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Dragonfly networks have significant advantages in data exchange due to the small network diameter, low cost and modularization. A graph |$G$| is |$vertex$| - |$pancyclic$| if for any vertex |$u\in V(G)$|⁠ , there exist cycles through |$u$| of every length |$\ell $| with |$3\leq \ell \leq |V(G)|$|⁠. A graph |$G$| is |$Hamiltonian$| - |$connected$| if there exists a Hamiltonian path between any two distinct vertices |$u,v\in V(G)$|⁠. In this paper, we mainly research the pancyclic and Hamiltonian properties of the dragonfly network |$D(n,h)$|⁠ , and find that it is Hamiltonian with |$n\geq 1,\,\,h\geq 2$|⁠ , pancyclic, vertex-pancyclic and Hamiltonian-connected with |$n\geq 4,\,\,h\geq 2$|⁠. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to advance the concept of region reaching control for a single robot to the study of region reaching consistency for uncertain fully‐actuated multi‐robot systems formulated by Lagrange dynamics. By introducing a directed network communication topology and utilizing the pinning‐like control methods, a distributed region reaching consensus control strategy is proposed. The desired region shape can be specified by selecting an appropriate potential objective function. A feature of the developed region reaching consensus algorithm is fully distributed, which is also an important generalization of pinning‐like set point tracking scheme based on the typical proportion‐integration‐differentiation control scheme. More importantly, the scope of consistency in this paper can be explicitly defined, which is different from traditional consistency control algorithms. Subsequently, numerical examples are presented to illustrate the performance of the designed controllers. [ABSTRACT FROM AUTHOR]

Purpose: The objective of this study was to investigate the efficacy of an artificial intelligence-assisted 3D planning system (AIHIP) in total hip arthroplasty by direct anterior approach and assess the reliability of the AIHIP preoperative program in terms of both interobserver and intraobserver agreement. Methods: A retrospective analysis was conducted on patients who underwent unilateral primary THA via direct anterior approach from June 2019 to March 2022. Participants were randomly assigned to receive either the AIHIP system (n = 220) or the 2D template (control group) (n = 220) for preoperative planning. The primary outcome aimed to evaluate the correspondence between the prosthesis selected intro-operation and the one planned preoperatively, as well as to calculate the intraclass correlation coefficient (ICC). Secondary outcomes included operation time, intraoperative blood loss, fluoroscopy times, Harris hip score (HHS), lower limb length difference (LLD), femoral offset (FO), and bilateral femoral offset difference. Results: No significant differences were observed in gender, age, body mass index (BMI), aetiology, and American Society of Anesthesiologists (ASA) score between the two groups. Both planning methods exhibited good intraobserver agreement for component planning (ICC: 0.941–0.976). Interobserver agreement for component planning was comparable between the two methods (ICC: 0.882–0.929). In the AIHIP group, the accuracy of acetabular cup and femoral stem prosthetics planning significantly improved, with accuracies within the size range of ± 0 and ± 1 being 76.8% and 90.5% and 79.5% and 95.5%, respectively. All differences between two groups were statistically significant (p < 0.05). Patients receiving AIHIP preoperative planning experienced shorter operation times, reduced intraoperative blood loss, fewer fluoroscopy times, and lower leg length discrepancy (LLD) (p < 0.05). Moreover, they demonstrated a higher Harris hip score (HHS) at three days post-surgery (p < 0.05). However, no significant differences were found in femoral offset (FO), difference of bilateral femoral offsets, and HHS at 1 month after the operation. Conclusion: Utilizing AIHIP for preoperative planning of direct anterior approach THA can significantly enhance the accuracy of prosthetic sizing with good reliability, decrease operation time, reduce intraoperative blood loss, and more effectively restore the length of both lower limbs. This approach has greater clinical application value. [ABSTRACT FROM AUTHOR]

Both respirators and surgical masks (SM) are used as source control devices. During the COVID-19 pandemic, there was much interest in understanding the extent of particle total outward leakage (TOL) from these devices. The objective of this study was to quantify the TOL for five categories of devices: SMs, National Institute for Occupational Safety and Health (NIOSH) Approved N95 filtering facepiece respirators (FFRs) without exhalation valves, NIOSH Approved N95 FFRs with exhalation valves (N95 FFRV), NIOSH Approved elastomeric half-mask respirators (EHMRs) with exhalation valves, and NIOSH Approved EHMRs with an SM covering the exhalation valve (EHMRSM). A benchtop test system was designed to test two models of each device category. Each device was mounted on a headform at three faceseal levels (0% faceseal, 50% faceseal, and 100% faceseal). At each faceseal level, the TOL was assessed at three flow rates of minute ventilations of 17, 28, and 39 L/min. The experimental design was a split-split-plot configuration. Device type, faceseal level, flow rate, and the interaction of device type and faceseal level were found to have a significant effect ( p - value < 0.05) on the TOL. This study found that the N95 FFRs without exhalation valves had the lowest mean TOL. The SMs had about three times higher TOL than the N95 FFRs without exhalation valves. The TOL of the N95 FFRV was comparable to that of the SM at 0% and 50% faceseal on average overall conditions, but the N95 FFRV had a significantly higher TOL than the SM at a 100% faceseal. The EHMRs had the highest TOL because of the exhalation valve. Using an SM to cover the exhalation valve did not improve the EHMRs' efficiency in mitigating the TOL. Caution should be exercised when using N95 FFRVs as a source control measure against respiratory activities with heavy work rates, such as performing CPR. Results of this study showed that reduced faceseal leakage for N95 FFRs and SMs improves source control. [ABSTRACT FROM AUTHOR]

Congenital aniridia is a rare autosomal dominant congenital ocular disorder. Genetic studies suggest that heterozygous mutations in the developmental regulator PAX6 gene or the related regulatory regions leading to haploinsufficiency are the main cause of congenital aniridia. In this study, the clinical characteristics and pathogenic mutation of a four-generation Chinese family with congenital aniridia were investigated. All members recruited in this study underwent comprehensive ophthalmic examinations. Targeted gene capture sequencing and Sanger sequencing were performed to screen and confirm the candidate pathogenicity gene and its mutation. A multiple alignment of homologous sequences covering the identified mutation from different species was investigated, and the mutant protein structure was predicted using Swiss-Model. Additionally, the prediction of pathogenicity was analyzed using the ACMG Guidelines. Thirteen patients in this pedigree were diagnosed with congenital aniridia. A novel heterozygous frameshift mutation (c.391_398dupATACCAAG, p.Ser133Argfs*8) in exon 7 of the PAX6 gene was identified in all affected individuals in the family. This study demonstrates that this frameshift mutation of the PAX6 gene might be the causative genetic defect of congenital aniridia in this family. This mutation is predicted to cause the premature truncation of the PAX6 protein, leading to the functional haploinsufficiency of PAX6, which may be the major molecular mechanism underlying the aniridia phenotype. To the best of our knowledge, this is the first report of a novel pathogenic PAX6 gene variant c.391_398dupATACCAAG(p.Ser133Argfs*8) identified in a Chinese family with congenital aniridia. [ABSTRACT FROM AUTHOR]

Fragmentation functions are important quantities in describing the hadronization process in high energy reactions. They can induce various azimuthal modulations which can be measured to reveal correlations between transverse momenta and polarizations. Without introducing initial state uncertainties, electron positron annihilation process is known as an ideal process to investigate the fragmentation functions. In this paper, therefore, we calculate the hadron pair production in the semi-inclusive electron positron annihilation process e + + e - → h 1 + h 2 + q ¯ + X at twist-4 to study dihadron fragmentation functions. Here q ¯ denotes an antiquark that corresponds to a jet of hadrons in experiments. Together with single hadron fragmentation functions, dihadron fragmentation functions can provide additional ways to extract nucleon parton distribution functions from the semi-inclusive deeply inelastic scattering experiments with two detected final state hadrons. We calculate the differential cross section of the hadron pair production semi-inclusive electron positron annihilation process at twist-4 level. The calculation is carried out by using the collinear expansion method. We also calculate azimuthal asymmetries in terms of dihadron fragmentation functions. Contributions from four-quark correlator are also taken into account. Both the electromagnetic and weak interactions are considered in this paper. [ABSTRACT FROM AUTHOR]

Given two graphs H and F, let ex(n, H, F) denote the maximum number of copies of H in an F-free graph on n vertices. In the paper, we show that e x (n , K r , 2 K r) = N (K r - 1 , T r - 1 (n - 1)) for n ≥ 3 r 5 and r ≥ 3 , where N (K r - 1 , T r - 1 (n - 1)) denotes the number of (r - 1) -cliques in (r - 1) -partite Turán graph on n - 1 vertices. For r = 3 , we determine e x (n , K 3 , 2 K 3) for all n. [ABSTRACT FROM AUTHOR]

Purpose. Elbow joint injuries are extremely common in most athletes. Athletes' chronic elbow injuries can involve multiple complex anatomical structures related to orthopedics. Therefore, it is of great significance to explore the characteristics of magnetic resonance (MR) images of chronic sports injuries of the elbow joint and the influence of acupuncture treatment on MR images and clinical symptoms. Methods. A total of 60 elbow joints of 39 athletes from 15-25 years old were selected for coronal, sagittal, and axial MR scans to observe the image characteristics; 60 elbow joints were randomly divided into acupuncture group and control group and observed changes in MR images and clinical symptoms after acupuncture treatment. Results. After acupuncture treatment, the clinical symptoms were significantly improved. MR images showed that the elbow joint effusion was reduced, and the bone marrow edema was reduced. The effective rate of acupuncture treatment is as high as 100%, while the effective rate of the control group is only 40%. Acupuncture treatment has significantly improved the range of motion of the elbow joint. Conclusion. Acupuncture treatment can significantly relieve athletes' elbow joint pain and locking symptoms, improve joint range of motion, and is beneficial to recovery of special training and high-level competitive competitions. It is a sensitive, effective, and noninvasive method. [ABSTRACT FROM AUTHOR]

Let S k be the star with k edges, and let L (K n) be the line graph of the complete graph K n on n vertices. In this paper, we show that if k > 2 is a prime and n ≥ k + 1 , then the line graph L (K n) has an S k -decomposition if and only if n ≡ 0 , 1 , 2 (mod k). [ABSTRACT FROM AUTHOR]

Objective. To improve the clinical detection rate of bone and joint fractures of the extremities and to explore the value and significance of the application of multislice spiral computed tomography (MSCT) postprocessing technology in diagnosis. Methods. 80 patients with bone and joint fractures of the extremities admitted to the hospital were selected as the research objects. The patients received X-ray digital radiography (DR) plain film examination and then MSCT examination. At the same time, multiplane reconstruction (MPR) and surface shadow display (SSD) and volume rendering three-dimensional imaging (VRT) technology and other postprocessing technologies compare the differences in the detection rate of limbs and joint fractures between the two inspection methods. Results. A total of 100 fractures were found in 80 patients. The detection rate of X-ray DR was 69%. After MSCT postprocessing technology, the detection rates of MPR, SSD, and VRT were 96%, 98%, and 99%, respectively. The accuracy of MSCT postprocessing technology in diagnosing extremity bone and joint fractures was significantly higher than that of DR, and the difference between groups was statistically significant. Conclusion. MSCT postprocessing technology for patients with extremity bone and joint fractures has a good effect. It is not only noninvasive but also has a high detection rate. It can significantly reduce the missed and misdiagnosed rate and provide detailed imaging data for the formulation of clinical treatment plans. [ABSTRACT FROM AUTHOR]

When tunneling events induced by nontrivial configurations of the quantum chromodynamics gauge fields are taken into consideration, parity violating quantities emerge. Based on this consideration, parity-odd fragmentation functions can be introduced in the high energy reactions. In this paper, we calculate the differential cross-section in terms of both the parity-even and parity-odd fragmentation functions in semi-inclusive electron positron annihilation process. Semi-inclusive implies that not only a vector meson in one jet but also the back-to-back jet is measured in this reaction. According to the differential cross-section, we further calculate the azimuthal asymmetries and hadron polarizations in terms of fragmentation functions. A method of measuring the parity violating effects in the semi-inclusive annihilation process is suggested. [ABSTRACT FROM AUTHOR]

Sun Yat-sen, an active christian in the 19th century, was established as a pious and great christian image in the 20th century, especially after his death. This was the result of the discourse construction of Chinese christians, especially liberal christians. Sun Yat-sen presented an image as a great christian revolution and national leader, who followed the teachings of faith and led the chinese to get rid of alien and autocratic rule and move towards a free and equal new China. However, such images were not a simple representation of the christian Sun Yatsen. When Kuomintang used Sun Yat-sen to establish party authority, chinese christians also made full use of this public resource to build Sun Yat-sen's religious image: chinese Moses or chinese Jesus. Their purposes were to effect a reconciliation with nationalism and revolutionary ideology through a creative interpretation, and to achieve their own multiple political and religious goals, and finally as a way to reconstruct religious self-identity, political identity and national identity. [ABSTRACT FROM AUTHOR]

In order to meet ever-increasing demands for reliable parallel and distributed systems, it is crucial to evaluate the reliability and fault tolerance of their underlying interconnection networks. Such an interconnection network is usually modeled as a connected graph G, where the vertex set and edge set represent the processors and links between processors in the network, respectively. In this paper, we combine Fàbrega's idea about h-extra edge-connectivity and Sampathkumar's concept about r-component edge-connectivity to introduce a more refined parameter for characterizing fault tolerance of interconnection networks, named as h-extra r-component edge-connectivity. Given a connected graph G, for two integers h ≥ 1 and r ≥ 2 , the h-extra r-component edge-connectivity of G, denoted as c λ r h (G) , is the minimum cardinality among all edge subsets F ⊂ E (G) , if any, such that G - F has at least r components, and each component has at least h vertices. As an enhancement on hypercube, the n-dimensional augmented cube AQ n , introduced by Choudum and Sunitha in 2002, reserves several excellent topological properties. As | V (AQ n) | = 2 n , the h-extra three-component edge-connectivity of AQ n is well-defined for each integer h with 1 ≤ h ≤ ⌊ 2 n / 3 ⌋ . In this paper, a generalization of Xu et al.'s conclusion is obtained that finds an upper bound for the exact value of general h-extra three-component edge-connectivity of AQ n and shows that it is sharp for 1 ≤ h ≤ 2 n 2 - 1 and h = 2 c where 1 ≤ c ≤ n - 2 . Let h = ∑ i = 0 s 2 t i be a positive integer with t 0 > t 1 > ⋯ > t s ≥ 0 . Let δ = 0 if h is even and δ = 1 if h is odd. Specifically, c λ 3 h (AQ n) = (4 n - 4) h - 2 ∑ i = 0 s (2 t i - 1) 2 t i - 2 ∑ i = 0 s 4 i · 2 t i - δ for n ≥ 4 , h ≤ 2 n 2 - 1 , and c λ 3 2 c (AQ n) = (2 n - 2 c - 1) 2 c + 1 for n ≥ 4 and 1 ≤ c ≤ n - 2 . [ABSTRACT FROM AUTHOR]

With the development of scalability and applications in many interconnection networks used for large-scale parallel computing, link failures are inevitable. Once fault-free processors are guaranteed to lie in specific undamaged subnetworks, the subtasks can still operate as originally intended or after slight redesigning. The hypercube Q n is one of the most promising networks, and many algorithms are designed based on it. As a variant of Q n , the (n, k)-enhanced hypercube Q n , k presents more desired topological properties. The modified embedded edge-connectivity of Q n , k , denoted by η l ∗ (Q n , k) , is defined as the minimum number of links whose removal disconnects Q n , k , if any, such that every processor in the resulting network lies in an undamaged Q l or Q l , k - n + l . For n ≥ 2 , 1 ≤ k ≤ n - 1 and 1 ≤ l ≤ n - 1 except for the case of k = 2 and l = n - 2 , this paper mainly determines that η l ∗ (Q n , k) = (n - l + 1) 2 l if l ≤ n - k and η l ∗ (Q n , k) = (n - l) 2 l if n - k + 1 ≤ l ≤ n - 1 . And the value in the exceptional circumstance is 2 n - 1 . After a slight modification of our conclusion for l = 2 , the cyclic edge-connectivity of Q n , k for n ≥ 3 is also determined as a by-product. Our work can offer a more accurate evaluation for the reliability and fault tolerance of interconnection networks. [ABSTRACT FROM AUTHOR]

Deep inelastic scattering is one of the best place to study hadron structures. In this paper we consider the target fragmentation region deep inelastic scattering process at leading twist. The calculations are carried out by applying the collinear expansion. In the collinear expansion formalism the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. Quantum chromodynamics is a non-Abelian gauge theory of strong interactions in which parity symmetry can be violated by the nontrivial 𝜃 -vacuum tunneling effects. As a result, the axial vector current is induced. By defining and decomposing the parity-odd correlator we calculate both the parity-even and parity-odd contributions to the cross-section of the target fragmentation region deep inelastic scattering. We also present the positivity bounds for these fracture functions. [ABSTRACT FROM AUTHOR]

Yoshimi Egawa [8] showed that a 5-connected graph G admits at most 2 | V (G) | − 1 0 3 5-shredders. In this paper we shown that a contraction-critical 5-connected graph G admits at most | G | − 6 2 5-shredders. Further we show that, for every contraction-critical 5-connected graph G, there is a contraction critical 5-connected graph G ̃ such that G is a spanning subgraph of G ̃ and G ̃ admits at most | G | − 1 4 5-shredders. [ABSTRACT FROM AUTHOR]

A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages so that no two edges on the same page cross. A planar graph of maximum degree k is called a planar k -graph. Bekos et al. described an O (n 2) time algorithm for computing two-page book embeddings for planar 4-graphs. In this paper, we embed planar 5-graphs into books of three pages by an O (n 2) time algorithm. [ABSTRACT FROM AUTHOR]

M.Kriesell conjectured that there existed b , h such that every 5-connected graph G with at least b vertices can be contracted to a 5-connected graph G 0 such that 0 < V G − V G 0 < h. We show that this conjecture holds for vertex transitive 5-connected graphs. [ABSTRACT FROM AUTHOR]

The k -matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect k -matchings nor almost perfect k -matchings. For many networks, their optimal k -matching preclusion sets are precisely those edges incident with a single vertex. In this paper, we introduce the concept of conditional k -matching preclusion, in which isolated vertices are not permitted in fault networks. We establish the conditional k -matching preclusion numbers and all possible minimum conditional k -matching preclusion sets for n -dimensional torus networks with n ≥ 3. In addition, we investigate the relationship between all optimal sets for three kinds of (conditional) matching preclusion problems. [ABSTRACT FROM AUTHOR]

Quantum chromodynamics is a fundamental non-Abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state is a linear superposition of the n -vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in this paper. We obtain 8 parity-odd parton distribution functions at leading twist for spin-1/2 hadrons and present their properties. By introducing the parity-odd quark–quark correlator, we find the parity-odd effects vanish from the macroscopic point of view. In this paper, we consider the high energy semi-inclusive deeply inelastic scattering process to investigate parity-odd effects by calculating the spin asymmetries. [ABSTRACT FROM AUTHOR]

Quantum chromodynamics is a non-Abelian gauge theory of strong interactions, in which the parity symmetry can be violated by the nontrivial 𝜃 -vacuum tunneling effects. The 𝜃 -vacuum induces the local parity-odd domains. Those reactions that occur in these domains can be affected by the tunneling effects and quantities become parity-odd. In this paper we consider the fragmentation process where parity-odd fragmentation functions are introduced. We present the fragmentation functions by decomposing the quark–quark correlator. Among the total 16 fragmentation functions, eight of them are parity conserved, and the others are parity violated. They have a one-to-one correspondence. Positivity bounds of these one-dimensional fragmentation functions are shown. To be explicit, we also introduce an operator definition of the parity-odd correlator. According to the definition, we give a proof that the parity-odd fragmentation functions are local quantities and vanish when sum over all the hadrons h. [ABSTRACT FROM AUTHOR]

To study the pore structure characteristics of middle-high rank coals (MHRC), five different kinds of coal samples from northern China were selected and pulverized, and the pore volume, pore size distribution, and fractal dimension were analyzed using N 2 /CO 2 adsorption and mercury intrusion porosimetry. The results show that the nanopores size of MHRC tends to decrease with the increase of coal rank, especially the ultra-micropores dominate in semi-anthracite coal. In addition, the fractal dimensions of the adsorption pore (pores >0.5 nm and pores <0.5 nm) are calculated, respectively. Both of these fractal dimension-fitting curves exhibit a U-shaped parabolic relationship with the R o. It can be found that the nanopores is affected by the coalification jumps by analyzing the relationship between the pore structure parameters and R o. The third coalification jump has a turning effect on the micropores development, and the fifth coalification jump significantly promoted the mesopores volume. Unlabelled Image • The pore structure of MHRC is characterized via MIP, N 2 /CO 2 adsorption. • We use fractal theory to analyze pore structure complexity of coal particles. • Ultra-micropores dominate pores in semi-anthracite. • The third coalification jump has a turning effect on the micropores structure. • The fifth coalification jump significantly promoted the development of mesopores. [ABSTRACT FROM AUTHOR]

A graph G is minimally t -tough if the toughness of G is t and deletion of any edge from G decreases its toughness. Kriesell conjectured that the minimum degree of a minimally 1-tough graph is 2, and Katona et al. proposed a generalized version of the conjecture that the minimum degree of a minimally t -tough graph is ⌈ 2 t ⌉. In this paper, we characterize the minimally 1 / a -tough, 2 K 2 -free graphs for an integer a. [ABSTRACT FROM AUTHOR]

Let r≥2 $r\ge 2$ and let F $F$ be an (r+1) $(r+1)$ ‐chromatic graph with a color‐critical edge, that is, there exists e∈E(F) $e\in E(F)$ such that F−e $F-e$ has chromatic number r $r$. Gerbner recently conjectured that every n $n$ ‐vertex maximal F $F$ ‐free graph with at least (1−1r)n22−o(nr+1r) $(1-\frac{1}{r})\frac{{n}^{2}}{2}-o({n}^{\frac{r+1}{r}})$ edges contains an induced complete r $r$ ‐partite graph on n−o(n) $n-o(n)$ vertices. Let Fs,k ${F}_{s,k}$ be a graph obtained from s $s$ copies of C2k+1 ${C}_{2k+1}$ by sharing a common edge. In this paper, we show that for all k≥2 $k\ge 2$ if G $G$ is an n $n$ ‐vertex maximal Fs,k ${F}_{s,k}$ ‐free graph with at least n2∕4−o(ns+2s+1) ${n}^{2}\unicode{x02215}4-o({n}^{\frac{s+2}{s+1}})$ edges, then G $G$ contains an induced complete bipartite graph on n−o(n) $n-o(n)$ vertices. We also construct graphs to show that the magnitude in o(ns+2s+1) $o({n}^{\frac{s+2}{s+1}})$ is best possible, which disproves Gerbner's conjecture for r=2 $r=2$. [ABSTRACT FROM AUTHOR]

A graph is l -path Hamiltonian if every path of length not exceeding l is contained in a Hamiltonian cycle. It is well known that a 2-connected, k -regular graph G on at most 3 k − 1 vertices is edge-Hamiltonian if for every edge uv of G , { u , v } is not a cut-set. Thus G is 1-path Hamiltonian if G − { u , v } is connected for every edge uv of G. Let P = u v z be a 2-path of a 2-connected, k -regular graph G on at most 2 k vertices. In this paper, we show that there is a Hamiltonian cycle containing the 2-path P if G − V (P) is connected. Therefore, the work implies a condition for a 2-connected, k -regular graph to be 2-path Hamiltonian. An example shows that the 2 k is almost sharp, i.e., the number is at most 2 k + 1. [ABSTRACT FROM AUTHOR]

We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron–positron annihilation process. When the nontrivial 𝜃 vacuum is taken into consideration, the parity symmetry of quantum chromodynamics is violated. As a consequence of the l o c a l 𝒫 -odd effects, 𝒫 -odd fragmentation functions would contribute to the azimuthal asymmetries. Azimuthal asymmetry coming from two interference terms with opposite signs vanishes when sum over many events. This symmetry only survives on the event-by-event basis. Azimuthal asymmetry coming from two interference terms with same signs survives and can be measured to extract the 𝒫 -odd fragmentation functions. We also present the hadron polarizations. [ABSTRACT FROM AUTHOR]

Diagnosability has played an important role in reliability of an interconnection network. In 2012, Peng et al. proposed a new measure of diagnosability, namely, g -good-neighbor diagnosability, which requires every fault-free vertex has at least g fault-free neighbors. The PMC model and MM ∗ model are widely adopted as the fault diagnosis model. The problems of g -good-neighbor diagnosability of many well-known networks under the PMC model and MM ∗ model have been widely explored. In this paper, we study the relationship between g -good-neighbor diagnosability under the PMC model and g -good-neighbor diagnosability under the MM ∗ model of a graph G. In addition, we give some sufficient conditions to ascertain g -good-neighbor diagnosability of a graph G under the PMC model and MM ∗ model. From this, many previous results can be directly obtained and g -good-neighbor diagnosability for many well-known networks under the PMC model and MM ∗ model, are derived. [ABSTRACT FROM AUTHOR]

The generalized k -connectivity of a graph G is a parameter that can measure the reliability of a network G to connect any k vertices in G , which is a generalization of traditional connectivity. Let S ⊆ V (G) and κ G (S) denote the maximum number r of edge-disjoint trees T 1 , T 2 , ... , T r in G such that V (T i) ⋂ V (T j) = S for any i , j ∈ { 1 , 2 , ... , r } and i ≠ j. For an integer k with 2 ≤ k ≤ n , the generalized k -connectivity of a graph G is defined as κ k (G) = m i n { κ G (S) | S ⊆ V (G) and | S | = k }. Data centers are essential to the business of companies such as Google, Amazon, Facebook and Microsoft et al. Based on data centers, the data center networks D k , n , introduced by Guo et al. in 2008, have many desirable properties. In this paper, we study the generalized 3 -connectivity of D k , n and show that κ 3 (D k , n) = n + k − 2 for k ≥ 0 and n ≥ 3. [ABSTRACT FROM AUTHOR]

Ultrafine and highly dispersed PdCu nanoalloys anchored on porous carbon were synthesized by a facile NaBH 4 reduction method in a ionic liquid (IL)/water solution system. During the synthesis, the IL solvent can act not only as a stabilizer to slow down the particle growth and prevent the agglomeration, but also as a functional agent to improve the hydrophilicity and sorption property of carbon support due to the functional groups. The resulting PdCu/porous carbon (PdCu/PC) exhibits a remarkable activity for ethanol oxidation in alkaline solution (ethanol oxidation specific activity of 6.54 mA cm−2, only 2.14 mA cm−2 for commercial Pd/C), high poison tolerance (i f /i b = 1.09), and excellent catalytic stability (only a loss of 4.3% of the initial ethanol oxidation reaction activity after 100 cycles). The superior performance of PdCu/PC can be ascribed to the abundant active reaction sites of porous carbon, uniform and good dispersion of PdCu nanoaolloys, as well as the strong metal-support interaction. This work is anticipated to be useful for the development of low-cost and highly active catalysts for fuel cells. Image 10799 • Ultrafine dispersed PdCu nanoalloys anchored on porous carbon are synthesized through an ionic liquid-assisted approach. • The ionic liquid solvent can improve the hydrophilicity of support and slow down the particle growth. • PdCu/PC shows high catalytic activity, durability, and tolerance toward ethanol oxidation in alkaline solution. • The superior performance of PdCu/PC arises from its advanced structure and composition. [ABSTRACT FROM AUTHOR]

Abstract The component connectivity is a kind of conditional connectivity. It is a generalization of the traditional connectivity, which is also a parameter for the reliability evaluation of interconnection networks. The g -component connectivity c κ g (G) of a non-complete connected graph G is the minimum number of vertices whose deletion results in a graph with at least g components. The results in Hsu et al. (2012) by Hsu et al. determine the component connectivity of the hypercube. As an invariant of the hypercube, in this paper, we first determine the minimum neighbourhood of g vertices in the folded hypercube for 1 ≤ g ≤ n + 2 , then we give the (g + 1) -component connectivity of the folded hypercube c κ g + 1 (F Q n) = g (n + 1) − 1 2 g (g + 1) + 1 for 1 ≤ g ≤ n − 1 and n ≥ 8. [ABSTRACT FROM AUTHOR]

Highlights • Molecular structure of the middle-high rank coals were systematically characterized. • The A(CH 2)/A(CH 3) of coal samples decrease with the increasing R o from 0.4 to 2.6%. • The new coalification jump at R o = 4.2–4.8% is unreported in previous studies. • Using chemical structure parameters to evaluate the coal rank has limitation. Abstract In recent years, the major coal producing areas in China have entered the period of deep mining, with coal rank changing from low-rank coal (LRC) to middle-high rank coal (MHRC). Even though material properties of MHRC, such as pore size and shape, have attracted increasing attentions, its molecular structures still remains unclear. This study probes molecular structural properties of five MHRC samples using X-ray diffraction (XRD), Raman and Fourier transform infrared (FTIR) spectroscopy. Test results show that with the deepening of coalification, the aromatic rings of MHRC increase gradually. The aliphatic side chains between the aromatic rings continuously fall off. The ordered structure of coal continues to enhance, resulting in an increase in the degree of graphitization of coal. The average lateral sizes (L a), stacking heights (L c) and interlayer spacing (d 002) of the crystallite structures of MHRC samples derived from the XRD range from 20.65 to 31.68, 10.62 to 19.21 and 3.42 to 3.66 Å, respectively. The L a values derived from the Raman spectra using the classical linear relationship between 1/L a and the I D1 /I G band ratio are higher (36.36–59.91 Å) than the values obtained from XRD. The FTIR spectra reveals that MHRC samples contain aliphatic functional groups such as CH 2 and CH 3 , aromatic functional groups such as C C and aromatic ring CH, and oxygen-containing functional groups such as OH, C O and C O. The aromaticity (f a) of the coal samples determined by FTIR ranges from 0.66 to 0.98, and compared with the f a valued from XRD (0.63 to 0.93), which shows that the MHRC contains abundant of aliphatic components. On the basis of these results, the structural parameters obtained by different spectral techniques are also used to comparatively study the effects of coalification on the molecular structure of coals. The structural parameters of coal derived by these methods reflect the coalification jumps at R o = 0.5, 0.7–0.9, 1.2, 2.6, 3.3, 3.5–4.0 and 4.2–4.8%. Among them, the jump at R o = 4.2–4.8% is unreported in previous studies and should be further studied in subsequent research. The application range of structure parameters used to evaluate the coal rank such as d 002 , L a (XRD), f a and G-D 1 should be considered because of coalification jumps. The parameters such as 'C', I D1 /I G and L a (Raman) are better choices for evaluating coal rank for their better correlation with R o. It is worth pointing out that these parameters have implications for coalification and should be concerned in further study. [ABSTRACT FROM AUTHOR]

Abstract For a set of graphs F , the extremal number e x (n ; F) is the maximum number of edges in a graph of order n not containing any subgraph isomorphic to some graph in F. If F contains a graph on n vertices, then we often call the problem a spanning Turán problem. A linear forest is a graph whose connected components are all paths and isolated vertices. In this paper, we let L n k be the set of all linear forests of order n with at least n − k + 1 edges. We prove that when n ≥ 3 k and k ≥ 2 , e x (n ; L n k) = n − k + 1 2 + O (k 2). Clearly, the result is interesting when k = o (n). [ABSTRACT FROM AUTHOR]

Abstract Various structured PbO 2 electrodes were prepared by surfactant-assisted anodic electrodeposition method. PbO 2 -PEG thin-film electrode is composed of small particles and shows a smooth surface. PbO 2 -PVA electrode displays a unique structure in which the PbO 2 particles are embed in the PVA network structure. PbO 2 -AOT electrode consists of bull-horn like particles. The morphologies and structures of PbO 2 electrodes are highly influenced by the surfactant. PEG and PVA can decrease the particle size of PbO 2 particle and AOT can dramatically alter the morphology of PbO 2 particle. PbO 2 -PEG, PbO 2 -PVA, and PbO 2 -AOT electrodes exhibit excellent electrocatalytic activity, stability, corrosion resistance, and long service life compared with bare PbO 2 electrode. This work demonstrates the relationship between the structure and electrochemical performances of PbO 2 electrodes, and provides a feasible approach to fabricate stable structured electrode. Highlights • Various structured PbO 2 thin-film electrodes are prepared. • Electrochemical performance of PbO 2 depends on its structure and morphology. • PbO 2 -PEG electrode exhibits the best performance. • The performance of PbO 2 -PEG electrode arises from its smooth and dense structure. [ABSTRACT FROM AUTHOR]

Application value of fiberoptic bronchoscopy combined with liquid-based cytology test (LCT) in the early diagnosis of lung cancer was investigated. Clinical data of 901 patients who had suspicious lung space-occupying lesions and underwent bronchoscopy combined with LCT in Shanxi Provincial Cancer Hospital from June 2012 to June 2016 were retrospectively analyzed. Patients were divided into four groups to receive different fiberoptic bronchoscopies combined with LCT. Patients in Group A (n=276) received bronchoscopic washing cultures (BWC), Group B (n=204) received bronchoalveolar lavage (BAL), Group C (n=187) underwent endobronchial ultrasound-guided transbronchial needle aspiration (EBUS-TBNA) and Group D (n=234) underwent transbronchial lung biopsy (TBLB). All patients received pathological biopsy to confirm the lesions. The diagnostic results of lung cancer and the incidence rates of postoperative adverse reactions/complications were analyzed and compared among the four groups. Among 901 patients, 741 cases were pathologically diagnosed with lung cancer. In Group A, there were 224 cases diagnosed with lung cancer, of which 193 cases were successfully detected with a detection rate of 86.17% and a κ-value of 0.426. In Group B, 171 cases were diagnosed with lung cancer, of which 149 cases were successfully detected with a detection rate of 87.13% and a κ-value of 0.430. In Group C, 154 cases were diagnosed with lung cancer, of which 146 cases were successfully detected with a detection rate of 94.81% and a κ-value of 0.769. In Group D, 192 cases were diagnosed with lung cancer, of which 170 cases were successfully detected with a detection rate of 88.54% and a κ-value of 0.440. Therefore, we conclude that fiberoptic bronchoscopy combined with LCT technique is safe and reliable for the diagnosis of the early-stage lung cancer. [ABSTRACT FROM AUTHOR]

Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The g -component edge connectivity c λ g (G) of a non-complete graph G is the minimum number of edges whose deletion results in a graph with at least g components. Let g be an integer and g = ∑ i = 0 s 2 t i be the decomposition of g such that t 0 = [ log 2 g ] , and t i = [ log 2 (g − ∑ r = 0 i − 1 2 t r ) ] for i ≥ 1. In this note, we determine the g -component edge connectivity of the hypercube Q n , c λ g (Q n) = n g − (∑ i = 0 s t i 2 t i − 1 + ∑ i = 0 s i ⋅ 2 t i ) for g ≤ 2 [ n 2 ] + 1 , n ≥ 7. Moreover, we classify the corresponding optimal solutions. [ABSTRACT FROM AUTHOR]

Given an integer 1 ≤  j  <  n , define the ( j )-coloring of a n -dimensional hypercube H n to be the 2-coloring of the edges of H n in which all edges in dimension i , 1 ≤  i  ≤  j , have color 1 and all other edges have color 2. Cheng et al. (2017) determined the number of distinct shortest properly colored paths between a pair of vertices for the (1)-colored hypercubes. It is natural to consider the number for ( j )-coloring, j  ≥ 2. In this note, we determine the number of different shortest proper paths in ( j )-colored hypercubes for arbitrary j . Moreover, we obtain a more general result. [ABSTRACT FROM AUTHOR]

Our understanding of the parton-level structure in the nucleon comes predominantly from the electron deeply inelastic scattering measurements with very high precision. It deserves further study. We therefore calculate the neutral current jet production semi-inclusive deeply inelastic scattering process in this paper. Neutral current implies that interactions can be mediated by the photon, Z 0 boson and their interference. The initial electron is assumed to be polarized and then scattered off by a target particle with spin 1. After obtaining the differential cross section, we calculate sets of quantities, including structure functions, azimuthal asymmetries, parity-violating asymmetries and charge asymmetries. They can be measured in the experiments. We find that these quantities are expressed in terms of the parton distribution functions and the electroweak coefficients. These coefficients are different from that in the γ ⁎ N collinear frame. As a result, our calculation provides a set of new quantities for determining the electroweak couplings as well as the parton distribution functions in the deeply inelastic scattering. It is helpful to test the universality of the parton distribution functions or to understand the hadronic weak interactions and strong interactions simultaneously. [ABSTRACT FROM AUTHOR]

The forward-backward asymmetry is an important measurable quantity which can enable independent determination of the neutral-current couplings of fermions. In this paper, we extend the definition of the asymmetry from the partonic level to the hadronic level by calculating this asymmetry of the hadron pair in the semi-inclusive electron position annihilation process. Semi-inclusive implies that a back-to-back jet is also measured in addition to the hadron pair. Due to the limitation of the factorization theorem, we calculate this process up to leading order twist-4 level by applying the collinear expansion formalism. After obtaining the differential cross section, we calculate the forward-backward asymmetries and show them in terms of the corresponding di-hadron fragmentation functions. Di-hadron fragmentation functions are introduced to describe the hadron pair productions in the fragmentation process. With available parameterization of the functions, we present a numerical estimation of the forward-backward asymmetry. On the flip side, measurements of the forward-backward asymmetry would give strict restrictions of parameterizations of the di-hadron fragmentation functions. We also present a numerical estimation of the twist-4 di-hadron fragmentation functions in order to illustrate their contributions. [ABSTRACT FROM AUTHOR]

Over binary-input memoryless symmetric (BMS) channels, the performance of polar codes under successive cancellation list (SCL) decoding can approach maximum likelihood (ML) algorithm when the list size L is greater than or equal to 2 M F , where MF, known as mixing factor of code, represents the number of information bits before the last frozen bit. Recently, Yao et al. showed the upper bound of the mixing factor of decreasing monomial codes with length n = 2 m and rate R ≤ 1 2 when m is an odd number; moreover, this bound is reachable. Herein, we obtain an achievable upper bound in the case of an even number. Further, we propose a new decoding hard-decision rule beyond the last frozen bit of polar codes under BMS channels. [ABSTRACT FROM AUTHOR]

The n-dimensional hypercube Qn is bipancyclic and contains a 3-regular, 3-connected subgraph on l vertices for every even l from 8 to 2n except 10. In this paper, we strengthen the previous works to Cartesian product of paths. The bipancyclicity and the existence of 3-regular subgraphs of Cartesian product of paths are studied in this paper. [ABSTRACT FROM AUTHOR]

We call an edge-coloring of a graph G a rainbow coloring if the edges of G are colored with distinct colors. For every even positive integer k≥4, let f(n,k) denote the minimum number of colors required to color the edges of the n-dimensional cube Qn, so that every copy of Ck is rainbow. Faudree et al. [6] proved that f(n,4)=n for n=4 or n>5. Mubayi et al. [8] showed that n≤f(n,6)

Let D be a digraph. A k -container of D between u and v , C ( u , v ) , is a set of k internally disjoint paths between u and v . A k -container C ( u , v ) of D is a strong (resp. weak) k ∗ -container ( k ≥ 2 ) if there is a set of k internally disjoint paths with the same direction (resp. with different directions allowed) between u and v and it contains all vertices of D . A digraph D is k ∗ -strongly (resp. k ∗ -weakly) connected if there exists a strong (resp. weak) k ∗ -container between any two distinct vertices for k ≥ 2 . Specially, we define D is 1 ∗ -connected if D is weakly Hamiltonian connected (a 1 ∗ -connected digraph is 1 ∗ -strongly and also 1 ∗ -weakly connected.) We define the strong (resp. weak) spanning connectivity of a digraph D , κ s ∗ ( D ) (resp. κ w ∗ ( D ) ), to be the largest integer k such that D is ω ∗ -strongly (resp. ω ∗ -weakly) connected for all 1 ≤ ω ≤ k . In this paper, we show that for k ≥ 0 , a ( 2 k + 1 ) -strong tournament is ( k + 2 ) ∗ -weakly connected and that for k ≥ 2 , a 2 k -strong tournament is k ∗ -strongly connected. Furthermore, we show that in a tournament with n vertices and irregularity i ( T ) ≤ k , if n ≥ 6 t + 5 k ( t ≥ 2 ) , then κ s ∗ ( T ) ≥ t and if n ≥ 6 t + 5 k − 3 ( t ≥ 2 ) , then κ w ∗ ( T ) ≥ t + 1 . [ABSTRACT FROM AUTHOR]

For a graph G = ( V , E ) , a subset F ⊂ V ( G ) is called an R k -vertex-cut of G if G − F is disconnected and each vertex u ∈ V ( G ) − F has at least k neighbors in G − F . The R k -vertex-connectivity of G , denoted by κ k ( G ) , is the cardinality of the minimum R k -vertex-cut of G , which is a refined measure for the fault tolerance of network G . In this paper, we study κ 2 for Cayley graphs generated by k -trees. Let S y m ( n ) be the symmetric group on { 1 , 2 , … , n } and T be a set of transpositions of S y m ( n ) . Let G ( T ) be the graph on n vertices { 1 , 2 , . . . , n } such that there is an edge i j in G ( T ) if and only if the transposition i j ∈ T . The graph G ( T ) is called the transposition generating graph of T . We denote by C a y ( S y m ( n ) , T ) the Cayley graph generated by G ( T ) . The Cayley graph C a y ( S y m ( n ) , T ) is denoted by T k G n if G ( T ) is a k -tree. We determine κ 2 ( T k G n ) in this work. The trees are 1-trees, and the complete graph on n vertices is a n − 1 -tree. Thus, in this sense, this work is a generalization of the results on Cayley graphs generated by transposition generating trees (Yang et al., 2010) and the complete-transposition graphs (Wang et al., 2015). [ABSTRACT FROM AUTHOR]

The line graph is a very popular research object in graph theory, in complex networks and also in social networks recently. In this paper, we show that if a line graph is Hamiltonian-connected, then the graphs in a special family of spanning subgraphs of the line graph are still Hamiltonian-connected. As an important corollary we prove that there exist at least m a x { 1 , ⌊ 1 8 δ ( G ) ⌋ − 1 } edge-disjoint Hamiltonian paths between any two vertices in a Hamiltonian-connected line graph L ( G ) . [ABSTRACT FROM AUTHOR]

The heat transfer and pressure loss characteristics on a square channel with two opposite surfaces roughened by high blockage ratio ribs are measured by systematic experiments. Reynolds number studied in the channel range from 1400 to 9000. The rib height (e) to the height of ribbed channel (H) ratios are 0.2 and 0.33, respectively. The rib spacing (S) to height ratio (S/e) ranges from 5 to 15. The rib orientations in the opposite surfaces are symmetric and staggered arrangement. The experimental results show that (1) the heat transfer coefficients are increased with the increase of Reynolds number, though at the cost of higher pressure losses; (2) when the rib spacing to height ratio is 10, it keeps a highest heat transfer coefficient in three kinds of rib spacing to height ratio 5, 10 and 15; (3) the heat transfer coefficient of symmetric arrangement ribs is higher than the staggered arrangement ribs, but the pressure losses of symmetric arrangement ribs is larger than the staggered arrangement ribs; (4) compared with one-side ribbed channel, the heat transfer coefficient of two-side ribbed channel is distinct higher than that of one-side ribbed channel. [ABSTRACT FROM AUTHOR]

Experimental investigations have been performed to investigate the enhanced film cooling performance caused by ellipse-shaped tabs located at the outlet of the film holes. Specific characteristics of three covering ratios of film holes and four blowing ratios are employed in this experiment and a numerical simulation is also performed to predict the flow fields and verify and to be validated by measured results. Both results showed that the presence of ellipse-tabs was in great decrease of intensity of kidney vortices and the penetration strength of coolant jet into mainstream, in consequence to improve the film cooling effectiveness and heat transfer coefficient than the ones without tabs. Furthermore, a generation of big pressure drop resulting from the ellipse tabs can be observed, resulting in the smaller discharge coefficient of film hole with ellipse tab than without tab. [ABSTRACT FROM AUTHOR]

It is known that edge disjoint paths is closely related to the edge connectivity and the multicommodity flow problems. In this paper, we study the edge disjoint paths in hypercubes and folded hypercubes with edge faults. We first introduce the F -strongly Menger edge connectivity of a graph, and we show that in all n -dimensional hypercubes (folded hypercubes, respectively) with at most 2 n − 4 ( 2 n − 2 , respectively) edges removed, if each vertex has at least two fault-free adjacent vertices, then every pair of vertices u and v are connected by min { deg ( u ), deg ( v )} edge disjoint paths, where deg ( u ) and deg ( v ) are the remaining degree of vertices u and v , respectively. [ABSTRACT FROM AUTHOR]

The r -component connectivity c κ r ( G ) of a non-complete graph G is the minimum number of vertices whose deletion results in a graph with at least r components. In this paper, we determine the component connectivity of the hypercube c κ r + 1 ( Q n ) = − r 2 2 + ( 2 n − 5 2 ) r − n 2 + 2 n + 1 for n + 1 ≤ r ≤ 2 n − 5 , n ≥ 6 . This paper extends the results in Hsu et al. (2012) [3] . [ABSTRACT FROM AUTHOR]