Article
Mathematics
Joachim Kerner
Summary: We study the spectral gap of one-dimensional Schrodinger operators with non-negative bounded potentials and Neumann boundary conditions. We establish an explicit lower bound, and provide an improved lower bound for a smaller class of potentials that holds on large intervals.
ARCHIV DER MATHEMATIK
(2022)
Article
Mathematics, Applied
Jazmin Garcia, Juan Monsalve, Juan Rada
Summary: This paper explores the spectral and trace norms of digraphs, providing lower bounds and introducing the concept of almost regular digraphs. It also gives new upper bounds for the trace norm of digraphs and identifies the digraphs for which these bounds are optimal, such as sink-source complete bipartite digraphs or symmetric balanced incomplete block designs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
B. Afshari, M. T. Saadati, R. Saadati
Summary: The text discusses the relationship between the Laplacian spectral radius of the graph G and related parameters, proving two inequalities for lambda(G) under certain conditions, involving concepts such as graph connectivity and maximum degree.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Peng-Li Zhang, Xiao-Dong Zhang
Summary: This paper presents lower bounds for the difference between the A(alpha)-spectral radius and the irregularity measures of connected k-uniform hypergraphs, as well as two lower bounds on the A(alpha)-spectral radius in terms of the maximum and minimum degrees of uniform hypergraphs.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
Zhi-Feng Wei
Summary: Using spectral embedding based on the probabilistic signless Laplacian, this article provides bounds on the spectrum of transition matrices on graphs. These bounds lead to constraints on return probabilities and uniform mixing time of simple random walk on graphs. In addition, spectral embedding is used to bound the spectrum of graph adjacency matrices. The method used in this article is adapted from Lyons and Oveis Gharan [13].
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Yuy Zhang, Yidu Yang
Summary: This paper obtains guaranteed lower bounds for eigenvalues of two spectral problems in fluid mechanics by using the min-max principles of weak form derived from operator forms. The positive semi-definiteness of associated bilinear forms is handled by adding constraints to the solution and finite element spaces. Numerical experiments are conducted to validate the theoretical results.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Physics, Multidisciplinary
Oskar Slowik, Adam Sawicki
Summary: Currently available quantum computers, known as Noisy Intermediate-Scale Quantum devices, have limited qubit numbers and moderate gate fidelities. Quantum error correction is currently impossible for these devices, resulting in modest performance and limited circuit depth. In this paper, lower bounds on the efficiency of universal sets of d-dimensional quantum gates are derived, using explicit bounds on the spectral gap at a certain scale. These bounds are applicable to physically feasible cases and can be determined through numerical calculations, providing a contrast to existing lower bounds that involve parameters with ambiguous values.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics
Yuzheng Ma, Yubin Gao, Yanling Shao
Summary: This study focuses on the generalized form of the reciprocal distance Laplacian matrix and its applications in graph theory. By investigating properties such as spectral radius and extremal graphs, it helps to provide a deeper understanding of the structure and characteristics of graphs.
Article
Mathematics, Applied
Zakaria El Allali, Evans M. I. I. I. I. Harrell
Summary: This passage characterizes the potential-energy functions V(x) that minimize the gap Gamma between the two lowest Sturm-Liouville eigenvalues. The study reveals that under the assumptions of convexity or single-well form, constant potentials can uniquely minimize Gamma for convex V, and a sharp bound of Gamma > 2.04575... is obtained for single-well potentials without restrictions on the position of the minimum.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Chunhong Fu, Jiajia Chen, Qingxiang Xu
Summary: This paper studies the Frobenius norm upper bounds and lower bounds of the unique solution to AX + XB = AC + DB, with improvements made to known results. Numerical tests demonstrate the sharpness of the newly obtained upper bounds, and numerical examples associated with the positivity of lower bounds are provided.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Software Engineering
Bruno P. Cavalar, Zhenjian Lu
Summary: In this paper, the study of average-case complexity and circuit analysis algorithms for comparator circuits is initiated. By utilizing the technique of shrinkage under random restrictions, new results are obtained for this model. These results include average-case lower bounds for comparator circuits, SAT algorithms, and pseudorandom generators and MCSP lower bounds.
Article
Mathematics, Applied
Maria Adam, Iro Oikonomou, Aikaterini Aretaki
Summary: In this article, we present new lower and upper bounds for the spectral radius of nonnegative matrices based on consecutive k-th powers. These bounds are formulated using the average (k + 1)-row sums and extreme entries of the matrix and offer tighter approximations. We analyze the properties of these bounds, including monotonicity and convergence, and provide conditions under which they are sharper than existing formulae. We also explore the cases of equality in the bounds for irreducible matrices and provide illustrative numerical examples.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Optics
Mario A. Ciampini, Alvaro Cuevas, Paolo Mataloni, Chiara Macchiavello, Massimiliano F. Sacchi
Summary: An experimental procedure using a fixed bipartite entangled state was demonstrated to certify the classical capacity for noisy qubit channels without resorting to full quantum process tomography. The method reconstructs sets of conditional probabilities, performs noise deconvolution, and optimizes the mutual information to achieve a witness to the classical capacity. The measured lower bounds showed high agreement with simulated data, considering experimental entanglement fidelity and imperfections.
Article
Quantum Science & Technology
Tristan Benoist, Lisa Haenggli, Cambyse Rouze
Summary: In this paper, we provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. By introducing and developing new non-commutative functional inequalities, we derive concentration inequalities for stochastic processes that satisfy these bounds. Additionally, we obtain an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form.
Article
Mechanics
H. Aibara, Z. Yoshida
Summary: This study examines the lower bounds on zonal enstrophy in two-dimensional barotropic flow, finding that energy, impulse, circulation, and total enstrophy serve as constraints in minimizing zonal enstrophy. The corresponding variational principle has a unique mathematical structure, with constraints working in an interesting way.
JOURNAL OF FLUID MECHANICS
(2021)
