Some properties of the LCM sequence

The main purpose of this paper is using the elementary method to study the properties of the Smarandache LCM sequence, and give some interesting identities

Local Model Checking Algorithm Based on Mu-calculus with Partial Orders

The propositionalμ-calculus can be divided into two categories, global model checking algorithm and local model checking algorithm. Both of them aim at reducing time complexity and space complexity effectively. This paper analyzes the computing process of alternating fixpoint nested in detail and designs an efficient local model checking algorithm based on the propositional μ-calculus by a group of partial ordered relation, and its time complexity is O(d2(dn)d/2+2) (d is the depth of fixpoint nesting,  is the maximum of number of nodes), space complexity is O(d(dn)d/2). As far as we know, up till now, the best local model checking algorithm whose index of time complexity is d. In this paper, the index for time complexity of this algorithm is reduced from d to d/2. It is more efficient than algorithms of previous research

Dibutyl 2,2′-bipyridine-4,4′-dicarboxyl­ate

In the title compound, C20H24N2O4, the mol­ecule lies on a centre of symmetry and is approximately planar (r.m.s. deviation= 0.013 Å for 26 non-H atoms). The carboxyl­ate group is inclined slightly to the neighbouring pyridine ring, forming a dihedral angle of 4.37 (2)°. The mol­ecules form stacks with an inter­planar separation of 3.547 (1) Å

Parametric analysis of pitch angle scattering and losses of relativistic electrons by oblique EMIC waves

This study analyzes the effects of electromagnetic ion cyclotron (EMIC) waves on relativistic electron scattering and losses in the Earth’s outer radiation belt. EMIC emissions are commonly observed in the inner magnetosphere and are known to reach high amplitudes, causing significant pitch angle changes in primarily >1 MeV electrons via cyclotron resonance interactions. We run test-particle simulations of electrons streaming through helium band waves with different amplitudes and wave normal angles and assess the sensitivity of advective and diffusive scattering behaviors to these two parameters, including the possibility of very oblique propagation. The numerical analysis confirms the importance of harmonic resonances for oblique waves, and the very oblique waves are observed to efficiently scatter both co-streaming and counter-streaming electrons. However, strong finite Larmor radius effects limit the scattering efficiency at high pitch angles. Recently discussed force-bunching effects and associated strong positive advection at low pitch angles are, surprisingly, shown to cause no decrease in the phase space density of precipitating electrons, and it is demonstrated that the transport of electrons into the loss cone balances out the scattering out of the loss cone. In the case of high-amplitude obliquely propagating waves, weak but non-negligible losses are detected well below the minimum resonance energy, and we identify them as the result of non-linear fractional resonances. Simulations and theoretical analysis suggest that these resonances might contribute to subrelativistic electron precipitation but are likely to be overshadowed by non-resonant effects

Comparative Component Analysis of Exons with Different Splicing Frequencies

Transcriptional isoforms are not just random combinations of exons. What has caused exons to be differentially spliced and whether exons with different splicing frequencies are subjected to divergent regulation by potential elements or splicing signals? Beyond the conventional classification for alternatively spliced exons (ASEs) and constitutively spliced exons (CSEs), we have classified exons from alternatively spliced human genes and their mouse orthologs (12,314 and 5,464, respectively) into four types based on their splicing frequencies. Analysis has indicated that different groups of exons presented divergent compositional and regulatory properties. Interestingly, with the decrease of splicing frequency, exons tend to have greater lengths, higher GC content, and contain more splicing elements and repetitive elements, which seem to imply that the splicing frequency is influenced by such factors. Comparison of non-alternatively spliced (NAS) mouse genes with alternatively spliced human orthologs also suggested that exons with lower splicing frequencies may be newly evolved ones which gained functions with splicing frequencies altered through the evolution. Our findings have revealed for the first time that certain factors may have critical influence on the splicing frequency, suggesting that exons with lower splicing frequencies may originate from old repetitive sequences, with splicing sites altered by mutation, gaining novel functions and become more frequently spliced

State-Aware Proximal Pessimistic Algorithms for Offline Reinforcement Learning

Pessimism is of great importance in offline reinforcement learning (RL). One broad category of offline RL algorithms fulfills pessimism by explicit or implicit behavior regularization. However, most of them only consider policy divergence as behavior regularization, ignoring the effect of how the offline state distribution differs with that of the learning policy, which may lead to under-pessimism for some states and over-pessimism for others. Taking account of this problem, we propose a principled algorithmic framework for offline RL, called \emph{State-Aware Proximal Pessimism} (SA-PP). The key idea of SA-PP is leveraging discounted stationary state distribution ratios between the learning policy and the offline dataset to modulate the degree of behavior regularization in a state-wise manner, so that pessimism can be implemented in a more appropriate way. We first provide theoretical justifications on the superiority of SA-PP over previous algorithms, demonstrating that SA-PP produces a lower suboptimality upper bound in a broad range of settings. Furthermore, we propose a new algorithm named \emph{State-Aware Conservative Q-Learning} (SA-CQL), by building SA-PP upon representative CQL algorithm with the help of DualDICE for estimating discounted stationary state distribution ratios. Extensive experiments on standard offline RL benchmark show that SA-CQL outperforms the popular baselines on a large portion of benchmarks and attains the highest average return

Modeling electron scattering and acceleration by whistler mode chorus waves in Jupiter's magnetosphere: effects of magnetic field model, total electron density, and electron injections

We evaluate the energetic electron scattering and acceleration due to whistler mode chorus waves using realistic magnetic field and density models in Jupiter's magnetosphere, and study the potential effects of electron injections. The bounce-averaged diffusion coefficients are calculated using the total electron density from the diffusive equilibrium model and the magnetic field strength from the VIP4 internal magnetic field and CAN current sheet model. The electron phase space density evolution due to chorus wave is simulated at M=10 . The typical chorus waves could cause fast pitch angle scattering loss of electrons from tens to several hundred keV, and gradual acceleration of relativistic electrons at several MeV. The latitudinally varying density and VIP4+CAN magnetic field model leads to faster pitch angle scattering and acceleration of electrons at energies above 100 keV than the constant density and dipolar magnetic field model. The simulation is compared to the electron dynamics during an electron injection event observed by Juno on 29 October, 2018. The electron flux is enhanced at low energies during the injection event, and the Fokker Planck simulation indicates an enhanced electron acceleration due to chorus waves subsequent to the injections. The modeling indicates an electron flux increase by nearly 1 order of magnitude within 1 day, suggesting the potentially important role of chorus waves in forming Jupiter's radiation belts after injections.First author draf

Oxygen ion dynamics in the Earth's ring current: Van Allen probes observations

Oxygen (O+) enhancements in the inner magnetosphere are often observed during geomagnetically active times, such as geomagnetic storms. In this study, we quantitatively examine the difference in ring current dynamics with and without a substantial O+ ion population based on almost 6 years of Van Allen Probes observations. Our results have not only confirmed previous finding of the role of O+ ions to the ring current but also found that abundant O+ ions are always present during large storms when sym-H < -60 nT without exception, whilst having the pressure ratio () between O+ and proton (H+) larger than 0.8 and occasionally even larger than 1 when L < 3. Simultaneously, the pressure anisotropy decreases with decreasing sym-H and increasing L shell. The pressure anisotropy decrease during the storm main phase is likely related to the pitch angle isotropization processes. In addition, we find that increases during the storm main phase and then decreases during the storm recovery phase, suggesting faster buildup and decay of O+ pressure compared to H+ ions, which are probably associated with some species dependent source and/or energization as well as loss processes in the inner magnetosphere.Accepted manuscrip