Non-degeneracy of solution for critical Lane-Emden systems with linear perturbation

In this paper, we consider the following elliptic system \begin{equation*} \begin{cases} -\Delta u = |v|^{p-1}v +\epsilon(\alpha u + \beta_1 v), &\hbox{ in }\Omega, \\-\Delta v = |u|^{q-1}u+\epsilon(\beta_2 u +\alpha v), &\hbox{ in }\Omega, \\u=v=0,&\hbox{ on }\partial\Omega, \end{cases} \end{equation*} where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq 3$, $\epsilon$ is a small parameter, $\alpha$, $\beta_1$ and $\beta_2$ are real numbers, $(p,q)$ is a pair of positive numbers lying on the critical hyperbola \begin{equation*} \begin{split} \frac{1}{p+1}+\frac{1}{q+1} =\frac{N-2}{N}. \end{split} \end{equation*} We first revisited the blowing-up solutions constructed in \cite{Kim-Pis} and then we proved its non-degeneracy. We believe that the various new ideas and technique computations that we used in this paper would be very useful to deal with other related problems involving critical Halmitonian system and the construction of new solutions.Comment: 44pag

DualMotion: Global-to-Local Casual Motion Design for Character Animations

Animating 3D characters using motion capture data requires basic expertise and manual labor. To support the creativity of animation design and make it easier for common users, we present a sketch-based interface DualMotion, with rough sketches as input for designing daily-life animations of characters, such as walking and jumping.Our approach enables to combine global motions of lower limbs and the local motion of the upper limbs in a database by utilizing a two-stage design strategy. Users are allowed to design a motion by starting with drawing a rough trajectory of a body/lower limb movement in the global design stage. The upper limb motions are then designed by drawing several more relative motion trajectories in the local design stage. We conduct a user study and verify the effectiveness and convenience of the proposed system in creative activities.Comment: 10 pages, 10 figures, under submission, video is here https://youtu.be/-tk8q8LSiL

Cost Allocation in PPP Projects: An Analysis Based on the Theory of “Contracts as Reference Points”

In recent years, the demand for infrastructure has been largely driven by the economic development of many countries. PPP has proved to be an efficient way to draw private capital into public utility construction, where ownership allocation becomes one of the most important clauses to both the government and the private investor. In this paper, we establish mathematical models to analyze the equity allocation problem of PPP projects through a comparison of the models with and without the effects of the theory of “contracts as reference points.” We then derive some important conclusions from the optimal solution of the investment ratio

Towards Visualization of Time-Series Ecological Momentary Assessment (EMA) Data on Standalone Voice-First Virtual Assistants.

Population aging is an increasingly important consideration for health care in the 21th century, and continuing to have access and interact with digital health information is a key challenge for aging populations. Voice-based Intelligent Virtual Assistants (IVAs) are promising to improve the Quality of Life (QoL) of older adults, and coupled with Ecological Momentary Assessments (EMA) they can be effective to collect important health information from older adults, especially when it comes to repeated time-based events. However, this same EMA data is hard to access for the older adult: although the newest IVAs are equipped with a display, the effectiveness of visualizing time-series based EMA data on standalone IVAs has not been explored. To investigate the potential opportunities for visualizing time-series based EMA data on standalone IVAs, we designed a prototype system, where older adults are able to query and examine the time-series EMA data on Amazon Echo Show - a widely used commercially available standalone screen-based IVA. We conducted a preliminary semi-structured interview with a geriatrician and an older adult, and identified three findings that should be carefully considered when designing such visualizations