Existence of multi-bump solutions for a system with critical exponent in RN

We consider the following system with critical exponent in ${\mathbb{R}}^N$:$\{\begin{array}{c}?\mathrm{\Delta }u=K_1(y)u^{2^{?}?1}+\frac{p}{2^{?}}V(y)u^{p?1}{v}^q\text{in}{\mathbb{R}}^N,\hfill \\ ?\mathrm{\Delta }v=K_2(y)v^{2^{?}?1}+\frac{q}{2^{?}}V(y)u^p{v}^{q?1}\text{in}{\mathbb{R}}^N,\hfill \\ u,v>0,y\in {\mathbb{R}}^N,\hfill \end{array}$ where $N\ge 5$, $p,q>1$ and $p+q=2^{?}=\frac{2N}{N?2}$. Using finite dimensional reduction method, we prove the existence of multi-bump solutions. Their bumps can be placed on arbitrarily many or even infinitely many lattice points in ${\mathbb{R}}^N$. Since $p<2$ or $q<2$, we introduce two new norms to avoid singularity.     

Characterizations of modalities and lex modalities

A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.     

Distinguishing and quantification of the human visual pathways using high-spatial-resolution diffusion tensor tractography

Quantification of the living human visual system using MRI methods has been challenging, but several applications demand a reliable and time-efficient data acquisition protocol. In this study, we demonstrate the utility of high-spatial-resolution diffusion tensor fiber tractography (DTT) in reconstructing and quantifying the human visual pathways. Five healthy males, age range 24–37 years, were studied after approval of the institutional review board (IRB) at The University of Texas Health Science Center at Houston. We acquired diffusion tensor imaging (DTI) data with 1-mm slice thickness on a 3.0-Tesla clinical MRI scanner and analyzed the data using DTT with the fiber assignment by continuous tractography (FACT) algorithm. By utilizing the high-spatial-resolution DTI protocol with FACT algorithm, we were able to reconstruct and quantify bilateral optic pathways including the optic chiasm, optic tract, optic radiations free of contamination from neighboring white matter tracts.     

Development of in-wheel sensor system for accurate measurement of wheel terrain interaction characteristics

Planetary rovers need high mobility on a rough terrain such as sandy soil, because such a terrain often impedes the rover mobility and causes significant wheel slip. Therefore, the accurate estimation of wheel soil interaction characteristics is an important issue. Recent studies related to wheel soil interaction mechanics have revealed that the classical wheel model has not adequately addressed the actual interaction characteristics observed through experiments. This article proposes an in-wheel sensor system equipped with two sensory devices on the wheel surface: force sensors that directly measure the force distribution between the wheel and soil and light sensors that accurately detect the wheel soil surface boundary line. This sensor design enables the accurate measurement of wheel terrain interaction characteristics such as wheel force distribution, wheel–soil contact angles, and wheel sinkage when the powered wheel runs on loose sand. In this article, the development of the in-wheel sensor system is introduced along with its system diagram and sensor modules. The usefulness of the in-wheel sensor system is then experimentally evaluated via a single wheel test bench. The experimental results confirm that explicit differences can be observed between the classical wheel model and practical data measured by the in-wheel sensor system.     

Biomimetic epoxidation in aqueous media catalyzed by cyclic dipeptides

We have developed a practical epoxidation of electron-deficient enones in aqueous media using cyclic dipeptides as bioinspired green catalyst. Optimizing the reaction conditions in a triphasic system led to efficient conditions providing epoxides with good enantioselectivities. Depending on the catalyst substituent chirality, both enantiomers are obtained. The cyclic rigidity impacts significantly the enantioselectivity.     

Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate long-time simulations. As an exponential integrator, the new scheme allows us to use large time steps compared to the size of the oscillations in the solution.     

Surplus division and investment incentives in supply chains: A biform-game analysis

In this paper, we use a biform-game approach for analyzing the impact of surplus division in supply chains on investment incentives. In the first stage of the game, firms decide non-cooperatively on investments. In the second stage, the surplus is shared according to the Shapley value. We find that all firms have inefficiently low investment incentives which, however, depend on their position in the supply chain. Cross-subsidies for investment costs can mitigate, but not eliminate the underinvestment problem. Vertical integration between at least some firms.yields efficient investments, but may nevertheless reduce the aggregated payoff of the firms. We show how the size of our effects depends on the structure of the supply chain and the efficiency of the investment technology. Various extensions demonstrate that our results are qualitatively robust.     

Proton transfer-assisted host–guest complexation between a difunctional pillar[5]arene and amine-based guests

Proton transfer from a difunctional pillar[5]arene containing two carboxylic acid moieties to amine-based guests occurs in the host–guest complexation. The binding affinities are enhanced effectively due to the existence of electrostatic interactions.     

Global dynamics of a reaction–diffusion system with mass conservation

We study global dynamics of a mass conserved reaction–diffusion system. First, we show the global-in-time existence of the solution with compact orbit. Then the dynamical stability of local minima associated with a variational function is proven.