Let Z=(Z1,…,Zd) be the d-dimensional Lévy processes where Zi’s are independent 1-dimensional with jump kernel Jϕ,1(u,w)=|u−w|−1ϕ(|u−w|)−1 for u,w∈R. Here ϕ is an increasing function weak scaling condition of order α̲,α¯∈(0,2). J(x,y)≍Jϕ(x,y) symmetric measurable Jϕ(x,y)≔Jϕ,1(xi,yi)if xi≠yi some i and xj=yj all j≠i0if more than one index iCorresponding to J, we show existence non-isotropic Markov...

Note that for f(x) = e − 1, (1.1) becomes a logistic equation with piecewise constant arguments. Definition 1.1 The zero solution of (1.1) is said to be uniformly stable, if for any ε > 0 and nonnegative integer n0, there is a δ = δ(ε) > 0 such that max{|x(n0 − j)| | j = −k,−k + 1, · · · , 0} < δ, implies that the solution {x(n)}n=0 of (1.1) satisfies |x(n)| < ε, n = n0, n0 + 1, · · · . Definit...

i,j cijxjdxi, cij ∈ C. The integrability condition ω ∧ dω = 0 implies that ω1 ∧ dω1 = 0. Let C be the matrix (cij)i,j ∈ Mn×n(C). Writing down explicitly the integrability condition, the coefficient of dxi ∧ dxj ∧ dxk (i < j < k) in ω1 ∧ dω1 is ci(ckj − cjk)− cj(cki − cik) + ck(cji − cij), where ci = ∑n j=1 cijxj . Two cases appear: (1) C is a symmetric matrix. (2) C is not symmetric. So, it exi...

The southern rock lobster (Jasus edwardsii) industry in Australia favours red lobsters, which are usually caught in shallow waters, over paler (brindle) lobsters. This preference is driven partly by the Chinese market, where red is associated with luck and prosperity, and additionally, by the widely held perception within the industry that brindles have greater mortality rates during out of wat...

In this paper, we prove that for any Kähler metrics $$\omega _0$$ and $$\chi $$ on M, there exists a metric _\varphi =\omega _0+\sqrt{-1}\partial {\bar{\partial }}\varphi >0$$ satisfying the J-equation $${\mathrm {tr}}_{\omega }\chi =c$$ if only $$(M,[\omega _0],[\chi ])$$ is uniformly J-stable. As corollary, find sufficient condition existence of constant scalar curvature with $$c_1<0$$ . Usin...

In the previous papers (Hu et al. in J Differ Equ 266(7):4106–4136, 2019; Kong 156(2):328–354, 1999), jump phenomena of j-th eigenvalue were completely characterized for Sturm–Liouville problems. this paper, we show that number these branches is exactly Maslov index path corresponding boundary conditions. Then determine sharp range jth on each layer space Finally, prove graph monodromy matrix t...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

This paper proposes a novel method for channel estimation in a single-carrier MIMO system with frequencydomain equalization/detection. To this end, we construct novel short MIMO training sequences that have constant envelope in the time domain to preclude the peak-to-mean power problem encountered in many systems that utilize the frequency domain for data recovery. Simultaneously, the spectrum ...