In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of ecomputability and we use it to prove that Strassen’s conjecture holds in infinitely many new cases.
Given a real projective plane S embedded in a 4？manifold X4 with Euler number 2 or ？？2, the Price twist is a surgery operation on .S/ yielding (up to) three different 4？manifolds: X4 , S.X4/ and ？S.X4/. This is of particular interest when X4 D S4 ,as then ？S.X4/ is a homotopy 4？sphere which is not obviously diffeomorphic to S4 . Here we show how to produce a trisection deion of each Price twist on S X4 by producing a relative trisection of X4 n .S/. Moreover, we show how to produce a trisection deion of general surface complements in 4？manifolds.
To estimate the causal impact of a change in the national health insurance policy to cover the cost of respiratory syncytial virus (RSV) antigen testing on the incidence of RSV infection by age-groups, we analyzed the sentinel datasets of RSV infection in Japan from 2009？2017.
The orthogonality sampling method (OSM) is a recently developed non-iterative technique for imaging and identifying targets in inverse scattering problems.
The recovery of 3D left ventricle(LV) shape using 2D echocardiography is very attractable topic in the field of ultrasound imaging. In this paper, we propose a mathematical model to determine the 3D position of LV contours extracted from multiple 2D echocardiography images.
We extend the classical Allen？Cahn (AC) equation to the fractional Allen？Cahn equation (FAC) with triple-well potential. By replacing the spatial Laplacian and double-well potential with fractional Laplacian and triple-well potential, we observe different dynamics.
n this paper, we take into account a two-dimensional inverse scattering problem for localizing small electromagnetic anomalies when they are surrounded by small, randomly distributed electromagnetic scatterers.
The aims of this study were to determine the predictive value of decision support analysis for the shock wave lithotripsy (SWL) success rate and to analyze the data obtained from patients who underwent SWL to assess the factors influencing the outcome by using machine learning methods.
In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author’s knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author’s previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability.
We study the effects of coupling strength inhomogeneity and coupling functions on locking behaviors of coupled identical oscillators, some of which are relatively weakly coupled to others while some are relatively strongly coupled.