This work develops asymptotic properties of randomly switching and time inhomogeneous dynamic systems under Brownian perturbation with a small diffusion. The switching process is modeled by a continuous-time Markov chain, which portraits discrete events that cannot be modeled by a diffusion process. In the model, there are two small parameters. One of them is ε associated with the generator of ...

Three bent-core nematic liquid crystals having the same core but with different terminal groups, short (C4) and long (C7,C9) tails, are investigated by dielectric and electro-optic contrast spectroscopic techniques. C4 shows sign reversal in the dielectric anisotropy Δε' as a function of both temperature and frequency, whereas C9 shows only negative Δε' in the entire mesophasic region. The beha...

The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

Lung tissue presents substantial nonlinear phenomena not accounted for by linear models; however, nonlinear approaches are less available. Our aim was to characterize the behavior of total harmonic distortion, an index of nonlinearity, in lung tissue strips under sinusoidal deformation at a single frequency as a function of strain amplitude and operational stress. To that end, lung parenchymal ...

We have developed an instrument for directly measuring the emissivity of reflective surfaces at near-millimeter wavelengths. The thermal emission of a test sample is compared with that of a reference surface, allowing the emissivity of the sample to be determined without heating. The emissivity of the reference surface is determined by one's heating the reference surface and measuring the incre...

The precise determination of the beam energy at BESIII is extremely important for many physics analyses, in particular, for the precise measurement of the τ mass. Fortunately, a method has been developed by physicists from the Budker Institute of Nuclear Physics (BINP) using back scattered Compton photons produced by CO2 laser beams on both the electron and positron beams in BESIII. This method...

The liquid crystal (LC) compound with the central linkage group Schiff-base was studied. molecular structure characterized FTIR. Mesomorphic properties were using differential scanning calamity (DSC) and polarizing optical microscopy (POM). dielectric constant (ε) conductivity (σ) anisotropy (Δε) have been measured in frequency range of 100 Hz to MHz from room temperature l00 °C. Dielectric con...