization cycles regardless of resin (A = 48.82, B = 53.46 and C = 57.68). Statistical diff erences were also found for the resin and cycle interaction (Classico: A = 52.32, B = 63.79 and C = 55.67; Vip Cril Plus: A = 45.32, B = 43.14 and C = 59.69). Diff erent polymerization cycles showed similar eff ects on hardness and different effects on the surface gloss of denture base acrylic resins

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page

High-temporal-resolution electron microscopy for imaging ultrafast electron dynamics

Ultrafast Electron Microscopy (UEM) has been demonstrated to be an effective table-top technique for imaging the temporally-evolving dynamics of matter with subparticle spatial resolution on the time scale of atomic motion. However, imaging the faster motion of electron dynamics in real time has remained beyond reach. Here, we demonstrate more than an order of magnitude (16 times) enhancement in the typical temporal resolution of UEM by generating isolated 30 fs electron pulses, accelerated at 200 keV, via the optical-gating approach, with sufficient intensity for efficiently probing the electronic dynamics of matter. Moreover, we investigate the feasibility of attosecond optical gating to generate isolated subfemtosecond electron pulses, attaining the desired temporal resolution in electron microscopy for establishing the Attomicroscopy to allow the imaging of electron motion in the act.Comment: 19 Pages, 4 Figure