For a harmonic map $u : M^3 \to S^1$ on closed, oriented $3$-manifold, we establish the identity \[ 2 \pi \int_{\theta \in S^1} \chi (\Sigma _\theta) \geq \frac{1}{2} \int_{\Sigma_\theta} \left( {\lvert du \rvert}^{-2} \mathit{Hess} (u) \rvert}^2 + R_M \right) \] relating scalar curvature $R_M$ of $M$ to average Euler characteristic level sets $\Sigma_\theta = u^{-1} {\lbrace \theta \rbrace}$. ...

The evolution of population dynamics in a stochastic environment is analysed under a general form of density-dependence with genetic variation in r and K, the intrinsic rate of increase and carrying capacity in the average environment, and in sigma(e)(2), the environmental variance of population growth rate. The continuous-time model assumes a large population size and a stationary distribution...

We have analyzed the kinematics of 9750 OB2 stars with proper motions and parallaxes selected by Xu et al. from Gaia EDR3 catalogue. The relative parallax errors for these do not exceed 10 $${\%}$$ . Based on entire sample stars, we found velocities $$(U,V)_{\odot}=(7.17,7.37)\pm(0.16,0.24)$$ km s $${}^{-1}$$ components angular velocity Galactic rotation: $$\Omega_{0}=29.700\pm 0.076$$ kpc , $$...

We used the time correlation of shadowgraph images to determine the angle Theta of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio Gamma identical with D/L=1 (D is the diameter and L approximately 87 mm is the height) in the Rayleigh-number range 7 x 10(7)</=R</=3 x 10(9) for a Prandtl number...

Theta correspondence θ over R was established by Howe in ( [5]). In [10], we proved that θ preserves unitarity under certain restrictions, generalizing the result of Jian-Shu Li ( [16]). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show that under a natural condition on the sizes of the related dual p...

Let ` > 0 be a square-free integer, ` ≡ 3 mod 4, K = Q( √ −`), and OK the ring of integers of K. Codes C over rings R := OK/pOK determine lattices Λ`(C) over K. The theta series θΛ`(C) of such lattice can be written in terms of the complete weight enumerator of C. For any `′ > ` the first `+1 4 terms of their corresponding theta functions are the same with those of Λ`(C). In [6] it was conjectu...

Theta correspondence y over R is established by Howe (J. Amer. Math. Soc. 2 (1989) 535). In He (J. Funct. Anal. 199 (2003) 92), we prove that y preserves unitarity under certain restrictions, generalizing the result of Li (Invent. Math. 97 (1989) 237). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show...

We present measurements of D--> KS0 pi and D--> KL0 pi branching fractions using 281 pb(-1) of psi(3770) data at the CLEO-c experiment. We find that B(D0--> KS0 pi 0) is larger than B(D0--> KL0 pi 0), with an asymmetry of R(D0)=0.108+/-0.025+/-0.024. For B(D+--> KS0 pi+) and B(D+--> KL0 pi+), we observe no measurable difference; the asymmetry is R(D+)=0.022+/-0.016+/-0.018. The D0 asymmetry is ...