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Let G be a graph and d i be the degree of a vertex v i in G. For a symmetric real function f (x , y) , one can get an edge-weighted graph in such a way that for each edge v i v j of G , the weight of v i v j is assigned by f (d i , d j). Hence, we have a weighted adjacency matrix A f (G) of G , in which the ij -entry is equal to f (d i , d j) if v i v j ∈ E (G) and 0 otherwise. In this paper, we use a unified approach to deal with the spectral properties of A f (G) for f (x , y) to be the functions of graphical or topological function-indices. Firstly, we obtain uniform interlacing inequalities for the weighted adjacency eigenvalues. For the edge-weight functions defined by almost a half of popularly used topological indices, it can be shown that our inequalities cannot be improved. Secondly, we establish a uniform equivalent condition for a connected graph G to have m distinct weighted adjacency eigenvalues. As an application, a combinatorial characterization for a graph to have two and three distinct weighted adjacency eigenvalues is presented, respectively. Moreover, bipartite graphs and unicyclic graphs with three distinct weighted adjacency eigenvalues are characterized. This paper attempts to unify the spectral study for weighted adjacency matrices of graphs with degree-based edge-weights. [ABSTRACT FROM AUTHOR]

Given two non-empty t -uniform hypergraphs G (t) , H (t) and a positive integer k , the hypergraph Gallai–Ramsey number gr k G (t) : H (t) is defined as the minimum positive integer N such that for all n ≥ N , every k -hyperedge-coloring of t -uniform complete hypergraph K n (t) contains either a rainbow subhypergraph G (t) or a monochromatic subhypergraph H (t) . A k -hyperedge-coloring of a hypergraph is exact if all colors are used at least once. In this paper, we get the exact values of hypergraph Gallai–Ramsey numbers for rainbow 3-uniform Berge triangles and monochromatic 3-uniform linear paths or cycles under exact k -hyperedge-coloring. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. Denote by d i the degree of a vertex v i in G. Let f (x , y) > 0 be a real symmetric function. Consider an edge-weighted graph in such a way that for each edge v i v j of G, the weight of v i v j is equal to the value f (d i , d j) . Therefore, we have a degree-based weighted adjacency matrix A f (G) of G, in which the (i, j)-entry is equal to f (d i , d j) if v i v j is an edge of G and is equal to zero otherwise. Let x be a positive eigenvector corresponding to the largest eigenvalue λ 1 (A f (G)) of the weighted adjacency matrix A f (G) . In this paper, we first consider the unimodality of the eigenvector x on an induced path of G. Second, if f(x, y) is increasing in the variable x, then we investigate how the largest weighted adjacency eigenvalue λ 1 (A f (G)) changes when G is perturbed by vertex contraction or edge subdivision. The aim of this paper is to unify the study of spectral properties for the degree-based weighted adjacency matrices of graphs. [ABSTRACT FROM AUTHOR]

Long non-coding RNAs (lncRNAs) play important roles in many pathophysiological processes, including cancer progression. Namely, lncRNA Receptor-tyrosine-kinase-like orphan receptor-1 antisense 1 (ROR1-AS1) is crucial for cancer occurrence and progression in organs such as the liver or bladder. However, its expression and role in cholangiocarcinoma (CCA) have not been thoroughly explored. Firstly, we assessed cell viability, proliferation, invasion, and migration using three cell lines (HuCCT-1, QBC399, and RBE) to explore the biological characteristics of ROR1-AS1 in CCA. Secondly, to determine the in vivo effect of ROR1-AS1 on tumor growth, ROR1-AS1 knockdown (KD) HuCCT-1 cells were subcutaneously injected into nude mice to evaluate tumor growth. Finally, we conducted a bioinformatic analysis to confirm the role of ROR1-AS1 in the prognosis and immunity of CCA. In this study, we found that lncRNA ROR1-AS1 was increased in CCA samples and patients with higher ROR1-AS1 expression had a shorter overall survival period. siRNA-mediated KD of ROR1-AS1 significantly reduced cell proliferation and inhibited the migration of CCA cells. In addition, ROR1-AS1 KD HuCCT-1 cells injected into nude mice grew slower than normal CCA cells. In summary, our results show that ROR1-AS1 can promote CCA progression and might serve as a new target for diagnosis and treatment of CCA. [ABSTRACT FROM AUTHOR]

Let G be a graph and d i denote the degree of a vertex v i in G , and let f (x , y) be a real symmetric function. Then one can get an edge-weighted graph in such a way that for each edge v i v j of G , the weight of v i v j is assigned by the value f (d i , d j). Hence, we have a weighted adjacency matrix A f (G) of G , in which the i j -entry is equal to f (d i , d j) if v i v j ∈ E (G) and 0 otherwise. In this paper, we obtain uniform interlacing inequalities for the weighted adjacency eigenvalues under some kinds of graph operations including edge subdivision, vertex deletion and vertex contraction. In addition, if f (x , y) is increasing in the variable x , then some examples are given to show that the interlacing inequalities are the best possible for each type of the operations. This paper attempts to unify the study of spectral properties for the weighted adjacency matrices of graphs with degree-based edge-weights. [ABSTRACT FROM AUTHOR]

Let G be an edge-colored graph. A triangle of G is called rainbow if any two edges of the triangle have distinct colors. We use m (G) and c (G) to denote the number of edges of G and the number of colors appearing on the edges of G , respectively. Li et al. in 2014 proved that every edge-colored graph of order n with m (G) + c (G) ≥ n (n + 1) / 2 contains a rainbow triangle and this result is best possible. In 2019, Fujita et al. characterized all graphs G satisfying m (G) + c (G) ≥ n (n + 1) / 2 − 1 but containing no rainbow triangle. In this paper, we conjecture that every edge-colored graph of order n with m (G) + c (G) ≥ n (n + 1) / 2 + 3 (k − 1) contains k edge-disjoint rainbow triangles. We show that the conjecture holds for k = 2 and 3 and these results are best possible. Furthermore, we characterize all graphs G satisfying m (G) + c (G) ≥ n (n + 1) / 2 + 2 but not containing two edge-disjoint rainbow triangles. At the end, we propose a conjecture on the number of vertex-disjoint rainbow triangles in an edge-colored graph. [ABSTRACT FROM AUTHOR]

Electro-mechanical transmission is the best choice for the transmission system of military, engineering and other heavy special vehicles. The scheme design is fundamental and key to realize the original innovation of the electro-mechanical transmission. Therefore, a novel design method of a planetary-gear scheme is proposed for electro-mechanical transmission. According to the distribution of mechanical points and the speed continuous condition of mode switching, the mode combination law of a dual-mode electro-mechanical transmission is obtained, i.e., the input split mode based on the scheme of three-degree-of-freedom (3-DOF) and the compound split mode based on the scheme of 2-DOF. Moreover, a design method for an electro-mechanical transmission scheme is proposed based on the mode combination law. Two single-mode schemes are combined to form a dual-mode scheme, and then mode jointing, control logic, isomorphism and other screening conditions are in turn used to screen schemes; therefore, two optimized schemes are obtained ultimately. Lastly, by analyzing the characteristics of speed, torque and the power split of the optimized schemes, the accuracy of the proposed design method in this paper is verified. The proposed design method can provide new ideas of designing multi-mode and multi-output electro-mechanical transmission schemes. [ABSTRACT FROM AUTHOR]

Let G be a vertex-colored connected graph. A subset U of the vertex set of G is called monochromatic, if all vertices of U are assigned the same color. The vertex-colored graph G is called monochromatic vertex-disconnected if for any two distinct vertices x and y, there is a monochromatic vertex-subset S of G such that x and y belong to different components of G - S if x and y are nonadjacent, and if x and y are adjacent, then x or y has the same color as S and x and y belong to distinct components of (G - x y) - S . The monochromatic vertex-disconnection number of a connected graph G, denoted by mvd (G) , is defined as the maximum number of colors that are allowed to make G monochromatic vertex-disconnected. The concept is inspired by the concepts of rainbow vertex-disconnection number rvd (G) and monochromatic disconnection number md (G) . In this paper, we present some sufficient conditions for a connected graph G to have mvd (G) = 1 and show that almost all graphs have monochromatic vertex-disconnection number 1. Moreover, we present Nordhaus–Gaddum-type results for the new parameter mvd (G) . At last, we investigate the monochromatic vertex-disconnection numbers for four graph products. [ABSTRACT FROM AUTHOR]

Let G be a vertex-colored connected graph. A subset X of the vertex-set of G is called proper if any two adjacent vertices in X have distinct colors. The graph G is called proper vertex-disconnected if for any two vertices x and y of G , there exists a vertex subset S of G such that when x and y are nonadjacent, S is proper and x and y belong to different components of G − S ; whereas when x and y are adjacent, S + x or S + y is proper and x and y belong to different components of (G − x y) − S. For a connected graph G , the proper vertex-disconnection number of G , denoted by p v d (G) , is the minimum number of colors that are needed to make G proper vertex-disconnected. In this paper, we firstly characterize the graphs of order n with proper vertex-disconnection number k for k ∈ { 1 , n − 2 , n − 1 , n }. Secondly, we give some sufficient conditions for a graph G such that p v d (G) = χ (G) , and show that almost all graphs G have p v d (G) = χ (G) and p v d (G ‾) = χ (G ‾). We also give an equivalent statement of the famous Four Color Theorem. Furthermore, we study the relationship between the proper disconnection number p d (G) of G and the proper vertex-disconnection number p v d (L (G)) of the line graph L (G) of G. Finally, we show that it is NP-complete to decide whether a given vertex-colored graph is proper vertex-disconnected, and it is NP-hard to decide for a fixed integer k ≥ 3 , whether the pvd-number of a graph G is no more than k , even if k = 3 and G is a planar graph with Δ (G) = 12. We also show that it is solvable in polynomial time to determine the proper vertex-disconnection number for a graph with maximum degree less than four. [ABSTRACT FROM AUTHOR]

Let G be a graph with an edge-coloring c, and let δ c (G) denote the minimum color-degree of G. A subgraph of G is called rainbow if any two edges of the subgraph have distinct colors. In this paper, we consider color-degree conditions for the existence of rainbow triangles in edge-colored graphs. At first, we give a new proof for characterizing all extremal graphs G with δ c (G) ≥ n 2 that do not contain rainbow triangles, a known result due to Li et al. Then, we characterize all complete graphs G without rainbow triangles under the condition δ c (G) = l o g 2 n , extending a result due to Li, Fujita and Zhang. Hu, Li and Yang showed that G contains two vertex-disjoint rainbow triangles if δ c (G) ≥ n + 2 2 when n ≥ 20 . We slightly refine their result by showing that the result also holds for n ≥ 6 , filling the gap of n from 6 to 20. Finally, we prove that if δ c (G) ≥ n + k 2 then every vertex of an edge-colored complete graph G is contained in at least k rainbow triangles, generalizing a result due to Fujita and Magnant. At the end, we mention some open problems. [ABSTRACT FROM AUTHOR]

With the development of science and the advancement of medicine, there are more and more treatment methods for repairing knee ligament sports injuries. At present, the common method of ligament repair is to implant artificial synthetic materials or natural biological materials into the body to form artificial ligaments to repair and reconstruct damaged ligaments. Existing ligament repair techniques are often accompanied by sequelae, and the implants are not well adapted. The purpose of this article is to compare the degree of repair of damaged ligaments after implantation of artificial ligaments made of different nanomaterials and to study the mechanical properties, biomechanical properties, and immunological properties of artificial ligaments implanted in the body, in order to explore the role of different artificial ligaments on knee ligament repair. According to the different synthetic materials of artificial ligaments, the experimental subjects were divided into three groups: silk fibroin polycaprolactone nanofiber membrane group (SF/PCL), polycaprolactone nanofiber membrane group (PCL), and control group. By comparing the biocompatibility, cell adhesion, cell proliferation rate, and repair ability of collagen fiber formation of the experimental scaffold after implantation in the body, as well as its immunological performance, the results of the study showed that compared with PCL, SF/PCL increased its biocompatibility by 25%, increased its cell proliferation by 57%, increased its somatic cell adhesion by 35%, and increased its collagen fiber formation by 12%, the porosity is about 60%, and the load is as high as 907 ± 132 N. The data shows that the silk fibroin polycaprolactone nanofiber membrane scaffold has good biocompatibility, degradability, and mechanical properties. [ABSTRACT FROM AUTHOR]

Let G be a graph of order n, and let Δ (G) , δ (G) and d ¯ be the maximum, minimum and average degrees of G, respectively. In 2020, Akbari and Hosseinzadeh proposed a conjecture that E (G) ≥ Δ (G) + δ (G) for all non-singular graphs G. Recently, they gave a strengthened version claiming that E (G) ≥ n - 1 + d ¯ for all non-singular graphs G, except two counterexamples of order 4. They proved this new conjecture for regular graphs, bipartite graphs, planar graphs and graphs with some other special properties. In this paper, we continue the study of the conjecture and find that it is true for the family of threshold graphs of order at least 5. [ABSTRACT FROM AUTHOR]

In an edge-colored graph G , a subgraph is rainbow if all its edges have different colors. A strongly edge-colored graph is an edge-colored graph in which each path of length three is rainbow. A cycle C in an edge-colored graph G of order n is called a rainbow Hamiltonian cycle if the cycle is rainbow and its length is n. An edge-colored graph G of order n is rainbow vertex(edge)-pancyclic if each vertex(edge) of G is contained in a rainbow cycle of length k for each k with 3 ≤ k ≤ n. Cheng et al. in 2019 showed that every strongly edge-colored graph G of order n with minimum degree δ ≥ 2 n 3 contains a rainbow Hamiltonian cycle. Later in 2021, Wang et al. extended this result and showed that every strongly edge-colored graph G of order n with minimum degree δ ≥ 2 n 3 is rainbow vertex-pancyclic. In this paper, we further show that every strongly edge-colored graph G of order n with minimum degree δ ≥ 2 n + 1 3 is rainbow edge-pancyclic. Moreover, from the proof we get a polynomial time algorithm for every given edge e in any such graph G to find a rainbow l -cycle for each 3 ≤ l ≤ n that contains the edge e. [ABSTRACT FROM AUTHOR]

The integration of technology into learning is a crucial capability for students to address future challenges. However, East Asian teachers exhibit a relatively lower level of support for students' technology use compared with the OECD average. The present study tries to uncover the foundational factors influencing teacher-supported student use of technology in five East Asian countries (economies) by analyzing Teaching and Learning International Survey (TALIS) 2018 data. The multilevel structural equation modeling was adopted to analyze the sample data, which combined the teacher-level and school-level factors. Additionally, teacher-level variables are aggregated to the school level to examine contextual effect. Results indicate that teachers' professional collaboration in lessons, team innovativeness, and self-efficacy in student engagement positively and significantly correlated with teacher-supported student use of technology. Notably, an opposing association is observed between teachers' perceptions of disciplinary climate and technology use in Shanghai and Singapore. However, in comparison to teacher-level variables, school-level and contextual variables, particularly fundamental school features such as material resources, budgets, and number of enrolled students, marginally explain associations. Importantly, these associations demonstrate variations across the five east Asian countries (economies), attributable to the fact that these economies have developed their educational technology policies grounded in technology determinism, emphasizing the necessity of equipping schools with the latest devices. Consequently, this study posits that there is a requisite shift in policy evolution from technology determinism to technology instrumentalism. This entails a pragmatic focus transition from merely distributing devices to the integration of technology within instructional practices. • Teachers' self-efficacy in student engagement significantly related with TSSUT. • School-level and contextual factors were found to have marginal effects on TSSUT. • The associations between T3COLES, T3TEAM, T3WLOAD varied across the subsamples. • A contextual effect found Korea teachers' T3COLES negatively related with TSSUT2. [ABSTRACT FROM AUTHOR]

Let G be a nontrivial connected and vertex-colored graph. A subset X of the vertex set of G is called rainbow if any two vertices in X have distinct colors. The graph G is called rainbow vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S such that when x and y are nonadjacent, S is rainbow and x and y belong to different components of G - S ; whereas when x and y are adjacent, S + x or S + y is rainbow and x and y belong to different components of (G - x y) - S . Such a vertex subset S is called an x–yrainbow vertex-cut of G. For a connected graph G, the rainbow vertex-disconnection number of G, denoted by rvd(G), is the minimum number of colors that are needed to make G rainbow vertex-disconnected. In this paper, we obtain bounds of the rainbow vertex-disconnection number of a graph in terms of the minimum degree and maximum degree of the graph. We give a tighter upper bound for the maximum size of a graph G with r v d (G) = k for k ≥ n 2 . We then characterize the graphs of order n with rainbow vertex-disconnection number n - 1 and obtain the maximum size of a graph G with r v d (G) = n - 1 . Moreover, we get a sharp threshold function for the property r v d (G (n , p)) = n and prove that almost all graphs G have r v d (G) = r v d (G ¯) = n . Finally, we obtain some Nordhaus–Gaddum-type results: n - 5 ≤ r v d (G) + r v d (G ¯) ≤ 2 n and n - 1 ≤ r v d (G) · r v d (G ¯) ≤ n 2 for the rainbow vertex-disconnection numbers of nontrivial connected graphs G and G ¯ with order n ≥ 24 . [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) and i , j ∈ V , denote by d i , d j the degrees of vertices i , j in G. Let f (d i , d j) > 0 be a function symmetric in i and j. Define a matrix A f (G) , called the weighted adjacency matrix of G , with the ij -entry A f (G) (i , j) = f (d i , d j) if i ∼ j and A f (G) (i , j) = 0 otherwise. In this paper, we find the extremal trees with the largest radius of A f when f (x , y) is increasing and convex in variable x. We also find the extremal tree with the smallest radius of A f when f (x , y) has a form P (x , y) or P (x , y) , where P (x , y) is a symmetric polynomial with nonnegative coefficients and zero constant term. This paper tries to unify the spectral study of weighted adjacency matrices of graphs weighted by some topological indices. [ABSTRACT FROM AUTHOR]

A directed path in a digraph is proper if any two consecutive arcs on the path have distinct colors. An arc-colored digraph D is proper connected if for any two distinct vertices x and y of D , there are both proper (x , y) -directed paths and proper (y , x) -directed paths in D. The proper connection number p c → (D) of a digraph D is the minimum number of colors that can be used to make D proper connected. Obviously, if a digraph has a proper connection number, it must be strongly connected, and p c → (D) = 1 if and only if D is complete. Magnant et al. showed that p c → (D) ≤ 3 for all strong digraphs D , and Ducoffe et al. proved that deciding whether a given digraph has proper connection number at most two is NP-complete. In this paper, we give a few classes of strong digraphs with proper connection number two, and from our proofs one can construct an optimal arc-coloring for a digraph of order n in time O (n 3). [ABSTRACT FROM AUTHOR]

For an edge-colored graph G , we call an edge-cut M of G monochromatic if the edges of M are colored with the same color. The graph G is called monochromatic disconnected if any two distinct vertices of G are separated by a monochromatic edge-cut. For a connected graph G , the monochromatic disconnection number (or M D -number for short) of G , denoted by m d (G) , is the maximum number of colors that are allowed in order to make G monochromatic disconnected. For graphs with diameter one, they are complete graphs and so their M D -numbers are 1. For graphs with diameter at least 3, we can construct 2-connected graphs such that their M D -numbers can be arbitrarily large; whereas for graphs G with diameter two, we show that if G is a 2-connected graph then m d (G) ≤ 2 , and if G has a cut-vertex then m d (G) is equal to the number of blocks of G. So, we will focus on studying 2-connected graphs with diameter two, and give two upper bounds of their M D -numbers depending on their connectivity and independent numbers, respectively. We also characterize the n 2 -connected graphs (with large connectivity) whose M D -numbers are 2 and the 2-connected graphs (with small connectivity) whose M D -numbers achieve the upper bound n 2 (these graphs are called extremal graphs). For graphs with connectivity less than n 2 , we show that if the connectivity of a graph is linear in its order n , then its M D -number is upper bounded by a constant, and this suggests us to leave a conjecture that for a k -connected graph G , m d (G) ≤ n k . [ABSTRACT FROM AUTHOR]

Grouting reinforcement is one of the most effective methods to enhance the stability of the goaf, and its scheme selection, hole location, and parameter determination directly affect the success or failure of goaf treatment. On the basis of discussion of the deformation mechanism and evolution law of the longwall goaf, this article comprehensively analyzed the grouting reinforcement mechanism of the goaf combined with filling theory, permeability theory, and fracturing theory and studied the physical and chemical reaction principles of two commonly used filling materials, cement-fly ash slurry and cement-clay slurry. Three grouting models have been established: whole grouting, local grouting in fracture zone, and strip grouting, and then simulated the grouting effect of the two more common methods of whole grouting and strip grouting by numerical simulation software (FLAC3D, tecplot, Surfer). Simulation analysis is carried out from the perspectives of settlement deformation, horizontal movement, vertical stress, and horizontal stress. Finally, the feasibility of grouting treatment in the goaf is verified by engineering example. The results show that a reasonable grouting scheme can effectively reduce the residual deformation of the goaf and its overlying rock and improve the poor stress state, so as to achieve the purpose of effective grouting. [ABSTRACT FROM AUTHOR]

For rock engineering in cold regions, the naturally fractured rock is susceptible to repeated freeze-thaw (F-T) weathering, coupled fatigue conditions of freeze-thaw (F-T), and stress disturbance act on rock mass, which can lead to the instability of rock engineering and even occurrence of geological hazards. Knowledge of how natural fracture affects the overall fracture evolution of freeze-thawed rock is crucial to rock mass stability. Laboratory multilevel cyclic loading tests are conducted to reveal the fatigue behavior and energy evolution for naturally fractured marble, as well as the influence of natural fracture volume on fracture evolution. The test results show that the preexisting natural fracture impacts fatigue strength, lifetime, and energy dissipation. The dissipated energy is correlated to all kinds of natural fracture (i.e., opening-mode, closing-mode, and filling-mode), and it decreases with the increase of the total natural fracture volume. The dissipated energy presents a first slow and then faster pattern as the cycle number grows. Compared with newly formed cracks, the proportion of energy consumed by stimulating natural cracks is smaller. [ABSTRACT FROM AUTHOR]

In an edge-colored graph (G , c) , let d c (v) denote the number of colors on the edges incident with a vertex v of G and δ c (G) denote the minimum value of d c (v) over all vertices v ∈ V (G). A cycle of (G , c) is called proper if any two adjacent edges of the cycle have distinct colors. An edge-colored graph (G , c) on n ≥ 3 vertices is called properly vertex-pancyclic if each vertex of (G , c) is contained in a proper cycle of length ℓ for every ℓ with 3 ≤ ℓ ≤ n. Fujita and Magnant conjectured that every edge-colored complete graph on n ≥ 3 vertices with δ c (G) ≥ n + 1 2 is properly vertex-pancyclic. Chen, Huang and Yuan partially solve this conjecture by adding an extra condition that (G , c) does not contain any monochromatic triangle. In this paper, we show that this conjecture is true if the edge-colored complete graph contain no joint monochromatic triangles. [ABSTRACT FROM AUTHOR]

A path in an edge-colored graph is called a monochromatic path if all edges of the path have a same color. We call k paths P 1 , ... , P k rainbow monochromatic paths if every P i is monochromatic and for any two i ≠ j , P i and P j have different colors. An edge-coloring of a graph G is said to be a rainbow monochromatic k-edge-connection coloring (or R M C k -coloring for short) if every two distinct vertices of G are connected by at least k rainbow monochromatic paths. We use r m c k (G) to denote the maximum number of colors that ensures G has an R M C k -coloring, and this number is called the rainbow monochromatic k-edge-connection number. We prove the existence of R M C k -colorings of graphs, and then give some bounds of r m c k (G) and present some graphs whose r m c k (G) reaches the lower bound. We also obtain the threshold function for r m c k (G (n , p)) ≥ f (n) , where n 2 > k ≥ 1 . [ABSTRACT FROM AUTHOR]

In an edge-colored graph G , let d m o n (v) denote the maximum number of edges with the same color incident with a vertex v in G , called the monochromatic-degree of v. The maximum value of d m o n (v) over all vertices v ∈ V (G) is called the maximum monochromatic-degree of G , denoted by Δ m o n (G). Li et al. in 2019 conjectured that every edge-colored complete graph G of order n with Δ m o n (G) ≤ n − 3 k + 1 contains k vertex-disjoint properly colored (PC for short) cycles of length at most 4, and they showed that the conjecture holds for k = 2. Han et al. showed that every edge-colored complete graph G of order n with Δ m o n (G) ≤ n − 2 k contains k PC cycles of different lengths. They further got the condition Δ m o n (G) ≤ n − 6 for the existence of two vertex-disjoint PC cycles of different lengths. In this paper, we consider the problems of the existence of edge-disjoint PC cycles of length at most 4 (different lengths) in an edge-colored complete graph G of order n. [ABSTRACT FROM AUTHOR]

This study determined the acute changes in kinematics and kinetics when an additional load equivalent to 5% body mass was attached to the torso during change of direction (COD). In this within-subject repeated measures study, 14 male soccer players (age: 18.29 ± 0.32 years) volunteered to participate. Subjects performed COD under two conditions in randomized order: (1) no WR, and (2) with WR. No significant differences between the loaded and unloaded conditions in actual COD angle, approach speed, braking time, propulsive time, contact time, COD completion time (all p > 0.05, ES = 0.05–0.11), and all measured kinematic parameters (all p > 0.05, ES = 0–0.18). Nonetheless, ankle plantar/dorsi flexion ROM had possibly small increase in the loaded condition (ES = 0.24). Kinetics analysis has shown that the loaded condition was likely to have small increase in relative peak vertical propulsive ground reaction force (GRF, p = 0.11, ES = 0.41), and possible small increases in relative peak braking GRF (vertical: p = 0.21, ES = 0.42; total: p = 0.22, ES = 0.38), relative peak total propulsive GRF (p = 0.24, ES = 0.26), and relative braking impulse (horizontal, vertical, and total; p = 0.27–0.41, ES = 0.26–0.28). WR did not significantly change the acute movement techniques, meanwhile induced small increases in important kinetic stimuli for potential adaptation in COD. [ABSTRACT FROM AUTHOR]

We propose an approach to designing smart wearables that act as partners to help people cope with stress in daily life. Our approach contributes to the developing field of smart wearables by addressing how technological capabilities can be designed to establish partnerships that consider the person, the situation, and the appropriate type of support. As such, this study also contributes to healthcare by opening up novel technology-supported routes to stress treatment and care. We present the results of a phenomenological study conducted with three war veterans who suffer from chronic posttraumatic stress disorder. We describe how their experiences of dealing with their stress informed our design approach, and discuss the implications of these results on smart wearables and stress management in general. We conclude by reflecting on the limitations of this study and directions for future work. [ABSTRACT FROM AUTHOR]

Let f (D (i , j) , d i , d j) be a real function symmetric in i and j with the property that f (d , (1 + o (1)) n p , (1 + o (1)) n p) = (1 + o (1)) f (d , n p , n p) for d = 1 , 2. Let G be a graph, d i denote the degree of a vertex i of G and D (i , j) denote the distance between vertices i and j in G. In this paper, we define the f -weighted Laplacian matrix for random graphs in the Erdös-Rényi random graph model G n , p , where p ∈ (0 , 1) is fixed. Four weighted Laplacian type energies: the weighted Laplacian energy LE f (G) , weighted signless Laplacian energy LE f + (G) , weighted incidence energy IE f (G) and the weighted Laplacian-energy like invariant LEL f (G) are introduced and studied. We obtain the asymptotic values of IE f (G) and LEL f (G) , and the values of LE f (G) and LE f + (G) under the condition that f (D (i , j) , d i , d j) is a function dependent only on D (i , j). As a consequence, we get that under the condition that f (D (i , j) , d i , d j) is a function dependent only on D (i , j) , for almost all graphs G p ∈ G n , p , the energy for the matrix with degree-distance-based entries of G p , E (W f (G p)) < LE f (G p) , the Laplacian energy of the matrix, which can be viewed as a generalization of a conjecture by Gutman et al. [ABSTRACT FROM AUTHOR]

Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems. [ABSTRACT FROM AUTHOR]

For an edge-colored graph G , we call an edge–cut M of G monochromatic if the edges of M are colored with the same color. The graph G is called monochromatically disconnected if any two distinct vertices of G are separated by a monochromatic edge–cut. For a connected graph G , the monochromatic disconnection number of G , denoted by m d (G) , is the maximum number of colors that are needed in order to make G monochromatically disconnected. We show that almost all graphs have monochromatic disconnection numbers equal to 1. We also obtain the Nordhaus–Gaddum-type results for m d (G). [ABSTRACT FROM AUTHOR]

In‐situ high content N‐doping carbon aerogel (NCA) is successfully prepared via low‐cost m‐phenylenediamine and formaldehyde reaction through the facile sol‐gel method and further high‐temperature carbonization process. NCA material with nanospheres presents the characteristics of large specific surface area and high loading sulfur owing to the specific cross‐linked framework structure. In addition, the NCA/S cathode with high content of nitrogen can achieve strong adsorption to lithium polysulfides (LiPSs) due to its inherent N active sites, and presents outstanding electrochemical performance. In details, the designed NCA/S electrode demonstrates the first discharge capacity of 1247 mAh g−1 at 0.2 C. Moreover, the NCA/S battery also displays excellent electrochemical stability with low capacity attenuation rate of 0.083 % per cycle within 300 cycles at 0.5 C. The remarkable electrochemical properties are mainly ascribed to intense adsorption of evenly‐distributed nitrogen in the carbon material, effectively preventing polysulfide (PS) escaping from host material, restraining shuttle effect and increasing sulfur utilization. [ABSTRACT FROM AUTHOR]

The concept of rainbow connection number of a graph was introduced by Chartrand et al. in 2008. Inspired by this concept, other concepts on colored version of connectivity in graphs were introduced, such as the monochromatic connection number by Caro and Yuster in 2011, the proper connection number by Borozan et al. in 2012, and the conflict-free connection number by Czap et al. in 2018, as well as some other variants of connection numbers later on. Chakraborty et al. proved that to compute the rainbow connection number of a graph is NP-hard. For a long time, it has been tried to fix the computational complexity for the monochromatic connection number, the proper connection number and the conflict-free connection number of a graph. However, it has not been solved yet. Only the complexity results for the strong version, i.e., the strong proper connection number and the strong conflict-free connection number, of these connection numbers were determined to be NP-hard. In this paper, we prove that to compute each of the monochromatic connection number, the proper connection number and the conflict free connection number for a graph is NP-hard. This solves a long standing problem in this field, asked in many talks of workshops and papers. [ABSTRACT FROM AUTHOR]

In this paper we study the flow properties of graphs containing a spanning triangle-tree. Our main results provide a structure characterization of graphs with a spanning triangle-tree admitting a nowhere-zero 3-flow. All these graphs without nowhere-zero 3-flows are constructed from K 4 by a so-called bull-growth operation. This generalizes a result of Fan et al. in 2008 on triangularly-connected graphs and particularly shows that every 4-edge-connected graph with a spanning triangle-tree has a nowhere-zero 3-flow. A well-known classical theorem of Jaeger in 1979 shows that every graph with two edge-disjoint spanning trees admits a nowhere-zero 4-flow. We prove that every graph with two edge-disjoint spanning triangle-trees has a flow strictly less than 3. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) and i , j ∈ V , denote the distance between i and j in G by D (i , j) and the degrees of i , j by d i , d j , respectively. Let f (D (i , j) , d i , d j) be a function symmetric in i and j. Define a matrix W f (G) , called the weighted distance matrix, of G , with the ij -entry W f (G) (i , j) = f (D (i , j) , d i , d j) if i ≠ j and W f (G) (i , j) = 0 if i = j. In this paper, we prove that if the symmetric function f satisfies that f (D (i , j) , (1 + o (1)) n p , (1 + o (1)) n p) = (1 + o (1)) f (D (i , j) , n p , n p) , then for almost all graphs G p in the E r d o ¨ s - R e ´ n y i random graph model G n , p , the energy of W f (G p) is { (8 3 π p (1 − p) + o (1)) ⋅ | f (1 , n p , n p) − f (2 , n p , n p) | + o (| f (2 , n p , n p) |) } ⋅ n 3 / 2. As a consequence, we give the asymptotic values of energies of a variety of weighted distance matrices with function f from distance-based only and mixed with degree-distance-based topological indices of chemical use. This generalizes our former result with only degree-based weights. [ABSTRACT FROM AUTHOR]

The inverse sum indeg (ISI) index is a vertex-degree-based topological index that was selected by Vukičević and Gašperov in 2010 as a significant predictor of the total surface area of octane isomers. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the ISI index from an algebraic viewpoint. We introduce suitably modified versions of the classical adjacency matrix and the Laplacian matrix involving the degrees of the vertices of a graph. Moreover, we formulate the ISI index in terms of these matrices. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the energy of a weighted random graph G p (f) in G n , p (f) , in which each edge i j takes the weight f (d i , d j) , where d v is a random variable, the degree of vertex v in the random graph G p of the Erdös–Rényi random graph model G n , p , and f is a symmetric real function on two variables. Suppose | f (d i , d j) | ≤ C n m for some constants C , m > 0 , and f ((1 + o (1)) n p , (1 + o (1)) n p) = (1 + o (1)) f (n p , n p). Then, for almost all graphs G p (f) in G n , p (f) , the energy of G p (f) is (1 + o (1)) f (n p , n p) 8 3 π p (1 − p) ⋅ n 3 ∕ 2 , where p ∈ (0 , 1) is any fixed and independent of n. Consequently, with this one basket we can get the asymptotic values of various kinds of graph energies of chemical use, such as Randić energy, ABC energy, and energies of random matrices obtained from various kinds of degree-based chemical indices. [ABSTRACT FROM AUTHOR]

An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph G , denoted by c f c (G) , is the smallest number of colors needed in order to make G conflict-free connected. In this paper, we show that almost all graphs have the conflict-free connection number 2. More precisely, let G (n , p) denote the Erdős–Rényi random graph model, in which each of the n 2 pairs of vertices appears as an edge with probability p independent from other pairs. We prove that for sufficiently large n , c f c (G (n , p)) ≤ 2 if p ≥ log n + α (n) n , where α (n) → ∞. This means that as soon as G (n , p) becomes connected with high probability, c f c (G (n , p)) ≤ 2. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some bounds for the ABC spectral radius of general graphs. In continuing, we get some properties of the ABC eigenvalues of graphs, and then we establish some new bounds for the ABC energy E A B C. Finally, we set up the correlation between the ABC energy and other classes of graph energies. [ABSTRACT FROM AUTHOR]

The ABC matrix of a graph G is a square matrix, where the (i , j) -entry A B C i j = d i + d j − 2 d i d j if there is an edge between vertices i and j in G , and A B C i j = 0 otherwise. The ABC spectral radius of G , denoted by ν 1 (G) , is the largest eigenvalue of the ABC matrix of G. In this paper, we prove that for a unicyclic graph G of order n ≥ 4 , 2 = ν 1 (C n) ≤ ν 1 (G) ≤ ν 1 (S n + e) , with equality if and only if G ≅ C n for the lower bound, and if and only if G ≅ S n + e for the upper bound. This solves a conjecture by Ghorbani et al. [ABSTRACT FROM AUTHOR]

Cadmium-doped carbon aerogels were successfully prepared via a microtemplate inducing strategy and subsequent high temperature carbonization. The controlled synthesis technology forms spherical carbon aerogels with uniform and interconnected porous structures. The as-prepared materials display large specific surface area and excellent conductivity. The loaded sulfur composites as cathode materials exhibit high discharge capacity and excellent cycling performance. Particularly, the designed P2-Cd-CA/S electrode with 78.9 wt% sulfur presents an initial discharge capacity of 1318 mA h g−1 at 0.2C. And it delivers an initial discharge capacity of 1189 mA h g−1 at 0.5C and still maintains 871 mA h g−1 after 300 cycles. The enhanced performance is mainly ascribed to the synergistic effect of the inductive graphitization of a microtemplate (3,4,9,10-perylenetetracarboxylic dianhydride) and the stronger anchoring for polysulfides of evenly distributed cadmium. Furthermore, the first-principles theoretical calculations further support the strong adsorption between CdO and polysulfides and affirmatively reveal the immobilizing mechanism. [ABSTRACT FROM AUTHOR]

Let G be an(a) edge(vertex)-colored graph. A path P of G is called a conflict-free path if there is a color that is used on exactly one of the edges(vertices) of P. The graph G is called conflict-free (vertex-)connected if any two distinct vertices of G are connected by a conflict-free path, whereas the graph G is called strongly conflict-free connected if any two distinct vertices u , v of G are connected by a conflict-free path of length of a shortest path between u and v in G. For a connected graph G , the (strong) conflict-free connection number of G , denoted by (s c f c (G)) c f c (G) , is defined as the smallest number of colors that are required to make G (strongly) conflict-free connected. In this paper, we first investigate the question: Given a connected graph G and a coloring c : E (o r V) → { 1 , 2 , ⋯ , k } (k ≥ 1) of G , determine whether or not G is, respectively, conflict-free connected, conflict-free vertex-connected, strongly conflict-free connected under the coloring c. We solve this question by providing polynomial-time algorithms. We then show that the problem of deciding whether s c f c (G) ≤ k (k ≥ 2) for a given graph G is NP-complete. Moreover, we prove that it is NP-complete to decide whether there is a k -edge-coloring (k ≥ 2) of G such that all pairs (u , v) ∈ P (P ⊂ V × V) are strongly conflict-free connected. [ABSTRACT FROM AUTHOR]

A signed graph Γ = (G , σ) is obtained from a simple graph G by assigning to each edge of G a sign + or −. Let A (Γ) denote the adjacency matrix of Γ and α (G) be the independence number of G. We study the rank of A (Γ) and the independence number α (G) . We show that r (Γ) + 2 α (G) ≥ 2 n - 2 d (G) , where n is the order of G and d(G) is the dimension of the cycle space of G. Moreover, we obtain sharp lower bounds for r (Γ) + α (G) , r (Γ) - α (G) , r (Γ) / α (G) and we characterize all corresponding extremal graphs. [ABSTRACT FROM AUTHOR]

A cage‐type composite was successfully prepared by attaching p‐sulfonatocalix[4]arene to a porous activated carbon aerogel (ACA). The resulting composite showed a high specific surface area of 1620.7 m2 g−1 and a high sulfur loading of 2.5 mg cm−2. The calixarene is uniformly dispersed on the carbon spheres and efficiently captures polysulfides by interaction with the sulfonate groups. Meanwhile, the cross‐linked porous structure of the composite restricts the migration of polysulfides. The cathode delivers an outstanding electrochemical performance with an initial capacity of 1304.7 mAh g−1 at 0.2 C. Furthermore, it displays excellent long‐term cycling stability, maintaining 884.7 mAh g−1 after 300 cycles at 0.5 C. Density functional theory (DFT) adsorption calculations support the strong interaction between the calixarenes and polysulfides and reveal the capture mechanism. [ABSTRACT FROM AUTHOR]

The signal-to-noise ratio (SNR), vertical resolution and fidelity of marine seismic data are closely related to the characteristics of hydrophones, namely the sensitivity and the frequency band range. In this article, we analyzed and processed seismic data collected in 2017 from a towed marine streamer equipped with optical fiber cable and hydrophones. Results from a pre-stack time migration section revealed that the optical fiber seismic data yielded high SNR, vertical resolution and fidelity. For validation purpose, a comparison of these data with those acquired by classic piezoelectric hydrophones along a migration section located in a very close location was carried out. This comparison showed that the SNR, fidelity and vertical resolution from the two means of measurements were comparable. [ABSTRACT FROM AUTHOR]

The total-coloring of a graph is a coloring of the edge set and vertex set. A path in a total-colored graph is a total proper path if the coloring of the edges and internal vertices is proper, that is, any two adjacent or incident elements of edges and internal vertices on the path differ in color. For a connected graph G, the total proper connection number of G, denoted by tpc(G), is defined as the smallest number of colors such that any two vertices of the graph are connected by a total proper path of G. These concepts are inspired by the concepts of total chromatic number χ ′ ′ (G) , proper connection number pc(G) and proper vertex connection number pvc(G) of a connected graph G. In this paper, we first determine the value of the total proper connection number tpc(G) for some special graphs G. Secondly, we obtain that t p c (G) ≤ 4 for any 2-(edge-)connected graph G and give examples to show that the upper bound 4 is sharp. For general graphs, we also obtain sharp upper bounds for tpc(G) in terms of the maximum degree of a vertex incident with a bridge in G and the minimum degree, respectively. Finally, we compare tpc(G) with pvc(G) and pc(G), respectively, and obtain that t p c (G) > p v c (G) for any nontrivial connected graph G and that there exist graphs G such that t p c (G) = p c (G) + t for 0 ≤ t ≤ 2 . [ABSTRACT FROM AUTHOR]

An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection number of a graph is the minimum number of colours needed to make the graph rainbow-connected. This parameter was introduced by G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang in 2008. Similar to rainbow connection coloring, an edge-coloring is a rainbow k-connection coloring if there are at least k internally disjoint rainbow u – v paths connecting any two distinct vertices u and v. And the rainbow k-connectivity rck(G) of G to be the minimum integer l such that there exists a l-edge-coloring which is a rainbow k-connection coloring. In [4], the authors determined the rck(G) of the complete graph Kn and r-regular complete bipartite graphs Kr, r. In this paper, we study the rainbow k-connectivity of the Cartesian product graphs K2□Kn for some k. We determine rck(K2□Kn) for k = 2, 3, 4 and prove that there exists Cartesian product graphs K2□Kn such that rck(K2□Kn) = 3 for each integer k ≥ 2. [ABSTRACT FROM AUTHOR]

Effective online monitoring of the spatial distribution of high‐energy radiation is of significant importance in various fields such as medical imaging, high‐energy physics, and homeland security. However, achieving radiation detectors with both high sensitivity and minimal disturbance is an enormous challenge. The present study introduces a solution to this bottleneck issue through the development of a full‐inorganic scintillating fiber, successfully demonstrating its application in constructing a radiation monitoring device. The scintillating fiber, activated with Ce3+ and fabricated using the melt‐in‐tube approach, is lightweight with a density of 2.5 g cm−3 and exhibits efficient scintillating emission with a light yield of 4000 photons MeV−1. These characteristics enable the achievement of radiation detection with high sensitivity while keeping disturbance to the incident radiation beam at a minimum. Furthermore, 2D and 3D radiation beam monitors are constructed based on these scintillating fibers, facilitating spatial radiation monitoring. The findings demonstrate that full‐inorganic scintillating fibers and devices offer a synergistic combination of high sensitivity and negligible disturbances. This progress not only introduces a novel full‐inorganic fiber for radiation detection but also suggests promising applications in various nuclear fields where 3D radiation beam tracking is essential. [ABSTRACT FROM AUTHOR]

A path in an edge-colored graph is called a proper path if no two adjacent edges of the path receive the same color. For a connected graph G , the proper connection number p c (G) of G is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of G is connected by at least one proper path in G. Recently, Li and Magnant in [8] posed the following conjecture: If G is a connected noncomplete graph of order n ≥ 5 and minimum degree δ (G) ≥ n / 4 , then p c (G) = 2. In this paper, we show that this conjecture is true except for two small graphs on 7 and 8 vertices, respectively. As a byproduct we obtain that if G is a connected bipartite graph of order n ≥ 4 with δ (G) ≥ n + 6 8 , then p c (G) = 2. [ABSTRACT FROM AUTHOR]

Abstract The air-conditioning units (ACUs) on high-speed trains are responsible for cooling the passenger compartment. Insufficient condensing air flux through the ACU may lead to a suboptimal cooling and causes dangerous levels of overheating or even a shutdown of the ACU itself. In this paper, the air flow through ACU at different speeds of a high-speed train is investigated numerically. A significant drop of the condensing air flux during the train operation at higher speed is observed. This phenomenon is related to the interaction of the air flow through the ACU and the boundary layer on the roof of the train. Simulations show that the motion of the train creates a region of negative pressure above the ACU inlets and a region of positive pressure above the outlets. Thus, a particular structural optimization of the air outlets aimed at reducing the pressure buildup is proposed. The proposed numerical method can be used serve to investigate and to optimize the performance the ACUs on high-speed trains under different structural modifications. [ABSTRACT FROM AUTHOR]

Abstract Lithium sulfur batteries have attracted significant attention owing to their remarkably high theoretical capacities and energy density for the potential next-generation energy storage system. Considerable efforts have been developed to improve the redox reversibility and suppress sulfur loss when maintaining their capacities. However, few strategies have enlightened to address shuttle issues via electric-field-responsive film. Here, we postulate a new strategy to create smart electric-field-responsive surface structure and design special molecular film with quaternary ammonium group. The responsive film bonded to carbon matrix can act as a switch to control the on-off of polysulfide channels. Meanwhile, the prepared carbon aerogel (CA) matrix presents highly cross-linked 3D framework, abundant hierarchical pore channels and high specific surface area. The results show the composite sulfur cathode with selective film exhibits outstanding high discharging capacities and long-term cycling stability. Specifically, the cathode with 61.6 wt% sulfur displays an initial specific capacity of 1307 mAh g−1 at 0.2C and maintains 84.0% after 100 cycles. The improved electrochemical performance may mainly benefit from the switch function of self-responsive film, effectively preventing polysulfides escaping from the cathode, suppressing shuttle effect and enhancing the utilization of sulfur. Furthermore, the adsorption calculation by the density functional theory (DFT) shows trapping role of beta-cyclodextrin quaternary ammonium (CDQA) to polysulfides. The DFT simulation further supports the confining and switching mechanism. [ABSTRACT FROM AUTHOR]

A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A path P in a total-colored graph G is called a total-proper path if (1) any two adjacent edges of P are assigned distinct colors; (2) any two adjacent internal vertices of P are assigned distinct colors; and (3) any internal vertex of P is assigned a distinct color from its incident edges of P. The total-colored graph G is total-proper connected if any two distinct vertices of G are connected by a total-proper path. The total-proper connection number of a connected graph G, denoted by tpc(G), is the minimum number of colors that are required to make G total-proper connected. In this paper, we first characterize the graphs G on n vertices with tpc(G)=n-1. Based on this, we obtain a Nordhaus-Gaddum-type result for total-proper connection number. We prove that if G and G¯ are connected complementary graphs on n vertices, then 6≤tpc(G)+tpc(G¯)≤n+2. Examples are given to show that the lower bound is sharp for n≥4. The upper bound is reached for n≥4 if and only if G or G¯ is the tree with maximum degree n-2. [ABSTRACT FROM AUTHOR]