Tattwa Shuddhi: The Tantric Practice of Inner Purification by Swami Satyasangananda Saraswati

By Swami Satyasangananda Saraswati

Comprises the speculation of the tattwas and targeted directions for the perform, together with the tantric instruments of yantra, mantra and mandala. Tattwa shuddhi is a sophisticated perform, that may be played as a sadhana in itself or as an accessory to kundalini kriyas and different better yogas.

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AB .. An−1 B]) = n. No satisfactory result similar to the pole-assignment theorem is known in infinite dimensions. e. θ ∈ [−h, 0), φ1 ∈ L2 (−h, 0; Rn ). 1. If the system is controllable, then there exists a feedback control u(t) = Kx(t) such that the closed loop system dx (t) = (A + BK)x(t) dt is asymptotically stable. 6 Stabilizability and detectability The structure theorem of linear systems and the pole-assignment theorem motivate the introduction of the concepts of stabilizability and detectability.

24) can be majorized by 28 I-1 Control of Linear Differential Systems ∞ t 0 M e−α(t−s) K |Cx(s)| ds 2 dt. 0 Now introduce the function f (s) = M K e−αs, s ≥ 0, 0, otherwise and |Cx(s)|, 0, g(s) = s ≥ 0, otherwise. Now f ∈ L1 (−∞, ∞; R) and g ∈ L2 (−∞, ∞; R). Hence by Young’s inequality f ∗g L2 ≤ f L1 . g L2 , where (f ∗ g)(t) = ∞ −∞ t f (t − s)g(s) ds = M K e−α(t−s)|Hx(s)| ds. 0 This proves the theorem. 4. This theorem and its proof generalize to certain infinite dimensional Hilbert space situations and have implications in the study of the algebraic Riccati equation.

N }. Let xi , i = 1, . . , n, be the corresponding eigenvectors. Hence xi = (λi I − A)−1 BKxi , Now (λI − A)−1 = i = 1, 2, . . , n. n ρj (λ)Aj−1 , j=1 where ρj (λ) are rational functions defined on the complement C\σ(A) of the spectrum σ(A) of A. Hence 2 Controllability, observability, stabilizability, and detectability n xi = 23 . . AB .. An−1 B]). j=1 . . AB .. An−1 B]) = n. No satisfactory result similar to the pole-assignment theorem is known in infinite dimensions. e. θ ∈ [−h, 0), φ1 ∈ L2 (−h, 0; Rn ).

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