A new fuzzy modeling method, which based on L - R fuzzy number, is discussed in this paper. First, the fuzzy state equation model is constructed based on fuzzy state variable,fuzzy Input variable and fuzzy output vari...A new fuzzy modeling method, which based on L - R fuzzy number, is discussed in this paper. First, the fuzzy state equation model is constructed based on fuzzy state variable,fuzzy Input variable and fuzzy output variable whkh are represented by L - R fuzzy number. And then, identification of time - varying parameter in this model is discussed further. At the end, a simulated application is given to Indicate the effectiveness of this fuzzy modeling method.展开更多
Objective:Interleukin-1(IL-1)is a pro-inflammatory cytokine which may be related to urolithiasis.Genetic polymorphisms of the interleukin-1beta(IL-1β)have been proposed as markers for urolithiasis in some areas.Due t...Objective:Interleukin-1(IL-1)is a pro-inflammatory cytokine which may be related to urolithiasis.Genetic polymorphisms of the interleukin-1beta(IL-1β)have been proposed as markers for urolithiasis in some areas.Due to the high incidence of urolithiasis in Uighur children(Xinjiang,China)and existence of ethnic difference,our aim is to explore the potential of IL-1 gene polymorphisms and urolithiasis among these children.Methods:Genomic DNA extracted from peripheral blood of 115 patients and 98 controls were used for genotype polymorphisms analyses.IL-1 receptor antagonist(IL-1RN)gene variable number of tandem repeat(VNTR)gene polymorphisms were analyzed by PCR method.PCR-based restriction analysis was done for the IL-1β(-511)and IL-1β(+3954)gene polymorphisms by endonucleases Ava I and Taq I,respectively.The genotype distribution,allele frequencies,carriage rate,and haplotype frequencies were statistically analyzed.Results:No significant differences were observed in genotypic frequencies between pediatric urolithiasis patients and control group for IL-1RN gene(χ^(2)=1.906,p=0.605),IL-1β(-511)gene(χ^(2)=0.105,p=0.949),or IL-1β(+3954)gene(χ^(2)=3.635,p=0.169).There were yet no significant differences of the allele frequencies of IL-1RN VNTR gene(p=0.779),IL-1β(-511)gene(p=0.941),and IL-1β(+3954)gene(p=0.418)in the case and control groups,as well as the carriage rate and haplotype of them(all p>0.05).Conclusions:The associations between IL-1RN VNTR,IL-1β(-511)and IL-1β(+3954)genes polymorphisms and urolithiasis were not significant in Uighur children.The results need to be confirmed in studies with larger population sample size,as well as in other ethnic groups.展开更多
To improve drying uniformity and anthocyanin content of the raspberry puree dried in a continuous microwave dryer,the effects of process parameters(microwave intensity,air velocity,and drying time)on evaluation indexe...To improve drying uniformity and anthocyanin content of the raspberry puree dried in a continuous microwave dryer,the effects of process parameters(microwave intensity,air velocity,and drying time)on evaluation indexes(average temperature,average moisture content,average retention rate of the total anthocyanin content,temperature contrast value,and moisture dispersion value)were investigated via the response surface method(RSM)and the artificial neural network(ANN)with genetic algorithm(GA).The results showed that the microwave intensity and drying time dominated the changes of evaluation indexes.Overall,the ANN model was superior to the RSM model with better estimation ability,and higher drying uniformity and anthocyanin retention rate were achieved for the ANN-GA model compared with RSM.The optimal parameters were microwave intensity of 5.53 W•g^(-1),air velocity of 1.22 m·s^(-1),and drying time of 5.85 min.This study might provide guidance for process optimization of microwave drying berry fruits.展开更多
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attract...We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent (MLE) for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 (month^- 1). Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.展开更多
INTRODUCTIONThe increased expression of ICAM-1 on a widerange of cells and in the sera of patients withmalignancies, chronic liver diseases andinflammation diseases has been described since thelate 1980s[1-22]. Recent...INTRODUCTIONThe increased expression of ICAM-1 on a widerange of cells and in the sera of patients withmalignancies, chronic liver diseases andinflammation diseases has been described since thelate 1980s[1-22]. Recently rapid progress in studieson expression of ICAM-1 in patients withhepatocellular carcinoma ( HCC ) have beenachieved, including clinical and experimentalresearches[23-31].展开更多
Objective: To investigate the association between IL-1 Ra variable number of tandem repeat(rs2234663), IL-6-597 GA(rs1800797), IL-6-572 GC(rs1800796) and the risk of CrimeanCongo hemorrhagic fever(CCHF) in the Turkish...Objective: To investigate the association between IL-1 Ra variable number of tandem repeat(rs2234663), IL-6-597 GA(rs1800797), IL-6-572 GC(rs1800796) and the risk of CrimeanCongo hemorrhagic fever(CCHF) in the Turkish patients. Methods: This study included 50 patients infected with CCHF and 50 healthy controls. These variants were genotyped using polymerase chain reaction and/or restriction fragment length polymorphism method. Results: The distribution of the IL-6-572 GC genotypes and alleles varied significantly between the patients and the controls. The subjects carrying IL-6-572 GC GG genotype and G allele had increased risk of developing CCHF compared to the control group(P=0.006, P=0.014, respectively). IL-6-572 GC GC genotype was higher in the controls than the patients(P=0.006). For the triple genotype combinations, the 1/2-GC-GG genotype combination was detected more frequently in the control group than CCHF patients(P=0.016). IL-6(-572/-597) GG-GG genotype was significantly higher in the patient group(P=0.015), while the GC-GG genotype was significantly lower in the patient group(P=0.005). Additionally, the G-G haplotype was significantly higher in the patient group(P=0.042), whereas C-G was found to be significantly lower in the patients than the control group(P=0.037). Conclusions: The results of this study suggest the IL-6-572 GC variant might be genetic markers of sensitivity to CCHF in the Turkish population and may facilitate greater protection against the disease.展开更多
Domain-domain interactions are important clues to inferring protein-protein interactions. Although about 8 000 domain-domain interactions are discovered so far,they are just the tip of the iceberg. Because domains are...Domain-domain interactions are important clues to inferring protein-protein interactions. Although about 8 000 domain-domain interactions are discovered so far,they are just the tip of the iceberg. Because domains are conservative and commonplace in proteins,domain-domain interactions are discovered based on pairs of domains which significantly co-exist in proteins. Meanwhile,it is realized that:( 1) domain-domain interactions may exist within the same proteins or across different proteins;( 2) only the domain-domain interactions across different proteins can mediate interactions between proteins;( 3) domains have biases to interact with other domains. And then,a novel method is put forward to construct protein-protein interaction network by using domain-domain interactions. The method is validated by experiments and compared with the state- of-art methods in the field. The experimental results suggest that the method is reasonable and effectiveness on constructing Protein-protein interactions network.展开更多
The GB/T 27930-2015 protocol is the communication protocol between the non-vehicle-mounted charger and the battery management system (BMS) stipulated by the state. However, as the protocol adopts the way of broadcast ...The GB/T 27930-2015 protocol is the communication protocol between the non-vehicle-mounted charger and the battery management system (BMS) stipulated by the state. However, as the protocol adopts the way of broadcast communication and plaintext to transmit data, the data frame does not contain the source address and the destination address, making the Electric Vehicle (EV) vulnerable to replay attack in the charging process. In order to verify the security problems of the protocol, this paper uses 27,655 message data in the complete charging process provided by Shanghai Thaisen electric company, and analyzes these actual data frames one by one with the program written by C++. In order to enhance the security of the protocol, Rivest-Shamir-Adleman (RSA) digital signature and adding random numbers are proposed to resist replay attack. Under the experimental environment of Eclipse, the normal charging of electric vehicles, RSA digital signature and random number defense are simulated. Experimental results show that RSA digital signature cannot resist replay attack, and adding random numbers can effectively enhance the ability of EV to resist replay attack during charging.展开更多
Various features of the atmospheric environment affect the number of migratory insects, besides their initial population. However, little is known about the impact of atmospheric low-frequency oscillation(10 to 90 day...Various features of the atmospheric environment affect the number of migratory insects, besides their initial population. However, little is known about the impact of atmospheric low-frequency oscillation(10 to 90 days) on insect migration. A case study was conducted to ascertain the influence of low-frequency atmospheric oscillation on the immigration of brown planthopper, Nilaparvata lugens(Stl), in Hunan and Jiangxi provinces. The results showed the following:(1) The number of immigrating N. lugens from April to June of 2007 through 2016 mainly exhibited a periodic oscillation of 10 to 20 days.(2) The 10-20 d low-frequency number of immigrating N. lugens was significantly correlated with a low-frequency wind field and a geopotential height field at 850 h Pa.(3) During the peak phase of immigration, southwest or south winds served as a driving force and carried N. lugens populations northward, and when in the back of the trough and the front of the ridge, the downward airflow created a favorable condition for N. lugens to land in the study area. In conclusion, the northward migration of N. lugens was influenced by a low-frequency atmospheric circulation based on the analysis of dynamics. This study was the first research connecting atmospheric low-frequency oscillation to insect migration.展开更多
Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantag...Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.展开更多
The new parity value of π0 was determined according to the hypothesis of conservation of particle number. The theo-retical pentaquark proton’s parity value was also determined, and it was found that the conservation...The new parity value of π0 was determined according to the hypothesis of conservation of particle number. The theo-retical pentaquark proton’s parity value was also determined, and it was found that the conservation of parity is account nicely for the τ-θ puzzle.展开更多
Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16...Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the <em>k</em>-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.展开更多
文摘A new fuzzy modeling method, which based on L - R fuzzy number, is discussed in this paper. First, the fuzzy state equation model is constructed based on fuzzy state variable,fuzzy Input variable and fuzzy output variable whkh are represented by L - R fuzzy number. And then, identification of time - varying parameter in this model is discussed further. At the end, a simulated application is given to Indicate the effectiveness of this fuzzy modeling method.
基金This work was supported by the Natural Science Foundation of Guangdong Province,China(No.2019A1515010891).
文摘Objective:Interleukin-1(IL-1)is a pro-inflammatory cytokine which may be related to urolithiasis.Genetic polymorphisms of the interleukin-1beta(IL-1β)have been proposed as markers for urolithiasis in some areas.Due to the high incidence of urolithiasis in Uighur children(Xinjiang,China)and existence of ethnic difference,our aim is to explore the potential of IL-1 gene polymorphisms and urolithiasis among these children.Methods:Genomic DNA extracted from peripheral blood of 115 patients and 98 controls were used for genotype polymorphisms analyses.IL-1 receptor antagonist(IL-1RN)gene variable number of tandem repeat(VNTR)gene polymorphisms were analyzed by PCR method.PCR-based restriction analysis was done for the IL-1β(-511)and IL-1β(+3954)gene polymorphisms by endonucleases Ava I and Taq I,respectively.The genotype distribution,allele frequencies,carriage rate,and haplotype frequencies were statistically analyzed.Results:No significant differences were observed in genotypic frequencies between pediatric urolithiasis patients and control group for IL-1RN gene(χ^(2)=1.906,p=0.605),IL-1β(-511)gene(χ^(2)=0.105,p=0.949),or IL-1β(+3954)gene(χ^(2)=3.635,p=0.169).There were yet no significant differences of the allele frequencies of IL-1RN VNTR gene(p=0.779),IL-1β(-511)gene(p=0.941),and IL-1β(+3954)gene(p=0.418)in the case and control groups,as well as the carriage rate and haplotype of them(all p>0.05).Conclusions:The associations between IL-1RN VNTR,IL-1β(-511)and IL-1β(+3954)genes polymorphisms and urolithiasis were not significant in Uighur children.The results need to be confirmed in studies with larger population sample size,as well as in other ethnic groups.
基金Supported by the National Natural Science Foundation of China(32072352)。
文摘To improve drying uniformity and anthocyanin content of the raspberry puree dried in a continuous microwave dryer,the effects of process parameters(microwave intensity,air velocity,and drying time)on evaluation indexes(average temperature,average moisture content,average retention rate of the total anthocyanin content,temperature contrast value,and moisture dispersion value)were investigated via the response surface method(RSM)and the artificial neural network(ANN)with genetic algorithm(GA).The results showed that the microwave intensity and drying time dominated the changes of evaluation indexes.Overall,the ANN model was superior to the RSM model with better estimation ability,and higher drying uniformity and anthocyanin retention rate were achieved for the ANN-GA model compared with RSM.The optimal parameters were microwave intensity of 5.53 W•g^(-1),air velocity of 1.22 m·s^(-1),and drying time of 5.85 min.This study might provide guidance for process optimization of microwave drying berry fruits.
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
基金the National Natural Science Foundation of China
文摘We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent (MLE) for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 (month^- 1). Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.
基金Supported by the grant from the Guangxi ScienceTechnology Committee, No. 9811003
文摘INTRODUCTIONThe increased expression of ICAM-1 on a widerange of cells and in the sera of patients withmalignancies, chronic liver diseases andinflammation diseases has been described since thelate 1980s[1-22]. Recently rapid progress in studieson expression of ICAM-1 in patients withhepatocellular carcinoma ( HCC ) have beenachieved, including clinical and experimentalresearches[23-31].
文摘Objective: To investigate the association between IL-1 Ra variable number of tandem repeat(rs2234663), IL-6-597 GA(rs1800797), IL-6-572 GC(rs1800796) and the risk of CrimeanCongo hemorrhagic fever(CCHF) in the Turkish patients. Methods: This study included 50 patients infected with CCHF and 50 healthy controls. These variants were genotyped using polymerase chain reaction and/or restriction fragment length polymorphism method. Results: The distribution of the IL-6-572 GC genotypes and alleles varied significantly between the patients and the controls. The subjects carrying IL-6-572 GC GG genotype and G allele had increased risk of developing CCHF compared to the control group(P=0.006, P=0.014, respectively). IL-6-572 GC GC genotype was higher in the controls than the patients(P=0.006). For the triple genotype combinations, the 1/2-GC-GG genotype combination was detected more frequently in the control group than CCHF patients(P=0.016). IL-6(-572/-597) GG-GG genotype was significantly higher in the patient group(P=0.015), while the GC-GG genotype was significantly lower in the patient group(P=0.005). Additionally, the G-G haplotype was significantly higher in the patient group(P=0.042), whereas C-G was found to be significantly lower in the patients than the control group(P=0.037). Conclusions: The results of this study suggest the IL-6-572 GC variant might be genetic markers of sensitivity to CCHF in the Turkish population and may facilitate greater protection against the disease.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61271346,61571163,61532014,91335112 and 61402132)the Fundamental Research Funds for the Central Universities(Grant No.DB13AB02)
文摘Domain-domain interactions are important clues to inferring protein-protein interactions. Although about 8 000 domain-domain interactions are discovered so far,they are just the tip of the iceberg. Because domains are conservative and commonplace in proteins,domain-domain interactions are discovered based on pairs of domains which significantly co-exist in proteins. Meanwhile,it is realized that:( 1) domain-domain interactions may exist within the same proteins or across different proteins;( 2) only the domain-domain interactions across different proteins can mediate interactions between proteins;( 3) domains have biases to interact with other domains. And then,a novel method is put forward to construct protein-protein interaction network by using domain-domain interactions. The method is validated by experiments and compared with the state- of-art methods in the field. The experimental results suggest that the method is reasonable and effectiveness on constructing Protein-protein interactions network.
文摘The GB/T 27930-2015 protocol is the communication protocol between the non-vehicle-mounted charger and the battery management system (BMS) stipulated by the state. However, as the protocol adopts the way of broadcast communication and plaintext to transmit data, the data frame does not contain the source address and the destination address, making the Electric Vehicle (EV) vulnerable to replay attack in the charging process. In order to verify the security problems of the protocol, this paper uses 27,655 message data in the complete charging process provided by Shanghai Thaisen electric company, and analyzes these actual data frames one by one with the program written by C++. In order to enhance the security of the protocol, Rivest-Shamir-Adleman (RSA) digital signature and adding random numbers are proposed to resist replay attack. Under the experimental environment of Eclipse, the normal charging of electric vehicles, RSA digital signature and random number defense are simulated. Experimental results show that RSA digital signature cannot resist replay attack, and adding random numbers can effectively enhance the ability of EV to resist replay attack during charging.
基金National Science Foundation of China(41075086,41475106)Science Research Program of Universities and Colleges in Jiangsu Province(14KJA170003)Priority Academic Program Development of Jiangsu Higher Education Institutions(IRT1147)
文摘Various features of the atmospheric environment affect the number of migratory insects, besides their initial population. However, little is known about the impact of atmospheric low-frequency oscillation(10 to 90 days) on insect migration. A case study was conducted to ascertain the influence of low-frequency atmospheric oscillation on the immigration of brown planthopper, Nilaparvata lugens(Stl), in Hunan and Jiangxi provinces. The results showed the following:(1) The number of immigrating N. lugens from April to June of 2007 through 2016 mainly exhibited a periodic oscillation of 10 to 20 days.(2) The 10-20 d low-frequency number of immigrating N. lugens was significantly correlated with a low-frequency wind field and a geopotential height field at 850 h Pa.(3) During the peak phase of immigration, southwest or south winds served as a driving force and carried N. lugens populations northward, and when in the back of the trough and the front of the ridge, the downward airflow created a favorable condition for N. lugens to land in the study area. In conclusion, the northward migration of N. lugens was influenced by a low-frequency atmospheric circulation based on the analysis of dynamics. This study was the first research connecting atmospheric low-frequency oscillation to insect migration.
基金Supported by the National Natural Science Foundation of China.
文摘Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.
文摘The new parity value of π0 was determined according to the hypothesis of conservation of particle number. The theo-retical pentaquark proton’s parity value was also determined, and it was found that the conservation of parity is account nicely for the τ-θ puzzle.
文摘Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the <em>k</em>-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.