‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

We present a new sampling-based algorithm for complete motion planning. Our algorithm relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point, called the guard, can see every point in the star-shaped region. The resulting set of guards capture the intraregion connectivity—the connectivity between points belonging...

We present near infrared broad band (J,H and K) and narrow band (H 2 S(1) 1 ! 0 and Br) images, and high resolution molecular observations (C 34 S(2-1), (3-2), (5-4) and 13 CO(2-1)) around the highly variable H 2 O maser located between the S235 A and B optical nebulosi-ties. These observations are part of an ongoing search for the sources of excitation of H 2 O masers in regions of star format...

i. Union, intersection, set concatenation, Kleene-star, set subtraction, complement Answer: Union: S ∪ T = { x | x ∈ S or x ∈ T} Intersection: S ∩ T = { x | x ∈ S and x ∈ T} Concatenation: S ◦ T = { xy | x ∈ S, y ∈ T} Kleene-star: S = { w1w2 · · ·wk | k ≥ 0, wi ∈ S ∀ i = 1, 2, . . . , k} Subtraction: S − T = { x | x ∈ S, x 6∈ T} Complement: S = { x ∈ Ω | x 6∈ S} = Ω− S, where Ω is the universe ...

We show that a set of reals is undetermined in Galvin’s point-open game iff it is uncountable and has property C′′, which answers a question of Gruenhage. Let X be a topological space. The point-open game G(X) of Galvin [G] is played as follows. Black chooses a point x0 ∈ X, then White chooses an open set U0 3 x0, then B chooses a point x1 ∈ X, then W chooses an open set U1 3 x1, etc. B wins th...

We present HST spectroscopy and imaging, along with new ground-based spectroscopy and ROSAT HRI imaging, of the He II emitting nebula N44C and its ionizing star. A GHRS spectrogram of the ionizing star yields a spectral type of about O7 for the star. The lack of P Cygni profiles for Si IV and C IV indicates that the star is not a supergiant. The nebular abundances in the ionized gas are consist...

We estimate the magnitude of spillovers generated by 112 academic "superstars" who died prematurely and unexpectedly, thus providing an exogenous source of variation in the structure of their collaborators' coauthorship networks. Following the death of a superstar, we find that collaborators experience, on average, a lasting 5 to 8% decline in their quality-adjusted publication rates. By explor...

We now know that long (duration > 2 s) gamma-ray burst (GRB) sources lie at distances comparable to the “radius” of the Universe and that they are momentarily the most luminous known objects: Several GRBs have now been observed to have associated X-ray, optical and radio counterparts following power-law decays that fit theoretical expectations for relativistic blastwaves. Three GRBs (and/or the...

Symmetry breaking is a well-known method for search reduction. It identifies state-space symmetries prior to search, and prunes symmetric states during search. A recent proposal, star-topology decoupled search, is to search not in the state space, but in a factored version thereof, which avoids the multiplication of states across leaf components in an underlying star-topology structure. We show...