The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.

We present several Orientifolds of M-Theory on K 3 × S 1 by additional projections with respect to the finite abelian automorphism groups of K 3. The resulting models correspond to anomaly free theories in six dimensions. We construct explicit examples which can be interpreted as models with eight, four, two and one vector multiplets and N = 1 supersymmetry in six dimensions.

Let $$g_t$$ be a smooth 1-parameter family of negatively curved metrics on closed hyperbolic 3-manifold M starting at the metric. We construct foliations Grassmann bundle $$Gr_2(M)$$ tangent 2-planes whose leaves are (lifts of) minimal surfaces in $$(M,g_t)$$ . These deformations foliation by totally geodesic planes projected down from universal cover $${\mathbb {H}}^3$$ Our construction contin...

Information on the early Holocene climate constrains the summer sea ice projections for the 21st century H. Goosse, E. Driesschaert, T. Fichefet, and M.-F. Loutre Université Catholique de Louvain, Institut d’Astronomie et de Géophysique G. Lemaı̂tre, Chemin du Cyclotron, 2, 1348 Louvain-la-Neuve, Belgium Received: 15 August 2007 – Accepted: 23 August 2007 – Published: 24 August 2007 Corresponden...

Let k be a field of characteristic 0 and let Vk be the category of smooth projective varieties over k. By ∼ we denote an adequate equivalence relation for algebraic cycles on varieties [Ja00]. For every X ∈ Vk let A i ∼(X) = (Z (X)/ ∼)⊗Q be the Chow group of codimension i cycles on X modulo the chosen relation ∼ with coefficients in Q. Let X, Y ∈ Vk, let X = ∪Xi be the connected components of X...

For the problems of nonparametric estimation of nonincreasing and symmetric unimodal density functions with bounded supports we determine the projections of estimates onto the convex families of possible parent densities with respect to the weighted integrated squared error We also describe the method of approx imating the analogous projections onto the respective density classes satisfying som...

Southern Asia experiences some of the most damaging climate events in world, with loss life from cyclones hundreds thousands. Despite this, research on extremes region is substantially lacking compared to other parts world. To understand narrative how an extreme event may change future, we consider Super Cyclone Amphan, which made landfall May 2020, bringing storm surges 2–4 m coastlines India ...

We discuss the use of a flat-plane slider for a surface acoustic wave (SAW) motor. For stable driving, the SAW motor requires a silicon slider with many microprojections on its surface. Previously, sliders with no projections on the flat-plane surface could not provide stable drive because of contact electrification occurring due to the low electrical conductivity of the lithium niobate stator....

In 1955, H. Dye defined certain projections of a C∗-matrix algebra by Pi,j(a) = (1 + aa ∗)−1 ⊗ Ei,i + (1 + aa∗)−1a⊗ Ei,j + a∗(1 + aa∗)−1 ⊗ Ej,i + a∗(1 + aa∗)−1a⊗ Ej,j , which was used to show that in the case of factors not of type I2n, the unitary group determines the algebraic type of that factor. We study these projections and we show that in M2(C), the set of such projections includes all t...

A Helson matrix is an infinite $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on product $mn$. We demonstrate orthogonal projection from Hilbert--Schmidt class $\mathcal{S}_2$ onto subspace of matrices does not extend to a bounded operator Schatten $\mathcal{S}_q$ for $1 \leq q \neq 2 < \infty$. In fact, we prove more general result showing large natural projections are u...