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Let $X$ and $Y$ be any two graphs of order $n$. The friends-and-strangers graph $\mathsf{FS}(X,Y)$ of $X$ and $Y$ is a graph with vertex set consisting of all bijections $\sigma :V(X) \mapsto V(Y)$, in which two bijections $\sigma$, $\sigma'$ are adjacent if and only if they differ precisely on two adjacent vertices of $X$, and the corresponding mappings are adjacent in $Y$. The most fundamental question that one can ask about these friends-and-strangers graphs is whether or not they are connected. Let $K_{k,n-k}$ be a complete bipartite graph of order $n$. In 1974, Wilson characterized the connectedness of $\mathsf{FS}(K_{1,n-1},Y)$ by using algebraic methods. In this paper, by using combinatorial methods, we investigate the connectedness of $\mathsf{FS}(K_{k,n-k},Y)$ for any $Y$ and all $k\ge 2$, including $Y$ being a random graph, as suggested by Defant and Kravitz, and pose some open problems.

A distributed zero-sequence-current (ZSC) carrier signal injection via current transformer (CT) is proposed for underground cable single-phase-to-ground fault location in neutral isolated medium voltage (MV) distribution networks. High-frequency ZSC carrier signal is directly injected to a high-voltage underground cable of an energized distribution network via CT. The injected carrier signal travels along the cable to the receiving center in the substation, and is processed for quick fault line selection and fault location. No external power supplies or signal generators are needed due to the self-contained nature of the injector. The device can be constructed as a sleeve to be mounted around the underground power cable. This permits economical retrofitting to existing installations of power line communication (PLC) devices. In this paper, the operational principle and the application considerations for such an injection device and fault location tricks are explained, followed by the theory behind the proposed technique. Finally, MATLAB based numerical simulations are performed and a low-voltage prototype is tested to verify the validity of the proposed approach.

Objective. This study aims to find the novel lncRNAs closely related to the progression of oral squamous cell carcinoma (OSCC) by comprehensively analyzing microarray. Methods. Chip dataset GSE84805 was downloaded from the Gene Expression Omnibus (GEO) database, lncRNA expression profiles of OSCC and paracancerous tissue were obtained, probes sequences reannotation was conducted, and differentially expressed lncRNAs (DELs) and differentially expressed genes (DEGs) were identified. Finally, these data were analyzed by constructing the lncRNA-function enrichment network. Results. We found that 465 lncRNAs are differentially expressed consisting of 193 upregulated lncRNAs and 272 downregulated lncRNAs. Meanwhile, 811 DEGs were identified with 498 upregulated genes and 313 downregulated genes. Analysis of the lncRNA-function enrichment network showed that these aberrant lncRNAs may be related to focal adhesion, inflammatory response pathway, cell cycle, matrix metalloproteinases, and other biological functions. Also, we found that some key lncRNAs such as LINC00152 and HOXA11-AS have been shown to play an important role in tumor proliferation and migration. Conclusion. The key lncRNAs may serve as potential molecular markers or therapeutic targets in OSCC formation and development. It can also help us to understand the molecular mechanism of occurrence and development in OSCC.

Solenoid valves are important electromagnetic devices which are used widely in various fields. Considering the uncertainty of failure mechanisms in practical operation, a thermal-structure coupled model of a direct action solenoid valve is constructed by using the finite element method. The coupled model provides useful information such as temperature distribution and stress distribution for failure mechanism study of the solenoid valve. The model results predict that the failure of the solenoid valve is closely related to the thermal expansion inside the coil, which means the high temperature generated by thermal expansion melts the insulation layers. Under the combined action of high temperature and coupled stress, the shorting of coils occurs and the resistance decreases which may cause the eventual failure of the solenoid valve. To verify the prediction of the finite element model, a degradation experiment is designed. The results suggest that the failure of the solenoid valve is a gradual degradation process, and there are several mutations of coil temperature and resistance. The high temperature melts the insulation layers and causes the shorting of coils, which further decreases the resistance and increases the current. Later more heat is generated to rise coil temperature and melt insulation layers, which will short out the coils and drop the resistance. With such a relationship, as the temperature rises alternately, the resistance decreases alternately until the solenoid valve completely fails. The model provides a reference for failure mechanism study and life prolonging research of solenoid valves.

Consider two graphs $X$ and $Y$, each with $n$ vertices. The friends-and-strangers graph $\mathsf{FS}(X,Y)$ of $X$ and $Y$ is a graph with vertex set consisting of all bijections $\sigma :V(X) \mapsto V(Y)$, where two bijections $\sigma$, $\sigma'$ are adjacent if and only if they differ precisely on two adjacent vertices of $X$, and the corresponding mappings are adjacent in $Y$. The most fundamental question that one can ask about these friends-and-strangers graphs is whether or not they are connected. Alon, Defant, and Kravitz showed that if $X$ and $Y$ are two independent random graphs in $\mathcal{G}(n,p)$, then the threshold probability guaranteeing the connectedness of $\mathsf{FS}(X,Y)$ is $p_0=n^{-1/2+o(1)}$, and suggested to investigate the general asymmetric situation, that is, $X\in \mathcal{G}(n,p_1)$ and $Y\in \mathcal{G}(n,p_2)$. In this paper, we show that if $p_1 p_2 \ge p_0^2=n^{-1+o(1)}$ and $p_1, p_2 \ge w(n) p_0$, where $w(n)\rightarrow 0$ as $n\rightarrow \infty$, then $\mathsf{FS}(X,Y)$ is connected with high probability, which extends the result on $p_1=p_2=p$, due to Alon, Defant, and Kravitz., Comment: 16 pages, 1 fighres. This is a version revised mainly under very careful comments from the anonymous referees. arXiv admin note: substantial text overlap with arXiv:2009.07840 by other authors

For k given graphs G 1 , G 2 , … , G k , k ≥ 2 , the k -color Ramsey number, denoted by R ( G 1 , G 2 , … , G k ) , is the smallest integer N such that if we arbitrarily color the edges of a complete graph of order N with k colors, then it always contains a monochromatic copy of G i colored with i , for some 1 ≤ i ≤ k . Let C m be a cycle of length m and K 1 , n a star of order n + 1 . In this paper, firstly we give a general upper bound of R ( C 4 , C 4 , … , C 4 , K 1 , n ) . In particular, for the 3-color case, we have R ( C 4 , C 4 , K 1 , n ) ≤ n + 4 n + 5 + 3 and this bound is tight in some sense. Furthermore, we prove that R ( C 4 , C 4 , K 1 , n ) ≤ n + 4 n + 5 + 2 for all n = l 2 − l and l ≥ 2 , and if l is a prime power, then the equality holds.

The unbalance current issue of the high-speed railway is the most prominent power quality of the traction power supply systems. Bullet trains can generate energy feedback when they brake, which should not be neglected. In this study, the effects of energy feedback on the unbalance issue are analysed, under different operating conditions of the trains. A collaborative unbalance compensation method (CUCM) for the high-speed railway is proposed in this work to lower the compensation capacity of the expensive power electronics compensation devices. To ensure that the CUCM works well, a further analysis of the two compensation principles, the railway power conditioner principle and Steinmetz principle, was carried out. The analysis results showed that the two compensation principles have different implementation methods and compensation current expressions, but the compensation essences were the same. According to the principle analysis results, a collaborative strategy was used. A capacity analysis of the CUCM, based on the actual operating situations of the bullet trains, was also completely done in this study. The simulation and experimental results showed that the proposed CUCM could adequately compensate the unbalance current of the high-speed railway power systems well with a low cost, in both traction and energy feedback situations.

For given graphs H 1 , . . . , H k , k ≥ 2 , the k -color Ramsey number R ( H 1 , . . . , H k ) is the smallest integer N such that every k -coloring of the edges of a complete graph K N contains a monochromatic copy of H i colored in i , for some i with 1 ≤ i ≤ k . Let C l , K 1 , m and P n denote a cycle of length l , a star of order m + 1 and a path of order n , respectively. In this paper, it is shown that R ( C 4 , K 1 , m , P n ) ≤ m + n − 1 + ⌈ m + n − 2 ⌉ for all m , n ≥ 2 and R ( C 4 , K 1 , m , P n ) ≤ m + n − 2 + ⌈ m + n − 2 ⌉ if m + n = l 2 + 3 and l ≥ 1 . Moreover, by discussing the local structure of the polarity graph whose vertices are points in the projective plane over Galois fields, we show that the two upper bounds can be attained for some special m and n . These results also extend some known results on R ( C 4 , K 1 , m ) obtained by Parsons in 1975 and by Zhang et al. recently.

In the networking designing phase, the network needs to be built according to certain indicators to ensure that the network has the ideal functions and can work smoothly. From a modeling perspective, each site in the network is represented by a vertex, channels between sites are represented by edges, and thus the entire network can be denoted as a graph. Problems in the network can be transformed into corresponding graph problems. In particular, the feasibility of data transmission can be transformed into the existence of fractional factors in network graph. This note gives an independent set neighborhood union condition for the existence of fractional factors in a special setting, and shows that the neighborhood union condition is sharp.

This paper proposes a hybrid active power filter (HAPF) with multi-coupled coils, applied to a medium- and high-voltage power grid. The passive filter of the proposed HAPF adopts the structure of multi-coupled coils to compress the traditional multiple LC branches into one branch which presents the same harmonic impedance characteristics as the former multiple LC branches. In the active power filter of the HAPF, a coupled inductor, instead of a transformer, is used to connect with the passive filter. The coupled inductor has mutual inductances with inductors of the passive filter. Through spatial magnetic coupling, the active power filter can inject compensation current into the power grid to eliminate the residual harmonics and absorb active power from the power grid to maintain the DC capacitor voltage. When the active power filter is open-circuited or short-circuited, the filtering effect of the passive filter can still be guaranteed, which improves the reliability of the filter. The benefits of the proposed HAPF with excellent harmonic filtering performance are that the inductors occupy only 1/3 space as compared with traditional three-tuned LC filter, and very small power of the active power filter. The feasibility of the proposed HAPF is verified through simulations and experiment.

In data transmission networks, the availability of data transmission is equivalent to the existence of the fractional factor of the corresponding graph which is generated by the network. Research on the existence of fractional factors under specific network structures can help scientists design and construct networks with high data transmission rates. A graph G is named as an all fractional (g, f, n′, m)-critical deleted graph if the remaining subgraph keeps being an all fractional (g, f, m)-critical graph, despite experiencing the removal of arbitrary n′ vertices of G. In this paper, we study the relationship between neighborhood conditions and a graph to be all fractional (g, f, n′, m)-critical deleted. Two sufficient neighborhood conditions are determined, and furthermore we show that the conditions stated in the main results are sharp.

Recently, many exciting achievements have been made in improving the cycling performance of SnO2-based electrode. However, the low initial Coulombic efficiency of SnO2-based electrode caused by the formation of solid electrolyte interphase and some of the irreversible formation of Li2O in SnO2 structure still remains unresolved. Here this work reports a primary-cell process to prelithiate the SnO2-based composites to compensate the irreversible loss during the first cycle. The primary-cell-prelithiated SnO2@C composites performs a high initial Coulombic efficiency from 92.7% to >100% with the prelithiation time extends. Even after 600 cycles, the prelithiated (24 h) SnO2@C composites show a high capacity retention of 95% (848 mAh g−1) at a current density of 0.5 A g−1.

Health management system of airborne missiles has a large amount and variety of knowledge, but such technical documents are lack of effective management in the knowledge level. According to the technical characteristics of knowledge in the field of airborne missile health management, a HTA analysis model (Hierarchy, time, and activity analysis model) based on multi-dimensional fuzzy ontology in the health management field of airborne missiles is constructed, and ontology description language OWL is introduced to express knowledge. It provides a theoretical and methodological basis for the dynamic management of health knowledge in the field of condition monitoring, prediction and evaluation, fault diagnosis, technical service.

For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that for any graph of order N, either G contains a copy of G1 or its complement contains a copy of G2. Let Cm be a cycle of length m and K1,n a star of order n+1. Parsons (1975) [6] shows that R(C4,K1,n)n+n1+2 for all n2 and the equality holds if n is the square of a prime power. Let q be a prime power. In this paper, we first construct a graph q on q21 vertices without C4 by using the Galois field Fq, and then we prove that R(C4,K1,(q1)2+t)=(q1)2+q+t for q4 is even and t=1,0,2, and R(C4,K1,q(q1)t)=q2t for q5 is odd and t=2,4,...,2q4.

For two given graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest integer N such that for any graph of order N , either G contains a copy of G 1 or its complement contains a copy of G 2 . Let C m be a cycle of length m and K 1 , n a star of order n + 1 . Parsons (1975) shows that R ( C 4 , K 1 , n ) ź n + ź n - 1 ź + 2 and if n is the square of a prime power, then the equality holds. In this paper, by discussing the properties of polarity graphs whose vertices are points in the projective planes over Galois fields, we prove that R ( C 4 , K 1 , q 2 - t ) = q 2 + q - ( t - 1 ) if q is an odd prime power, 1 ź t ź 2 ź q 4 ź and t ź 2 ź q 4 ź - 1 , which extends a result on R ( C 4 , K 1 , q 2 - t ) obtained by Parsons (1976).

For a graph $H$ and an integer $k\ge1$, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the cycle on $m\ge4$ vertices and let $\Theta_m$ denote the family of graphs obtained from $C_m$ by adding an additional edge joining two non-consecutive vertices. Unlike Ramsey number of odd cycles, little is known about the general behavior of $R_k(C_{2n})$ except that $R_k(C_{2n})\ge (n-1)k+n+k-1$ for all $k\ge2$ and $n\ge2$. In this paper, we study Ramsey number of even cycles with chords under Gallai colorings, where a Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles. For an integer $k\geq 1$, the Gallai-Ramsey number $GR_k(H)$ of a graph $H$ is the least positive integer $N$ such that every Gallai $k$-coloring of the complete graph $K_N$ contains a monochromatic copy of $H$. We prove that $GR_k(\Theta_{2n})=(n-1)k+n+1$ for all $k\geq 2$ and $n\geq 3$. This implies that $GR_k(C_{2n})=(n-1)k+n+1$ all $k\geq 2$ and $n\geq 3$. Our result yields a unified proof for the Gallai-Ramsey number of all even cycles on at least four vertices., Comment: arXiv admin note: text overlap with arXiv:1809.00227

Network virtualization provides a promising solution to overcome the ossification of current networks, allowing multiple Virtual Network Requests (VNRs) to be embedded on a common infrastructure. The major challenge in network virtualization is the Virtual Network Embedding (VNE) problem, which is to embed VNRs onto a shared substrate network and known to be $\mathcal {NP}$ -hard. The topological heterogeneity of VNRs is one important factor hampering the performance of the VNE. However, in many specialized applications and infrastructures, VNRs are of some common structural features, e.g., paths and cycles. To achieve better outcomes, it is thus critical to design dedicated algorithms for these applications and infrastructures by taking into accounting topological characteristics. Besides, paths and cycles are two of the most fundamental topologies that all network structures consist of. Exploiting the characteristics of path and cycle embeddings is vital to tackle the general VNE problem. In this paper, we investigate the path and cycle embedding problems. For path embedding, we prove its $\mathcal {NP}$ -hardness and inapproximability. Then, by utilizing Multiple Knapsack Problem (MKP) and Multi-Dimensional Knapsack Problem (MDKP), we propose an efficient and effective MKP-MDKP-based algorithm. For cycle embedding, we propose a Weighted Directed Auxiliary Graph (WDAG) to develop a polynomial-time algorithm to determine the least-resource-consuming embedding. Numerical results show our customized algorithms can boost the acceptance ratio and revenue compared to generic embedding algorithms in the literature.

The input part of the high-voltage test power supply is usually composed of switching devices; however, the pulse-type periodic interference caused by the switching devices makes the monitoring of the test power supply partial discharge more difficult. Therefore, this paper proposes a high-efficiency and distortion-free linear power supply based on piecewise-linearization with all N-type transistor. Under the same DC input, multiple power transistors are connected to different taps of the same transformer. By controlling the period of linear conduction of each power transistor in turn, we ensure that the power transistor works on the linear side (biased towards saturation) to reduce its conduction voltage drop and the output realizes sinusoidal piecewise linearization, so that the converter can greatly improve the system efficiency. After that, from the perspective of the lowest sum of the transistor loss, an optimization method for the design of the multi-winding transformer ratio at each stage is proposed. Finally, a power supply prototype based on four-piece linear converter with an output voltage of 220 V was built. The experimental efficiency reaches 87.03%, and, additionally, if the linear amplification is divided into more sections, the efficiency can be further improved.

Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cm denote a cycle of order m, K1,n a star of order n + 1 and Wn a wheel of order n + 1. Already back in the 1970s, exact values of the Ramsey numbers R(Cm,K1,n) have been determined for all m ≥ 2n and for all odd m ≤ 2n − 1, but for even m < 2n not many exact values are known. In this paper, we use a result of Bondy on pancyclicity to fill a considerable part of this gap. We show that R(Cm,K1,n) = 2n for even m with n < m < 2n, and that R(Cm,K1,n) = 2m−1 for even m with 3n/4+1 ≤ m ≤ n. In addition, we determine another six formerly unknown exact values of Ramsey numbers, namely R(C6,K1,n) for 7 ≤ n ≤ 11, and R(C6,W9).

Given two graphs $$G_1$$G1 and $$G_2$$G2, the Ramsey number $$R(G_1, G_2)$$R(G1,G2) is the smallest integer $$N$$N such that, for any graph $$G$$G of order $$N$$N, either $$G_1$$G1 is a subgraph of $$G$$G, or $$G_2$$G2 is a subgraph of the complement of $$G$$G. We consider the case that $$G_1$$G1 is a cycle and $$G_2$$G2 is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels versus cycles of even order; and large cycles versus generalized odd wheels.

The topology of the distribution network often changes during routine maintenance and expansion. In addition, the real-time measurement data and the number of configured sensors is limited, and the switch state lacks of real-time telemetry, which causes the topology generator to often fail to obtain actual structure of distribution network. At present, the common topology identification methods are not well adapted to the above characteristics of the distribution network. Therefore, in order to avoid the state estimation distortion of the distribution network caused by serious errors in the distribution network topology, a new topology identification method is proposed. The method determines the possible topologies based on the matching loop power and performs state estimation on the possible topologies based on the common measured values. According to the state evaluation result and the measured value, thereby based on the highest matching degree, it is determined that the topology is a trusted topology, that is, an actual topology. The proposed method realizes the quantitative evaluation of the topology, simplifies the topology identification process, and reduces the computational complexity of the topology identification process. Finally, the effectiveness and practicality of the method are verified through related cases.

We consider proper edge colorings of a graph G using colors of the set { 1 , … , k } . Such a coloring is called neighbor sum distinguishing if for any u v ∈ E ( G ) , the sum of colors of the edges incident to u is different from the sum of the colors of the edges incident to v . The smallest value of k in such a coloring of G is denoted by ndi Σ ( G ) . Let mad ( G ) and Δ ( G ) denote the maximum average degree and the maximum degree of a graph G , respectively. In this paper we show that, for a graph G without isolated edges, if mad ( G ) 8 3 , then ndi Σ ( G ) ≤ max { Δ ( G ) + 1 , 7 } ; and if mad ( G ) 3 , then ndi Σ ( G ) ≤ max { Δ ( G ) + 2 , 7 } .

In this paper, an immune algorithm (IA)-based dead-time elimination PWM control strategy is proposed. For existing dead-time elimination applications, one of the major problems is the dead-time control around the zero-current-crossing points. To deal with this problem, this paper proposes a different PWM control method which first restricts the control sequence to a specified level around the zero-crossing zone. Also, the proposed method can improve the current waveform quality by using the IA approach and three-level control strategy. Compared with conventional dead-time elimination methods, this technique has the features of simple hardware requirement and adaptive control. Moreover, this control strategy effectively eliminates the effect of dead-time, while at the same time significantly reducing the total harmonic distortion of output current and improving the amplitude of output RMS value in different modulation indexes and loads conditions. To verify the analysis, an experimental platform based on DSP and field-programmable gate array is built. The simulation and experimental results are given to demonstrate the effectiveness and feasibility of this new method.

This paper focuses on analysis and suppression of circulating harmonic currents in a modular multilevel converter (MMC) considering the impact of dead time in medium-voltage applications. A continuous equivalent model of the MMC containing two ideal transformer models is presented. Using this model, the impact of a harmonic voltage upon the dc side is analyzed and the production mechanism of circulating harmonic currents is elucidated. At the same time, the impact of dead time and insulated gate bipolar transistor (IGBT) voltage drop (DTVD) is studied, which indicates that capacitor voltages, output harmonics, and circulating harmonic currents are influenced. Based on this analysis, an open-loop control strategy to suppressing circulating harmonic currents caused by the output current and DTVD is presented. Finally, all these conclusions are verified using a simulation platform with 14 modules per arm fed by a 14-kV dc voltage source and a downscaled experimental platform with four modules per arm fed by a 560-V dc voltage source.

For two given graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest integer N such that, for any graph G of order N , either G contains G 1 as a subgraph or the complement of G contains G 2 as a subgraph. Let T n be a tree of order n , S n a star of order n , and F m a fan of order 2 m + 1 , i.e.,� m triangles sharing exactly one vertex. In this paper, we prove that R ( T n , F m ) = 2 n - 1 for n � 3 m 2 - 2 m - 1 , and if T n = S n , then the range can be replaced by n � max { m ( m - 1 ) + 1 , 6 ( m - 1 ) } , which is tight in some sense.

For two given graphs $G_{1}$ and $G_{2}$, the Ramsey number $R(G_{1},G_{2})$ is the smallest integer $N$ such that, for any graph $G$ of order $N$, either $G$ contains $G_{1}$ as a subgraph or the complement of $G$ contains $G_{2}$ as a subgraph. A fan $F_{l}$ is $l$ triangles sharing exactly one vertex. In this note, it is shown that $R(F_{n},F_{m})=4n+1$ for $n\geq \max \{m^{2}-m/2,11m/2-4\}$.

Let G be a connected graph of order n ? 3 . The remoteness ? = ? ( G ) is the maximum, over all vertices, of the average distance from a vertex to all others. The radius r = r ( G ) is the minimum, over all vertices, of the eccentricity of a vertex. Aouchiche and Hansen (2011) conjectured that ? - r ? 3 - n 4 if n is odd and ? - r ? 2 n - n 2 4 ( n - 1 ) if n is even. In this paper, we confirm this conjecture. In addition, we completely characterize extremal graphs attaining the lower bound.

As an efficient theoretical tool, graph theory is widely used in computing chemistry. In terms of index computation on molecular graphs, the researchers can learn the potential properties of chemical compounds, including drugs, materials, and organics. In this paper, by means of distance computation, we study the eccentric version indices of cycloalkanes which occur quite frequently in the chemical drugs and other compounds. The promising prospects of the application for the physical, chemical, medical, and pharmacy engineering are illustrated by theoretical conclusions obtained in this article.

For two given graphs G 1 and G 2 , the planar Ramsey number P R ( G 1 , G 2 ) is the smallest integer N such that for any planar graph G on N vertices, either G contains G 1 or its complement contains G 2 . Let C n denote a cycle of length n and K l a complete graph of order l . Sun, Yang, Lin and Song conjectured that P R ( C 4 , K l ) = 3 l + ⌊ ( l − 1 ) / 5 ⌋ − 2 and the conjecture was proved for l ≤ 7 . In this paper, it is shown that P R ( C 4 , K 8 ) = 23 which confirms the conjecture for l = 8 .

Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that for any graph G of order N, either G contains G1 or its complement contains G2. Let Cm denote a cycle of order m and Wn a wheel of order n+1. In this paper, it is shown that R(Wn,Cm)=2n+1 for m odd, n≥3(m−1)/2 and (m,n)≠(3,3),(3,4), and R(Wn,Cm)=3m−2 for m,n odd and m

In this paper, an immune algorithm (IA) is developed for optimization of the harmonic performance of a three-phase inverter under the space-vector pulsewidth-modulation (SVPWM) control strategy. The presented algorithm employs the immune approach as the search method for finding the best optimal control vectors and action time of the three-phase inverter. As a result, the optimal control vectors and action time are calculated to minimize the objective function of the weighted total harmonic distortion of the output voltage waveforms. In addition, an experimental platform based on DSP and field-programmable gate array is built. This paper provides a detailed performance analysis of the method with comparison to the conventional SVPWM. The simulation and experimental results verify the superiority of the best control sequences generated by IA compared with the existing conventional control strategies.

For graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest integer N such that, for any graph G of order N , G contains G 1 as a subgraph or the complement of G contains G 2 as a subgraph. Let T n denote a tree of order n , W n a wheel of order n + 1 and F n a fan of order 2 n + 1 . We establish Ramsey numbers for fans and trees versus wheels of even order, thereby extending several known results. In particular, we prove that R ( F n , W m ) = 6 n + 1 for odd m ź 3 and n ź ( 5 m + 3 ) / 4 , and that R ( T n , W m ) = 3 n - 2 for odd m ź 3 and n ź m - 2 , and T n being a tree for which the Erdźs-Sos Conjecture holds.

For two given graphs G"1 and G"2, the Ramsey number R(G"1,G"2) is the smallest integer n such that for any graph G of order n, either G contains G"1 or the complement of G contains G"2. Let C"n denote a cycle of order n and W"m a wheel of order m+1. Surahmat, Baskoro and Tomescu conjectured that R(C"n,W"m)=3n-2 for m odd, n>=m>=3 and (n,m) (3,3). In this paper, we confirm the conjecture for n>=20.

A graph G is 3-domination-critical (3-critical, for short), if its domination number @c is 3 and the addition of any edge decreases @c by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with @[email protected][email protected], Discrete Mathematics 271 (2003) 1-12; Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with @[email protected]+2, European Journal of Combinatorics 23 (2002) 777-784; Y.J. Chen, T.C.E. Cheng, C.T. Ng, Hamilton-connectivity of 3-domination critical graphs with @[email protected]+1>=5, Discrete Mathematics 308 (2008) (in press)], we solve the following conjecture: a connected 3-critical graph G is Hamilton-connected if and only if @t(G)>1, where @t(G) is the toughness of G.

For two given graphs G"1 and G"2, the Ramsey number R(G"1,G"2) is the smallest integer n such that for any graph G of order n, either G contains G"1 or the complement of G contains G"2. Let C"m denote a cycle of length m and K"n a complete graph of order n. In this paper, it is shown that R(C"6,K"8)=36.