Generalization of the Zlámal condition for simplicial finite elements in ℝ<Superscript><Emphasis Type=Italic>d</Emphasis></Superscript>

The famous Zlámal’s minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in 2d. In this paper we present and discuss its generalization to simplicial partitions in any space dimension.     

On the asymptotic optimality of the <Emphasis Type=Italic>cμ</Emphasis>/<Emphasis Type=Italic>θ</Emphasis> rule under ergodic cost

We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served. For class i, service is provided at rate μ _i , and abandonment occurs at rate θ _i . In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c _i μ _i /θ _i asymptotically minimizes an ergodic holding cost, where c _i denotes the equivalent holding cost per unit time for class i.     

Upper bounds for the first dirichlet eigenvalue of a tube around an algebraic complex curve of ℂ<Emphasis Type=Italic>P</Emphasis><Superscript><Emphasis Type=Italic>n</Emphasis></Superscript>(<Emphasis Type=Italic>λ</Emphasis>)

We give an upper bound for the first Dirichlet eigenvalue of a tube around a complex curve P of ℂP ⁿ (λ) which depends only on the radius of the tube and the degrees of the polynomials defining P. The bound is sharp on a totally geodesic ℂP ¹(λ) and gives a gap between the eigenvalue of a tube around ℂP ¹(λ) and around other complex curves.     

On the identification <Emphasis Type=Italic>H</Emphasis> = <Emphasis Type=Italic>H</Emphasis>′ in the Lions theorem and a related inaccuracy

We show that the common identification of H with its dual space in the famous functional frame V ⊂ H = H′ ⊂ V′ is incompatible with the distributional frame for some standard pdes and we recall an error related to this unnecessary identification which is repeated from years.     

Strengthening of the Kneser theorem on zeros of solutions of the equation <Emphasis Type=Italic>u</Emphasis>″ + <Emphasis Type=Italic>q</Emphasis>(<Emphasis Type=Italic>t</Emphasis>)<Emphasis Type=Italic>u</Emphasis> = 0 using one functional equation

We present conditions under which a linear homogeneous second-order equation is nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.     

Calibration relations for <Emphasis Type=Italic>B</Emphasis><Subscript><Emphasis Type=Italic>φ</Emphasis></Subscript>-splines of fourth order

We study necessary and sufficient conditions for the smoothness of (not necessarily polynomial) splines of fourth order. We establish the uniqueness of a space of splines of maximal smoothness and prove embeddings on refined grids. We also obtain the corresponding calibration relations. Bibliography: 12 titles.     

Dark matter interpretations of the cosmic-ray <Emphasis Type=Italic>e</Emphasis><Superscript>±</Superscript> excesses

The cosmic-ray excess observed by PAMELA in the positron fraction and by FERMI and HESS in e⁻+e⁺ can be interpreted in terms of dark matter annihilations or decays. We summarize the main possibilities and their possible tests.     

Sur la rigidité des groupes de triangles (<Emphasis Type=Italic>r</Emphasis>, <Emphasis Type=Italic>p</Emphasis>, <Emphasis Type=Italic>q</Emphasis>)

We show the length spectral rigidity for the family of fuchsian triangular groups.     

Kinetic Spanners in ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

We present a new (1+ε)-spanner for sets of n points in ℝ ^d . Our spanner has size O(n/ε ^d−1) and maximum degree O(log  ^d n). The main advantage of our spanner is that it can be maintained efficiently as the points move: Assuming that the trajectories of the points can be described by bounded-degree polynomials, the number of topological changes to the spanner is O(n ²/ε ^d−1), and using a supporting data structure of size O(nlog  ^d n), we can handle events in time O(log  ^d+1 n). Moreover, the spanner can be updated in time O(log n) if the flight plan of a point changes. This is the first kinetic spanner for points in ℝ ^d whose performance does not depend on the spread of the point set.