Spirocyclic Tetramates by Sequential Knoevenagel and [1,5]-Prototropic Shift

Preparation of neuroprotective condensed 1,4-benzoxazepines by regio- and diastereoselective domino Knoevenagel–[1,5]-hydride shift cyclization reaction

Condensed O,N-heterocycles containing tetrahydro-1,4-benzoxazepine and tetrahydroquinoline moieties were prepared by a regio- and diastereoselective domino Knoevenagel-[1,5]-hydride shift cyclization reaction of a 4-aryl-2-phenyl-1,4-benzoxazepine derivative obtained from flavanone. The relative configuration of products were determined by the correlation of (3) J H,H coupling data with the geo...

Synthesis of spirocyclic thiazolidinediones using ring-closing metathesis and one-pot sequential ring-closing/cross metathesis.

A novel synthetic route to spirocyclic thiazolidinediones is reported by utilizing ring-closing metathesis (RCM). A selective cross metathesis (CM) of N-allyl azaspiro derivatives with different olefins has been demonstrated to prepare substituted azaspiro-[4.4]nonenediones. The X-ray crystal structure of a spirocyclic thiazolidinedione dimer is described, which has been prepared in two steps f...

Lecture 15: Chernoff bounds and Sequential detection

1 Chernoff Bounds 1.1 Bayesian Hypothesis Test A test using log-likelihood ratio statistic has the form, T (Y ) = logL(Y ) T τ. (1) Bound-1: The probability of error Pe is bounded as, Pe ≤ (π0 + π1e )eμT,0(s0)−s0τ , (2) where μT,0(s) = logE0[e ], and μ ′ T,0(s0) = τ . Bound-2: ∀ s ∈ [0, 1], Pe ≤ max(π0, π1e )eμT,0(s)−sτ . (3) Derivation of the above bound: Consider, Pe = π0P0(Γ1) + π1P1(Γ0), = ...

Unitary Shift-Register Realizations of Sequential Machines

On Shift Register Realization of Sequential Circuits

Realizing a sequential machine with shift registers is an attractive approach to the design for testability. It requires little extra circuit for scan and since feed-backs are always to the rst ip-op of a shift register test generation is expected to be easier than that for circuits with unstructured feedbacks. Though the shift register realization of sequential machines was studied by several ...