Results 21 to 30 of about 2,396 (56)

A note on Johansen's rank conditions and the Jordan form of a matrix

Journal of Time Series Analysis, Volume 46, Issue 4, Page 796-805, July 2025.
This note presents insights on the Jordan structure of a matrix which are derived from an extension of the I(1) and I(2) conditions in Johansen (1996). It is first observed that these conditions not only characterize, as it is well known, the size (1 or 2) of the largest Jordan block in the Jordan form of the companion matrix but more generally the ...
Massimo Franchi
wiley   +1 more source

N$N$‐Soliton Matrix mKdV Solutions: Some Special Solutions Revisited

Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.
ABSTRACT In this article, a general solution formula is derived for the d×d${\sf d}\times {\sf d}$‐matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as N$N$‐solitons (in the sense of Goncharenko) with common phase matrix. It turns out
Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold   +2 more
wiley   +1 more source

The Granger–Johansen representation theorem for integrated time series on Banach space

Journal of Time Series Analysis, Volume 46, Issue 3, Page 432-457, May 2025.
We prove an extended Granger–Johansen representation theorem (GJRT) for finite‐ or infinite‐order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is analytic on and inside the unit circle except for an isolated singularity at unity.
Phil Howlett, Brendan K. Beare, Massimo Franchi, John Boland, Konstantin Avrachenkov   +4 more
wiley   +1 more source

Mean‐field limit of non‐exchangeable systems

Communications on Pure and Applied Mathematics, Volume 78, Issue 4, Page 651-741, April 2025.
Abstract This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent systems consisting of non‐identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis but also graph theory through a new concept ...
Pierre‐Emmanuel Jabin, David Poyato, Juan Soler   +2 more
wiley   +1 more source

Jordan weak amenability and orthogonal forms on JB*-algebras [PDF]

, 2014
We prove the existence of a linear isometric correspondence between the Banach space of all symmetric orthogonal forms on a JB$^*$-algebra $\mathcal{J}$ and the Banach space of all purely Jordan generalized derivations from $\mathcal{J}$ into $\mathcal{J}
A. Siddiqui, Akhlaq, Antonio M. Peralta, Fatmah B. Jamjoom   +3 more
core  

From the conformal anomaly to the Virasoro algebra

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract The conformal anomaly and the Virasoro algebra are fundamental aspects of two‐dimensional conformal field theory and conformally covariant models in planar random geometry. In this article, we explicitly derive the Virasoro algebra from an axiomatization of the conformal anomaly in terms of real determinant lines, one‐dimensional vector spaces
Sid Maibach, Eveliina Peltola
wiley   +1 more source

Solvability and uniqueness of solution of generalized ★$\star$‐Sylvester equations with arbitrary coefficients

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We analyze the consistency and uniqueness of solution of the generalized ★$\star$‐Sylvester equation AXB+CX★D=E$AXB+CX^\star D=E$, with A,B,C,D$A,B,C, D$, and E$E$ being complex matrices (and ★$\star$ being either the transpose or the conjugate transpose). In particular, we obtain characterizations for the equation to have at most one solution
Fernando De Terán, Bruno Iannazzo
wiley   +1 more source

Asymptotics of block Toeplitz determinants with piecewise continuous symbols

Communications on Pure and Applied Mathematics, Volume 78, Issue 1, Page 120-160, January 2025.
Abstract We determine the asymptotics of the block Toeplitz determinants detTn(ϕ)$\det T_n(\phi)$ as n→∞$n\rightarrow \infty$ for N×N$N\times N$ matrix‐valued piecewise continuous functions ϕ$\phi$ with a finitely many jumps under mild additional conditions.
Estelle Basor, Torsten Ehrhardt, Jani A. Virtanen   +2 more
wiley   +1 more source

Integer–Fractional Order of Identical Eigenvalues Chaotic Oscillator: Analysis and Shadow Economy Application

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
This study introduces a new three‐dimensional chaotic oscillator system characterized by zero eigenvalues, with stability localized in the center manifold, an uncommon feature in chaotic system design. The proposed system is constructed entirely from nonlinear terms and demonstrates complex dynamics validated through bifurcation analysis and Lyapunov ...
Ali Shukur, Faruk Ozger, Nasser Saeed, Surma Ibrabim, Viet-Thanh Pham, Giuseppe Grassi, Peiguang Wang   +6 more
wiley   +1 more source

Derivations and Extensions in JC‐Algebras

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
A well‐known result by Upmeier states that every derivation on a universally reversible JC‐algebra A⊆B(H)sa extends to the C∗‐algebra [A] generated by A in B(H). In this paper, we significantly strengthen this result by proving that every Jordan derivation on a universally reversible JC‐algebra A extends to ∗‐derivations on its universal enveloping ...
Fatmah B. Jamjoom, Doha A. Abulhamail, Armando Sánchez-Nungaray   +2 more
wiley   +1 more source