The model matching problem ${\bf min}_{R(z)}\|W(z)−R(z)E(z)\|_\infty$ involved in multirate filter banks design is addressed. A method is presented to design the synthesis filter bank $R(z)$ with the order of $W(z)$ which is the polyphase representation of the time delay of the reconstructed signal. The existence conditions of such low−order $R(z)$ are given in linear matrix inequalities (LMIs)...

We investigate how the galaxy reservoirs of molecular gas fuelling star formation are transformed while host galaxies infall onto cluster cores. As part Spatially Extended ESO Distant Cluster Survey (SEEDisCS), we present CO(3-2) observations 27 star-forming obtained with Atacama Large Millimeter Array (ALMA). These sources located inside and around CL1411.1$-$1148 at $z=0.5195$, within five ti...

Abstract Two matrices $$H_1$$ H 1 and $$H_2$$ 2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by $$H_1\cong H_2$$ ≅ , if one of the can obtained other via sequence row co...

We present a systematic study of deuterated molecular hydrogen (HD) at high redshift, detected in absorption the spectra quasars. four new identifications HD lines associated with known $\rm H_2$-bearing Damped Lyman-$\alpha$ systems. In addition, we measure upper limits on HD$ column density twelve recently identified DLAs. find that detections have similar $N({\rm HD})/N(\rm H_2)$ ratios as p...

‎Using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{R}^N$‎. ‎The existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $V(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.