On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group

In this paper, we classify the m-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive m-ovoids.

Scaling Behavior for the Susceptibility of the Vacuum

Using the two-component superfluid model of Winterberg for space, two models for the susceptibility of the cosmic vacuum as a function of the cosmic scale parameter, a, are presented. We also consider the possibility that Newton’s constant can scale, i.e., G-1=G-1(a), to form the most general scaling laws for polarization of the vacuum. The positive and negative values for the Planckion mass, which form the basis of the Winterberg model, are inextricably linked to the value of G, and as such, both G and Planck mass are intrinsic properties of the vacuum. Scaling laws for the non-local, smeared, cosmic susceptibility, , the cosmic polarization, , the cosmic macroscopic gravitational field, , and the cosmic gravitational field mass density, , are worked out, with specific examples. At the end of recombination, i.e., the era of last scattering, using the polarization to explain dark matter, and the gravitational field mass density to explain dark energy, we find that, . While this is an unconventional assignment, differing from the ΛCDM model, we believe this is correct, as localized dark matter (LDM) contributions can be much higher in this epoch than cosmic smeared values for susceptibility. All density parameter assignments in Friedmanns’ equation are cosmic averages, valid for distance scales in excess of 100 Mpc in the current epoch. We also evaluate the transition from ordinary matter dominance, to dark matter dominance, for the cosmos as a whole. We obtain for the transition points, z=1.66, for susceptibility model I, and, z=2.53 , for susceptibility model II.

Air-Stable Dy(III)-Macrocycle Enantiomers:From Chiral to Polar Space Group

Magnetoelectric(ME)multiferroic materials have unique advantages in low-power and high-density information storage,because they can simultaneously display ferroelectricity and ferromagnetism.However,research on how to construct air-stable highperformance ME single-molecule magnets(SMMs)is nonexistent.Herein,by introducing homochirality while reducing molecular symmetry,two doubledecker Dy(III)enantiomers adopting the polar space group P2_(1) and exhibiting excellent thermal stability were obtained.They displayed zero field SMM behavior with an anisotropy barrier(Ueff)of ca.100 cm^(−1).This work establishes a rational chemical design strategy for crystallizing SMMs in polar space groups and elucidates the direction for future research,that is,engineering small-size high-performance SMMs.

Morphology-dependent space charge polarization and dielectric relaxation of CdO nanomorphotypes

A versatile approach signifying the morphology-dependent dielectric polarization and relaxation mechanisms of cadmium oxide(CdO)nanosphere,nanoflakes and nanoparallelepiped morphotypes as a function of frequency and temperature is presented.Variation of dielectric property is observed due to the changes of space charge/interfacial polarization resulting from the variations of surface to volume ratio of nanomorphology.Accordingly,colossal dielectric constant value has been observed in CdO nano-sphere having larger surface to volume ratio.The order of dielectric constant(dc)values observed for the present nanomorphologies is:dc of sphere>dc of flakes>dc of parallelepiped resembles the order of surface to volume ratios of the present morphologies respectively.The experimental data of complex impedance values are numerically fitted using theoretical models which provide the information of role of grain resistance on dielectric polarization and Cole–Cole type mechanism of dielectric relaxation process.The activation energies for electron transport are found to be 0.087 eV for spheres,0.074 eV for flakes and 0.067 for parallelepiped nanomorphotypes of CdO.The dielectric and impedance spectroscopic analysis of the present material opens up wide scope for morphology-dependent tuning of nanomaterials for electrical applications.

Magnetic manganese-based composites with multiple loss mechanisms towards broadband absorption

The weak dielectric properties and the lack of magnetic loss of manganese-based absorbers are obstructed as the new generation of electromagnetic wave absorption(EMA)materials applying in microelectronic devices.Herein,the sulfuration and subsequent compounding strategies have been employed to enhance the EMA performance of multi-shell nanosphere-shaped Mn_(2)O_(3)materials.With the narrow bandgap,the as-obtained MnS possesses reinforced electrical conductivity,which is conducive to conductivity loss.More importantly,the presence of potential difference between different phases will form space charge region at the heterogeneous interface,thus favoring interfacial polarization.Additionally,the improvement of magnetic loss is attributed to the presence of Co_(3)O_(4)nanoparticles.Consequently,the composites present enhanced EMA performance than original Mn_(2)O_(3).Specifically,the minimum reflection loss of as-prepared composites is−51.4 dB at the thickness of 1.8 mm and the broad effective absorption bandwidth reaches 6.2 GHz at 1.9 mm.The low matching thickness and high absorption efficiency in this work can provide a convincing reference when designing distinguished manganese-based absorbers.

Theorems of Erds-Ko-Rado type in geometrical settings

The original Erdos-Ko-Rado problem has inspired much research. It started as a study on sets of pairwise intersecting k-subsets in an n-set, then it gave rise to research on sets of pairwise non-trivially intersecting k-dimensional vector spaces in the vector space V（n, q） of dimension n over the finite field of order q, and then research on sets of pairwise non-trivially intersecting generators and planes in finite classical polar spaces. We summarize the main results on the Erdos-Ko-Rado problem in these three settings, mention the ErdSs-Ko-Rado problem in other related settings, and mention open problems for future research.