Results 21 to 30 of about 13,270 (218)

Cramer’s rules for the system of quaternion matrix equations with η-Hermicity

4 open, 2019
The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1 A 1 X A 1 η * = C 1 $ {\mathbf{A}}_1\mathbf{X}{\mathbf{A}}_1^{\eta \mathrm{*}}={\mathbf{C}}_1$ , A2XA2η* = C2 A 2 X A 2 η ...
Kyrchei Ivan I.
doaj   +1 more source

CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA

Barekeng
A min-plus algebra is a set ,  where  is the set of all real numbers, equipped with the minimum  and addition  operations. The system of linear equations  in min-plus algebra can be solved using Cramer's rule.
Siswanto Siswanto, Ade Safira Septiany
doaj   +1 more source

Berezinians, Exterior Powers and Recurrent Sequences

, 2003
We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations
A. Connes, A.N. Sergeev, A.N. Sergeev, H. M. Khudaverdian, H. Weyl, I. Gelfand, I. Kantor, I. Kantor, I. Kantor, I.G. Macdonald, J.N. Bernstein, M.J. Bergvelt, TH. TH. Voronov, V.G. Kac   +13 more
core   +3 more sources

Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations

Journal of Mathematics, 2018
Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion ...
Ivan I. Kyrchei
doaj   +1 more source

Fluid Biomarkers of Disease Burden and Cognitive Dysfunction in Progressive Supranuclear Palsy

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Identifying objective biomarkers for progressive supranuclear palsy (PSP) is crucial to improving diagnosis and establishing clinical trial and treatment endpoints. This study evaluated fluid biomarkers in PSP versus controls and their associations with regional 18F‐PI‐2620 tau‐PET, clinical, and cognitive outcomes.
Roxane Dilcher, Charles B. Malpas, Stuart J. McDonald, William T. O’Brien, Craig Despott, Kelly L. Bertram, Matthew P. Pase, Lukas Frontzkowski, Meng Law, Terence J. O’Brien, Lucy Vivash   +10 more
wiley   +1 more source

On Quasilinear Algebra of Linear Interval Equations and Interval Cramer’s Rule

Mathematics
Determining the solution set of a system of linear interval equations is often a difficult task. Establishing a general theory that includes the classical theory of systems of linear equations as a special case opens the door to extensive and challenging
Yılmaz Yılmaz
doaj   +1 more source

Mesoscale Recovery of Microglial and Neuronal Dynamics After Craniotomy Across Wide Cortex in Transgenic Mice

Advanced Science, EarlyView.
This study employs longitudinal fluorescence imaging in transgenic mice to map post‐craniotomy cortical recovery. We identify distinct neuroimmune recovery phases: microglial structural inflammation peaks at ∼10 days, neuronal structural intensity peaks at ∼14 days and correlates with microglial activity, and functional network modularity is most ...
Guihua Xiao, Zhilei Wang, Pengchang Zheng, Jingyu Xie, Yangzhen Wang, Yun Chen, Zilin Wang, Ao Li, Minghuan Wang, Quanbo Ji, Can Gao, Di Yao, Lingbo Li, Jiangbei Cao   +13 more
wiley   +1 more source

High‐Fidelity Synthetic Data Replicates Clinical Prediction Performance in a Million‐Patient Diabetes Cohort

Advanced Science, EarlyView.
This study generates high‐fidelity synthetic longitudinal records for a million‐patient diabetes cohort, successfully replicating clinical predictive performance. However, deeper analysis reveals algorithmic biases and trajectory inconsistencies that escape standard quality metrics. These findings challenge current validation norms, demonstrating why a
Francisco Ortuño, Víctor M. de la Oliva Roque, Javier‐Ignacio Ramirez‐Lopez, David P. Kreil, Joaquín Dopazo, Carlos Loucera   +5 more
wiley   +1 more source

A novel interpretation of least squares solution

International Journal of Mathematics and Mathematical Sciences, 1992
We show that the well-known least squares (LS) solution of an overdetermined system of linear equations is a convex combination of all the non-trivial solutions weighed by the squares of the corresponding denominator determinants of the Cramer's rule ...
Jack-Kang Chan
doaj   +1 more source

Beyond Transconductance: Cell‐Polymer Coupling Determines Fidelity in Action Potential Recording via Electrolyte‐Gated Polymer Transistors

Advanced Science, EarlyView.
High electrical performance alone does not guarantee efficient bioelectronic signal transduction. Despite excellent mixed ionic‐electronic conduction, recordings from cardiomyocytes reveal that p(g2T‐TT)‐based OECTs predominantly transduce field potential FP‐like signals due to weak cell‐polymer coupling.
Giulia Zoe Zemignani, Elena Mancinelli, Gabriele Tullii, Aleksandr Khudiakov, Cristiano Bortolotti, Shubham Tanwar, Peter J. Schwartz, Luca Sala, Maria Rosa Antognazza, Mario Caironi, Adrica Kyndiah   +10 more
wiley   +1 more source