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It is shown that (special) relativistically dilated time is the vector sum of rest time and time induced by movement in three dimensional space exeeding the rest time component and that the first vector is orthogonally directed relative to…
The study of correlations between brain regions is an important chapter of the analysis of large-scale brain spatiotemporal dynamics. In particular, novel methods suited to extract dynamic changes in mutual correlations are needed. Here we…
The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision,…
In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…
Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the PT symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
Recently, Bapat and Kurata [\textit{Linear Algebra Appl.}, 562(2019), 135-153] defined the Cartesian product of two square matrices $A$ and $B$ as $A\oslash B=A\otimes \J+\J\otimes B$, where $\J$ is the all one matrix of appropriate order…
Herein it is shown that mass and time in the rest frame as well as relativistically enlarged mass and dilated time in the moving frame are of like origin. This implies that the former are generated by the movement of a fourth spatial…
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…
Let $D$ be an oriented link diagram with the set of regions $\operatorname{r}_{D}$. We define a symmetric map (or matrix) $\operatorname{\tau}_{D}\colon\operatorname{r}_{D}\times \operatorname{r}_{D} \to \mathbb{Z}[x]$ that gives rise to an…
This short note provides an explicit description of the Fr\'echet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fr\'echet derivatives of…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
The evolute of a plane curve is the envelope of its normals. Replacing the normals by the lines that make a fixed angle with the curve yields a new curve, called the evolutoid. We prefer the term ``skew evolute", and we study the geometry…
The problem of finding a generic star product on R^n is reduced to the computation of a skew-symmetric biderivation.
We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special…
An instantaneous time mirror (ITM) is an interesting approach to manipulate wave propagation from the time boundaries. In the time domain, the reversed wave is previously proven to be the temporal derivative of the original pattern. Here,…
Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has…
The logarithmic corotational derivative is a key concept in rate-type constitutive relations in continuum mechanics. The derivative is defined in terms of the logarithmic spin tensor, which is a skew-symmetric tensor/matrix given by a…