We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke ...operators acting on period polynomials of modular forms, and it generalizes an approach developed by Don Zagier and the author for the modular group. This approach leads to a very simple formula for the trace on the space of cusp forms plus the trace on the space of modular forms. As applications, we investigate what happens when one varies the weight or the level in the trace formula.
The mesoporous silica KIT-6 was synthesized and functionalized with 3-aminopropyltriethoxysilane (APTES) by grafting at 110 °C. The composites were prepared with three different concentrations of ...APTES: 20, 30 and 40 wt.%. The as-prepared samples were characterized by thermal gravimetric analysis in air and nitrogen atmosphere (TG/DTA), Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction and nitrogen adsorption–desorption. In this study, CO2 adsorption–desorption was investigated using temperature programmed desorption mass spectrometry (TPD-MS) at different temperatures. The adsorption capacity of the prepared composites is 2.23 mmol CO2/g at 40 °C and decreases to 0.95 mmol/g at 70 °C. Regarding the efficiency of the amino groups, the best result was obtained for APTES-grafted KIT-6 at 40 °C, with 0.512 mmol CO2/mmol NH2. The results showed good cyclical stability in adsorption capacities even after nine adsorption–desorption cycles.
The ordered mesoporous silica MCM-48 with cubic Ia3d structure was synthesized using the cationic surfactant hexadecyltrimethylammonium bromide (CTAB) as a template agent and tetraethylorthosilicate ...(TEOS) as a silica source. The obtained material was first functionalized with (3-glycidyloxypropyl)trimethoxysilane (KH560); further, two types of amination reagents were used: ethylene diamine (N2) and diethylene triamine (N3). The modified amino-functionalized materials were characterized by powder X-ray diffraction (XRD) at low angles, infrared spectroscopy (FT-IR) and nitrogen adsorption–desorption experiments at 77 K. Characterization from a structural point of view reveals that the ordered MCM-48 mesoporous silica has a highly ordered structure and a large surface area (1466.059 m2/g) and pore volume (0.802 cm3/g). The amino-functionalized MCM-48 molecular sieves were tested for CO2 adsorption–desorption properties at different temperatures using thermal program desorption (TPD). Promising results for CO2 adsorption capacities were achieved for MCM-48 sil KH560-N3 at 30 °C. At 30 °C, the MCM-48 sil KH560-N3 sample has an adsorption capacity of 3.17 mmol CO2/g SiO2, and an efficiency of amino groups of 0.58 mmol CO2/mmolNH2. After nine adsorption–desorption cycles, the results suggest that the performance of the MCM-48 sil KH N2 and MCM-48 sil KH N3 adsorbents is relatively stable, presenting a low decrease in the adsorption capacity. The results reported in this paper for the investigated amino-functionalized molecular sieves as absorbents for CO2 can be considered as promising.
Modular forms and period polynomials Paşol, Vicenţiu; Popa, Alexandru A.
Proceedings of the London Mathematical Society,
October 2013, Letnik:
107, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We study the space of period polynomials associated with modular forms of integral weight for finite‐index subgroups of the modular group. For the modular group, this space is endowed with a pairing, ...corresponding to the Petersson inner product on modular forms via a formula of Haberland, and with an action of Hecke operators, defined algebraically by Zagier. We generalize Haberland's formula to (not necessarily cuspidal) modular forms for finite‐index subgroups, and we show that it conceals two stronger formulas. We extend the action of Hecke operators to period polynomials of modular forms, we show that the pairing on period polynomials appearing in Haberland's formula is nondegenerate, and we determine the adjoints of Hecke operators with respect to it. We give a few applications for Γ1(N): an extension of the Eichler–Shimura isomorphism to the entire space of modular forms; the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms, which are independent of the period relations; and an explicit formula for Fourier coefficients of Hecke eigenforms in terms of their period polynomials, generalizing the Coefficient theorem of Manin.
We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by \mathrm {PSL}_2(\mathbb{Z}) that may be of ...independent interest.
In this study, the preparation of some large-pore ordered mesoporous silicas using a proper surfactant with different swelling agents was carried out. The synthesis of conventional SBA-15 was ...modified to obtain pore-expanded materials, with pore diameters up to 10 nm. To use a micelle swelling agent with a moderate swelling ability, three swelling agents were selected: 1-phenyl-decane (Dec), butyl benzene (BB), and mesitylene (Mes). These syntheses aimed to achieve a pore diameter enlargement but at the same time to avoid the formation of heterogeneous and/or poorly defined nanostructure of silica. The CO
2
adsorbents were obtained by post-synthesis functionalization treatments carried out by grafting with 3-aminopropyl triethoxysilane. The CO
2
adsorption/desorption experiments showed that carbon dioxide sorption capacities depend on the textural characteristics and the temperature used for the adsorption process. Good CO
2
adsorption capacities were obtained for all prepared adsorbents, especially for SSBA-15-Mes-sil and SSBA-15-BB-sil samples. At 50 °C, the SSBA-15-Mes-sil sample has an adsorption capacity of 3.58 mmol CO
2
/g SiO
2
, and an efficiency of amino groups of 0.99 mmol CO
2
/mmol NH
2
. The results of adsorption capacities are comparable or even superior with the ones reported in literature for mesoporous silica functionalized with different amines. After nine adsorption–desorption cycles, the performance of the SSBA-15-Mes-sil adsorbent is relatively stable, with a low decrease in the adsorption capacity (0.1 mmol/g of CO
2
, i.e., 2.8% of initial capacity). These studies show the potential of mesoporous silica for carbon dioxide capture.
Diminutive polyps present a unique challenge in colorectal cancer (CRC) prevention strategies. This study aims to assess the characteristics and variables of diminutive polyps in a Romanian cohort, ...intending to develop a combined resect-and-retrieve or resect-and-discard strategy that reduces the need for an optical diagnosis.
A prospective cohort study was conducted at two endoscopy centers in Romania from July to December 2021. Adult patients undergoing colonoscopies where polyps were identified and resected were included. Endoscopic procedures employed advanced diagnostic features, including blue-light imaging (BLI) and narrow-band imaging (NBI). Logistic regression analysis was utilized to determine factors impacting the probability of adenomatous polyps with high-grade dysplasia (HGD).
A total of 427 patients were included, with a mean age of 59.42 years (±11.19), predominantly male (60.2%). The most common indication for a colonoscopy was lower gastrointestinal symptoms (42.6%), followed by screening (28.8%). Adequate bowel preparation was achieved in 87.8% of cases. The logistic regression analysis revealed significant predictors of HGD in adenomatous polyps: age (OR = 1.05, 95% CI: 1.01-1.08,
= 0.01) and polyp size (>5 mm vs. ≤5 mm, OR = 4.4, 95% CI: 1.94-10.06,
< 0.001). Polyps classified as Paris IIa, Ip, and Isp were significantly more likely to harbor HGD compared to the reference group (Is), with odds ratios of 6.05, 3.68, and 2.7, respectively.
The study elucidates significant associations between the presence of HGD in adenomatous polyps and factors such as age, polyp size, and Paris classification. These findings support the feasibility of a tailored approach in the resect-and-discard and resect-and-retrieve strategies for diminutive polyps, potentially optimizing CRC prevention and intervention practices. Further research is warranted to validate these strategies in broader clinical settings.
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