The fundamental gap of a kind of two dimensional sub-elliptic operator

This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials $V(x)$ when $V(x)$ is subject to $L^\infty$ norm constraint

A fleet arithmetic on overlay capacity of multi-aircraft cooperative detect base on transformed chameleon

In allusion to the particularity of Multi-Fighter Cooperative Detection, this paper analyzes the influence of different formation modes of the aircraft.. The framework of basic formation modes is established, moreover, the solutions of these models are also introduced. There is some disadvantage of gridding-method on real-time performance. A transformed chameleon method is used to divide up the big formation and cluster it into the basic ones. The rules-less formations’ detect an overlay area and divided into basic ones, can be figured out on the ground of dividing results. In this way, we can reduce the fighter formations to calculate the overlay capacity fleetly. The simulation results indicate that the method meet the real-time needs with error permissibility

Empirical likelihood-based portmanteau tests for autoregressive moving average models with possible infinite variance innovation

It is an important task in the literature to check whether a fitted autoregressive moving average (ARMA) model is adequate, while the currently used tests may suffer from the size distortion problem when the underlying autoregressive models have low persistence. To fill this gap, this paper proposes two empirical likelihood-based portmanteau tests. The first one is naive but can serve as a benchmark, and the second is for the case with infinite variance innovations. The asymptotic distributions under the null hypothesis are derived under mild moment conditions, and their usefulness is demonstrated by simulation experiments and two real data examples.Comment: 23 pages, 2 figure

Evolution of magnetic component in Yang-Mills condensate dark energy models

The evolution of the electric and magnetic components in an effective Yang-Mills condensate dark energy model is investigated. If the electric field is dominant, the magnetic component disappears with the expansion of the Universe. The total YM condensate tracks the radiation in the earlier Universe, and later it becomes $w_y\sim-1$ thus is similar to the cosmological constant. So the cosmic coincidence problem can be avoided in this model. However, if the magnetic field is dominant, $w_y>1/3$ holds for all time, suggesting that it cannot be a candidate for the dark energy in this case.Comment: 12 pages, 4 figures, minor typos correcte

Mimicking Intermolecular Interactions of Tight Protein–Protein Complexes for Small-Molecule Antagonists

Tight protein–protein interactions (Kd1000 Å2) are highly challenging to disrupt with small molecules. Historically, the design of small molecules to inhibit protein–protein interactions has focused on mimicking the position of interface protein ligand side chains. Here, we explore mimicry of the pairwise intermolecular interactions of the native protein ligand with residues of the protein receptor to enrich commercial libraries for small-molecule inhibitors of tight protein–protein interactions. We use the high-affinity interaction (Kd=1 nm) between the urokinase receptor (uPAR) and its ligand urokinase (uPA) to test our methods. We introduce three methods for rank-ordering small molecules docked to uPAR: 1) a new fingerprint approach that represents uPA′s pairwise interaction energies with uPAR residues; 2) a pharmacophore approach to identify small molecules that mimic the position of uPA interface residues; and 3) a combined fingerprint and pharmacophore approach. Our work led to small molecules with novel chemotypes that inhibited a tight uPAR⋅uPA protein–protein interaction with single-digit micromolar IC50 values. We also report the extensive work that identified several of the hits as either lacking stability, thiol reactive, or redox active. This work suggests that mimicking the binding profile of the native ligand and the position of interface residues can be an effective strategy to enrich commercial libraries for small-molecule inhibitors of tight protein–protein interactions