Results 31 to 40 of about 1,994 (184)

An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

Special Matrices, 2021
A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.
Hutchinson George
doaj   +1 more source

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix [PDF]

, 2017
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite).
openaire   +2 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Real factorization of positive semidefinite matrix polynomials

Linear Algebra and its Applications
Suppose $Q(x)$ is a real $n\times n$ regular symmetric positive semidefinite matrix polynomial. Then it can be factored as $$Q(x) = G(x)^TG(x),$$ where $G(x)$ is a real $n\times n$ matrix polynomial with degree half that of $Q(x)$ if and only if $\det(Q(x))$ is the square of a nonzero real polynomial.
Sarah Gift, Hugo J. Woerdeman
openaire   +2 more sources

Ising Solver Using Vertical NAND Flash Memory

Advanced Intelligent Systems, EarlyView.
Commercial V‐NAND flash memory is repurposed as a discrete‐time Ising solver by exploiting in‐memory current summation and read‐voltage‐controlled intrinsic noise. The system implements Hopfield neural‐network updates with simulated‐annealing‐like behavior, solving max‐cut problems with high accuracy and energy efficiency while using mass‐produced ...
Sung‐Ho Park, Yeongheon Yang, Jong‐Won Back, Jiseong Im, Ryun‐Han Koo, Jonghyun Ko, Dongseok Kwon, Jong‐Ho Lee   +7 more
wiley   +1 more source

Overcoming the Phase Discontinuity Problem in RIS Optimization: A Robust and Scalable Phase‐Aware Deep Regression Framework via Hybrid CNN–LSTM Architecture

Advanced Intelligent Systems, EarlyView.
The phase discontinuity problem—where the cyclic nature of phase angles causes catastrophic errors near the ±π boundary—is a fundamental obstacle in learning‐based reconfigurable intelligent surface (RIS) optimization. A phase‐aware hybrid CNN–LSTM framework resolves this by decomposing phase predictions into sine–cosine components, mapping circular ...
Seda Savaşçı Şen, Ali Çalhan, Murtaza Cicioğlu, Oğuzhan Demiryürek   +3 more
wiley   +1 more source

Purifications of multipartite states: limitations and constructive methods

New Journal of Physics, 2013
We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D ; and (ii) as a purification that is written as a ...
Gemma De las Cuevas, Norbert Schuch, David Pérez-García, J Ignacio Cirac   +3 more
doaj   +1 more source

The Unintended Consequences of Sugar‐Sweetened Beverage Taxes on Sales and Prices of Beer Beverages

Health Economics, EarlyView.
ABSTRACT This paper estimates the causal effect of Berkeley's sugar‐sweetened beverage (SSB) tax on beer purchases and prices using retail scanner data from 2014 to 2015. Applying both synthetic control and difference‐in‐differences (DID) approaches, we find that the tax reduced beer purchases within Berkeley by 8.9%, while having a negligible effect ...
Lei Pan, Xiaoyong Zheng
wiley   +1 more source

有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)

Zhejiang Daxue xuebao. Lixue ban, 2019
In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成), HENingxin(贺宁馨)   +1 more
doaj   +1 more source

On the range of a Hadamard power of a positive semidefinite matrix

Linear Algebra and its Applications, 2006
For a polynomial mapping \(F:\mathbb{C}^n\to\mathbb{C}^n\) the Jacobian conjecture asserts that \(F\) is invertible if \(JF\in\mathbb{C}^*\), where \(JF\) denotes the Jacobian matrix of \(F\). \textit{L. M. Druzkowski} [Math. Ann. 264, 303--313 (1983; Zbl 0504.13006)] showed that it suffices to prove the Jacobian conjecture for all cubic-linear ...
Sun, Xiaosong, Du, Xiankun, Liu, Dayan
openaire   +1 more source