Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of the secant variety, and give conditions on the variety that are equivalent to the secant variety being arithmetically Cohen-Macaulay. Under this same condition, we then show that if X satisfies Np+2dim(X), then the se...

An explicit time differencing technique is introduced to approximate nonlinear conservation laws. This differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments. Previous stability requirements, i.e. the CFL condition, placed a global bound on the size of the time increments. For scalar, monotone, approximations in one space dimension,...

posed on some finite x-interval along with initial and boundary conditions, and where the function a is piecewise continuous and satisfies a(u) ≥ 0 for all u. In particular, a(u) = 0 is possible on u-intervals of positive length, so (1) may turn into a first-order hyperbolic conservation law where the location of the type-change interface is unknown a priori. Thus, solutions of (1) are in gener...

In the current discussion about the capacity of Bayesianism in reasoning under uncertainty, there is a conceptual and notational confusion between the explicit condition and the implicit condition of a probability evaluation. Consequently, the limitation of Bayesianism is often seriously underestimated. To represent the uncertainty of a belief system where revision is needed, it is not enough t...

We investigate classical formation of a trap surface in D-dimensional Einstein gravity in the process of a head-on collision of two high-energy particles, which are treated as Aichelburg-Sexl shock waves. From the condition of the trap surface volume local maximality we deduce an explicit form of the inner trap surface. Imposing the continuity condition on the fronts we obtain a time-dependent ...

We study the stabilization problem of discrete-time planar switched linear systems with impulse. When all subsystems are controllable, based on an explicit estimation on the state transitionmatrix, we establish a sufficient condition such that the switched impulsive system is stabilizable under arbitrary switching signal with given switching frequency. When there exists at least one uncontrolla...

In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d -dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of d = 2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and q...

A celebrated theorem by Herman and Yoccoz asserts that if the rotation number α of a C∞-diffeomorphism of the circle f satisfies a Diophantine condition, then f is C∞-conjugated to a rotation. In this paper, we establish explicit relationships between the Ck norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow a suitably modified version of Yoccoz’s p...

We develop some of the foundations of affinoid pre-adic spaces without Noetherian or finiteness hypotheses. We give explicit examples of non-adic affinoid pre-adic spaces, and also a new condition ensuring that the structure presheaf on Spa(R,R) is a sheaf. This condition can be used to give a new proof that the spectrum of a perfectoid algebra is an adic space.