A calibrated model of local food system of Hawaii: What are the economic implications of the state's food goals and policies?

We develop a fully calibrated positive mathematical programming model for Hawaii's local food systems—which captures the production and the consumer sides of the market. Then we use the model to assess two proposed policies—a general excise tax (GET) exemption on locally produced foods, and an investment in agricultural infrastructure. For the GET exemption case, our results indicate an economic gain of $118 per $100 cost. On the other hand, an investment in 1,200 acres of land injected to support local production may generate an economic gain of up to $357 per $100 annual cost of the investment. However, these estimates should be considered preliminary, and thus viewed with caution. Although the model is used to capture Hawaii's local food systems, we believe that our model is generalizable and can be adopted by other economies to assess their respective food localization policies. Recommendations for Resource Managers

• Local food policies need to be based on quantitative terms instead of mere armchair speculation because often their potential outcomes may vary significantly.

• The current modeling framework demonstrates the potential of using positive mathematical programming (PMP) in capturing the intricacies of local food systems. However, this exploratory exercise should be viewed as preliminary in nature and the ensuing results were taken with caution because many important factors such as labor availability may have been left out.

• Thus, further model refinements are necessary to better capture the complexities of local food systems such as farm heterogeneity, availability of farm labor, water availability, and interisland transportation of farm products in the case of Hawaii.

     

Painlevé analysis,lump-kink solutions and localized excitation solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

In this paper the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is investigated. The integrability test is performed yielding a positive result. Through the Painlevé–Bäcklund transformation, we derive four types of lump-kink solutions composed of two quadratic functions and N exponential functions. It is shown that fission and fusion interactions occur in the lump-kink solutions. Furthermore, a new variable separation solution with two arbitrary functions is obtained, the localized excitations including lumps, dromions and periodic waves are analyzed by some graphs.     

Using block designs in crossing number bounds

The crossing number $\mathrm{\text{CR}}\left(G\right)$ of a graph $G=\left(V,E\right)$ is the smallest number of edge crossings over all drawings of $G$ in the plane. For any $k\ge 1$, the $k$‐planar crossing number of $G,{\mathrm{\text{CR}}}_k\left(G\right)$, is defined as the minimum of $\text{CR}\left(G_1\right)+\text{CR}\left(G_2\right)+?+\text{CR}\left(G_k\right)$ over all graphs $G_1,G_2,\dots ,G_k$ with ${\cup }_{i=1}^k{G}_i=G$. Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every $k\ge 1$, we have ${\text{CR}}_k\left(G\right)\le (2/k^2?1/k^3)\text{CR}\left(G\right)$ and that this bound does not remain true if we replace the constant $2/k^2?1/k^3$ by any number smaller than $1/k^2$. We improve the upper bound to $(1/k^2)\left(1+o\left(1\right)\right)$ as $k\to \infty$. For the class of bipartite graphs, we show that the best constant is exactly $1/k^2$ for every $k$. The results extend to the rectilinear variant of the $k$‐planar crossing number.     

Embedding hypertrees into steiner triple systems

In this paper, we are interested in the following question: given an arbitrary Steiner triple system on vertices and any 3‐uniform hypertree on vertices, is it necessary that contains as a subgraph provided ? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.