Powers of vertex cover ideals of simplicial trees

Abstract

In 2011, Herzog et al. conjectured that if J is the cover ideal of a chordal graph, then is componentwise linear for all . In 2022, Hà and Van Tuyl considered objects more general than chordal graphs and posed the following problem: let be the cover ideal of a simplicial tree Γ. Is it true that is componentwise linear for all In this paper, we give an affirmative answer to this problem.

A Review of Epidermal Flexible Pressure Sensing Arrays

“…Metal-and carbon-based materials are also widely used in flexible sensing arrays because of their extraordinary flexibility, fantastic electrical conductivity, biocompatibility, and a series of other advantages. These functional materials determine the overall performance of the sensor [24].…”

“…Metal-and carbon-based materials are also widely used in flexible sensing arrays because of their extraordinary flexibility, fantastic electrical conductivity, biocompatibility, and a series of other advantages. These functional materials determine the overall performance of the sensor [24]. In this section, flexible materials are introduced in three main aspects: substrate materials, electrode materials, and sensitive layer materials.…”

“…PDMS has extraordinary flexibility and chemical stability [24] and is often used to make flexible pressure sensing arrays with fantastic sensitivity. In addition, PDMS has excellent mechanical properties with a Young's modulus of 2.2 ± 0.2 MPa [42], which is shown in Figure 2 in comparison with the skin modulus of elasticity [43].…”

“…The materials used for flexible wearable pressure sensing arrays are generally classified as carbon-based materials [14][15][16], metallic materials [17,18], polymeric materials [19,20], and some new materials [21,22]. Polymers such as polydimethylsiloxane (PDMS), polyethylene terephthalate (PET), polyimide (PI), Ecoflex, and polyurethane (PU) that have excellent biocompatibility, a low Young's modulus, and ductility [23,24] would allow sensing arrays to better fit the skin for the purpose of collecting weak physiological signals. Liquid metal, carbon-based materials, and some new materials such as poly (3,4-ethylenedioythiophene):poly(styrenesulfonate) (PEDOT:PSS) possess fantastic electrical conductivity as electrode materials [7], and various electrode material systems are described in order to help researchers develop electrodes with more excellent properties.…”