Related papers: A necessary condition for the logarithmic Minkowks…
In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski…
In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately…
We study the truncation error of the COS method and give simple, verifiable conditions that guarantee convergence. In one dimension, COS is admissible when the density belongs to both L1 and L2 and has a finite weighted L2 moment of order…
In the case of symmetries with respect to n independent linear hyperplanes, the stability of the solution of the Logarithmic Minkowski problem on S^{n-1} is established.
In this paper, we firstly establish the weak laws of large numbers on the canonical space $(\br^\bn,\cb(\br^\bn))$ by traditional truncation method and Chebyshev's inequality as in the classical probability theory. Then we extend them from…
Conditions for the unique solvability of the Cauchy problem for a family of scalar functional differential equations are obtained. These conditions are sufficient for the solvability of the Cauchy problem for every equation from the family…
Some exact solutions of the SU(2) Seiberg-Witten equations in Minkowski spacetime are given.
We explore the consequences of assuming that the bounded space-time subsets contain a finite number of degrees of freedom. A physically natural hypothesis is that this number is additive for spatially separated subsets. We show that this…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
For proper minimizers of parabolic variational integrals with linear growth with respect to $|Du|$, we establish a necessary and sufficient condition for $u$ to be continuous at a point $(x_o,t_o)$, in terms of a sufficient fast decay of…
A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating…
We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.
We consider a Dirichlet problem for the mean curvature operator in the Minkowski spacetime, obtaining a necessary and sufficient condition for the existence of a spacelike solution, with prescribed mean curvature, which is the graph of a…
This is a sequel to [2] and [3], which study the second boundary value problems for mean curvature flow. Consequently, we construct the translating solitons with prescribed Gauss image in Minkowski space.
Necessary and sufficient conditions for the existence of a composite-system statistical operator, and, separately, for the possibility of its being correlated or uncorrelated, are derived in terms of its range dimension and the range…
This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $\Phi(u)=\int_a^b f(x,u(x),u'(x))\,dx$, where $u\in C^1([a,b],{\mathbb R}^N)$. We first derive conditions which are simpler than the…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
We extend the non-perturbative time-dependent bosonic string action of [3] to a N=1 supersymmetric world sheet action with graviton background, and assume a superpotential, function of the time super coordinate.
It is shown that in order for the solutions of the Lindblad equation never to give a decreasing von Neumann entropy, it is necessary and sufficient that the operators appearing in this equation should be unitary linear combinations of their…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…