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The augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and $d(v_i)$ denotes the degree of the vertex $v_i$. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs. \\[2mm] {\bf Keywords:} Agumented Zagreb index; molecular trees; Triangle-free graph

Let G be a graph and u,v,w ∈ V (G). The vertex w is said to resolve a pair u and v if and only if dG(w,u)≠dG(w,v). A set W ⊆ V (G) is defined as a resolving set of G if for all u,v ∈ V (G), the pair (u,v) is resolved by some w ∈ W. The minimum cardinality of a resolve set of G is defined as dim(G). A set R ⊆ V (G) is a local resolve set of G if for all u,v ∈ V (G) such that uv ∈ E(G), the pair (u,v) is resolved by some r ∈ R. The minimum cardinality of a local resolve set of G is defined as dimℓ(G). An edge uv ∈ E(G) is said to be monitored by x ∈ V (G) if dG(x,u)≠dG−uv(x,u) or dG(x,v)≠dG−uv(x,v). A set M ⊆ V (G) is a distance-edge-monitoring (DEM) set if for all e ∈ E(G), e is monitored by some v ∈ M. The minimum cardinality of a DEM set of G is defined as dem(G).In this paper, we obtained that 1 ≤dimℓ(G) ≤dem(G) ≤ n − 1 for all non trivial graphs with order n, and the exact value of dimℓ(G) and dem(G) for G ∈{Tn,Kn,Bn,NEn, Koch(n)}. Also, we obtained that if dimℓ(G) = 1 then dem(G) ≤⌊n 2 ⌋. With respect to the relation between the defined graph invariants, it was proved a bound for (dem −dim)(n) for G ∈ 픊n = {G||V (G)| = n} and the exact values of (dim −dimℓ)(n) for G ∈ 픊n, where (dem −dim)(n) (resp, (dim −dimℓ)(n))is the maximum value of dem(G) −dim(G) (resp, dem(G) −dimℓ(G)) over all graphs G with order n. Finally, we proved that for 2 ≤ s ≤ t ≤ s + ⌊n−2s 3 ⌋, there exists a graph with order n such that dimℓ(G) = s and dem(G) = t. [ABSTRACT FROM AUTHOR]

The B6 metamorphic buried hill condensate gas reservoir exhibits a highly compact matrix, leading to a rapid decline in bottom-hole pressure during initial production. The minimal difference between formation and saturation pressures results in severe retrograde condensation, with multiphase flow further increasing resistance. Conventional numerical simulations often overestimate reservoir energy supply due to their failure to account for this additional resistance, leading to inaccuracies in bottom-hole pressure predictions and gas–oil ratio during history matching. To address these challenges, this study conducted research on nonlinear numerical simulation for buried hill condensate gas reservoirs and established a method for calculating a multiphase pressure sweep range based on the well testing theory. By correcting and fitting the pressure propagation boundaries with numerical simulation, the nonlinear flow parameters applicable to the B6 gas field were inversed. This study revealed that conventional Darcy flow is inadequate for predicting pressure propagation boundaries and that it is possible to reasonably characterize the pressure sweep range through nonlinear flow. This approach resulted in an improvement in the accuracy of historical matching for bottom-hole pressure and gas–oil ratio, which improve the historical fitting accuracy to 85%, providing valuable insights for the development of similar reservoirs. [ABSTRACT FROM AUTHOR]

Let G be a graph. For any u v ∈ E (G) , if there exists w ∈ V (G) such that d G (w , u) ≠ d G (w , v) , we say that w resolving u , v. A set W of vertices in G is a local resolving set of G if there exists w ∈ W such that d G (w , v) ≠ d G (w , u) for any u v ∈ E (G). The local metric dimension dim l (G) of G is the minimum cardinality of all the local resolving sets of G. In this paper, we study the relation between dim l (G) and dim l (L (G)). Furthermore, we construct a graph G s , t such that dim l (G s , t) = s and dim l (L (G s , t)) = t. Finally, we investigate the local metric dimension of several special line graphs. [ABSTRACT FROM AUTHOR]

For a vertex set M , we say that M is a monitoring-edge-geodetic set (MEG-set for short) of graph G , that is, some vertices of M can monitor an edge of the graph, if and only if we can remove that edge would change the distance between some pair of vertices in the set. The monitoring-edge-geodetic number meg (G) of a graph G is defined as the minimum cardinality of a monitoring-edge-geodetic set of G. The line graph L (G) of G is the graph whose vertices are in one-to-one correspondence with the edges of G , that is, if two vertices are adjacent in L (G) if and only if the corresponding edges have a common vertex in G. In this paper, we study the relation between meg (G) and meg (L (G)) , and prove that 2 ≤ meg (L (G)) ≤ | E (G) |. Next, we have determined the exact values for a MEG-set of some special graphs and their line graphs. For a graph G and its line graph L (G) , we prove that meg (L (G)) − meg (G) can be arbitrarily large. [ABSTRACT FROM AUTHOR]

Many scenes need facial gender identification with good accuracy. Deep convolutional neural networks (CNN) with large set of training data normally give good accuracy, however, to achieve good accuracy with uncertain training data is a difficult task due to their lower explanation and potential information loss. Moreover, the uncertain-ties resulted from illumination, postures and facial expressions can lead to low accuracy of the classification. In this paper, a shadowed sets based two-level model for gender classification is proposed to address the problem. Deep convolutional neural networks are used as one-level classifier. Combining the concept of shadowed sets, one-level classification results are divided into three parts: accept domain, reject domain and uncertain domain. Samples in the uncertain domain are selected as uncertain facial images for two-level reclassification. Results show that the proposed method can further improve the accuracy compared with several existing state-of-the-art methods on the LFW dataset and Adience dataset.

Gas injection for enhanced oil and gas reservoir recovery is a crucial method in offshore Carbon Capture, Utilization, and Storage (CCUS). The B6 buried hill condensate gas reservoir, characterized by high CO2 content, a deficit in natural energy, developed fractures and low-pressure differentials between formation and saturation pressures, requires supplementary formation energy to mitigate retrograde condensation near the wellbore area through gas injection. However, due to the connected fractures, the B6 gas reservoir exhibits strong horizontal and vertical heterogeneity, resulting in severe gas channeling and a futile cycle, which affects the gas injection efficiency at various levels of fracture development. Based on these findings, we conducted gas injection experiments and numerical simulations on fractured cores. A characterization method for oil and gas relative permeability considering dissolution was established. Additionally, the gas injection development boundary for this type of condensate gas reservoir was quantified according to the degree of fracture development, and the gas injection mode of the B6 reservoir was optimized. Research indicates that the presence of fractures leads to the formation of a dominant gas channel; the greater the permeability difference, the poorer the gas injection effect. The permeability gradation (fracture permeability divided by matrix permeability) in the gas injection area should be no higher than 15; gas injection in wells A1 and A2 is likely to achieve a better development effect under the existing well pattern. Moreover, early gas injection timing and pulse gas injection prove beneficial in enhancing the recovery rate of condensate oil. The study offers significant guidance for the development of similar gas reservoirs and for reservoirs with weakly connected fractures; advancing the timing of gas injection can mitigate the retrograde condensation phenomenon, whereas initiating gas injection after depletion may reduce the impact of gas channeling for reservoirs with strongly connected fractures. [ABSTRACT FROM AUTHOR]

Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Given a graph G = (V(G), E(G)), a set M ⊆ V(G) is a distance-edge-monitoring set if for every edge e ∈ E(G), there is a vertex x ∈ M and a vertex y ∈ V(G) such that the edge e belongs to all shortest paths between x and y. The smallest size of such a set in G is denoted by dem(G). Denoted by G – e (resp. G\u) the subgraph of G obtained by removing the edge e from G (resp. a vertex u together with all its incident edges from G). In this paper, we first show that dem(G – e) – dem(G) ≤ 2 for any graph G and edge e ∈ E(G). Moreover, the bound is sharp. Next, we construct two graphs G and H to show that dem(G) – dem(G\u) and dem(H \ v) – dem(H) can be arbitrarily large, where u ∈ V(G) and v ∈ V(H). We also study the relation between dem(H) and dem(G), where H is a subgraph of G. In the end, we give an algorithm to judge whether the distance-edge-monitoring set still remain in the resulting graph when any edge of a graph G is deleted. [ABSTRACT FROM AUTHOR]

Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Given a graph G = (V(G), E(G)), a set M ⊆ V(G) is a distance-edge-monitoring set if for every edge e ∈ E(G), there is a vertex x ∈ M and a vertex y ∈ V(G) such that the edge e belongs to all shortest paths between x and y. The smallest size of such a set in G is denoted by dem(G). Denoted by G – e (resp. G\u) the subgraph of G obtained by removing the edge e from G (resp. a vertex u together with all its incident edges from G). In this paper, we first show that dem(G – e) – dem(G) ≤ 2 for any graph G and edge e ∈ E(G). Moreover, the bound is sharp. Next, we construct two graphs G and H to show that dem(G) – dem(G\u) and dem(H \ v) – dem(H) can be arbitrarily large, where u ∈ V(G) and v ∈ V(H). We also study the relation between dem(H) and dem(G), where H is a subgraph of G. In the end, we give an algorithm to judge whether the distance-edge-monitoring set still remain in the resulting graph when any edge of a graph G is deleted. [ABSTRACT FROM AUTHOR]

Traditional reservoir numerical simulation software just only consider the static fractures but cannot simulate the impact of fracture expansion on well network development during long-term water injection, and the simulation results are poorly fitted to the actual production dynamic data. To address this problem, a characterization method for complex dynamic fracture networks is developed based on the embedded discrete fracture model ( ED-FM) with dynamic improvement of pre-processing algorithms. The study shows that an efficient waterflood-induced fracture simulation method is established by coupling cross-fracture discrimination criteria, which can efficiently simulate the dynamic changes of fractures during reservoir injection and development and reflect the influence of natural fractures on the main fracture propagation path; the results are consistent compared with Abaqus software, while the computational efficiency is higher. The application example shows that the method has good adaptability for numerical simulation of waterflood-induced fractures, can accurately achieve the fitting of the water cut rising rules of the field water injection well cluster, which and has good reference significance for production dynamic analysis of ultra-low permeability reservoirs and later well pattern adjustment. [ABSTRACT FROM AUTHOR]