NbSe$_3$ and monoclinic-TaS$_3$ ($m$-TaS$_3$) are quasi-1D metals containing three different types of chains undergoing two charge density wave (CDW) Peierls transitions at T$_{P_1}$ T$_{P_2}$. The nature these is discussed on the basis first-principles DFT calculation their electron-hole Lindhard response function. As a result stronger inter-chain interactions Fermi surface (FS) function consi...

Let $${{\mathfrak {A}}}\, $$ and '$$ be two $$C^*$$ -algebras with identities $$I_{{{\mathfrak }$$ '}$$ , respectively, $$P_1$$ $$P_2 = I_{{{\mathfrak } - P_1$$ nontrivial projections in . In this paper, we study the characterization of multiplicative $$*$$ -Lie–Jordan-type maps, where notion these maps arise here. particular, if $${\mathcal {M}}_{{{\mathfrak is a von Neumann algebra relative $...

We study the persistent homology of an Erdős–Rényi random clique complex filtration on n vertices. Here, each edge e appears independently at a uniform time $$p_e \in [0,1]$$ , and persistence cycle $$\sigma $$ is defined as $$p_2(\sigma ) / p_1(\sigma )$$ where $$p_1(\sigma are birth death times . show that if $$k \ge 1$$ fixed, then with high probability maximal k-cycle order $$n^{1/k(k+1)}$$

We design a Fortin operator for the lowest-order Taylor-Hood element in any dimension, which was previously constructed only 2D. In construction we use tangential edge bubble functions divergence correcting operator. This naturally leads to an alternative inf-sup stable reduced finite pair. Furthermore, provide counterexample stability and hence existence of $P_2$-$P_0$ augmented 3D.

We study coexistence in discrete time multi-type frog models. first show that for two types of particles on $\mathbb{Z}^d$, $d\geq2$, any jumping parameters $p_1, p_2 \in (0,1)$, occurs with positive probability sufficiently rich deterministic initial configuration. extend this to the case random distribution particles. question multiple and $2^d$ $\mathbb{Z}^d$ enough also an instance infinite...

For two graphs J and H, the generalized Turán number, denoted by ex(n, J, H), is maximum number of copies in an H-free graph order n. A linear forest F disjoint union paths. In this paper, we determine $$ex(n,S_r,F)$$ when n large enough, which generalizes results on $$ex(n, S_r, P_k)$$ (k+1) P_2)$$ . Finally, prose a problem related to F-free under shifting operations.

Let N1 = p1q1 and N2 = p2q2 be two different RSA moduli. Suppose that p1 = p2 mod 2 t for some t, and q1 and q2 are α bit primes. Then May and Ritzenhofen showed that N1 and N2 can be factored in quadratic time if t ≥ 2α+ 3. In this paper, we improve this lower bound on t. Namely we prove that N1 and N2 can be factored in quadratic time if t ≥ 2α+ 1. Further our simulation result shows that our...

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

The orbit of the outer satellite Alexhelios (216) Kleopatra is already constrained by adaptive-optics astrometry, obtained with VLT/SPHERE instrument. However, there also a preceding occultation event in 1980 attributed to this satellite. Hereinafter, we try link all observations, spanning 1980--2018. We find nominal exhibits an unexplained shift $+60^\circ$ true longitude. Using both periodogr...

Metric spaces can be generalized to partial metric spaces. Partial have a unique concept related distance. In usual case, there is no distance from two same points. But, we obtain the points in It means that not absolutely zero. Using basic of spaces, find analogy between and We define d^p formed by p, with applying characteristics metric. At beginning, implement determine sequences L_2 (P). th...