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1 Sep 2011: APPROXIMATION THEORY:A volume dedicated to Borislav Bojanov(D. K. Dimitrov, G. Nikolov, and R. Uluchev, Eds.)additional information (to be provided by the publisher). Twelve Proofs of the Markov Inequality. Aleksei Shadrin. This is the story of the

1 Sep 2011: f (tj ) = g(tj ) on {a = t0 < t1 <. < tn < tn1 = b}. Then, there exists a spline z such that. ... be such thatg(tj ) = p(tj ) on {a = t0 < t1 <. < tn < tn1 = b}. Then, there exists a spline z such that.

1 Sep 2011: 2. Condition number and related constantsLet fN̂jg be the B-spline basis of order k on a knot sequence t = (tj), tj < tjk,normalized with respect to the Lp-norm (1 ... p 1), i.e.,N̂j(x) = (k=(tjk tj))1=pNj(x);where fNjg is the B-spline basis which

1 Sep 2011: More details on the problems relevant to k;p can befound in [1],[2],[5].Recall that Nj(t) := (tjk tj) [tj; tj1; : : :; tjk] ( t)k1+ ;so that suppNj = (tj; tjk); ... degree p such thatsuppMj;p = (tj; tjp1); Z tjp1tj Mj;p(x)dx = 1;and by!

22 Nov 2011: Tj(x) = cos(j arccos x), j = 0, 1, 2,. ,. and c0 = 1π , cj =. 2π , j 6= 1. ... Given that the polynomials Tj are orthogonal with respect to the weight.

13 Apr 2011: F(x) = 12xT{ n. j=1 100(j1)/(n1) vj v. Tj. }x, xRn.

27 Nov 2011: THE ROTARY MOTOR OF BACTERIALFLAGELLA. Howard C. BergDepartment of Molecular and Cellular Biology, Harvard University, 16 DivinityAvenue, Cambridge, Massachusetts 02138; email: hberg@biosun.harvard.edu. Key Words Escherichia coli, motility,

6 Oct 2011: 52 predicts for a single receptor if IJ = TJ(1 - p).

10 Apr 2011: Magar V, Goto T, Pedley TJ (2003) Q J Mech Appl Math 56:65–91.35.

10 Apr 2011: Nature 2001; 413: 39–44. Wilson DR, Beveridge TJ: Bacterial f lagellar fila-ments and their component f lagellins.