4,554 Result(s)
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On minimality and scalar curvature of CMC triharmonic hypersurfaces in pseudo-Riemannian space forms
In this paper, we first study the minimality of triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms under the assumption that the shape operator is diagonalizable. Then, we ...
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Moments of quadratic twists of modular \(L\) -functions
We prove an asymptotic for the second moment of quadratic twists of a modular L \(L\) ...
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Approximate Calculation for a Debate Between Two Chinese Children More Than Two Thousand Years Ago
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Nonexistence for Lane-Emden system involving Hardy potentials with singularities on the boundary
Our purpose of this article is to study nonexistence of positive super solutions for Lane-Emden system involving inverse-square potentials
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Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process
The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup, which is defined by the backward differential equation. We provide a proof of t...
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Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions
How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory. Motsch and Tadmor in 2011 also stressed the significance to assume that the intera...
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On the solutions to the weighted biharmonic equation in the unit disk
In this paper, we investigate the solutions of the weighted biharmonic differential equation \(\Delta \big ((1-|z|^2)^{-1}\Delta \big ) \Phi =0\) ...
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Conditional Regularity for the 3D Damped Boussinesq Equations with Zero Thermal Diffusion
The main purpose of this paper is to establish regularity criteria of the 3D damped Boussinesq equations with zero thermal diffusion. It is shown that if two components of the velocity or the gradient of veloc...
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A note on Majorana representation of quantum states
By the Majorana representation, for any \(d > 1\) d > 1 ...
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Open AccessCorrection to: p-Parabolicity and a Generalized Bochner’s Method with Applications
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Open AccessGlobal dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition
We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone ...
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On a ternary diophantine inequality with prime numbers of a special type II
Suppose that N is a sufficiently large real number and E is an arbitrarily large constant. In this paper, it is proved that, for $$1< c < \frac{7}{6}$...
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On the characterization of harmonic functions with initial data in Morrey space
Let (X, d, μ) be a metric measure space satisfying the doubling condition and an L2-Poincaré inequality. Consider the nonnegative operator $$\...
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The Pointwise Convergence Along Curve Associated with Boussinesq Operator
In this paper, we study the almost everywhere pointwise convergence of the Boussinesq operator along curve γ(x, t) in ℝ. It is shown that $${\...
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Refinements of the norm of two orthogonal projections
In this paper, some refinements of norm equalities and inequalities of combination of two orthogonal projections are established. We use certain norm inequalities for positive contraction operator to establish...
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Weak-strong uniqueness for three dimensional incompressible active liquid crystals
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models. In this paper, we study the weak-strong uniqueness for the Leray-Hopf ty...
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A Liouville-type theorem in conformally invariant equations
Given a smooth function K(x) satisfying a polynomially cone condition and \(x\cdot \nabla K\le 0\) ...
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Open AccessGreen functions and smooth distances
In the present paper, we show that for an optimal class of elliptic operators with non-smooth coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly rectifiable if and only if the ...
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Some Abstract Critical Point Theorems and Applications in Wave Equations
With the index defined in [J. Differential Equations, 2016, 260(4): 3749–3784] and [Front. Math., 2023, 18(3): 731–742], we get some critical point theorems for abstract operator equation without compactness a...
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Existence and Asymptotic Behavior of Solutions for a Quasilinear Schrödinger–Poisson System in ℝ3 with a General Nonlinearity
In this paper, we are concerned with the following quasilinear Schrödinger–Poisson system in ℝ3 $$\begin{cases}-\Delta u+u+\lambda\phi u=f(u), & \text...
