Given an initial point, x0, sets Si for i = 1, . . . , r and their corresponding nearest point projections PSi , the method of alternating projections (MAP) attempts to finds a point in ∩i=1Si by cyclically projecting onto the sets. The original alternating projection result was due to von Neumann (1933) who was able to prove that if the sets are subspaces MAP converges in norm to P∩i=1Si . Usi...

Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences. 2000 Mathematics Subject Classification . 03E05 (Combinatorial set theory), 03E50 (Continuum hypothesis and Martin’s axiom), 03E35 ( Consisten...

We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A2n(2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape 〈n, n, n〉, and between the set A2n+1(2143) of alternating permutations of length...

Fe3O4 nanofluid fully developed forced convection inside a copper tube is empirically investigated under the effect of a magnetic field. All of the investigations are performed under laminar flow regime (670≤Re≤1700) and thermal boundary conditions of the tube with uniform thermal flux. The tube is under the effect of a magnetic field in certain points. This research aims to study the effect of...

1 Fa ulty of Mathemati s, Informati s, and Me hani s Warsaw University, Poland E-mail address: {shummel,henrykm,niwinski} mimuw.edu.pl Abstra t. The game tree languages an be viewed as an automata-theoreti ounterpart of parity games on graphs. They witness the stri tness of the index hierar hy of alternating tree automata, as well as the xed-point hierar hy over binary trees. We onsider a game ...

We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set Sn(132) of 132-avoiding permutations and the set A2n+1(132) of alternating, 132avoiding permutations. For every set p1, . . . , pk of patterns and certain related patterns q1, . . . , qk, our bijection restricts to a bijection between Sn(...

We consider a graph with colored edges. A trail (vertices may repeat but not edges) is called alternating when successive edges have different colors. Given a set of vertices called terminals, the alternating reachability problem is to find an alternating trail connecting distinct terminals, if one exists. A special case with two colors is searching for an augmenting path with respect to a give...

Abstract. In this paper, we establish bijections between the set of 4123-avoiding In this paper, we establish bijections between the set of 4123-avoiding down-up alternating permutations of length 2n and the set of standard Young tableaux of shape (n, n, n), and between the set of 4123-avoiding down-up alternating permutations of length 2n−1 and the set of shifted standard Young tableaux of sha...

We consider a graph with colored edges. A trail (vertices may repeat but not edges) is called alternating when successive edges have different colors. Given a set of vertices called terminals, the alternating reachability problem is to find a trail connecting distinct terminals, if one exists. A special case with two colors is searching for an augmenting path with respect to a given matching. I...