The structure of IR divergences in celestial gluon amplitudes

The all-loop resummation of SU(N) gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity.We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite N.In the large N limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $$ \mathcal{N} $$ N = 4 SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

Wavelet Transform Based Estimation of 1 Dimensional Signal

The key idea of this manuscript is denoising of noisy biological signals. For this wavelet thresholding technique is suggested. To eliminate the noise existing in the signal, mixed thresholding function is considered which is the median of Hard, Soft and Garrote functions. The mixed thresholding function is applied by degraded white gaussian noise Electrocardiogram signal. Two methods that are used to calculate the threshold value is FDR technique and Visu shrink technique. The outcomes of mixed functions are compared with remaining functions using Signal to Noise Ratio (SNR) and Mean Square Error (MSE). It is obvious that the mixed function performs superior than remaining functions using Visu shrink technique and performs better than only Hard function using FDR technique.

Preparation and Properties of Alcohol-Soluble Acrylate Adhesive

A kind of alcohol-soluble acrylate adhesive was synthesized by solution-polymerization. The influences of monomer ratio of soft to hard, function monomer and initiator content were studied on adhesive performance. The optimal conditions: ethanol as solvent, MA : MMA : AA : VAc = 4.5 : 4 : 1.5 : 2 : 0.8, and BPO is 0.8% of total mass, the temperature is 73 °C for 3.5 h. The properties of adhesive were determined.