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We construct TBA equations for D-type Argyres-Douglas theories with an SU(2) flavor symmetry based on their spectral networks. We show that the solutions of these TBA equations agree with the quantum periods of the corresponding quantum…
In this paper, to the best of our knowledge, we make the first attempt at studying the parametric semilinear elliptic eigenvalue problems with the parametric coefficient and some power-type nonlinearities. The parametric coefficient is…
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…
Let $\Omega$ be an unbounded open subset of ${\mathbb R}^n$, $n \ge 2$, and $A : \Omega \times {\mathbb R}^n \to {\mathbb R}^n$ be a function such that $$ C_1 |\zeta|^p \le \zeta A (x, \zeta), \quad |A (x, \zeta)| \le C_2 |\zeta|^{p-1} $$…
Following a review of the dual description of the non-linear sigma model we investigate the one-loop quadratic divergences. We use the covariant background field method for the general case and apply the results to the important example of…
Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P\sim M^\eta$ with $0 < \eta < 2/5$. We simplify the proof of subconvexity bounds for $L(\frac{1}{2},f\otimes\chi)$ when $f$ is a primitive…
We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x^{\frac{3}{4}}$.…
We describe the behavior of the Perdew-Zunger self-interaction-corrected local density approximation (SIC-LDA) functional when implemented in a plane-wave pseudopotential formalism with Wannier functions. Prototypical semiconductors and…
The number $\nu_d(n)$ of linearly independed homogeneous invariants of degree $n$ for the ternary form of degree $d$ is calculated.
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…
Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational…
We consider an asymptotically free, vectorial, ${\cal N}=1$ supersymmetric gauge theory with gauge group $G$ and $N_f$ pairs of chiral superfields in the respective representations ${\cal R}$ and $\bar {\cal R}$ of $G$, having an infrared…
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
We investigate a relaxation of the notion of fractional treewidth-fragility, namely fractional tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for meta-problems such as finding a…
We report the results of a measurement of susceptibilities in noncompact $QED_4$ in $8^4, 10^4$ and $12^4$ lattices. Due to the potentialities of the $MFA$ approach, we have done simulations in the chiral limit which are therefore free from…
We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose…
The problem of estimating the initial state of 1-D wave equations with globally Lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers, and…
We consider the diagonal paraproduct arising in the nonlinearity $(u\cdot \nabla) u$ for the three-dimensional Navier-Stokes equations. On scale-critical windows and in the range $1/6 < \delta \le 5/8$ we obtain a log-free estimate at the…
Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via…
We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is…