Quantitative Regularity for p-Minimizing Maps Through a Reifenberg Theorem

In this article we extend to arbitrary p-energy minimizing maps between Riemannian manifolds a regularity result which is known to hold in the case $$p=2$$ p = 2 . We first show that the set of singular points of such a map can be quantitatively stratified: we classify singular points based on the number of almost-symmetries of the map around them, as done in Cheeger and Naber (Commun Pure Appl Math 66(6): 965–990, 2013). Then, adapting the work of Naber and Valtorta (Ann Math (2) 185(1): 131–227, 2017), we apply a Reifenberg-type Theorem to each quantitative stratum; through this, we achieve an upper bound on the Minkowski content of the singular set, and we prove it is k-rectifiable for a k which only depends on p and the dimension of the domain.

Calculation of the resource use limiting factors in the management digital transformation context

On the basis of the equation of entropy-information balance, which can describe the macromodel of control of equipment operation, consumption of materials, energy carriers, the limiting values of the coefficients of their use and losses are obtained. It turned out that the ratio of the latter satisfies with high accuracy the proportions of the golden section. This quantitative regularity, which is of a systemic nature, should be taken into account as a standard in the feasibility study of projects of information systems for production management, which has a probabilistic nature.

Space regularity for evolution operators modeled on Hörmander vector fields with time dependent measurable coefficients

We consider a heat-type operator $$\mathcal {L}$$ L structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, with a uniformly positive matrix of bounded measurable coefficients depending only on time. We prove that if $$\mathcal {L}u$$ L u is smooth with respect to the space variables, the same is true for u, with quantitative regularity estimates in the scale of Sobolev spaces defined by right invariant vector fields. Moreover, the solution and its space derivatives of every order satisfy a 1/2-Hölder continuity estimate with respect to time. The result is proved both for weak solutions and for distributional solutions, in a suitable sense.

Core/Double-Cone Emission-Beam Structure in a Millisecond Pulsar

Slow pulsars show a great deal of qualitative and quantitative regularity in the structure of their radio emission beams as described by the core/double-cone model; however, millisecond pulsars (MSPs) have shown little. It is thus arresting to encounter a 2.7-s MSP with what appears to be a double-cone/core profile—and even more so to find that the arrangement of the cones around the core suggest aberration/retardation emission heights that are very reasonable. This and several other pulsars then represent rare opportunities for analysis and raise questions about why a few MSPs show such orderly beam structure while so many do not.

Challenge Analysis and Schemes Design for the CFD Simulation of PWR

CFD simulation for a PWR is an important part for the development of Numerical Virtual Reactor (NVR) in Harbin Engineering University of China. CFD simulation can provide the detailed information of the flow and heat transfer process in a PWR. However, a large number of narrow flow channels with numerous complex structures (mixing vanes, dimples, springs, etc.) are located in a typical PWR. To obtain a better CFD simulation, the challenges created by these structural features were analyzed and some quantitative regularity and estimation were given in this paper. It was found that both computing resources and time are in great need for the CFD simulation of a whole reactor. These challenges have to be resolved, so two schemes were designed to assist/realize the reduction of the simulation burden on resources and time. One scheme is used to predict the combined efficiency of the simulation conditions (configuration of computing resources and application of simulation schemes), so it can assist the better choice/decision of the combination of the simulation conditions. The other scheme is based on the suitable simplification and modification, and it can directly reduce great computing burden.