Related papers: On the effective secular equation
When a torus acts on a compact oriented manifold with isolated fixed points, the equivariant localization formula of Atiyah--Bott--Berline--Vergne converts the integral of an equivariantly closed form to a finite sum over the fixed points,…
We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
An exact differential equation is derived for the evolution of the Liouville effective action with the mass parameter. This derivation is based on properties of the exponential potential and some consequences of the equation are discussed.
In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the…
Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the…
We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medium modelled by a highly oscillatory coefficient. This…
We develop a superfield approach to the effective potential in the supersymmetric Chern-Simons theory coupled to matter, and, in Landau gauge, calculate the one-loop Kahlerian effective potential and give some qualitative prescriptions for…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
We prove that the generalized Benjamin-Ono equations $\partial_tu+\mathcal{H}\partial_x^2u\pm u^k\partial_xu=0$, $k\geq 4$ are locally well-posed in the scaling invariant spaces $\dot{H}^{s_k}(\R)$ where $s_k=1/2-1/k$. Our results also hold…
A family of special cases of the integrable Euler equations on $so(n)$ introduced by Manakov in 1976 is considered. The equilibrium points are found and their stability is studied. Heteroclinic orbits are constructed that connect unstable…
We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
We study the impact of saturable nonlinearity on the presence and location of exceptional points in a non-Hermitian dimer system. The inclusion of the saturable nonlinearity leads to the emergence of multiple eigenvalues, exceeding the…
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…
In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…