Related papers: New Quantitative Deformation Lemma and New Mountai…

We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.

We study mathematical programs with switching constraints (MPSC)from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous defor-mation of lower level sets can be…

Easy lowering local minima, after introducing valley functions on smooth manifolds gives, without gluing technicities, "M. Morse's lemma's" canonical form, moving critical values and eliminating pair of critical points theorems, reducing…

For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations.…

The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this…

Recently Wolff obtained a nearly sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. We obtain the endpoint of Wolff's estimate and generalize to the case when one of the subsets is large. As a…

At a generic quantum critical point, the thermal expansion $\alpha$ is more singular than the specific heat $c_p$. Consequently, the "Gr\"uneisen ratio'', $\GE=\alpha/c_p$, diverges. When scaling applies, $\GE \sim T^{-1/(\nu z)}$ at the…

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point…

The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem \[ \bar J(u)\ =\ \frac1p\ \int_\Omega \bar A(x,u)|\nabla u|^p dx - \int_\Omega G(x,u) dx \]…

We study the phase diagram of $N_f = 2+1$ QCD in the $T - \mu_B$ plane and investigate the critical point corresponding to the onset of the Roberge-Weiss transition, which is found for imaginary values of $\mu_B$. We make use of stout…

We present a method for computing transition points of the random cluster model using a generalization of the Newman-Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is…

Deconfined quantum criticality of two-dimensional $SU(2)$ quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP$^1$ model…

We consider the Grueneisen parameter and the magnetocaloric effect near a pressure and magnetic field controlled quantum critical point, respectively. Generically, the Grueneisen parameter (and the thermal expansion) displays a…

We study a topologically exact, negative Schwarzian unimodal map whose critical point is non-recurrent and flat. Assuming the critical order is either logarithmic or polynomial, we establish the Large Deviation Principle and give a partial…

In this note we consider boundary point principles for partial differential inequalities of elliptic type. Firstly, we highlight the difference between conditions required to establish classical strong maximum principles and classical…

We describe characteristic physical properties of the recently introduced class of deconfined quantum critical points. Using some simple models, we highlight observables which clearly distinguish such critical points from those described by…

In this paper, we study the sufficient conditions for the existence of solutions of first-order Hamiltonian stochastic impulsive differential equations under Dirichlet boundary value conditions. By using the variational method, we first…

We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional…

In the influential paper \cite{Caflish-1980-CPAM} which was the starting point of the employment of Hilbert expansion method to the rigorous justifications of the fluid limits of the Boltzmann equation, Caflisch discovered an elegant and…

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field…