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Thermal desorption (TD) has been widely used for remediation of soils contaminated with volatile/semi-volatile contaminants. There is a need to reduce the temperature of TD technology to minimize energy consumption and soil damage. The effect of low-temperature TD coupled with steam injection (SI) on the remediation of PAH-contaminated soil was investigated in this study. It was shown that the addition of SI to the TD at both 150 and 250 °C improved the removal of LPAHs from soil, with better performance at 150 °C, especially for LPAHs with boiling points between 295 and 340 °C. In contrast, the addition of SI to the TD at both 150 and 250 °C reduced the removal of HPAHs from soil, particularly at 250 °C. Under TD at 150 °C, the removal of LPAHs and HPAHs were further promoted and limited with increasing SI flow rates, respectively. It was noted that the introduction of steam in the low-temperature TD only promoted the removal of LPAHs, and the effect was better with higher steam flow rate. The addition of 4 g/min steam to TD at 150 °C could accelerate 259.18% of the removal process of LPAHs, and could improve the removal of LPAHs by 17.88% while reducing the energy consumption by 29.18%. This promotion is likely attributed to the fact that the introduced steam facilitates the release of LPAHs inside the soil matrix through steam replacement, steam distillation, and stripping. In addition, the addition of SI to the TD has little effect on soil physicochemical properties. [ABSTRACT FROM AUTHOR]

Let X and Y be any two graphs of order n. The friends-and-strangers graph FS (X , Y) of X and Y is a graph with vertex set consisting of all bijections σ : V (X) → V (Y) , in which two bijections σ , σ ′ are adjacent if and only if they differ precisely on two adjacent vertices of X, and the corresponding mappings are adjacent in Y. The most fundamental question that one can ask about these friends-and-strangers graphs is whether or not they are connected. Let Lollipop n - k , k be a lollipop graph of order n obtained by identifying one end of a path of order n - k + 1 with a vertex of a complete graph of order k. Defant and Kravitz started to study the connectedness of FS (Lollipop n - k , k , Y) . In this paper, we give a sufficient and necessary condition for FS (Lollipop n - k , k , Y) to be connected for all 2 ≤ k ≤ n , which interpolates between two previous results on paths and complete graphs. [ABSTRACT FROM AUTHOR]

For given graphs G 1 , G 2 , ⋯ , G k , k ≥ 2 , the k-color Ramsey number, denoted by R (G 1 , G 2 , … , G k) , is the smallest integer N such that if we arbitrarily color the edges of a complete graph of order N with k colors, then it always contains a monochromatic copy of G i in color i, for some 1 ≤ i ≤ k . Let C m be a cycle of length m and W n a wheel of order n + 1 . In this paper, we show that R (C 4 , C 4 , W n) ≤ n + 4 n + 5 + 3 for n = 42 , 48 , 49 , 50 , 51 , 52 or n ≥ 56 . Furthermore, we prove that R (C 4 , C 4 , W ℓ 2 - ℓ) ≤ ℓ 2 + ℓ + 2 for ℓ ≥ 9 , and if ℓ is a prime power, then the equality holds. [ABSTRACT FROM AUTHOR]

For given 3-uniform hypergraphs H and G , the Ramsey number R (H , G) is the smallest number N such that each red-blue coloring of the edges of the complete 3-uniform hypergraph K N 3 contains either a red copy of H or a blue copy of G . Let C n 3 , P n 3 and S n 3 denote the 3-uniform loose cycle, loose path and star with n edges, respectively. The 2-color Ramsey number of 3-uniform loose path and loose cycle has been determined completely by several researchers. In this paper, we prove that R (P m 3 , S n 3) = 2 n + 1 + m - 1 2 for all m, n with n ≥ 2 m ≥ 2 and R (P m 3 , S n 3) = 2 m + 1 for all m, n with m ≥ 9 4 n . [ABSTRACT FROM AUTHOR]

For two graphs G 1 and G 2 , the star-critical Ramsey number r ∗ (G 1 , G 2) is the minimum integer k such that any red/blue edge-coloring of K r - 1 ⊔ K 1 , k contains a red copy of G 1 or a blue copy of G 2 , where r is the classical Ramsey number R (G 1 , G 2) and K r - 1 ⊔ K 1 , k is the graph obtained from a K r - 1 and an additional vertex v by joining v to k vertices of K r - 1 . Let C n denote a cycle of order n and W m a wheel of order m + 1 . Hook (2010) proved that r ∗ (C n , W 3) = 2 n for n ≥ 5 . In this paper, it is shown that r ∗ (C n , W m) = 2 n for m odd, n ≥ m ≥ 5 and n ≥ 60 . [ABSTRACT FROM AUTHOR]

The generalized Turán number e x (n , K s , H) is defined to be the maximum number of copies of a complete graph K s in any H-free graph on n vertices. Let F be an even linear forest, that is, F consists of paths of even order. In this paper, we determine the value of e x (n , K s , F) , which generalizes or improves some known results on generalized Turán number and classical Turán number. [ABSTRACT FROM AUTHOR]

Let G = (V (G) , E (G)) be a graph and s, t integers with s ≤ t . If we can assign an s-subset ϕ (v) of the set { 1 , 2 , ... , t } to each vertex v of V(G) such that ϕ (u) ∩ ϕ (v) = ∅ for every edge u v ∈ E (G) , then G is called (t : s)-colorable, and such an assignment ϕ is called a (t : s)-coloring of G. Let C n denote a cycle of length n. In this paper, we show that every planar graph without C 4 and C 6 is (7 : 2)-colorable and thus has fractional chromatic number at most 7/2. [ABSTRACT FROM AUTHOR]

In the past ten years, researchers have always attached great importance to the application of ontology to its relevant specific fields. At the same time, applying learning algorithms to many ontology algorithms is also a hot topic. For example, ontology learning technology and knowledge are used in the field of semantic retrieval and machine translation. The field of discovery and information systems can also be integrated with ontology learning techniques. Among several ontology learning tricks, multi-dividing ontology learning is the most popular one which proved to be in high efficiency for the similarity calculation of tree structure ontology. In this work, we study the multi-dividing ontology learning algorithm from the mathematical point of view, and an approximation conclusion is presented under the linear representation assumption. The theoretical result obtained here has constructive meaning for the similarity calculation and concrete engineering applications of tree-shaped ontologies. Finally, linear combination multi-dividing ontology learning is applied to university ontologies and mathematical ontologies, and the experimental results imply that the higher efficiency of the proposed approach in actual applications. [ABSTRACT FROM AUTHOR]

For two given graphs G 1 and G 2 , the planar Ramsey number P R (G 1 , G 2) is the smallest integer N such that every planar graph G on N vertices either contains a copy of G 1 or its complement contains a copy of G 2 . In this paper, we determine all planar Ramsey numbers for the complete graphs versus trees. [ABSTRACT FROM AUTHOR]

For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or its complement G¯ contains G2. Let Pn,Sn and Tn denote a path, a star and a tree of order n, respectively. A generalized wheel, denoted by Ws,m, is the join of a complete graph Ks and a cycle Cm. In this paper, we show that R(Tn,Ws,4)=(n-1)(s+1)+1 for n≥3,s≥2 and R(Tn,Ws,5)=(n-1)(s+2)+1 for n≥3,s≥1. These generalize some known results on Ramsey numbers for a tree versus a wheel. [ABSTRACT FROM AUTHOR]

Purpose: Understanding the effect of biochar on surface albedo and soil CO2 fluxes is a crucial issue in evaluating the impact of biochar on carbon sequestration and greenhouse gas mitigation. In this study, we consider the following research questions: (1) Under bare soil and crop coverage conditions, do different dosages of biochar decrease the surface albedo? (2) How does the application of biochar affect soil CO2 fluxes? (3) What are the influencing factors of surface albedo and soil CO2 fluxes after biochar is applied?Materials and methods: We examined the influence of biochar applications on farmland on the surface albedo, soil CO2 flux, soil temperature, soil moisture, and soil organic carbon fractions over a period of 15 months. There are six treatments (CK+, CK−, BC5+, BC5−, BC45+, and BC45−) in this study, and three biochar application rates, which are as follows: 0 t ha−1 year−1 (CK), 5 t ha−1 year−1 (BC5), and 45 t ha−1 year−1 (BC45) of biochar, and each application is rated with two crop coverage conditions, a wheat-maize crop rotation (+) and bare soil (−).Results and discussion: We found that in the early stage of crop growth, the surface albedo of BC45+ and BC5+ were decreased significantly compared with the control treatment (P < 0.05). As the crop canopy structures developed, the surface albedo reduction weakened or even disappeared. Under the bare soil condition, the surface albedos of BC45− and BC5− was decreased significantly in most of the measurements (P < 0.05). The soil CO2 fluxes of the biochar treatments were increased significantly (P < 0.05). However, the growth rates of the soil CO2 fluxes of BC45+, BC5+, BC45−, and BC5− gradually decreased with time. The increase in the CO2 emissions of biochar treatments may be due to mineralization of the readily oxidizable organic carbon (e.g., water-soluble organic carbon) in the biochar-soil system. Adding biochar to the soil reduced the sensitivity of the soil respiration to temperature changes.Conclusions: The leaf area index is one of the factors that affects the surface albedo. The surface albedo did not decrease proportionally with the increase in biochar application. Readily oxidizable organic carbon played an important role in the soil CO2 emissions. The reduction of surface albedo caused by the biochar has no direct effect on soil CO2 fluxes. The findings were helpful in evaluating the effects of adding biochar to soil and its consequences for C sequestration in agricultural soils. [ABSTRACT FROM AUTHOR]

We consider proper edge colorings of a graph G using colors in $$\{1,\ldots ,k\}$$ . Such a coloring is called neighbor sum distinguishing if for each pair of adjacent vertices u and v, the sum of the colors of the edges incident with u is different from the sum of the colors of the edges incident with v. The smallest value of k in such a coloring of G is denoted by $${\mathrm ndi}_{\Sigma }(G)$$ . In this paper we show that if G is a 2-degenerate graph without isolated edges, then $${\mathrm ndi}_{\Sigma }(G)\le \max \{\Delta (G)+2,7\}$$ . [ABSTRACT FROM AUTHOR]

For two given graphs $$G_1$$ and $$G_2$$ , the planar Ramsey number $$PR(G_1,G_2)$$ is the smallest integer $$N$$ such that for any planar graph $$G$$ of order $$N$$ , either $$G$$ contains $$G_1$$ or the complement of $$G$$ contains $$G_2$$ . Let $$K_m$$ denote a complete graph of order $$m$$ and $$W_n$$ a wheel of order $$n+1$$ . In this paper, we determine all planar Ramsey numbers $$PR(K_m,W_n)$$ . [ABSTRACT FROM AUTHOR]

Given two graphs $$G_1$$ and $$G_2$$ , the Ramsey number $$R(G_1, G_2)$$ is the smallest integer $$N$$ such that, for any graph $$G$$ of order $$N$$ , either $$G_1$$ is a subgraph of $$G$$ , or $$G_2$$ is a subgraph of the complement of $$G$$ . We consider the case that $$G_1$$ is a cycle and $$G_2$$ is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels versus cycles of even order; and large cycles versus generalized odd wheels. [ABSTRACT FROM AUTHOR]

The effect of matrix cracking on the bifurcation creep buckling of viscoelastic laminated circular cylindrical shells is investigated. The viscoelastic behavior of laminas is modeled by Schapery’s integral constitutive equation with growing matrix cracks. The values of damage variables are correlated to non-dimensional density of matrix cracks relying on the formulas from meso-mechanics approach, and the evolution equation predicting the growth rate of density of matrix cracks is assumed to follow a power type relation with transverse tensile stress. The governing equations for pre-buckling creep deformation and bifurcation buckling of laminated circular cylindrical shells under axial compression are obtained on the basis of the Donnell type shallow shell theory and Kármán-Donnell geometrically nonlinear relationship. Corresponding solution strategy is constructed by integrating finite-difference technique, trigonometric series expansion method and Taylor’s numerical recursive scheme for convolution integration. The bifurcation creep buckling of symmetrically laminated glass-epoxy circular cylindrical shells with matrix creep cracking coupled are examined for various geometrical parameters and parameters of damage evolution as well as boundary conditions. The numerical results show that matrix creep cracking remarkably shortens the critic time of bifurcation buckling and reduces the durable critic loads, and its effects become weak and finally vanish with the increase of the ratio of radius to thickness in the case of short laminated circular cylindrical shells, also the influence of the matrix creep cracking is mainly dependent on the boundary conditions at two ends for moderately long circular cylindrical shells. [ABSTRACT FROM AUTHOR]

Let G be a connected graph of order n and suppose that n=∑ i =1 k n i, where n i≥2 are integers. In this paper we give some sufficient conditions in terms of degree sums to ensure that G contains a spanning subgraph consisting of vertex disjoint paths of orders n1, n2,..., n k. [ABSTRACT FROM AUTHOR]