We present a task duplication based scalable scheduling algorithm for Symmetric Multiprocessors (SMP), called S3MP (Scalable Scheduling for SMP), to address the problem of task scheduling. The algorithm pre-allocates network communication resources so as to avoid potential communication conflicts, and generates a schedule for the number of processors available in a SMP. This algorithm employs h...

This paper considers feasible long-step primal-dual path-following methods for semidefinite programming based on Newton directions associated with central path equations of the form Φ(PXP T , P−T SP−1) − νI = 0, where the map Φ and the nonsingular matrix P satisfy several key properties. An iteration-complexity bound for the long-step method is derived in terms of an upper bound on a certain sc...

Let X be a projective manifold of dimension n, a symmetric differential of degree m is a section of the m-th symmetric power of the sheaf of holomorphic 1-forms, SΩX . A symmetric differential w of degree m is of rank 1 if it can be locally written in the form w|U = fμ, where μ ∈ H(U,ΩX) and f ∈ O(U). Symmetric differentials of degree 1, i.e. holomorphic 1-forms, are trivially of rank 1. Holomo...

Let X be a CAT (−1)-space which is spherically symmetric around some point x0 ∈ X and whose boundary has finite positive s−dimensional Hausdorff measure. Let μ = (μx)x∈X be a conformal density of dimension d > s/2 on ∂X. We prove that μx0 is a weak limit of measures supported on spheres centered at x0. These measures are expressed in terms of the total mass function of μ and of the d−dimensiona...

This paper following a geometric approach proves new, and reproves old, vanishing and nonvanishing results on the space of twisted symmetric differentials, H(X, SΩX⊗ OX(k)) with k ≤ m, on subvarieties X ⊂ P . The case of k = m is special and the nonvanishing results are related to the space of quadrics containing X and lead to interesting geometrical objects associated to X, as for example the ...

Let us say that a relation r is symmetric iff whenever x bears r to y, y bears r to x; otherwise, r is non-symmetric. In this paper, I will argue for the thesis that necessarily, there are no non-symmetric relations. What is this predicate ‘. . . bears . . . to . . . ’ in terms of which ‘symmetric’ was defined? According to one important theory of relations, this predicate is primitive, in the ...

a $p$-group $g$ is $p$-central if $g^{p}le z(g)$‎, ‎and $g$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin‎ ‎g$‎. ‎we prove that for $g$ a finite $p^{2}$-abelian $p$-central ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $g$ divides the ‎order of $text{aut}(g)$‎.

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT-symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occ...

Let (E, ‖·‖E) be a symmetric space and let Y ⊂ X be a nonempty subset. For x ∈ X denote PY (x) = {y ∈ Y : ‖x− y‖ = dist(x, Y )}. Any element y ∈ PY (x) is called a best approximant in Y to x. A nonempty set Y ⊂ X is called proximinal or set of existence if PY (x) 6= ∅ for any x ∈ X. A nonempty set Y is said to be a Chebyshev set if it is proximinal and PY (x) is a singleton for any x ∈ E. A sym...

We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...