Unpaired Many-to-Many Disjoint Path Covers in Nonbipartite Torus-Like Graphs With Faulty Elements by Jung-Heum Park

“…Given disjoint source and sink sets, <inline-formula> <tex-math notation="LaTeX">$S = \{ s_{1},\ldots,s_{k}\}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$T = \{t_{1},\ldots, t_{k}\}$ </tex-math></inline-formula>, in graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, an unpaired many-to-many <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-disjoint path cover joining <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> is a disjoint path cover <inline-formula> <tex-math notation="LaTeX">$\{ P_{1}, \ldots, P_{k}\}$ </tex-math></inline-formula>, in which each path <inline-formula> <tex-math notation="LaTeX">$P_{i}$ </tex-math></inline-formula> runs from source <inline-formula> <tex-math notation="LaTeX">$s_{i}$ </tex-math></inline-formula> to some sink <inline-formula> <tex-math notation="LaTeX">$t_{j}$ </tex-math></inline-formula>. …”
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Image-to-Image Training for Spatially Seamless Air Temperature Estimation With Satellite Images and Station Data by Peifeng Su, Temesgen Abera, Yanlong Guan, Petri Pellikka

“…Plus, the strong linear relationships between observed daily mean <inline-formula><tex-math notation="LaTeX">$T_{a}$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">$T_{\rm{mean}}$</tex-math></inline-formula>), daily minimum <inline-formula><tex-math notation="LaTeX">$T_{a}$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">$T_{\min}$</tex-math></inline-formula>), and daily maximum <inline-formula><tex-math notation="LaTeX">$T_{a}$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">$T_{\max}$</tex-math></inline-formula>) make the estimation of <inline-formula><tex-math notation="LaTeX">$T_{\rm{mean}}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$T_{\min}$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">$T_{\max}$</tex-math></inline-formula> simultaneously possible. …”
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Maximal Augmented Zagreb Index of Trees With at Most Three Branching Vertices by Roberto Cruz, Juan Daniel Monsalve, Juan Rada

“…The Augmented Zagreb index of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is defined to be <inline-formula> <tex-math notation="LaTeX">$\mathcal {AZI}\left ({G}\right) =\sum _{uv\in E\left ({G}\right) } \left ({\frac { d\left ({u}\right) d\left ({v}\right) }{d\left ({u}\right) +d\left ({v}\right) -2} }\right) ^{3}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$E\left ({G}\right) $ </tex-math></inline-formula> is the edge set of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$d\left ({u}\right) $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d\left ({v}\right) $ </tex-math></inline-formula> are the degrees of the vertices <inline-formula> <tex-math notation="LaTeX">$u$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula> of edge <inline-formula> <tex-math notation="LaTeX">$uv$ </tex-math></inline-formula>. …”
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Set-to-Set Disjoint Path Routing in Bijective Connection Graphs by Keiichi Kaneko, Antoine Bossard, Frederick C. Harris

“…The bijective connection graph encompasses a family of cube-based topologies, and <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-dimensional bijective connection graphs include the hypercube and almost all of its variants with the order <inline-formula> <tex-math notation="LaTeX">$2^{n}$ </tex-math></inline-formula> and the degree <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>. …”
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Feature Extraction and NN-Based Enhanced Test Maneuver Deployment for 2 DoF Vehicle Simulator by Ugur Demir, Gazi Akgun, Mustafa Caner Akuner, Bora Demirci, Omer Akgun, Tahir Cetin Akinci

“…Then, a hardware in the loop (HIL) model with 2 inputs (torque, <inline-formula> <tex-math notation="LaTeX">$\tau _{1}$ </tex-math></inline-formula>- <inline-formula> <tex-math notation="LaTeX">$\tau _{2}$ </tex-math></inline-formula>) and 3 outputs (acceleration, <inline-formula> <tex-math notation="LaTeX">$\text{a}_{\mathrm {x}}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\text{a}_{\mathrm {y}}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\text{a}_{\mathrm {z}}$ </tex-math></inline-formula>) is created. …”
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On the Minimal General Sum-Connectivity Index of Connected Graphs Without Pendant Vertices by Akbar Ali, Shahzad Ahmed, Zhibin Du, Wei Gao, Muhammad Aslam Malik

“…The general sum-connectivity index of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, denoted by <inline-formula> <tex-math notation="LaTeX">$\chi _{_\alpha }(G)$ </tex-math></inline-formula>, is defined as <inline-formula> <tex-math notation="LaTeX">$\sum _{uv\in E(G)}(d(u)+d(v))^{\alpha }$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$uv$ </tex-math></inline-formula> is the edge connecting the vertices <inline-formula> <tex-math notation="LaTeX">$u,v\in V(G)$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$d(w)$ </tex-math></inline-formula> denotes the degree of a vertex <inline-formula> <tex-math notation="LaTeX">$w\in V(G)$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> is a non-zero real number. …”
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Amalgamations and Cycle-Antimagicness by Yijun Xiong, Huajun Wang, Mustafa Habib, Muhammad Awais Umar, Basharat Rehman Ali

“…A finite simple graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is called a <inline-formula> <tex-math notation="LaTeX">$(c,d)$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-antimagic if <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> satisfies the following properties: (i) <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> has an <inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-covering by the family of subgraphs <inline-formula> <tex-math notation="LaTeX">$H_{1},H_{2}, {\dots },H_{r}$ </tex-math></inline-formula> where every <inline-formula> <tex-math notation="LaTeX">$H_{t}\cong H, 1\leq t\leq r$ </tex-math></inline-formula>, (ii) there exists a bijection <inline-formula> <tex-math notation="LaTeX">$\beta: V\cup E \rightarrow \{1,2,3, {\dots },|V\cup E|\}$ </tex-math></inline-formula> such that the <inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula>-weights constitute an arithmetic progression with initial term <inline-formula> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> and common difference <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$c &gt; 0, d \ge 0$ </tex-math></inline-formula> are integers. …”
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On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3<italic>p^s</italic> Over F_{<italic>p^m</italic>} &#x002B; <italic>u</italic>F<it... by Hai Q. Dinh, Bac T. Nguyen, Hiep T. Luu, Woraphon Yamaka

“…Let <inline-formula> <tex-math notation="LaTeX">$p\not =3$ </tex-math></inline-formula> be any prime. …”
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Resistance Distances and Kirchhoff Indices Under Graph Operations by Yujun Yang, Yue Yu

“…The resistance distance between any two vertices of a connected graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is defined as the net effective resistance between them in the electrical network constructed from <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> by replacing each edge with a unit resistor. …”
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Vertex-Fault-Tolerant Cycles Embedding in Four-Conditionally Faulty Enhanced Hypercube Networks by Min Liu

“…Let <inline-formula> <tex-math notation="LaTeX">$F_{v}^{*}$ </tex-math></inline-formula> be the set of faulty vertices in <inline-formula> <tex-math notation="LaTeX">$Q_{n,k}$ </tex-math></inline-formula>. …”
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Key Generation in Cryptography Using Radio Path Coloring by Dhanyashree, K. N. Meera, Said Broumi

“…An <inline-formula> <tex-math notation="LaTeX">$L(p_{1},~p_{2},~p_{3},~{\dots },~p_{m})$ </tex-math></inline-formula>- labeling of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> is an assignment of positive integers to the vertices of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> such that the difference in the labels assigned to the vertices at distance <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> should be at least <inline-formula> <tex-math notation="LaTeX">$p_{i}$ </tex-math></inline-formula>. …”
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Two Algorithms for Constructing Independent Spanning Trees in (<italic>n,k</italic>)-Star Graphs by Jie-Fu Huang, Eddie Cheng, Sun-Yuan Hsieh

“…In a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, two spanning trees <inline-formula> <tex-math notation="LaTeX">$T_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$T_{2}$ </tex-math></inline-formula> are rooted at the same vertex <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>. …”
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r, s, t-Spherical Fuzzy VIKOR Method and Its Application in Multiple Criteria Group Decision Making by Jawad Ali, Muhammad Naeem

“…In <inline-formula> <tex-math notation="LaTeX">$\textsf {r},\textsf {s},\textsf {t}$ </tex-math></inline-formula>-SFS the sum of the <inline-formula> <tex-math notation="LaTeX">$\textsf {r}$ </tex-math></inline-formula>th power of membership grade, <inline-formula> <tex-math notation="LaTeX">$\textsf {s}$ </tex-math></inline-formula>th power of neutral grade and the <inline-formula> <tex-math notation="LaTeX">$\textsf {t}$ </tex-math></inline-formula>th power of non-membership grade is less than or equal to 1, where <inline-formula> <tex-math notation="LaTeX">$\textsf {r}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\textsf {s}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\textsf {t}$ </tex-math></inline-formula> are natural numbers. …”
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New Systematic MDS Array Codes With Two Parities by Lan Ma, Liyang Zhou, Shaoteng Liu, Xiangyu Chen, Qifu Sun

“…Row-diagonal parity (RDP) code is a classical <inline-formula> <tex-math notation="LaTeX">$(k+2,~k)$ </tex-math></inline-formula> systematic maximum distance separable (MDS) array code with <inline-formula> <tex-math notation="LaTeX">$k \leq L-1$ </tex-math></inline-formula> under sub-packetization level <inline-formula> <tex-math notation="LaTeX">$l = L-1$ </tex-math></inline-formula>, where L is a prime integer. …”
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Duty-Cycle Dependent Phase Shift Modulation of Dual Three-Phase Active Bridge Four-Port AC–DC/DC&#x2013;AC Converter Eliminating Low Frequency Power Pulsations by Morris J. Heller, Florian Krismer, Johann W. Kolar

“…A recently introduced Dual Three-Phase Active Bridge Converter (D3ABC) provides two three-phase ac ports (ac<inline-formula><tex-math notation="LaTeX">${}_{1}$</tex-math></inline-formula> and ac<inline-formula><tex-math notation="LaTeX">${}_{2}$</tex-math></inline-formula>), two dc ports (dc<inline-formula><tex-math notation="LaTeX">${}_{1}$</tex-math></inline-formula> and dc<inline-formula><tex-math notation="LaTeX">${}_{2}$</tex-math></inline-formula>), and galvanic isolation between the ports ac<inline-formula><tex-math notation="LaTeX">${}_{1}$</tex-math></inline-formula>, dc<inline-formula><tex-math notation="LaTeX">${}_{1}$</tex-math></inline-formula> (primary side) and ac<inline-formula><tex-math notation="LaTeX">${}_{2}$</tex-math></inline-formula>, dc<inline-formula><tex-math notation="LaTeX">${}_{2}$</tex-math></inline-formula> (secondary side). …”
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Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems by Muhammad Rahim, Kamal Shah, Thabet Abdeljawad, Maggie Aphane, Alhanouf Alburaikan, Hamiden Abd El-Wahed Khalifa

“…The <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOF) set, an extension of the <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair fuzzy set (<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ROF) set, offers a more comprehensive approach to information representation, adept at managing data uncertainties. …”
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Analytical Modeling and Optimization of Partitioned Permanent Magnet Consequent Pole Switched Flux Machine With Flux Barrier by Wasiq Ullah, Faisal Khan, Shahid Hussain, Muhammad Yousaf, Siddique Akbar

“…However, conventional SFPMM exhibits demerits of high PM volume <inline-formula> <tex-math notation="LaTeX">$(V_{PM})$ </tex-math></inline-formula>, high torque ripples <inline-formula> <tex-math notation="LaTeX">$(T_{rip})$ </tex-math></inline-formula>, higher cogging torque <inline-formula> <tex-math notation="LaTeX">$(T_{cog})$ </tex-math></inline-formula>, lower torque density <inline-formula> <tex-math notation="LaTeX">$(T_{den})$ </tex-math></inline-formula> and significant stator flux leakage. …”
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A Small Metaline Array Antenna for Circularly Polarized Dual-Band Beam-Steering by Hisamatsu Nakano, Tomoki Abe, Junji Yamauchi

“…The antenna has the following features: 1) dual-band operation at low frequency <inline-formula> <tex-math notation="LaTeX">$f_{\mathrm {LOW}}$ </tex-math></inline-formula> (wavelength <inline-formula> <tex-math notation="LaTeX">$\lambda _{\mathrm {LOW}}$ </tex-math></inline-formula>) and at high frequency <inline-formula> <tex-math notation="LaTeX">$f_{\mathrm {HIGH}}$ </tex-math></inline-formula> (wavelength <inline-formula> <tex-math notation="LaTeX">$\lambda _{\mathrm {HIGH}}$ </tex-math></inline-formula>); 2) a small antenna volume of less than <inline-formula> <tex-math notation="LaTeX">$0.01\lambda _{\mathrm {LOW}}^{3}$ </tex-math></inline-formula>; 3) a small antenna height on the order of <inline-formula> <tex-math notation="LaTeX">$\lambda _{\mathrm {LOW}}$ </tex-math></inline-formula>/100; 4) a small conducting antenna footprint of <inline-formula> <tex-math notation="LaTeX">$0.62\lambda _{\mathrm {LOW}}\times 0.49\lambda _{\mathrm {LOW}}$ </tex-math></inline-formula>; and 5) a phased array antenna consisting of minimum array elements (two elements). …”
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The Lee Weight Distributions of a Class of Quaternary Codes by Zongbing Lin, Kaimin Cheng

“…Let <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{n}$ </tex-math></inline-formula> be the integer ring of residue classes modulo <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>. …”
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Hermitian Rank Metric Codes and Duality by Javier De La Cruz, Jorge Robinson Evilla, Ferruh Ozbudak

“…We analyze the duality for <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{q^{2}}$ </tex-math></inline-formula>-linear matrix codes in the ambient space <inline-formula> <tex-math notation="LaTeX">$(\mathbb {F}_{q^{2}})_{n,m}$ </tex-math></inline-formula> and for both <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{q^{2}}$ </tex-math></inline-formula>-additive codes and <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{q^{2m}}$ </tex-math></inline-formula>-linear codes in the ambient space <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{q^{2m}}^{n}$ </tex-math></inline-formula>. …”
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