SynopsisTwo non-singular conies ω and α are said to be related by a pentagram if there exist pentads ofdistinct points {Oi} on ω and {Ai} on α (1 ≦ i ≦ 5) such that A1 ≡ O2O4. O3O5, A2 ≡ O3O5. O1O4, A3 ≡ O1O4. O2O5, A4 ≡ O2O5. O1O3 and A5 ≡ O1O3. O2O4. It is shown that relation by a pentagram is a poristic property; and a necessary condition on their mutual projective invariants that two nonsingular conies be so related is derived. Some ramifications are discussed.
SynopsisIf the conic α, a0x2 + a1y2 + a2z2 + 2a3yz + 2a4zx + 2a5xy=0, is represented by the point (a0, a1, a2, a3, a4, a5) of S5, the transforms of α by projectivities that fix a second conic ω will generally be represented by points of a threefold in S5 containing (a0, a1,…, a5). It is shown that this threefold is in general a rational sextic belonging to an ∞2 family, that is composed of ∞1 sets of projectively equivalent threefolds. Special, exceptional members of the family are discussed.Equations for the threefold are found in terms of the mutual projection invariants of ω and α.
Infducfion: Multi-unit m i -'c d i e s quantifying muscle sympatWc nave activity (MSNA) in essdal aad 'bordsfine' hypatension havebeon inconSiracd Fathe first time smgle vamamhictor lmits (S-MSNA) wac studied in subject groups with a range of severity of essential hypertension compared to normotension. MelhodF: Seveaty four matched CaucaSiaa subjects (FM, 38:36; 22-75 years) fire from therapy, were grouped Bccording to their resting blood pnssurcs (BP) using the JNC-VI (1997) classification, into twHmd (NT), high n o d 0, Stage 1 (Em-I) and Stage 2 or 3 hypatcasion (EHT-2B). Continuous heart rate (HR), respiration, BP and synpalhdc activity were rccordtd in the resting state. N e d activity was quantified pcr 100 cardiac beats to allow for d i h c e s in HR.Results: Using ANOVA, d t s from the two methods of sympathdc assessment in the four groups of subjects are illustratcd below, s-MSNA (Fig. 1) and MSNA (Fig.2).
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