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Synthesis and characterization of new aromatic esters based on 4,16-pregnadiene-6,20-dione skeleton
Juan Li1,
Hongqi Li1 &
Yijing Li1
Chemistry Central Journal volume 4, Article number: 18 (2010) Cite this article
A series of new aromatic esters based on 4,16-pregnadiene-6,20-dione skeleton, namely 3β-benzoyloxy-4,16-pregnadiene-6,20-dione and 3β-furoyloxy-4,16-pregnadiene- 6,20-dione, which may be good inhibitors for the 5α-reductase enzyme and show high antiandrogenic activity, were synthesized starting from diosgenin. The structures of the steroids were characterized by elemental analysis, 1H NMR, 13C NMR, IR and mass spectrum. Single crystal X-ray diffraction measurement on one of the new compounds, 3β-(p-methoxybenzoyloxy)-4,16-pregnadiene-6,20-dione revealed that the A, B, C, and D ring adopted half chair, distorted chair, distorted chair, and distorted envelope conformation, respectively. The molecules in the crystal were packed face-to-face at the normal van der Waals distances.
Studies on steroids stimulated renewed interest because apart from their estrogenic and anabolic/androgenic activity [1–3] steroids were found to show various biological activities including cytotoxicity [4], antiproliferative activity [5], antimicrobial activity [6], anti-glioma activity [7], inhibition of cholesterol α-glucosyltransferase [8], neuromuscular blocking activity [9], differential activities on prostate cancer cells [10], anti-osteoporosis activity [11], and anti-aging activity [12]. Up until now steroids have showed potential applications as 5α-reductase inhibitors [13], as modulators of inflammation and immunity [14], as inhibitors of 17α-hydroxylase/C17,20-lyase [15], as predictor of tamoxifen response in premenopausal breast cancer [16], as progesterone receptor antagonist [17], as glucocorticoid receptor imaging agents [18], as inhibitors of protein tyrosine phosphatase 1B [19], as reversal agents of multidrug resistance in cancer cells [20], as inhibitors of 17β-hydroxysteroid dehydrogenase [21], and as ligands for drug vectors [22]. Some steroidal compounds were used for photodynamic therapy [23], for cancer chemotherapy [24], and for DNA delivery [25]. Moreover, cholesteric liquid crystal [26] and steroid-based organogelator [27] were also studied. Recently Cabeza and collegues synthesized a series of 3β-benzoyloxy-4,16-pregnadiene-6,20-dione (1a-e, Figure 1) and 3β- cycloalkylcarbonyloxy-4,16-pregnadiene-6,20-dione (2a-d, Figure 1) compounds starting from 16-dehydropregnenolone acetate (16-DPA) and evaluated their biological activities. Of these steroids 1a is a good inhibitor for the 5α-reductase enzyme [13] while 1b-e and 2a-d showed high antiandrogenic activity [28, 29]. In continuation of our study on steroids [30, 31] and to explore an improved way for synthesis of new steroidal compounds from the cheap starting material diosgenin, herein we report the synthesis and structural characterization of a series of new aromatic esters based on 4,16-pregnadiene-6,20-dione skeleton.
Chemical structure of compound 1a-e and 2a-d.
All chemical reagents were purchased from commercial sources and used as received unless stated otherwise. Melting points were determined on a XT-4 melting apparatus and the quoted temperatures were uncorrected. Elemental analysis was carried out on an Elmentar Vario EL III system. 1H NMR and 13C NMR spectra were recorded on a Bruker AM 400 spectrometer. CDCl3 was used as solvent and chemical shifts recorded were internally referenced to Me4Si (0 ppm). IR spectra were obtained on a Thermo Electron Corporation Nicolet 380 FT-IR spectrophotometer. Mass spectra were recorded on a Shimadzu QP-2010 instrument using electron impact ionization (EI) at 70 eV. LC-MS spectra were obtained on an Agilent 6000 LC-MS instrument equipped with a SunFire C18 column (4.6 × 50 mm, 3.5 μm) under the following conditions: mobile phase: H2O (0.05% trifluoroacetic acid (TFA)) (A)/acetonitrile (0.05% TFA) (B); elution program: gradient from 5 to 95% of B in 1.6 min at 2.2 ml/min; temperature: 50°; detection: UV (214 nm) and MS (ESI, pos mode, 70 to 1000 amu). All of the measured samples were dissolved in methanol. X-Ray crystal structure was measured on a Bruker Smart CCD diffractometer by using Mo Kα radiation at 293 K.
Pseudodiosgenin diacetate (4) [32]
To a solution of diosgenin 3 (16.0 g, 38.6 mmol) and ammonium chloride (2.5 g, 46.7 mmol) in acetic anhydride (82 ml) was added pyridine (1.5 ml) and the mixture was heated at 140°C for 8-9 h. The resulting solution was cooled to room temperature and poured into ice water. The precipitate was filtered and recrystallized from methanol to give the product pseudodiosgenin diacetate (4) as yellow solid (16.6 g, 86%). M.p. 70-72°C.
3β-Acetoxy-5,16-pregnadiene-20-one (5)
A solution of pseudodiosgenin diacetate (4) (15.4 g, 30.8 mmol) in acetic anhydride (76 ml) was diluted with water (4.8 ml) and acetic acid (50 ml). The mixture was cooled to 0°C then a solution of chromium(VI) oxide (8.9 g, 89.0 mmol) in acetic acid (25 ml) was added dropwise in 1 h. After the addition the solution was allowed to warm to 10-16°C and the stirring was continued for 5 h at this temperature. Sodium bisulphite (9.3 g, 89.4 mmol) in water (30 ml) was added then the mixture was refluxed for 3 h, cooled and poured into water to give sticky solids. The crude product was crystallized from methanol then purified by means of column chromatography on silica gel with petroleum ether (b.p. 60-90°C) and ethyl acetate (4:1, v/v) as eluent to afford product 5 (4.5 g, 41%) as yellow needles. M.p. 170-172°C (literature [32] value: 171-172°C). Rf 0.58 (petroleum ether/ethyl acetate, 4:1, v/v).
Compound 6 was synthesized as described in literature [33] in 90% yield and as described in literature [13] in 95% yield. M.p. 170-172°C (literature [13] value: 170-172°C). Rf 0.57 (petroleum ether/ethyl acetate, 4:1, v/v).
Compound 7 was synthesized as described in literature [13] in 84% yield. M.p. 243-245°C (literature [13] value: 244-245°C). Rf 0.56 (petroleum ether/ethyl acetate, 4:1, v/v).
3β-Hydroxypregna-4,16-diene-6,20-dione (9)
A solution of steroid 8 (0.3 g, 0.8 mmol) in methanol (45 ml) and 2% aqueous sodium hydroxide (3 ml) was stirred for 30 min at room temperature. The resulting solution was poured into ice water (45 ml) then extracted with ethyl acetate (3 × 30 ml). The organic phase was dried over anhydrous magnesium sulfate and the solvent was removed in vacuum. The residue was purified by column chromatography on silica gel with petroleum ether and ethyl acetate (1:1, v/v) as eluent to afford product 9 (0.25 g, 74%) as pale yellow needles. M.p. 168-170°C (literature [13] value: 168-170°C). Rf 0.52 (petroleum ether/ethyl acetate, 4:1, v/v).
3β-(p-Methoxybenzoyloxy)pregna-4,16-diene-6,20-dione (10a)
A solution containing steroid 9 (0.10 g, 0.3 mmol), p-methoxybenzoic acid (0.13 g, 0.7 mmol), 1,3-dicyclohexylcarbodiimide (DCC, 0.10 g, 0.5 mmol) and 4-dimethylaminopyridine (DMAP, 0.06 g, 0.5 mmol) in methylene dichloride (6 ml) was stirred for 2 h at about 10°C. Ice water was added and the reaction mixture was extracted with chloroform (3 × 20 ml). The organic phase was dried over anhydrous magnesium sulfate and the solvent was removed in vacuum. The crude product was dissolved in ethyl acetate and filtered through a column containing silica gel. The organic solvent was removed in vacuum to give a white crystalline solid 10a (0.14 g, 71%). M.p. 244-246°C. Rf 0.50 (petroleum ether/ethyl acetate, 4:1, v/v). 1H NMR (CDCl3): 0.94 (s, 3 H, H-C(18)); 1.10 (s, 3 H, H-C(19)); 2.28 (s, 3 H, H-C(21)); 3.87 (s, 3 H, OMe); 5.56 (m, 1 H, H-C(3)); 6.23 (m, 1 H, H-C(4)); 6.71 (t, 1 H, J = 1.3 Hz, H-C(16)); 6.93 (m, 2 H, H-Ph); 8.02 (m, 2 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.7 (C(19)); 27.1 (C(21)); 69.5 (C(3)); 131.8 (C(4)); 143.8 (C(16)); 147.9 (C(5)); 154.9 (C(17)); 165.9 (ester C = O); 196.6 (C(20)); 201.9 (C(6)). IR (KBr): 3075, 2958, 1706, 1690, 1656, 1629. EI-MS: 312 (12, M+ + 1 - p-MeO-C6H4COO), 175 (31), 157 (38), 121 (30), 105 (41), 93 (33), 91 (66), 79 (51), 77 (46), 43 (100). LC-MS: 485.4 (M+ + Na, retention time 2.20 min). Anal. Calcd. for C29H34O5: C, 75.30; H, 7.41; Found: C, 75.12; H, 7.37.
Other steroidal compounds 10b-j were prepared in a similar procedure and the physical data of the new steroids were as follows.
3β-(o-Methoxybenzoyloxy)pregna-4,16-diene-6,20-dione (10b)
White powder. Yield 45%. M.p. 240-242°C. Rf 0.42 (petroleum ether/ethyl acetate, 4:1, v/v). 1H NMR (CDCl3): 0.93 (s, 3 H, H-C(18)); 1.07 (s, 3 H, H-C(19)); 2.27 (s, 3 H, H-C(21)); 3.89 (s, 3 H, OMe); 5.56 (m, 1 H, H-C(3)); 6.23 (m, 1 H, H-C(4)); 6.73 (t, J = 1.6 Hz, H-C(16)); 6.96 (m, 2 H, H-Ph); 7.46 (m, 1 H, H-Ph); 7.80 (m, 1 H, H-Ph). 13C NMR (CDCl3): 17.5 (C(18)); 22.0 (C(19)); 26.5 (C(21)); 71.8 (C(3)); 136.0 (C(4) and C(16)); 146.1 (C(5)); 149.9 (C(17)); 167.0 (ester C = O); 198.9 (C(20)); 203.8 (C(6)). IR (KBr): 3040, 2946, 1688. LC-MS: 485.4 (M+ + Na, retention time 2.13 min). Anal. Calcd. for C29H34O5: C, 75.30; H, 7.41; Found: C, 75.04; H, 7.46.
3β-(o-Methylbenzoyloxy)pregna-4,16-diene-6,20-dione (10c)
White powder. Yield 62%. M.p. 182-184°C. Rf 0.39 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.94 (s, 3 H, H-C(18)); 1.08 (s, 3 H, H-C(19)); 2.28 (s, 3 H, H-C(21)); 2.60 (s, 3 H, Me-Ph); 5.56 (m, 1 H, H-C(3)); 6.24 (m, 1 H, H-C(4)); 6.72 (t, 1 H, J = 1.8 Hz, H-C(16)); 7.23 (m, 2 H, H-Ph); 7.40 (m, 1 H, H-Ph); 7.93 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.7 (C(19)); 27.1 (C(21)); 69.6 (C(3)); 132.1 (C(4)); 143.9 (C(16)); 148.0 (C(5)); 154.9 (C(17)); 168.4 (ester C = O); 196.7 (C(20)); 201.8 (C(6)). IR (KBr): 3070, 2946, 1688. LC-MS: 469.4 (M+ + Na, retention time 2.28 min). Anal. Calcd. for C29H34O4: C, 78.00; H, 7.67; Found: C, 77.81; H, 7.63.
3β-(m-Methylbenzoyloxy)pregna-4,16-diene-6,20-dione (10d)
White powder. Yield 69%. M.p. 138-140°C. Rf 0.42 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.95 (s, 3 H, H-C(18)); 1.11 (s, 3 H, H-C(19)); 2.27 (s, 3 H, H-C(21)); 5.60 (m, 1 H, H-C(3)); 6.24 (m, 1 H, H-C(4)); 6.71 (t, 1 H, J = 1.8 Hz, H-C(16)); 7.32 (m, 2 H, H-Ph); 7.44 (m, 1 H, H-Ph); 7.84 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.7 (C(19)); 27.1 (C(21)); 69.8 (C(3)); 138.0 (C(4)); 143.9 (C(16)); 148.0 (C(5)); 154.9 (C(17)); 166.4 (ester C = O); 196.6 (C(20)); 201.9 (C(6)). IR (KBr): 3060, 2945, 1688, 1589, 1457. LC-MS: 469.4 (M+ + Na, retention time 2.29 min). Anal. Calcd. for C29H34O4: C, 78.00; H, 7.67; Found: C, 78.18; H, 7.71.
3β-(p-Nitrobenzoyloxy)pregna-4,16-diene-6,20-dione (10e)
Pale yellow powder. Yield 46%. M.p. 174-176°C. Rf 0.36 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.95 (s, 3 H, H-C(18)); 1.12 (s, 3 H, H-C(19)); 2.28 (s, 3 H, H-C(21)); 5.62 (m, 1 H, H-C(3)); 6.21 (m, 1 H, H-C(4)); 6.72 (t, 1 H, J = 1.8 Hz, H-C(16)); 8.23 (m, 2 H, H-Ph); 8.28 (m, 2 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.6 (C(19)); 27.1 (C(21)); 71.0 (C(3)); 130.8 (C(4)); 135.4 (C(16)); 148.6 (C(5)); 154.9 (C(17)); 164.3 (ester C = O); 196.6 (C(20)); 201.8 (C(6)). IR (KBr): 3062, 2946, 1688, 1528, 1456. LC-MS: 500.3 (M+ + Na, retention time 2.17 min). Anal. Calcd. for C28H31NO6: C, 70.42; H, 6.54; N, 2.93; Found: C, 70.57; H, 6.52; N, 2.87.
3β-(o-Nitrobenzoyloxy)pregna-4,16-diene-6,20-dione (10f)
Pale yellow powder. Yield 55%. M.p. 158-161°C. Rf 0.29 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.92 (s, 3 H, H-C(18)); 1.05 (s, 3 H, H-C(19)); 2.27 (s, 3 H, H-C(21)); 5.60 (m, 1 H, H-C(3)); 6.17 (m, 1 H, H-C(4)); 6.70 (t, 1 H, J = 1.8 Hz, H-C(16)); 7.63-7.68 (m, 2 H, H-Ph); 7.72 (m, 1 H, H-Ph); 7.95 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.6 (C(19)); 27.1 (C(21)); 71.5 (C(3)); 133.0 (C(4)); 143.8 (C(16)); 148.6 (C(5)); 154.9 (C(17)); 165.1 (ester C = O); 196.6 (C(20)); 201.6 (C(6)). IR (KBr): 3033, 2945, 1732, 1687, 1656, 1628, 1587, 1540, 1456. LC-MS: 500.3 (M+ + Na, retention time 2.11 min). Anal. Calcd. for C28H31NO6: C, 70.42; H, 6.54; N, 2.93; Found: C, 70.25; H, 6.49; N, 2.90.
3β-(m-Nitrobenzoyloxy)pregna-4,16-diene-6,20-dione (10g)
Pale yellow powder. Yield 47%. M.p. 176-178°C. Rf 0.38 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.94 (s, 3 H, H-C(18)); 1.12 (s, 3 H, H-C(19)); 2.27 (s, 3 H, H-C(21)); 5.63 (m, 1 H, H-C(3)); 6.20 (m, 1 H, H-C(4)); 6.71 (t, J = 1.2 Hz, H-C(16)); 7.66 (m, 1 H, H-Ph); 8.36-8.43 (m, 2 H, H-Ph); 8.86 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.6 (C(19)); 27.1 (C(21)); 71.0 (C(3)); 135.4 (C(4)); 143.8 (C(16)); 148.6 (C(5)); 154.9 (C(17)); 164.1 (ester C = O); 196.6 (C(20)); 201.7 (C(6)). IR (KBr): 3040, 2945, 1689, 1526, 1456. LC-MS: 500.3 (M+ + Na, retention time 2.17 min). Anal. Calcd. for C28H31NO6: C, 70.42; H, 6.54; N, 2.93; Found: C, 70.27; H, 6.58; N, 2.88.
3β-(3,5-Dinitrobenzoyloxy)pregna-4,16-diene-6,20-dione (10h)
Pale yellow powder. Yield 45%. M.p. 168-170°C. Rf 0.59 (petroleum ether/ethyl acetate, 2:1, v/v). 1H NMR (CDCl3): 0.95 (s, 3 H, H-C(18)); 1.15 (s, 3 H, H-C(19)); 2.29 (s, 3 H, H-C(21)); 5.70 (m, 1 H, H-C(3)); 6.20 (m, 1 H, H-C(4)); 6.72 (t, 1 H, J = 1.4 Hz, H-C(16)); 9.16 (m, 2 H, H-Ph); 9.24 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.5 (C(19)); 27.1 (C(21)); 72.2 (C(3)); 133.8 (C(4)); 143.8 (C(16)); 148.6 (C(5)); 154.8 (C(17)); 162.2 (ester C = O); 196.6 (C(20)); 201.6 (C(6)). IR (KBr): 3037, 2946, 1689, 1543, 1457. LC-MS: 500.3 (M+ + Na, retention time 3.14 min). Anal. Calcd. for C28H30N2O8: C, 64.36; H, 5.79; N, 5.36; Found: C, 64.22; H, 5.75; N, 5.19.
3β-(o-Chlorobenzoyloxy)pregna-4,16-diene-6,20-dione (10i)
White powder. Yield 64%. M.p. 192-194°C. Rf 0.32 (petroleum ether/ethyl acetate, 3:1, v/v). 1H NMR (CDCl3): 0.95 (s, 3 H, H-C(18)); 1.11 (s, 3 H, H-C(19)); 2.27 (s, 3 H, H-C(21)); 5.59 (m, 1 H, H-C(3)); 6.24 (m, 1 H, H-C(4)); 6.71 (t, 1 H, J = 1.8 Hz, H-C(16)); 7.32 (m, 1 H, H-Ph); 7.36 (m, 2 H, H-Ph); 7.87 (m, 1 H, H-Ph). 13C NMR (CDCl3): 15.8 (C(18)); 19.6 (C(19)); 27.1 (C(21)); 70.5 (C(3)); 133.9 (C(4)); 143.8 (C(16)); 148.2 (C(5)); 154.9 (C(17)); 165.2 (ester C = O); 196.6 (C(20)); 201.7 (C(6)). IR (KBr): 3040, 2946, 1688, 1522, 1456. LC-MS: 490.2 (M+ + Na, retention time 2.23 min). Anal. Calcd. for C28H31ClO4: C, 72.01; H, 6.69; Found: C, 71.83; H, 6.65.
3β-(2-Furoyloxy)pregna-4,16-diene-6,20-dione (10j)
White powder. Yield 77%. M.p. 180-182°C. Rf 0.40 (petroleum ether/ethyl acetate, 2:1, v/v). 1H NMR (CDCl3): 0.94 (s, 3 H, H-C(18)); 1.09 (s, 3 H, H-C(19)); 2.28 (s, 3 H, H-C(21)); 5.57 (m, 1 H, H-C(3)); 6.20 (m, 1 H, H-C(4)); 6.52 (t, 1 H, J = 1.8 Hz, H-C(16)); 6.71 (m, 1 H, H-Ar); 7.20 (m, 1 H, H-Ar); 7.59 (m, 1 H, H-Ar). 13C NMR (CDCl3): 15.8 (C(18)); 19.6 (C(19)); 27.1 (C(21)); 69.9 (C(3)); 128.7 (C(4)); 143.8 (C(16)); 148.1 (C(5)); 154.8 (C(17)); 158.3 (ester C = O); 196.6 (C(20)); 201.8 (C(6)). IR (KBr): 3042, 2946, 1720, 1689, 1657, 1580, 1523, 1457. LC-MS: 445.2 (M+ + Na, retention time 2.06 min). Anal. Calcd. for C26H30O5: C, 73.91; H, 7.16; Found: C, 73.73; H, 7.21.
The synthetic route of the target steroids 3β-benzoyloxypregna-4,16-diene-6,20-dione (10a-i) and 3β-furoyloxypregna-4,16-diene-6,20-dione (10j) was showed in Figure 2. At first the starting material diosgenin was transformed by acetylation and oxidation to 3β-acetoxy-5,16-pregnadiene-20-one (16-DPA, 5). The transformation could be achieved stepwise or in a one-pot reaction [32]. We adopted the former in consideration that the purification of the product was easier to yield 16-DPA of higher purity. Epoxidation of 16-DPA to form steroid 6 was conducted by using 30% H2O2/HCO2H [33] or m-chloroperoxybenzoic acid (m-CPBA) [13] oxidation system in 90% or 95% yield.
Synthetic route of target steroids 10a-j.
Conversion of compound 6 to 7 was carried out in a similar way as reported in literature [13] and the yield of steroid 7 was improved from 81% to 84%. Dehydration of 7 with thionyl chloride in pyridine resulted compound 8. We found that the quality of the solvent pyridine had an effect on the yield of the steroid 8. When dried pyridine (refluxed in the presence of potassium hydroxide for 2 h before distillation) was used instead of pyridine of analytically pure grade without treatment, the yield of 8 was improved to 73% from the literature [13] value 66%. Compound 8 was hydrolyzed with aqueous sodium hydroxide in methanol to afford 3β-hydroxypregna-4,16-diene-6,20-dione (9). The procedure for workup was improved by using extraction (with ethyl acetate) and concentration replacing filtration and subsequent recrystallization and pure product 9 was obtained in 74% yield, significantly higher than the literature [13] value 60%.
The target steroids 3β-benzoyloxypregna-4,16-diene-6,20-dione (10a-i) and 3β- furoyloxypregna-4,16-diene-6,20-dione (10j) were synthesized through Steglich reaction from 9, substituted benzoic acid or furoic acid, and DCC catalyzed by DMAP in fair to good yields (45%-77%), depending upon the structure of the aryl acids. It seems that the steric hindrance from the aryl acid structure leads to decrease in the yield. Therefore the highest yield of the Steglich reaction came from furoic acid (77%) while the reactions with dinitrobenzoic acid or nitrobenzoic acid gave the lowest yield.
The chemical structures of steroids 10a-j were fully characterized by elemental analysis, 1H NMR, 13C NMR, IR and mass spectrum and melting point measurements. Characteristic chemical shifts in 1H NMR spectra of steroids 10a-j were summarized in Table 1. All the chemical shifts of protons in methyl groups, OCH moieties, C = CH moieties, and aryl rings were in the reasonable range and the spectra data were in good accordance with the structures.
Table 1 Characteristic chemical shifts in 1H NMR spectra of steroids 10a-j
Single crystals of 10a suitable for X-ray crystal diffraction measurement were obtained by slow evaporation of a solution of 10a in 1:1 petroleum ether and ethyl acetate. X-Ray data for crystals of 10a were collected by graphite-monochromatized Mo Kα radiation at 293 K and the crystal data and experimental details for compound 10a were summarized in Table 2. The structure was solved by direct methods and refined by full-matrix least-squares with anisotropic temperature factors for the non-hydrogen atoms. The hydrogen atoms bonded to the carbon atoms were assigned based on the expected bonding geometry. The hydrogen atoms were refined isotropically in the final least-squares cycles.
Table 2 Crystal data and experimental details for compound 10a
The crystal structure and molecular packing of steroid 10a were shown in Figure 3 and Figure 4 respectively. It can be seen that the molecule consists of three six-membered rings (A, B, and C ring) and one five-membered ring (D ring), all trans fused. The six-membered rings A, B, and C occur in a half chair, distorted chair, and distorted chair conformation, respectively. Ring D adopts a distorted envelope conformation. The molecules in the crystal were packed face-to-face at the normal van der Waals distances, similar to the crystal structure of 3β-(p-fluorobenzoyloxy)-4,16-pregnadiene-6,20-dione [34]. CCDC-787721 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/data_request/cif
Crystal structure of compound 10a.
View of the molecular packing in 10a.
In summary, ten new aromatic esters based on 4,16-pregnadiene-6,20-dione skeleton, namely 3β-benzoyloxy-4,16-pregnadiene-6,20-dione and 3β-furoyloxy-4,16-pregnadiene-6,20- dione were synthesized starting from diosgenin. The structures of the steroids were characterized by elemental analysis, 1H NMR, 13C NMR, IR and mass spectrum. Single crystal X-ray diffraction measurement on one of the new compounds, 3β-(p-methoxybenzoyloxy)-4,16-pregnadiene-6,20-dione revealed that the A, B, C, and D ring adopted half chair, distorted chair, distorted chair, and distorted envelope conformation, respectively. The molecules in the crystal were packed face-to-face at the normal van der Waals distances. These new steroids may show high antiandrogenic activity and serve as good inhibitors for the 5α-reductase enzyme. Investigation of the inhibitory activity of the new steroids for the 5α-reductase enzyme will be conducted in the near future.
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Gunasekara S, Vrielink A, Stubbs KA: Preliminary studies into the inhibition of the cholesterol α-glucosyltransferase from Helicobacter pylori using azasugars. Carbohyd Res. 2010, 345: 960-964. 10.1016/j.carres.2010.03.003.
Dubey S, Sharma AK, Jindal DP, Harvey A, Singh R, Bodhankar SL: Synthesis and neuromuscular blocking activity of 16-(2- and 3-pyridylmethylene) dehydroepiandrosterone derivatives. Steroids. 2010, 75: 323-329. 10.1016/j.steroids.2010.01.009.
Bastien D, Leblanc V, Asselin É, Bérubé G: First synthesis of separable isomeric testosterone dimers showing differential activities on prostate cancer cells. Bioorg Med Chem Lett. 2010, 20: 2078-2081. 10.1016/j.bmcl.2010.02.077.
Liu J, Zhang X, Zhao M, Peng S: Synthesis, evaluation and 3D QSAR analysis of novel estradiol-RGD octapeptide conjugates with oral anti-osteoporosis activity. Eur J Med Chem. 2009, 44: 1689-1704. 10.1016/j.ejmech.2008.09.036.
Weng Y, Xiang L, Matsuura A, Zhang Y, Huang Q, Qi J: Ganodermasides A and B, two novel anti-aging ergosterols from spores of a medicinal mushroom Ganoderma lucidum on yeast via UTH1 gene. Bioorg Med Chem. 2010, 18: 999-1002. 10.1016/j.bmc.2009.12.070.
Pérez-Ornelas V, Cabeza M, Bratoeff E, Heuze I, Sánchez M, Ramírez E, Naranjo-Rodríguez E: New 5α-reductase inhibitors: in vitro and in vivo effects. Steroids. 2005, 70: 217-224.
Chapman KE, Odermatt A: Steroids: modulators of inflammation and immunity. J Steroid Biochem Mol Biol. 2010, 120: 67-68. 10.1016/j.jsbmb.2010.04.022.
Iványi Z, Wölfling J, Görbe T, Szécsi M, Wittmann T, Schneider G: Synthesis of regioisomeric 17β-N-phenylpyrazolyl steroid derivatives and their inhibitory effect on 17α-hydroxylase/C17,20-lyase. Steroids. 2010, 75: 450-456.
Källström A-C, Salme R, Rydén L, Nordenskjöld B, Jönsson P-E, Stål O: 17β-Hydroxysteroid dehydrogenase type 1 as predictor of tamoxifen response in premenopausal breast cancer. Eur J Cancer. 2010, 46: 892-900.
Cabeza M, García-Lorenzana M, Garcés M, Heuze I, Teran N, Bratoeff E: New-D- homoandrost-4,6-diene derivatives as potent progesterone receptor antagonist. Steroids. 2010, 75: 101-108. 10.1016/j.steroids.2009.11.001.
Wuest F, Carlson KE, Katzenellenbogen JA: Expeditious synthesis of steroids containing a 2-methylsulfanyl-acetyl side chain as potential glucocorticoid receptor imaging agents. Steroids. 2008, 73: 69-76. 10.1016/j.steroids.2007.08.013.
Xu J-Q, Shen Q, Li J, Hu L-H: Dammarans from Gynostemma pentaphyllum and synthesis of their derivatives as inhibitors of protein tyrosine phosphatase 1B. Bioorg Med Chem. 2010, 18: 3934-3939. 10.1016/j.bmc.2010.04.073.
Xiong J, Taniguchi M, Kashiwada Y, Sekiya M, Yamagishi T, Takaishi Y: Papyriferic acid derivatives as reversal agents of multidrug resistance in cancer cells. Bioorg Med Chem. 2010, 18: 2964-2975. 10.1016/j.bmc.2010.02.046.
Bydal P, Luu-The V, Labrie F, Poirier D: Steroidal lactones as inhibitors of 17β-hydroxysteroid dehydrogenase type 5: chemical synthesis, enzyme inhibitory activity, and assessment of estrogenic and androgenic activities. Eur J Med Chem. 2009, 44: 632-644. 10.1016/j.ejmech.2008.03.020.
Yaya AR, Touaibia M, Massarweh G, Rochon FD, Breau L: Synthesis of 17α- substituted ethynylestradiols: potential ligands for drug vectors. Steroids. 2010, 75: 489-498. 10.1016/j.steroids.2010.03.004.
Novakova V, Zimcik P, Miletin M, Kopecky K, Ivincová J: A phthalocyanine- mestranol conjugate for photodynamic therapy prepared via click chemistry. Tetrahedron Lett. 2010, 51: 1016-1018. 10.1016/j.tetlet.2009.12.075.
Oaksmith JM, Ganem B: Synthesis of a COMC-estradiol conjugate for targeted, tissue-selective cancer chemotherapy. Tetrahedron Lett. 2009, 50: 3497-3498. 10.1016/j.tetlet.2009.03.083.
Radchatawedchakoon W, Watanapokasin R, Krajarng A, Yingyongnarongkul B: Solid phase synthesis of novel asymmetric hydrophilic head cholesterol-based cationic lipids with potential DNA delivery. Bioorg Med Chem. 2010, 18: 330-342. 10.1016/j.bmc.2009.10.057.
Köysal O: Conductivity and dielectric properties of cholesteric liquid crystal doped with single wall carbon nanotube. Synth Met. 2010, 160: 1097-1100.
Edelsztein VC, Burton G, Di Chenna PH: Self-assembly of a silylated steroid-based organogelator and its use as template for the in situ sol-gel polymerization of tetraethyl orthosilicate. Tetrahedron. 2010, 66: 2162-2167. 10.1016/j.tet.2010.01.065.
Cabeza M, Heuze I, Sánchez M, Bratoeff E, Ramírez E, Rojas A, Orozco A, Mungía A, Agustín G, Cuatepotzo L, Gonzalez C, Palma S, Padilla D, Perez V, Jimenez G: Relative binding affinity of novel steroids to androgen receptors in hamster prostate. J Enzyme Inhib Med Chem. 2005, 20: 357-364. 10.1080/14756360500148924.
Cabeza M, Bratoeff E, Ramírez E, Heuze I, Recillas S, Berrios H, Cruz A, Cabrera O, Perez V: Biological activity of novel progesterone derivatives having a bulky ester side chains at C-3. Steroids. 2008, 73: 838-843. 10.1016/j.steroids.2008.03.006.
Li H, Song Y, Peng X: Improved synthesis of mestranol and ethinyl estradiol (EE) related degradation products as authentic references. Steroids. 2008, 73: 488-494. 10.1016/j.steroids.2007.12.024.
Li H, Song Y, Ge F: 17α-Ethynyl-3-methoxyestra-1,3,5(10),9(11)-tetraen-17-ol. Acta Crystallogr E. 2008, 64: o783-10.1107/S1600536808005254.
Bandhoria P, Gupta VK, Gupta DK, Jain SM, Varghese B: Crystal structure of 3β-acetoxy-pregna-5,16-dien-20-one (16 DPA). J Chem Crystallogr. 2006, 36: 161-166. 10.1007/s10870-005-9000-5.
Sun F, Lu H, Ge W: Synthesis of epoxy-progesterone derivatives and spectroscopic analysis. J Mol Sci (in Chinese). 2007, 23: 209-212.
Soriano-García M, Valencia N, Flores E, Bratoeff E, Ramírez E, Cabeza M: Crystal structure and synthesis of β-(p-fluorobenzoyloxy)-4,16-pregnadiene-6,20-dione. Anal Sci. 2003, 19: x79-x80.
The authors acknowledge the financial support of the project by Shanghai Natural Science Foundation (No. 06ZR14001).
Key Laboratory of Science & Technology of Eco-Textile, Ministry of Education, College of Chemistry, Chemical Engineering & Biotechnology, Donghua University, 2999 North Renmin Road, Shanghai, 201620, P. R, China
Juan Li, Hongqi Li & Yijing Li
Juan Li
Hongqi Li
Yijing Li
Correspondence to Hongqi Li.
JL carried out the synthetic experiments and drafted the manuscript. HL completed the molecular design, the arrangement of the work and modification of the manuscript. YL participated in the separation and purification of compounds, acquisition of data, and collection of literature and helped to draft the manuscript. All authors read and approved the final manuscript.
Li, J., Li, H. & Li, Y. Synthesis and characterization of new aromatic esters based on 4,16-pregnadiene-6,20-dione skeleton. Chemistry Central Journal 4, 18 (2010). https://doi.org/10.1186/1752-153X-4-18
CDCl3
Anhydrous Magnesium Sulfate
Aromatic Ester


M. J. McDermott speaks plainly of the need to master basic math by the end of the 5th grade or age 10. Explanations are provided on various teaching techniques taught in schools. She closes the video by stressing the need to teach the basics. TeachMeWell.com provides you and your child with a cost effective solution that follows a streamline process in learning the basics in an independent learning format.


text:
Sync Review: Five Missions More
Posted 5 June 2014
In our latest sync review we get the low down on the trailer for Mad Men Season Seven.
Alice Russell's latest album To Dust is proving to be one of her most popular so far with both the record buying public and music supervisors. Abla El-Sharnouby from Five Missions More tells M how Alice Russell's LP has yielded 15 music placements to date, including a lucrative sync in the trailer for Mad Men Season Seven…
How did the Mad Men sync happen?
We've worked with an agent in the US called David Steel, from a company called Steel Feet, for about 10 years. He handled all the licensing for Moby's Play, which was a watershed momentfor sync. David has really strong relationships with US music supervisors including at [entertainment giant] AMC. An AMC supervisor was arranging music for the Mad Men trailer and he hooked it up.
Have other syncs come from that record?
That song has been placed in Magic Mike, the Black List, the Client List and the Inbetweeners. Mad Men is probably the most high-profile. Alice's latest album To Dust is her most commercial to date and has done incredibly well sync-wise.
What was it about Breakdown that appealed to the Mad Men producers?
The song's dramatic edge works well in this context. Alice's music is rooted in fifties, sixties, seventies soul. While the album has a contemporary edge production-wise, the songs hark back to the era of the series. Aesthetically, it's a great fit.
Were there any challenges you had to overcome?
In this case, there weren't. But there can be many where US syncs are concerned. You can sometimes be looking for stems and trying to call producers at two in the morning so they can make changes. But not this time.
How does this sort of placement help an artist?
The US is a huge territory so artists can feel like a needle in a haystack and find it hard to get traction. The great thing about a high profile US TV show, particularly one as popular as Mad Men, is that there's a lot of hype about the music.
The song lists are hosted and discussed online. People are genuinely interested in the music and tend to check these lists for inspiration to find new artists. For example, Breakdown was used in Black List, another successful US show, and there was a tangible spike in sales after that. Alice is very hard working, has been touring the US for years but once the light is shone on an artist this way, it can generate much more interest.
Why have the songs from Alice's To Dust gained so many placements?
It's a combination of all the pieces in the jigsaw coming together at the same time. The work her label Tru Thoughts does, our efforts as publishers, in addition to the hard work Alice and her producer Alex Cowan (TM Juke) put in, in the studio and on the road.
Her music is very heartfelt and honest. She has such an amazing voice – anyone who sees her live will know she has this goosebump effect and this album is her best work. It's the hard work from all her camps plus a great LP that has facilitated the placements.
www.fivemissionsmore.com
Read our interview with Alice about the songwriting process for her latest album and working with David Byrne.
Check out our recent interview with music publishers Five Mission More about how they started their business.
five missions more
Interview: My Bus
'I come up with the melodies and Gary's job is just basically to put the apocalypse on basically anything I do': Butterfly Child's Joe Cassidy and Gary McKendry, aka Papa Sprain chat collaboration.
Interview: Gengahr
'From a slightly unfortunate set of circumstances we've found ourselves in a position to start releasing music,' say Gengahr's Felix Bushe.
Interview: Monarchy
'I think music (and art) is the expression of life, if all you have is music in your life then your music has no substance,' says Monarchy's Ra Black.

redpajama_set_name: RedPajamaCommonCrawl


text:
Dravid given break for New Zealand tour, Laxman to coach India
2mESPNcricinfo staff
WPL player auction likely to take place on February 11 or 13, Mumbai could host first edition
9minNagraj Gollapudi
The coaching staff has been given a break after the T20 World Cup
ESPNcricinfo staff
Rahul Dravid will return to his duties for the tour of Bangladesh • Peter Della Penna
Rahul Dravid has been given a break now that India's T20 World Cup campaign is over with VVS Laxman taking over as acting head coach for the team's white-ball tour of New Zealand starting on November 18.
A PTI report also suggests that Hrishikesh Kanitkar and Sairaj Bahutule will join the New Zealand-bound squad, taking up the roles of batting and bowling coach respectively.
'Not only mental but also physical burnout' - Ashwin defends Dravid's absence in New Zealand
Guptill, Boult left out of New Zealand's white-ball squads for India series
Hardik Pandya, Shikhar Dhawan to lead India in New Zealand
Dravid: Difficult to let Indian players play overseas T20 leagues
Tacky pitch and old habits haunt India in semi-final flop show
Laxman, who runs the National Cricket Academy, has had other short-term stints as India's coach, namely the tours of Ireland and Zimbabwe earlier this year, as well as the last month's home ODI series against South Africa. He was also in charge of the India Under-19 side that won the ODI World Cup in February.
India's tour of New Zealand will kick off with a three-match T20I series next Friday in Wellington.
Dravid will return to his coaching duties when India travel to Bangladesh immediately after the New Zealand tour. India play the third ODI against New Zealand on November 30 and will then play the first of three ODIs against Bangladesh on December 4.
Apart from the coaching team being given a break, India have also rested regular captain Rohit Sharma and senior batters Virat Kohli and KL Rahul.
Allrounder Hardik Pandya will captain India in the T20I series, while Shikhar Dhawan will lead the team in the ODIs.
On Thursday, India were knocked out of the T20 World Cup as England thrashed them by 10 wickets in the semi-final. The members of the Indian team who are not part of the New Zealand tour have already started dispersing from Australia, according to reports. While Kohli left from Adelaide, Rahul and Rohit are also expected to fly out soon.
Rahul DravidVVS LaxmanHrishikesh KanitkarSairaj BahutuleIndiaIndia in New Zealand


Is Kylo Ren a double agent?
I'm being torn apart. I want to be free of this pain. I know what I have to do but I don't know if I have the strength to do it. Will you help me?
Your son is gone. He was weak and foolish like his father, so I destroyed him.
Do you mean the murderers, traitors and thieves you call friends? You'll be relieved to hear I have no idea.
We know Luke is the last Jedi so maybe Kylo/Ben and Rey are the beginnings of a new order or force users who are more open than either Sith or Jedi. After all the Jedi close themselves off from temptation to stave off the Dark Side, but against an entity like Snoke abstinence may not be effective. It may be a little bit stupid but its possible that Kylo heard Snokes call and recognized it for what it was and was disgusted with Luke's ability to deal with it and decided that the needs of the many out weighted the needs of the few. I am well aware I just quoted Star Trek and that I am comparing Kylo to Itachi Uchiha but this is all plausible.
What might appear as innocuous fantasy or role-playing, when conducted under stressful or life-and-death situations exacts a heavy toll on the individual forced to slide in and out of character.
This could help explain Kylo's extreme mood shifts, one of the best examples is when he destroyed a console for no reason other than anger.
This could be another reason he wears the mask, though apparently it is a Sith Mask, but it helps hide is true emotions. Ben could be buried under Kylo just waiting to come out.


text:
"Our Philosophy"
Since opening our doors in 2012, we've prescribed to a fundamental philosophy: do what's right. This basic mantra sounds simple, but it extends to every area of our evolution. Do what's right for the world by giving back to charitable organizations, rescue groups and animal shelters. Do what's right for the community by supporting the neighborhood that has so wonderfully and wholly welcomed us as their own pet shop. Do what's right for our employees by constantly offering further information and education on pet health and products, so that they may provide exceptional service to all who shop with us. Do what's right for our customers by carrying only top-quality, all-natural and holistic pet food and supplies that we'd give to our own healthy pets.


We will propose the concept of progressions to comprehensively cover the factorial on the set of natural cadenced. In this context, it is necessary to propose new notations hopelessly and new methods to facilitate applications and encompass this whole concept. Before that, we agreed that all the manifestations of logical truth must coexist with the simple matematic, but mostly get away from the confusion. Thus it is not preferable to new notations for what is already established. Thus we present the formulas for solving factorial progressions having as main focus the division operation that is relatively parallel multiplication.


Volcanic Jalapeño is much like an actual volcano. At first taste, it is sweet and harmless. Then you feel a little heat, which quickly erupts into an explosion of great tasting jerky. Volcanic Jalapeño is the perfect answer for those who have tried so-called hot jerky before and found it to be too mild. This jerky has been designed with 5 different types of pepper (Jalapeño, habanero, cayenne, red and black pepper) as well as a custom blend of spices and gourmet ingredients. It was critical to make sure that underneath all the heat, it is still an amazing jerky.
My husband says he "definitely enjoyed the jalapeno jerky, it was good stuff"
Manly Man, bouquet of jerky flowers in tumbler with the Volcanic Jalapeño sampler.
My husband loved the jalapeno beef jerky and the .mixed "meat bouquet" I had delivered to him. I would definitely order again. The only thing that upset me about the delivery was the gift message card was not included.


Warm, dynamic, ready to be used in your tracks, productions and projects! Produced with attention to all details and processed on top quality hardware like SLL, Manley and others! Diginoiz proudly presents 'Modern Drum Shots'! 312 highest quality modern style drum one shots! Inspired by top modern pop and urban style artists. You will find here 214 Mb multiformat material. 62 Claps, 63 HiHats, 58 Kicks, 62 Shakes, 65 Snares and 2 Perc sounds.
'Modern Drum Shots' contains 312 Drum One Shots (62 Claps, 63 HiHats, 58 Kicks, 62 Shakes, 65 Snares and 2 Perc sounds). 214 Mb multi-format material (24-bit WAV, 24-bit Aiff and 16-bit WAV) ready to use in your favorite sampler or sequencer, both hardware and software, including: Logic, GarageBand, Soundtrack, Digital Performer, Sony Acid, Ableton Live, Adobe Audition, Cakewalk Sonar, Pro Tools, Emagic EXS24 and many more.


Federal Way police report that a firearm was discharged inside the Commons mall about 4:10 p.m. Sunday.
Police say two parties were involved in a physical altercation near Kohl's and Target when the gun was discharged. It is unknown if the gunshot was accidental or intentional, according to the police department.
Retailers were placed on lockdown and people inside the mall were evacuated. No injuries have been reported, according to police, who are investigating.
More information will be reported when available.


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text:
Q: sqlite3 autoincrement - am I missing something? I want to create unique order numbers for each day. So ideally, in PostgreSQL for instance, I could create a sequence and read it back for these unique numbers, because the readback both gets me the new number and is atomic. Then at close of day, I'd reset the sequence.
In sqlite3, however, I only see an autoincrement for the integer field type. So say I set up a table with an autoincrement field, and insert a record to get the new number (seems like an awfully inefficient way to do it, but anyway...) When I go to read the max back, who is to say that another task hasn't gone in there and inserted ANOTHER record, thereby causing me to read back a miss, with my number one too far advanced (and a duplicate of what the other task reads back.)
Conceptually, I require:

*

*fast lock with wait for other tasks

*increment number

*retrieve number

*unlock

...I just don't see how to do that with sqlite3. Can anyone enlighten me?

A: In SQLite, autoincrementing fields are intended to be used as actual primary keys for their records.
You should just it as the ID for your orders table.
If you really want to have an atomic counter independent of corresponding table records, use a table with a single record.
ACID is ensured with transactions:
BEGIN;
SELECT number FROM MyTable;
UPDATE MyTable SET number = ? + 1;
COMMIT;

A: ok, looks like sqlite either doesn't have what I need, or I am missing it. Here's what I came up with:

*

*declare zorder as integer primary key autoincrement, zuid integer in orders table
this means every new row gets an ascending number, starting with 1

*generate a random number:
rnd = int(random.random() * 1000000) # unseeded python uses system time

*create new order (just the SQL for simplicity):
'INSERT INTO orders (zuid) VALUES ('+str(rnd)+')'

*find that exact order number using the random number:
'SELECT zorder FROM orders WHERE zuid = '+str(rnd)

*pack away that number as the new order number (newordernum)

*clobber the random number to reduce collision risks
'UPDATE orders SET zuid = 0 WHERE zorder = '+str(newordernum)
...and now I have a unique new order, I know what the correct order number is, the risk of a read collision is reduced to negligible, and I can prepare that order without concern that I'm trampling on another newly created order.
Just goes to show you why DB authors implement sequences, lol.

redpajama_set_name: RedPajamaStackExchange


Despite the horrifically high death toll among civilians, Israel continues its war in the Gaza Strip, even threatening to launch a full invasion. So far the United Nations and the European Union have failed in their attempts to bring about a cease-fire.
They return after the sun has set over Gaza. All that can be heard at first is the droning of diesel engines. Then the headlights cut through the darkness and Israeli Merkava tanks emerge from the clouds of dust churned up by their heavy chains.
Soldiers covered in sweat and dirt climb from the cockpits, young conscripts hardly 20 years old. They have spent the last three days and nights in their tanks, where they have eaten, slept and relieved themselves.
They embrace each other, sing songs and talk about how smoothly everything went. "How many terrorists did you kill?" someone asks Benni from Petach Tikva. "Three," says Benni, which earns him a congratulatory slap on the back. But Benni isn't in the mood for celebration. "I had to do it, but they are humans, too." "Oh, come on," says the other soldier, "you're a great guy."
A female soldier appears carrying a white plastic bag containing mobile phones, which the soldiers were required to drop off before going into battle. Now they reach into the bag, pull out their phones and call home: "Ima, hakol beseder" -- "Mama, everything is all right." Friends from Jerusalem have brought a dozen pizzas. They are cold, but the soldiers don't mind. Who knows when they will be eating pizza again? "We're supposed to go back in again," one of them says, nodding in the direction of Gaza.
The soldiers are confident that their mission was a success. Unlike the 2006 Lebanon war, communications between intelligence and the troops is functioning well this time, says an officer as he bites into his pizza. "We are hitting our targets and eliminating the terrorists."
From ordinary soldiers to the military leadership, from vegetable vendors to cabinet ministers, at the end of week two of Operation Cast Lead, Israel is relatively free of doubt when it comes to making sense of its war against the Palestinian militant group Hamas.
And why shouldn't it be? The Israeli army has systematically advanced from the north, east and south, divided the Gaza Strip into two zones, encircled Gaza City and captured Khan Yunis, a city in the southern Gaza Strip.
Nevertheless, this is a war without victory, a war that can hardly be won any more, be it morally or militarily. How can these young Israeli soldiers defeat Hamas fighters who carry children in their arms as living shields, mingle with civilians and hide out in hospitals and schools? Hamas celebrates a triumph with each Israeli soldier it kills or abducts, no matter how small that number is. But Israel loses with each dead civilian.
There is growing international pressure to end this war soon. According to a UN report, by Saturday morning the conflict had already claimed 800 Palestinian lives, including more than 60 women and 250 children. Last Friday, the UN Security Council called for an immediate cease-fire, a demand that both the Israeli government and Hamas promptly rejected. At least the two sides have agreed to a daily three-hour pause in the fighting.
The war is still considered a success in Israel, where most newspapers have celebrated "our heroes," and the death toll among Israeli troops -- 11 soldiers by Saturday morning -- has not raised any significant doubts yet. After the first phase of air attacks, after the second phase of tank incursions in Gaza, the third phase of this war, an invasion with ground troops, could change everything. The previous balance could very well tip in the opposite direction.
In the third phase of the war, tens of thousands of reservists would be sent to fight in street battles in Gaza City, a deadly, booby-trapped labyrinth where snipers lie in waiting. There would undoubtedly be many dead on both sides, and the strategic gains would once again be minimal. The Israeli government knows this, which is why it is currently pursuing a double strategy. On the one hand, the army is preparing for the third phase while, on the other hand, cease-fire negotiations are underway behind closed doors.
The Israeli government is deeply divided. While Defense Minister Ehud Barak favors a cease-fire brokered by Egypt, Foreign Minister Tzipi Livni remains unbending. "We are not thinking about pulling back," says Livni.
By the end of the second week of Operation Cast Lead, both war and peace were options for Prime Minister Ehud Olmert, for whom this war will be among his last official acts.
In that second week, the world emerged from its shocked apathy and looked on with horror as the Israelis used enormous firepower against densely populated cities.
The aerial bombardments were followed, more or less inevitably, by the dirty war. Hundreds of thousands protested around the world. The Pope condemned the carnage, Belgium wanted to evacuate injured children, Venezuela expelled the Israeli ambassador and the International Red Cross sharply criticized the Israeli army for blocking emergency aid for wounded civilians. And John Ging, director of the UN's Gaza relief operations, attracted widespread attention when he criticized Israel for inflicting immense suffering on Palestinian civilians.
Since then, the world's attention has been focused on the Gaza Strip, that tiny sliver of land along the Mediterranean so full of misery and despair. The UN became involved, as did the European Union and various governments. Negotiators flew back and forth and consultations were held at every level. French President Nicolas Sarkozy took a leading role, traveling hurriedly from one Arab capital to the next, disproving his reputation of doing everything only for effect. Sarkozy, together with Egyptian President Hosni Mubarak, eventually presented a plan that could lead to a ceasefire.
US President-elect Barack Obama broke his silence for the first time. After all, the United States could see terrorist attacks as the expected consequence of this latest Middle East war, following a demonstrated pattern of violence begetting violence, in the Middle East and elsewhere. The war could also destabilize the region's more moderate regimes, which often face difficulties containing extremist groups of their own. And it will probably benefit Iran once again, the mullah-controlled state that has gained in prominence in the region since the 2003 Iraq war.
German Chancellor Angela Merkel, on unusually good terms with Sarkozy last week, said that there is no time to be lost. The situation is by no means hopeless. The peace place hammered out by the French and Egyptian presidents addresses two important issues: a secret tunnel system Hamas has developed in southern Gaza, which is part of the reason Israeli decided to launch its offensive, and the Israeli blockade of Gaza, one of the main reasons behind Hamas's rocket attacks on Israel.
The Israelis are holding a man who could become a key figure in peace negotiations: Marwan Barghouti, a senior official with the Palestinian Fatah movement. Impartial observers believe that he could serve as a middleman between the Gaza Strip and the West Bank, perhaps contributing a small step to achieving the two-state solution that most diplomats continue to believe represents the only chance of achieving lasting peace.
Even a tiny step would be significant in this conflict. The Palestinians and the Israelis have been fighting each other for decades, and Israel has already invaded Gaza four times. But it will not succeed in its efforts to permanently eliminate Hamas.


Every now and then I lose patience with some of my stocks. I see other folks trading in and out of the same stocks that I have held on to steadfastly because I believe they are under-valued. I start to wonder if i should engage in a bit of trading. At such times, I find it comforting to read material that will keep me true to the discipline of value investing.
Here is such material. The below is taken from a presentation made by Zeke Ashton who runs Centaur Capital Partners.
This entry was posted in Investing Rules, value investing, Zeke Ashton. Bookmark the permalink.


text:
Harry Potter and Torah
Harry Potter and Torah, a collection of Jewish insights related to the Harry Potter series, written by Dov Krulwich.
Haskama
REPOST: Fawkes the Phoenix in Noah's Ark
Could Fawkes, Dumbeldore's immortal phoenix, have been in the Garden of Eden or on Noah's Ark?Read the answer in the following excerpt from Harry Potter and Torah, which was printed in the Washington Jewish Week last July:
Was Fawkes the Phoenix on Noah's Ark?
When we think about Noah collecting the animals to bring into the ark, most of us tend to imagine lions and tigers, cows and rams, and other "regular" animals. After all, Torah does not talk about mythical animals like those found in Harry Potter.
Or does it? Might Fawkes the Phoenix have been on Noah's ark?
The Talmud tells the following midrashic story about Noah on the ark:"Noah found the phoenix hiding in the bottom of the Ark. He said to it, 'Don't you want food?' It replied, 'I saw you were busy, and did not want to trouble you.' He said to it, 'May it be God's will that you never die.' "
The midrash elaborates on the phoenix's immortality as follows: "It lives for a thousand years, and at the end of this thousand years, a fire emerges from its nest and incinerates it. A volume equivalent to an egg is left, which grows limbs and lives." The Prophet Job refers to the phoenix's immortality when he says "Like a phoenix I increase my life's days."
So we see the magical phoenix quite clearly in Torah literature! This sounds just like Dumbeldore's explanation to Harry in the middle of Chamber of Secrets (chapter 12):
"Fawkes is a phoenix, Harry. Phoenixes burst into flame when it is time for
themto die and are reborn from the ashes."
Interestingly, the same midrash gives a second, very different explanation of the phoenix's immortality: "Eve fed the animals and birds from the Tree of Knowledge. They all listened to her, except for one bird, called the phoenix."
Since all people and animals were immortal until eating from the tree of knowledge, the phoenix's not eating from the tree of knowledge meant it would never die.
So which is the reason that the midrashic phoenix lives forever? Is it because it did not eat from the tree of knowledge, or because of Noah's blessing?
Commentaries on the midrash give two possibilities. One is that the sages simply disagree, that the sage quoted in the midrash attributes the phoenix's longevity to the Garden of Eden, and the sage quoted in the Talmud attributes it to Noah's blessing.
The second possibility is that the phoenix's longevity was earned in two stages. It lives a long time, and does not die a natural death like other animals, because it did not eat from the tree of knowledge. Then Noah's blessing added to its immortality, either by giving it the process of rejuvenation by burning up and being reborn, or by giving it Divine protection from hunters and accidents.
Many commentaries, however, take all the biblical and midrashic discussions of the phoenix to be metaphorical. The Book of Job, for example, used the bird as a metaphor for long life, and did not refer to actually seeing one. Both the above stories from the midrash can be understood this way, as lessons about the importance of caring for other people's difficulties (the midrash of Noah) and about doing the right thing in the face of a temptation (the midrash of Eve). Each, according to the midrash, merits a lot of Divine reward, metaphorically earning long life or immortality.
Other commentaries say that the phoenix is used by our sages as a metaphor for "the soaring of the intellect, which continues even when man's body becomes weak." Others see the phoenix as a metaphor for the Jewish people throughout history, often appearing "burnt up" but always being reborn.
All in all, the magical phoenix has left us a lot to think about. Anyone intrigued by the existence of magical animals has no shortage of Torah sources for them. And anyone looking for metaphors for a soaring intellect or the everlasting Jewish people need look no further.
But, most important, we see two things that we can think about in our own lives, doing what is right when we're given a temptation not to (as in the story of Eve) and caring that others not work too hard for our own sake (the story of Noah). According to the midrash, these are how immortality is earned, either real or metaphorical. Even without spells or incantations, our own behavior can be as hot as a phoenix.
Interested in more about magical creatures in Torah? Harry Potter and Torah discusses talking snakes, owl post, and more! I also recommend Rabbi Slifkin's new book Sacred Monsters.
Posted by Bruce Krulwich at 10:48 PM No comments:
I think that a lot of fans of Harry Potter and Torah will like a new book written by my neighbor Rabbi Dov Lipman, called Timeout: Sports Stories as a Game Plan for Spiritual Success:
http://www.amazon.com/dp/1932687963?tag=hpt-20&creativeASIN=1932687963
The book is a great collection of lessons learned from sports, and how they relate to Jewish teachings. From Michigan's "Fab 5" to Rick Barry to Gilbert Arenas, there's no end to the lessons that can be learned from sports stories.
Posted by Bruce Krulwich at 8:14 AM No comments:
Harry Potter thoughts related to the story of creation
On Simchat Torah we re-start the Torah cycle from the beginning, starting with the creation story. The following articles from the Harry Potter and Torah blog relate to the creation story:
Snape's love for Lily: True Love or Obsession?
http://harrypottertorah.blogspot.com/2008/01/snapes-love-for-lily-true-love.html
Love, Relationships, and Souls
http://harrypottertorah.blogspot.com/2008/02/love-relationships-and-souls.html
The Divine Hallows
http://harrypottertorah.blogspot.com/2007/08/divine-hallows.html
I hope everyone has a great holiday!
Starting the new Torah cycle
If you haven't bought Harry Potter and Torah, now's the time!
We're about to start the new cycle of Torah portions back at Bereisheet (Genesis), and Harry Potter and Torah has chapters for every Torah portion in Bereisheet, along with many throughout the rest of the Torah. So you can have Harry Potter perspectives for every week's Torah portion!
Below is the full table of contents. Click here to buy it now!
In the Beginning There Were Magic Words
Talking Snakes and Human Souls
Day of Rest, Day of Magic
Noah's Care of Magical Creatures
Owl post, Raven post, and dove post
Ghosts and curtains
Mudbloods, Moabites, and Moshiach
Whomping Willows & Monotheistic Maples
Everyday Magic, Everyday Miracles
Nicolas Flamel and the Children of Ketura
When One Rises, the Other Will Fall
Destiny and Decisions
Go to the Hippogriff, thy Sluggard
Creating Bodies
Rights of Magical Creatures
Dreams: Divination or Digestion?
Everything Happens for a Reason
We are as Strong as we are United
Magic Shows: Kosher Fun or Idolatry?
Magical Protection
Laws of a Sukkah according to Dr. Seuss
I just came across this on a few other Web sites, and thought that readers of Harry Potter and Torah would enjoy it:
You can build it very small (1)
You can build it very tall (2)
You can build it very large (3)
You can build it on a barge
You can build it on a ship (4)
Or on a roof but please don't slip (5)
You can build it in an alley (6)
You shouldn't build it in a valley (7)
You can build it on a wagon (8)
You can build it on a dragon (9)
You can make the s'chach of wood (10)
Would you, could you, yes you should
Make the s'chach from leaves of tree
You shouldn't bend it at the knee (11)
Build your Succah tall or short
No Succah is built in the Temple Court
You can build it somewhat soon
You cannot build it in the month of June (12)
If your Succah is well made
You'll have the right amount of shade (13)
You can build it very wide
You can not build it on its side
Build if your name is Jim
Or Bob or Sam or even Tim
Build it if your name is Sue (14)
Do you build it, yes you do!
From the Succah you can roam
But you should treat it as your home (15)
You can invite some special guests
Don't stay in it if there are pests
You can sleep upon some rugs
Don't you build it where there's bugs
In the Succah you should sit
And eat and drink but never...
If in the Succah it should rain
To stay there would be such a pain (16)
And if it should be very cold
Stay there only if you're bold
So build a Succah one and all
Make it large or make it small
Succah rules are short and snappy
Enjoy Succos, rejoice be happy.
1. Maimonides (RMBM) Mishne Torah, Hilchot Succah, Chapter 4, Section 1. The minimum height of a Succah is 10 tefachim. A tefach is a measure of the width of the four fingers of one's hand. My hand is 3 1/4 inches wide for a minimum Succah height of 32 1/2 inches. The minimum allowable width is 7 tefachim by 7 tefachim. This would result in a Succah of 22 3/4 inches by 22 3/4 inches.
2. The maximum height is 20 Amot. An Amah is the length from the elbow to the tip of the middle finger. My Amah is 15 1/2 inches for a maximum height of 25 feet. Others say that 30 feet is the maximum.
3. According to RMBM the Succah can be built to a width of several miles. Shulchan Aruch also says there is no limit on the size of the width.
4. RMBM Hilchot Succah Chapter 4, Section 6.
5. RMBM Hilchot Succah Chapter 4, Section 11. RMBM states that one may construct a Succah by wedging poles in the four corners of the roof and suspending s'chach from the poles. The walls of the building underneath are considered to reach upward to the edge of the s'chach.
6. RMBM Hilchot Succah Chapter 4, Section 8-10 discusses the ins and outs of building your Succah in an alley or passageway.
7. There is a location referred to in the Talmud called Ashtarot Karnayim. According to the discussion there are two hills, with a valley in between where the Sun does not reach. Therefore it is impossible to sit in the shade of the roof of the Succah. I can't find the reference...hopefully next year.
8. RMBM Hilchot Succah Chapter 4, Section 6. You can go into a Succah built on a wagon or a ship even on Yom Tov.
9. RMBM Hilchot Succah Chapter 4, Section 6. OK, RMBM says a camel but dragon rhymes with wagon a lot better, don't you agree. Anyway, RMBM says you can build your Succah on a wagon or in the crown of a tree, but you can't go into it on Yom Tov. There is a general rule against riding a beast or ascending into the crown of a tree on Yom Tov.
10. Chapter 5 deals with the rules for the s'chach. Basically, you can use that which has grown from the ground, and is completely detached from the ground. So, for example, you cannot bend the branches of a tree over the Succah to form the s'chach. But you can cut the branches from a tree and use them as s'chach.
11. This would be a violation of the rule cited in the prior footnote.
12. Shulchan Aruch, Hilchot Succah, Perek 636, Section 1. The Succah should not be built sooner than 30 days before the Chag. However, if the structure is built prior to 30 days, as long as something new is added within the 30 days, the Succah is kosher.
13. Of course it's a well known rule that you must sit in the shade from the roof of the Succah and not in the shade that may be cast by the walls. It seems that this might affect the height of the walls, depending on the longitude of the location where you are building your Succah.
14. Technically, women, servants and minors are exempt from the Mitzvah of Succah. In our day we hope we know better than to read out half the Jewish people from the observance of Mitzvot. Of course, that's just a personal opinion of the author.
15. RMBM ibid Chapter 6, Section 6 explains that you should eat, drink and live in the Succah for the 7 days as you live in your own home. One should not even take a nap outside of the Succah.
16. RMBM ibid, Section 10. If it rains one should go into the house. How does one know if it is raining hard enough? If sufficient raindrops fall through the s'chach (roof covering) and into the food so that the food is spoiled - go inside!
Buy the book now!
Other books you may enjoy:
I think that a lot of fans of Harry Potter and To...
Harry Potter thoughts related to the story of crea...


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Mon, 03 Jun 2019 03:51:44 GMT
11: Sequences and Series (Exercises)
[ "article:topic", "showtoc:yes" ]
Exercises (Calculus)
Exercises: Calculus (Guichard)
11.2: Series
11.3: The Integral Test
11.4: Alternating Series
11.5: Comparison Test
11.6: Absolute Convergence
11.7: The Ratio and Root Tests
11.8: Power Series
11.9: Calculus with Power Series
11.10: Taylor Series
11.11: Taylor's Theorem
11.12: Additional Exercises
These are homework exercises to accompany David Guichard's "General Calculus" Textmap. Complementary General calculus exercises can be found for other Textmaps and can be accessed here.
11.1: Sequences
Ex 11.1.1 Compute \(\lim_{x\to\infty} x^{1/x}\). (answer)
Ex 11.1.2 Use the squeeze theorem to show that \(\lim_{n\to\infty} {n!\over n^n}=0\).
Ex 11.1.3 Determine whether \(\{\sqrt{n+47}-\sqrt{n}\}_{n=0}^{\infty}\) converges or diverges. If it converges, compute the limit. (answer)
Ex 11.1.4 Determine whether \(\left\{{n^2+1\over (n+1)^2}\right\}_{n=0}^{\infty}\) converges or diverges. If it converges, compute the limit. (answer)
Ex 11.1.5 Determine whether \(\left\{{n+47\over\sqrt{n^2+3n}}\right\}_{n=1}^{\infty}\) converges or diverges. If it converges, compute the limit. (answer)
Ex 11.1.6 Determine whether \(\left\{{2^n\over n!}\right\}_{n=0}^{\infty}\) converges or diverges. (answer)
Ex 11.2.1 Explain why \(\sum_{n=1}^\infty {n^2\over 2n^2+1}\) diverges. (answer)
Ex 11.2.2 Explain why \(\sum_{n=1}^\infty {5\over 2^{1/n}+14}\) diverges. (answer)
Ex 11.2.3 Explain why \(\sum_{n=1}^\infty {3\over n}\) diverges. (answer)
Ex 11.2.4 Compute \(\sum_{n=0}^\infty {4\over (-3)^n}- {3\over 3^n}\). (answer)
Ex 11.2.5 Compute \(\sum_{n=0}^\infty {3\over 2^n}+ {4\over 5^n}\). (answer)
Ex 11.2.6 Compute \(\sum_{n=0}^\infty {4^{n+1}\over 5^n}\). (answer)
Ex 11.2.7 Compute \(\sum_{n=0}^\infty {3^{n+1}\over 7^{n+1}}\). (answer)
Ex 11.2.8 Compute \(\sum_{n=1}^\infty \left({3\over 5}\right)^n\). (answer)
Ex 11.2.9 Compute \(\sum_{n=1}^\infty {3^n\over 5^{n+1}}\). (answer)
Determine whether each series converges or diverges.
Ex 11.3.1 \(\sum_{n=1}^\infty {1\over n^{\pi/4}}\) (answer)
Ex 11.3.2 \(\sum_{n=1}^\infty {n\over n^2+1}\) (answer)
Ex 11.3.3 \(\sum_{n=1}^\infty {\ln n\over n^2}\) (answer)
Ex 11.3.4 \(\sum_{n=1}^\infty {1\over n^2+1}\) (answer)
Ex 11.3.5 \(\sum_{n=1}^\infty {1\over e^n}\) (answer)
Ex 11.3.6 \(\sum_{n=1}^\infty {n\over e^n}\) (answer)
Ex 11.3.7 \(\sum_{n=2}^\infty {1\over n\ln n}\) (answer)
Ex 11.3.8 \(\sum_{n=2}^\infty {1\over n(\ln n)^2}\) (answer)
Ex 11.3.9 Find an \(N\) so that \(\sum_{n=1}^\infty {1\over n^4}\) is between \(\sum_{n=1}^N {1\over n^4}\) and \(\sum_{n=1}^N {1\over n^4} + 0.005\). (answer)
Ex 11.3.10 Find an \(N\) so that \(\sum_{n=0}^\infty {1\over e^n}\) is between \(\sum_{n=0}^N {1\over e^n}\) and \(\sum_{n=0}^N {1\over e^n} + 10^{-4}\). (answer)
Ex 11.3.11 Find an \(N\) so that \(\sum_{n=1}^\infty {\ln n\over n^2}\) is between \(\sum_{n=1}^N {\ln n\over n^2}\) and \(\sum_{n=1}^N {\ln n\over n^2} + 0.005\). (answer)
Ex 11.3.12 Find an \(N\) so that \(\sum_{n=2}^\infty {1\over n(\ln n)^2}\) is between \(\sum_{n=2}^N {1\over n(\ln n)^2}\) and \(\sum_{n=2}^N {1\over n(\ln n)^2} + 0.005\). (answer)
Determine whether the following series converge or diverge.
Ex 11.4.1 \(\sum_{n=1}^\infty {(-1)^{n-1}\over 2n+5}\) (answer)
Ex 11.4.2 \(\sum_{n=4}^\infty {(-1)^{n-1}\over \sqrt{n-3}}\) (answer)
Ex 11.4.3 \(\sum_{n=1}^\infty (-1)^{n-1}{n\over 3n-2}\) (answer)
Ex 11.4.4 \(\sum_{n=1}^\infty (-1)^{n-1}{\ln n\over n}\) (answer)
Ex 11.4.5 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^3}\) to two decimal places. (answer)
Determine whether the series converge or diverge.
Ex 11.5.1 \(\sum_{n=1}^\infty {1\over 2n^2+3n+5} \) (answer)
Ex 11.5.2 \(\sum_{n=2}^\infty {1\over 2n^2+3n-5} \) (answer)
Ex 11.5.3 \(\sum_{n=1}^\infty {1\over 2n^2-3n-5} \) (answer)
Ex 11.5.4 \(\sum_{n=1}^\infty {3n+4\over 2n^2+3n+5} \) (answer)
Ex 11.5.5 \(\sum_{n=1}^\infty {3n^2+4\over 2n^2+3n+5} \) (answer)
Ex 11.5.6 \(\sum_{n=1}^\infty {\ln n\over n}\) (answer)
Ex 11.5.8 \(\sum_{n=2}^\infty {1\over \ln n}\) (answer)
Ex 11.5.9 \(\sum_{n=1}^\infty {3^n\over 2^n+5^n}\) (answer)
Ex 11.5.10 \(\sum_{n=1}^\infty {3^n\over 2^n+3^n}\) (answer)
Determine whether each series converges absolutely, converges conditionally, or diverges.
Ex 11.6.1 \(\sum_{n=1}^\infty (-1)^{n-1}{1\over 2n^2+3n+5}\) (answer)
Ex 11.6.2 \(\sum_{n=1}^\infty (-1)^{n-1}{3n^2+4\over 2n^2+3n+5}\) (answer)
Ex 11.6.4 \(\sum_{n=1}^\infty (-1)^{n-1} {\ln n\over n^3}\) (answer)
Ex 11.6.5 \(\sum_{n=2}^\infty (-1)^n{1\over \ln n}\) (answer)
Ex 11.6.6 \(\sum_{n=0}^\infty (-1)^{n} {3^n\over 2^n+5^n}\) (answer)
Ex 11.6.8 \(\sum_{n=1}^\infty (-1)^{n-1} {\arctan n\over n}\) (answer)
Ex 11.7.1 Compute \(\lim_{n\to\infty} |a_{n+1}/a_n|\) for the series \(\sum 1/n^2\).
Ex 11.7.2 Compute \(\lim_{n\to\infty} |a_{n+1}/a_n|\) for the series \(\sum 1/n\).
Ex 11.7.3 Compute \(\lim_{n\to\infty} |a_n|^{1/n}\) for the series \(\sum 1/n^2\).
Ex 11.7.4 Compute \(\lim_{n\to\infty} |a_n|^{1/n}\) for the series \(\sum 1/n\).
Determine whether the series converge.
Ex 11.7.5 \(\sum_{n=0}^\infty (-1)^{n}{3^n\over 5^n}\) (answer)
Ex 11.7.6 \(\sum_{n=1}^\infty {n!\over n^n}\) (answer)
Ex 11.7.7 \(\sum_{n=1}^\infty {n^5\over n^n}\) (answer)
Ex 11.7.8 \(\sum_{n=1}^\infty {(n!)^2\over n^n}\) (answer)
Ex 11.7.9 Prove theorem 11.7.3, the root test.
Find the radius and interval of convergence for each series. In exercises 3 and 4, do not attempt to determine whether the endpoints are in the interval of convergence.
Ex 11.8.1 \(\sum_{n=0}^\infty n x^n\) (answer)
Ex 11.8.2 \(\sum_{n=0}^\infty {x^n\over n!}\) (answer)
Ex 11.8.3 \(\sum_{n=1}^\infty {n!\over n^n}x^n\) (answer)
Ex 11.8.4 \(\sum_{n=1}^\infty {n!\over n^n}(x-2)^n\) (answer)
Ex 11.8.5 \(\sum_{n=1}^\infty {(n!)^2\over n^n}(x-2)^n\) (answer)
Ex 11.8.6 \(\sum_{n=1}^\infty {(x+5)^n\over n(n+1)}\) (answer)
Ex 11.9.1 Find a series representation for \(\ln 2\). (answer)
Ex 11.9.2 Find a power series representation for \(1/(1-x)^2\). (answer)
Ex 11.9.3 Find a power series representation for \( 2/(1-x)^3\). (answer)
Ex 11.9.4 Find a power series representation for \( 1/(1-x)^3\). What is the radius of convergence? (answer)
Ex 11.9.5 Find a power series representation for \(\int\ln(1-x)\,dx\). (answer).
For each function, find the Maclaurin series or Taylor series centered at $a$, and the radius of convergence.
Ex 11.10.1 \(\cos x\) (answer)
Ex 11.10.2 \( e^x\) (answer)
Ex 11.10.3 \(1/x\), \(a=5\) (answer)
Ex 11.10.4 \(\ln x\), \(a=1\) (answer)
Ex 11.10.6 \( 1/x^2\), \(a=1\) (answer)
Ex 11.10.7 \(1/\sqrt{1-x}\) (answer)
Ex 11.10.8 Find the first four terms of the Maclaurin series for \(\tan x\) (up to and including the \( x^3\) term). (answer)
Ex 11.10.9 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( x\cos (x^2)\). (answer)
Ex 11.10.10 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( xe^{-x}\). (answer)
Ex 11.11.1 Find a polynomial approximation for \(\cos x\) on \([0,\pi]\), accurate to \( \pm 10^{-3}\) (answer)
Ex 11.11.2 How many terms of the series for \(\ln x\) centered at 1 are required so that the guaranteed error on \([1/2,3/2]\) is at most \( 10^{-3}\)? What if the interval is instead \([1,3/2]\)? (answer)
Ex 11.11.3 Find the first three nonzero terms in the Taylor series for \(\tan x\) on \([-\pi/4,\pi/4]\), and compute the guaranteed error term as given by Taylor's theorem. (You may want to use Sage or a similar aid.) (answer)
Ex 11.11.4 Show that \(\cos x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as N approaches infinity.
Ex 11.11.5 Show that \(e^x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as \(N\) approaches infinity.
10: Polar Coordinates, Parametric Equations (Exercises)
12: Three Dimensions (Exercises)


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EP's pesticides committee chief 'silent' over toxic organic agent
By Sarantis Michalopoulos | EURACTIV.com
Andrieu, a fierce opponent of glyphosate from the S&D is also the chief of the PEST committee, which was created to monitor the transparency of the pesticides' authorisation in the EU. [European Parliament]
The head of the European Parliament's pesticides committee has warned the European Commission about the possible impact on organic wine-growing if the use of copper, a toxic substance according to EFSA and ECHA, is outlawed.
Eric Andrieu, a fierce opponent of weed-killer glyphosate from the Group of the Progressive Alliance of Socialists and Democrats (S&D group) is also the chief of the PEST committee, which was created to monitor the transparency of pesticide authorisation in the EU.
Following the heated debate on the re-approval of Monsanto's glyphosate, the Parliament established earlier this year this special committee in order to examine the authorisation procedure of pesticides in the EU.
Copper compounds, including copper sulphate, are authorised in the EU as bactericides and fungicides. They are approved for use in organic farming, particularly for potato, grape, tomato and apple production systems.
EFSA (the European Food Safety Authority) and ECHA (the European Chemicals Agency) have identified risks to farm workers, birds, mammals and soil organisms, as well as the impact of copper compounds on the wider environment. As such, copper compounds are included on the EU substitution list.
EU renews toxic pesticide amid safety uncertainty
The European Commission and the member states extended once again the authorisation for copper sulphate, a controversial pesticide used in organic farming, which is on the EU's "substitution" list and its effects on consumers are still unknown.
On 13 March 2018, the Court of Justice of the European Union confirmed that the substance "fulfilled the conditions to be met to be regarded as a persistent and toxic substance".
In December 2017, the Commission and member states agreed to extend the use of copper compounds for one year. Twenty-six member states voted in favour of that while France and Sweden opposed it.
On 23 May 2018, the Andrieu submitted a question to the EU executive about the renewal of the authorisation of copper.
In his question, he noted that he was contacted by all of Europe's professional winemaking associations, who "wished to express concerns, particularly among organic winegrowers, regarding the draft text renewing the authorisation for use of copper on vines to combat bacteria and fungi".
"Copper is one of the only minerals authorised under EU rules for use in organic farming," Andrieu said.
He warned that outlawing the use of copper in 2019 without any "alternative solutions" could mean the end for organic wine-growing.
"If the use of copper is prohibited this would appear to place winemakers, particularly organic growers, in a state of technical deadlock. What does the Commission intend to do about this?" the French politician asked.
EURACTIV asked the MEP if he was concerned about the assessments of EFSA and ECHA as well as if social and economic implications should also be considered when it comes to the re-authorisation of pesticides.
Despite the repeated calls and emails, the MEP declined to provide any answer.
On the other hand, the S&D was particularly critical of glyphosate, despite the fact that it received the green light from EFSA and ECHA.
At an event recently organised by EURACTIV, British MEP Anthea McIntyre (ECR coordinator for PEST), was asked if the PEST committee will achieve results.
"The PEST committee is about politics, we have elections next year and political groups will always come up with an idea, like the PEST committee to leverage it with voters," she said.
PAN Europe, a network of European NGOs promoting sustainable alternatives to pesticides, stated that copper was proved to be toxic and has to be phased-out.
Eric Andrieu on Efsa, PEST committee and France
French MEP Eric Andrieu discusses the role of the EP's PEST Committee, which he chairs, to respond to comments suggesting that it is at a dead-end.
"The assessment of the toxicity of copper by the EFSA indicates that there is a necessity to phase out this substance within a few years. Until then, the Commission should fix maximum limits of use to protect soil's health and the environment as a whole," PAN Europe chemical officer Hans Muilerman told EURACTIV.
Martin Dermine, PAN Europe health and environment policy officer, added that for many productions such as apples and potatoes, fungi-resistant varieties are already available.
"Farmers should focus on resistant varieties and more public investments are necessary to develop more resistant varieties and non-toxic alternatives to pesticides. Pesticides should be used after the many available alternatives as determined by the principles of integrated pest management."
Éric Andrieu
pesticide regulation


Tony Raines picked up the 4th last-place finish of his NASCAR Nationwide Series career in Saturday's Great Clips 200 at the Phoenix International Raceway when his unsponsored #91 TriStar Motorsports Toyota fell out with a vibration after he completed 5 of the race's 204 laps.
It was Raines' second last-place finish of 2012, his first since Dover, twenty races ago.
Raines qualified 31st for Saturday's race at an average speed of 128.041 mph, ranking him ninth among the fifteen "go-or-go-homers" who attempted to make the race. This secured the third start of the season for TriStar's #91 team. The team debuted at Iowa in August with 2012 LASTCAR Nationwide Series Champion Jeff Green driving it to his tenth of twelve last-place finishes this season.
On Satuday, Raines' car was the first behind the wall. Three laps later, Chase Miller parked his #46, and all three of his teammates at The Motorsports Group followed suit. This resulted in TMG's #40 scoring its first DNF since Bristol in August, finishing 37th with Erik Darnell.
Meanwhile, Jeff Green not only finished under power for the first time since last month at Charlotte, but also made his first full-race run in the #10, the car number he parked in eleven of his last-place finishes this season. Green came home 23rd, three laps down.
*This was the first last-place finish for both Raines and the #91 in a Nationwide Series race at Phoenix.


Just kinda curious how everyone else's 7month old acted or is acting. DS is 7 months and 1 week. He is now saying mama......usually when he fusses but I'm counting it. He is very close to crawling...rocks back and forth like crazy. He sits all by himself, and can almost pull himself up. He laughs constantly,mostly at our dogs....he loves them. He loves to play. He still doesn't respond to his name a whole lot. He chooses to listen to DH more than me...He could play in his exersaucer and I could be right in front of him trying to talk to him, and he just continues to play.....>BUT, if DH or grandma walks in the room, he'll stop and smile and get excited for them. Any other mom's out there feel like their kid ignores the already? At times, I still feel like he stares off and looks at strange things, the blinds, curtains, TV, LOVES remotes controls and telephones. Does anyone elses's 7 month old do this? I figured he'd outgrow it by now. OH, and I think we are starting separation anxiety. This weekend everytime I'd leave the room, he's start to cry and put his arms out to pick him up. It was cute the first 30 times he did it, but now 30 more times later, I'm thinking "Oh c__p, what do we do now?"
Yes, yes & yes. My ds is also 7 months & 1 week. He babbles da-da, ma-ma ect. Sits by himself, rocks back and forth on hands & knees, laughs at the dog. He is fascinated with remotes, cellphones, toothbrushes, paper ect. All those silly things...Your ds sounds like he is doing great!! Oh, and my lo started his seperation anxiety about 2-3 wks ago. He is starting to get a little better about that now though. My ds does respond to me when I talk to him. I could be just that you're a face he always sees so it's nothing different...but that fact that he is feeling seperation anxiety means that he feels safe and comforted by you. He LOVES you more than anything!
Hello, my ds is also 7 months 1 week. He does basically the same things that your lo does. He is fasinated by the blinds, telephone, music screen on the computer, keys and lights. He also love to bite paper and anything else that he finds. He is just now learning to pull himself up to the standing position and crawls on his tummy to everywhere he needs to go. Its as if he is swimming on the floor. I dont know if he will ever crawl on his hands and knees lol. I have also noticed that he doesnt b___stfeed as much as he used to, guess its because he is so much more mobile now. He loves to look in the mirror and laugh at himself (soo cute).
Yup. my dd is almost 8 months and she is still fascinated by the remote control and sometimes our ceiling fans!! The separation anxiety has kicked in big time for us...although when I leave her with my MIL or at daycare she could care less if I leave. She is pretty responsive to her name most of the time, but sometimes she'll just stare off out the window and ignore me. She is big-time babbling lately...mamamamadadadadabababa, all day long!
My dd is 7 months and 1 week too. She dosent babble mama or dada yet :((( but babbles gooo....aaaa...ga....agooo etc.. She says mama when she cries (I can count them) She loves the TV remote a lot. She has started the seperation anxiety about 2-3 weeks ago and cries so hard when I leave the room. She loves to go out in her stroller and I take her everyday to a water fountain and she loves it. She loves the swings in the park . She responds to her name very well. she can sit by herself and play with her toys, she has mastered crawling and pulling and standing up.


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Q: Propensity score matching after multiple imputation I refer to this paper:
Hayes JR, Groner JI.
"Using multiple imputation and propensity scores to test the effect of car seats and seat belt usage on injury severity from trauma registry data."
J Pediatr Surg. 2008 May;43(5):924-7.
In this study, multiple imputation was performed to obtain 15 complete datasets. Propensity scores were then computed for each dataset. Then, for each observational unit, a record was chosen randomly from one of the completed 15 datasets (including the related propensity score) thereby creating a single final dataset for which was then analysed by propensity score matching.
My questions are: Is this valid way to perform propensity score matching following multiple imputation ? Are there alternative ways to do it ?
For context: In my new project, I aim to compare the effects of 2 treatment methods using propensity score matching. There is missing data and I intend to use the MICE package in R to impute missing values, then twang to do the propensity score matching, and then lme4 to analyse the matched data.
Update1:
I have found this paper which takes a different approach:
Mitra, Robin and Reiter, Jerome P. (2011) Propensity score matching with missing covariates via iterated, sequential multiple imputation
[Working Paper]
In this paper the authors compute propensity scores on all the imputed datasets and then pool them by averaging, which is in the spirit of multiple imputation using Rubin's rule's for a point estimate - but is it really applicable for a propensity score ?
It would be really nice if anyone on CV could provide an answer with commentary on these 2 different approaches, and/or any others....

A: The first thing to say is that, for me, method 1 (sampling) seems to be without much merit - it is discarding the benefits of multiple imputation, and reduces to single imputation for each observation, as mentioned by Stas. I can't see any advantage in using it.
There is an excellent discussion of the issues surrounding propensity score analysis with missing data in Hill (2004):
Hill, J. "Reducing Bias in Treatment Effect Estimation in Observational Studies Suffering from Missing Data"
ISERP Working Papers, 2004.
It is downloadable from here.
The paper considers two approaches to using multiple imputation (and also other methods of dealing with missing data) and propensity scores :

*

*averaging of propensity scores after multiple imputation, followed by causal inference (method 2 in your post above)

*causal inference using each set of propensity scores from the multiple imputations followed by averaging of the causal estimates.
Additionally, the paper considers whether the outcome should be included as a predictor in the imputation model.
Hill asserts that while multiple imputation is preferred to other methods of dealing with missing data, in general, there is no a priori reason to prefer one of these techniques over the other. However, there may be reasons to prefer averaging the propensity scores, particularly when using certain matching algorithms. Hill did a a simulation study in the same paper and found that averaging the propensity scores prior to causal inference, when including the outcome in the imputation model produced the best results in terms of mean squared error, and averaging the scores first, but without the outcome in the imputation model, produced the best results in terms of average bias (absolute difference between estimated and true treatment effect).  Generally, it is advisable to include the outcome in the imputation model (for example see here).
So it would seem that your method 2 is the way to go.

A: There might be a clash of two paradigms. Multiple imputation is a heavily model-based Bayesian solution: the concept of the proper imputation essentially states that you need to sample from the well-defined posterior distribution of the data, otherwise you are screwed. Propensity score matching, on the other hand, is a semi-parametric procedure: once you have computed your propensity score (no matter how, you could've used a kernel density estimate, not necessarily a logit model), you can do the rest by simply taking the differences between the treated and non-treated observations with the same propensity score, which is kinda non-parametric now, as there is no model left that controls for other covariates. I don't feel good about the discontinuities introduced by the literal implementation of matching (find the control with the closest possible value of the propensity score, and ignore the rest; Abadie and Imbens (2008) discussed that it makes it impossible to actually get the standard errors right in some of the matching situations). I would give more trust to the smoother approaches like weighting by the inverse propensity. My favorite reference on this is "Mostly Harmless Econometrics", subtitled "An Empiricist Companion", and aimed at economists, but I think this book should be a required reading for other social scientists, most biostatisticians, and non-bio statisticians as well so that they know how other disciplines approach data analysis.
At any rate, using only one out of 15 simulated complete data lines per observation is equivalent to a single imputation. As a result, you lose efficiency compared to all 15 completed data sets, and you can't estimate the standard errors properly. Looks like a deficient procedure to me, from any angle.
Of course, we happily sweep under the carpet the assumption that both the multiple imputation model and the propensity model are correct in the sense of having all the right variables in all the right functional forms. There is little way to check that (although I'd be happy to hear otherwise about diagnostic measures for both of these methods).

A: I can't really speak to the theoretical aspects of the question, but I'll give my experience using PS/IPTW models and multiple imputation.

*

*I've never heard of someone using multiply imputed data sets and random sampling to build a single data set. That doesn't necessarily mean it's wrong but it's a strange approach to use. The data set also isn't big enough that you'd need to get creative to get around running 3-5 models instead of just one to save time and computation.

*Rubin's rule and the pooling method is a pretty general tool. Given the pooled, multiply imputed result can be calculated using only the variance and estimates, there's no reason I can see that it couldn't be used for your project - creating the imputed data, performing the analysis on each set, and then pooling. It's what I've done, it's what I've seen done, and unless you have a specific justification not to do it, I can't really see a reason to go with something more exotic - especially if you don't understand what's going on with the method.


Home / Case Studies / After completing a fact find, we identified an important gap in our client's investment planning.
After completing a fact find, we identified an important gap in our client's investment planning.
Although he had various offshore investments with a number of fund companies and a few advisers in Thailand, they were all targeted at providing an income for him and his family in retirement. His investments hadn't really taken consideration of his young son who was currently in an international school. He wanted to be able to send his son to university in the UK or US and knew that this wouldn't come cheap. So the first step was to set up a monthly savings plan with a term suited to his son's age, with a figure that he was happy with.
For the second step, we had a few complications to deal with: our client was a partner in an Accountancy firm – which meant that he couldn't invest in funds that the firm audits. (He'd already been 'bitten' with this issue before with another company, and had learned his lesson!) Our solution was to set up a personal portfolio bond, which only held funds that had been given the all-clear from his firm.
He wanted to send his son to university in the UK or US. Then there was a slight complication to deal with.