Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?

The Miller–Tucker–Zemlin (MTZ) Subtour Elimination Constraints (SECs) and the improved version by Desrochers and Laporte (DL) have been and are still in regular use to model a variety of routing problems. This paper presents a systematic way of deriving inequalities that are more complicated than the MTZ and DL inequalities and that, in a certain way, “generalize” the underlying idea of the original inequalities. We present a polyhedral approach that studies and analyses the convex hull of feasible sets for small dimensions. This approach allows us to generate generalizations of the MTZ and DL inequalities, which are “good” in the sense that they define facets of these small polyhedra. It is well known that DL inequalities imply a subset of Dantzig–Fulkerson–Johnson (DFJ) SECs for two-node subsets. Through the approach presented, we describe a generalization of these inequalities which imply DFJ SECs for three-node subsets and show that generalizations for larger subsets are unlikely to exist. Our study presents a similar analysis with generalizations of MTZ inequalities and their relation with the lifted circuit inequalities for three node subsets.     

Viscous dissipation effect on heat transfer characteristics of rectangular microchannels under slip flow regime and H1 boundary conditions

Viscous dissipation effect on heat transfer characteristics of a rectangular microchannel is studied. Flow is governed by the Navier–Stokes equations with the slip flow and temperature jump boundary conditions. Integral transform technique is applied to derive the temperature distribution and Nusselt number. The velocity distribution is taken from literature. The solution method is verified for the case where viscous dissipation is neglected. It is found that, the viscous dissipation is negligible for gas flows in microchannels, since the contribution of this effect on Nu number is about 1%. However, this effect should be taken into account for much more viscous flows, such as liquid flows. Neglecting this effect for a flat microchannel with an aspect ratio of 0.1 for Br=0.04 underestimates the Nu number about 5%.     

Symplectic tori in rational elliptic surfaces

Let E(1)_p denote the rational elliptic surface with a single multiple fiber f_p of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive 2-dimensional homology class [f_p] in E(1)_p when p>1. As a consequence, we get infinitely many non-isotopic symplectic tori in the fiber class of the rational elliptic surface . We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.     

Minimal Surfaces in Three-Dimensional Riemannian Manifold Associated with a Second-Order ODE

We show that a surface corresponding to a first-order ODE is minimal in three-dimensional Riemannian manifold which is determined by the first prolongation of \({\text {d}}y/\mathrm{d}x=p(x,y)\) if and only if \(p_{yy}=0\). Accordingly, any linear first-order ODE describes a minimal surface which is not necessarily totally geodesic.     

The unique minimal dual representation of a convex function

Suppose (i) X is a separable Banach space, (ii) C is a convex subset of X that is a Baire space (when endowed with the relative topology) such that aff(C) is dense in X, and (iii) f:C→R is locally Lipschitz continuous and convex. The Fenchel-Moreau duality can be stated as

     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.     

Wearable Sweat Sensors: Background and Current Trends

Sweat‐related physiology research has been well established over the years. However, it has only been around ten years that sweat‐based sensing devices started to be explored. With the recent advancements in wearable activity and physiology monitoring devices, sweat was investigated for its contents similar to blood and corresponding wearable devices were studied intensively. This article provides a thorough review on sweating mechanisms, sweat sensing devices, and electronic technologies for sweat sensor implementations. Potential future directions and recommendations based on current research trends were provided in each section. This review aims to offer a unique perspective from both physiology and engineering point‐of‐view to draw a complete landscape of the sweat sensing research.