2013 Vol. 45 No. 4
2013, 45(4)
Abstract：
An optimal control problem in a PBN with the help of the theory of Semi-Markov decision processes is studied. Specifically, a control model for a PBN as a first passage model for semi-Markov decision processes is firstly formulated and then an optimal control problem is solved for choosing optimal control inputs in a PBN such that an objective function related to system behavior is minimal. In order to illustrate the validity of our approach, an example is also displayed.
An optimal control problem in a PBN with the help of the theory of Semi-Markov decision processes is studied. Specifically, a control model for a PBN as a first passage model for semi-Markov decision processes is firstly formulated and then an optimal control problem is solved for choosing optimal control inputs in a PBN such that an objective function related to system behavior is minimal. In order to illustrate the validity of our approach, an example is also displayed.
Abstract：
A new local constant kernel weighted computational method based on MM-algorithm is proposed in this paper. The proposed method makes that the calculated quantile regression estimation curve is continuous and smooth under some mild conditions. The selection problem of the tuning parameter is also discussed. Finally, simulation studies and a real data analysis illustrate that the quantile regression estimation curve based on our proposed computational method is robust under the model with heavy-tailed error.
A new local constant kernel weighted computational method based on MM-algorithm is proposed in this paper. The proposed method makes that the calculated quantile regression estimation curve is continuous and smooth under some mild conditions. The selection problem of the tuning parameter is also discussed. Finally, simulation studies and a real data analysis illustrate that the quantile regression estimation curve based on our proposed computational method is robust under the model with heavy-tailed error.
Abstract：
In the case of non-conservative system, a further study on orthogonality and normalization relationships of state vectors is firstly proposed in this paper．A new normalized technique about state vectors is presented accordingly．Secondly by using the orthogonality and normalization condition in sensitivity analysis of structural optimization, modal sensitivity expressions are derived．It could simultaneously avoid the effect on solving the coefficient of modal sensitivity, which is caused by the singular property．The expressions are concise and easy to be implemented．Finally the usefulness and effectiveness of the derived expressions are demonstrated by considering an example of a non-conservative damped four degrees-of-freedom system．
In the case of non-conservative system, a further study on orthogonality and normalization relationships of state vectors is firstly proposed in this paper．A new normalized technique about state vectors is presented accordingly．Secondly by using the orthogonality and normalization condition in sensitivity analysis of structural optimization, modal sensitivity expressions are derived．It could simultaneously avoid the effect on solving the coefficient of modal sensitivity, which is caused by the singular property．The expressions are concise and easy to be implemented．Finally the usefulness and effectiveness of the derived expressions are demonstrated by considering an example of a non-conservative damped four degrees-of-freedom system．
2013, 45(4)
Abstract：
By using the interlacing theorem of the signless Laplacian eigenvalues, the relationship on the signless Laplacian spread of a graph and an pendent vertex-deleted subgraph is established. Combined the graph operation of gradually deleting pendent vertices of uncyclic graph, and calculated the signless Laplacian spread of some special unicyclic graphs, the graph with minimum signless Laplacian spread is determined among the class of unicyclic graphs with n vertices.
By using the interlacing theorem of the signless Laplacian eigenvalues, the relationship on the signless Laplacian spread of a graph and an pendent vertex-deleted subgraph is established. Combined the graph operation of gradually deleting pendent vertices of uncyclic graph, and calculated the signless Laplacian spread of some special unicyclic graphs, the graph with minimum signless Laplacian spread is determined among the class of unicyclic graphs with n vertices.
2013, 45(4)
Abstract：
The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. The classic coefficients theorem of simple graph is generalized to the case of signed graph. With the help of this theorem, the nullity of signed graph is studied. The upper bound of the nullity of n(n≥5)-vertex unicyclic signed graphs is shown to be n−4. The unicyclic signed graphs with nullity equal to n-2(n-3 or n-4, respectively) are charaterized. Moreover, the nullity set is concerned.
The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. The classic coefficients theorem of simple graph is generalized to the case of signed graph. With the help of this theorem, the nullity of signed graph is studied. The upper bound of the nullity of n(n≥5)-vertex unicyclic signed graphs is shown to be n−4. The unicyclic signed graphs with nullity equal to n-2(n-3 or n-4, respectively) are charaterized. Moreover, the nullity set is concerned.
Abstract：
Let H be a complex Hilbert space, the set of all bounded linear operators on H is denoted by B(H). In this note, by using the block-operator matrix technique, the group inverses of multiplicative combinations associated with two idempotents on a Hilbert space is established under some conditions.
Let H be a complex Hilbert space, the set of all bounded linear operators on H is denoted by B(H). In this note, by using the block-operator matrix technique, the group inverses of multiplicative combinations associated with two idempotents on a Hilbert space is established under some conditions.
Abstract：
The algebraic structure and features of right-e wlpp semigroups are discussed. Then a new structure theorem of right-e wlpp semigroups is obtained. A wlpp semigroup S is right-e wlpp semigroup. This kind of semigroups is a spined product of C-wlpp semigroup and left normal band with respect to a semilattice Y. Finally, the result that right-e wlpp semigroup is strong semilattice of L -right cancellative planks is proved.
The algebraic structure and features of right-e wlpp semigroups are discussed. Then a new structure theorem of right-e wlpp semigroups is obtained. A wlpp semigroup S is right-e wlpp semigroup. This kind of semigroups is a spined product of C-wlpp semigroup and left normal band with respect to a semilattice Y. Finally, the result that right-e wlpp semigroup is strong semilattice of L -right cancellative planks is proved.
2013, 45(4)
Abstract：
By using the way of weight coefficient and the idea of real analysis, two new reverse half-discrete reverse Hilbert-type inequalities with homogeneous kernel as are established. The constant factor on the plane is the best value. As applications, best extensions with multi-parameter and equivalent form are also considered.
By using the way of weight coefficient and the idea of real analysis, two new reverse half-discrete reverse Hilbert-type inequalities with homogeneous kernel as are established. The constant factor on the plane is the best value. As applications, best extensions with multi-parameter and equivalent form are also considered.
Abstract：
The best speed limit value using mathematical modeling and regression analysis method was studied to construct the generalized cost function based on the previous research on the multi-objective optimization road maximum speed limit value model. The Guangzhou Inner Ring Road (IRR) is taken as a research sample. Taking the mortality rate as a constraint condition and combining with the actual road parameters on the curve section and flat straight sections model modification, the best speed limit value of Guangzhou IRR is calculated. The rationality of the optimized speed limit value is proved through applying ArcGIS software platform and the theoretical basis of the optimal speed limit value is proposed.
The best speed limit value using mathematical modeling and regression analysis method was studied to construct the generalized cost function based on the previous research on the multi-objective optimization road maximum speed limit value model. The Guangzhou Inner Ring Road (IRR) is taken as a research sample. Taking the mortality rate as a constraint condition and combining with the actual road parameters on the curve section and flat straight sections model modification, the best speed limit value of Guangzhou IRR is calculated. The rationality of the optimized speed limit value is proved through applying ArcGIS software platform and the theoretical basis of the optimal speed limit value is proposed.
Abstract：
The regional and provincial differences of the development of express service in China were studied from the angle of geography. The effects of charge of express service, resident income, economic development level, transportation and population in different region on express service were analyzed. It is discovered that there is a significant imbalance of regional development in express service in China. The business volume of express delivery in the eastern part of China is much larger than the middle China, western of China, and the Northeast China. The difference of resident income and economic development level is the major reason which restricts the development of express industry. Furthermore, by applying the analysis tool of SPSS, this paper establishes the optimal regression model which indicates the relationship among all the elements in different areas, to analyze the factors that affect the regional difference of the development of express service.
The regional and provincial differences of the development of express service in China were studied from the angle of geography. The effects of charge of express service, resident income, economic development level, transportation and population in different region on express service were analyzed. It is discovered that there is a significant imbalance of regional development in express service in China. The business volume of express delivery in the eastern part of China is much larger than the middle China, western of China, and the Northeast China. The difference of resident income and economic development level is the major reason which restricts the development of express industry. Furthermore, by applying the analysis tool of SPSS, this paper establishes the optimal regression model which indicates the relationship among all the elements in different areas, to analyze the factors that affect the regional difference of the development of express service.
2013, 45(4)
Abstract：
The NBMO of alternant hydrocarbons could be determined by the “star notation” method. The coefficients of the NBMO of odd alternant hydrocarbons are easy to be calculated using the “zero-sum rule” through undetermined coefficient method. Since multiple NBMOs may exist in some even alternant hydrocarbons, more than one algebra number must be employed for the star notation in the determination of the coefficients. A good agreement was observed between the results from “star notation” method and DFT calculations.
The NBMO of alternant hydrocarbons could be determined by the “star notation” method. The coefficients of the NBMO of odd alternant hydrocarbons are easy to be calculated using the “zero-sum rule” through undetermined coefficient method. Since multiple NBMOs may exist in some even alternant hydrocarbons, more than one algebra number must be employed for the star notation in the determination of the coefficients. A good agreement was observed between the results from “star notation” method and DFT calculations.
Abstract：
Once antibiotics enter the environment, there will be a series of biological transformation process to eliminate them, such as hydrolysis, photolysis, biodegradation. In the laboratory, iron nanoparticles are proved better to degrade metronidazole. Numerous experimental studies have improved the efficiency of metronidazole degradation, few theoretical studies focused on the mechanism. This work investigated the degradation mechanism of metronidazole with density functional theory (DFT). Experimental results suggest a stepwise process catalyzed by Fe nano particles, finally the reactant nitro was catalyzed to amino through a series of reactions. Each intermediate product was simulated, the two oxygen atoms of nitro group are gradually replaced by hydrogens. The solvent effect is also considered. Calculation results show that the irons provide electrons, thus increasing the activity of the system, and the solvent promoted the reaction.
Once antibiotics enter the environment, there will be a series of biological transformation process to eliminate them, such as hydrolysis, photolysis, biodegradation. In the laboratory, iron nanoparticles are proved better to degrade metronidazole. Numerous experimental studies have improved the efficiency of metronidazole degradation, few theoretical studies focused on the mechanism. This work investigated the degradation mechanism of metronidazole with density functional theory (DFT). Experimental results suggest a stepwise process catalyzed by Fe nano particles, finally the reactant nitro was catalyzed to amino through a series of reactions. Each intermediate product was simulated, the two oxygen atoms of nitro group are gradually replaced by hydrogens. The solvent effect is also considered. Calculation results show that the irons provide electrons, thus increasing the activity of the system, and the solvent promoted the reaction.
Abstract：
GMDH-type neural network was used to optimize the experiment of Cu(Ⅱ) ion absorption by oil shale. In order to build a mathematical adsorption model on the absorption process, mass proportion for absorbate and absorbent, pH value and contact time were considered as independent variables, while the absorption rate as dependent variable. According to the analysis by using the GMDH-type neural network model, the effect of pH values on the absorption rate is higher than the others. Additionally, GMDH-type neural network explains the absorption mechanism based on the three variables. What’s more, a comparative study was made to confirm the good correlation between GMDH and Langmuir models on sorption isotherms, while the coefficient of correlation was 0.907.
GMDH-type neural network was used to optimize the experiment of Cu(Ⅱ) ion absorption by oil shale. In order to build a mathematical adsorption model on the absorption process, mass proportion for absorbate and absorbent, pH value and contact time were considered as independent variables, while the absorption rate as dependent variable. According to the analysis by using the GMDH-type neural network model, the effect of pH values on the absorption rate is higher than the others. Additionally, GMDH-type neural network explains the absorption mechanism based on the three variables. What’s more, a comparative study was made to confirm the good correlation between GMDH and Langmuir models on sorption isotherms, while the coefficient of correlation was 0.907.
2013, 45(4)
Abstract：
A new method for detection of formaldehyde in undamaged textiles was established. In the experiment, the formaldehyde was absorbed by self-designed equipment and measured by the spectrophotography. The detection limit was 10.9 mg/kg which is lower than that in the GB18401-2001 for determination of the formaldehyde content in textiles. The experimental conditions such as temperature, rotational speed and absorption solvent were optimized. The optimum test conditions: 300 mL absorption liquid (water), maximum drum speed V＝12.5 r/min, at 45℃ thermostatic. The result showed that this new method was superior to that of GB18401-2001 when the formaldehyde content was low.
A new method for detection of formaldehyde in undamaged textiles was established. In the experiment, the formaldehyde was absorbed by self-designed equipment and measured by the spectrophotography. The detection limit was 10.9 mg/kg which is lower than that in the GB18401-2001 for determination of the formaldehyde content in textiles. The experimental conditions such as temperature, rotational speed and absorption solvent were optimized. The optimum test conditions: 300 mL absorption liquid (water), maximum drum speed V＝12.5 r/min, at 45℃ thermostatic. The result showed that this new method was superior to that of GB18401-2001 when the formaldehyde content was low.
2013, 45(4)
Abstract：
Rectorite was intercalative modified with three novel Gemini surfactants to form three kinds of organic-modified rectorite (OREC) by the conventional method. The results indicated that the interlayer distances of the three ORECs were enlarged from 2.49 nm to 3.77 nm, 3.00 nm and 3.33 nm, respectively. Besides, the adsorption results showed that the OREC with larger interlayer space displayed more adsorption capacities than the OREC with smaller interlayer space in the same work condition. The max adsorption amount of the three ORECs can be reached to 45.56 mg/g, 37.81 mg/g, 40.82 mg/g at 25℃, respectively.
Rectorite was intercalative modified with three novel Gemini surfactants to form three kinds of organic-modified rectorite (OREC) by the conventional method. The results indicated that the interlayer distances of the three ORECs were enlarged from 2.49 nm to 3.77 nm, 3.00 nm and 3.33 nm, respectively. Besides, the adsorption results showed that the OREC with larger interlayer space displayed more adsorption capacities than the OREC with smaller interlayer space in the same work condition. The max adsorption amount of the three ORECs can be reached to 45.56 mg/g, 37.81 mg/g, 40.82 mg/g at 25℃, respectively.
2013, 45(4)
Abstract：
LiMn2O4 and its Bismuth modified materials were synthesized by sol-gel method, PAA-Bi/LiMn2O4 was prepared by calcining the precursor after LiMn2O4 powders were immersed in polyacrylic acid (PAA) chelated Bi(NO3)3 solution. The performance of three samples were studied by thermogravimetric analysis (TGA), powder X-ray diffraction (XRD), scanning electron microscope (SEM), cyclic voltammograms (CV) and galvanostatic cycle (GC). The cycle stability of both Bi modified samples is improved. The advantage of PAA-immersing-calcining method is to avoid the formation of impure phases as Bi2Mn4O10. The first cycle discharge capacity of PAA-Bi/LiMn2O4 is decreased slightly, and the cycle stability is greatly improved.
LiMn2O4 and its Bismuth modified materials were synthesized by sol-gel method, PAA-Bi/LiMn2O4 was prepared by calcining the precursor after LiMn2O4 powders were immersed in polyacrylic acid (PAA) chelated Bi(NO3)3 solution. The performance of three samples were studied by thermogravimetric analysis (TGA), powder X-ray diffraction (XRD), scanning electron microscope (SEM), cyclic voltammograms (CV) and galvanostatic cycle (GC). The cycle stability of both Bi modified samples is improved. The advantage of PAA-immersing-calcining method is to avoid the formation of impure phases as Bi2Mn4O10. The first cycle discharge capacity of PAA-Bi/LiMn2O4 is decreased slightly, and the cycle stability is greatly improved.
2013, 45(4)
Abstract：
A multiscale total variation algorithm is proposed. By taking advantage of the multiscale structure after wavelet transform, the proposed algorithm applies different regularization parameters to low frequency and high frequency blocks. Numerical experiments show that the proposed algorithm eliminates the noise better while preserving the meaningful edges comparing to using Wavelet method or total variation method alone.
A multiscale total variation algorithm is proposed. By taking advantage of the multiscale structure after wavelet transform, the proposed algorithm applies different regularization parameters to low frequency and high frequency blocks. Numerical experiments show that the proposed algorithm eliminates the noise better while preserving the meaningful edges comparing to using Wavelet method or total variation method alone.
2013, 45(4)
Abstract：
In order to generate virtual scene or work of art by non-photorealistic graphics rendering, a tree-creating model based on stroke and multi-pass rendering is proposed. The model enables painters to select an appropriate paintbrush model of leaf and its parameters in multi-pass rendering and to optimize repeatedly the paintbrush stickup position till the satisfactory tree morphology is obtained, thus to render painting works with distinct hand-painted Chinese painting style. This method is a good try in creating non-photorealistic artistic works by using stroke rendering technique.
In order to generate virtual scene or work of art by non-photorealistic graphics rendering, a tree-creating model based on stroke and multi-pass rendering is proposed. The model enables painters to select an appropriate paintbrush model of leaf and its parameters in multi-pass rendering and to optimize repeatedly the paintbrush stickup position till the satisfactory tree morphology is obtained, thus to render painting works with distinct hand-painted Chinese painting style. This method is a good try in creating non-photorealistic artistic works by using stroke rendering technique.
2013, 45(4)
Abstract：
In this paper, a robust real time lane departure warning system for safe driving assistant is proposed. The design of hardware and software is achieved by using an ALTERA CycloneⅡFPGA with on-chip NIOS Ⅱ system on it as the process core, a robust algorithm for quick lane departure warning is applied in the design, while the IP core is customized with Avalon bus. Test result shows that the accuracy and real-time performance of the system can meet the needs of lane departure warning all day.
In this paper, a robust real time lane departure warning system for safe driving assistant is proposed. The design of hardware and software is achieved by using an ALTERA CycloneⅡFPGA with on-chip NIOS Ⅱ system on it as the process core, a robust algorithm for quick lane departure warning is applied in the design, while the IP core is customized with Avalon bus. Test result shows that the accuracy and real-time performance of the system can meet the needs of lane departure warning all day.
Abstract：
A multithreading disaster tolerance backup log transmission system was devoloped based on Oracle Dataguard software. The system support all kinds of host hardware system, and its transmission rate was improved to 10 times higher than the Oracle software. MD5 checksum algorithm was applied to automaticly resume the broken transmission, and the reliability of database log transmission was improved.
A multithreading disaster tolerance backup log transmission system was devoloped based on Oracle Dataguard software. The system support all kinds of host hardware system, and its transmission rate was improved to 10 times higher than the Oracle software. MD5 checksum algorithm was applied to automaticly resume the broken transmission, and the reliability of database log transmission was improved.
Abstract：
A data caching model based on the regional supply and demand equilibrium is proposed and a distributed solution using a distributed consensus algorithm is provided. Experimental results show that, with the help of appropriate neighbor selection mechanism, the proposed model can effectively improve the playback performance of the P2P media streaming systems, and reduce the media traffics among network regions.
A data caching model based on the regional supply and demand equilibrium is proposed and a distributed solution using a distributed consensus algorithm is provided. Experimental results show that, with the help of appropriate neighbor selection mechanism, the proposed model can effectively improve the playback performance of the P2P media streaming systems, and reduce the media traffics among network regions.
Abstract：
The readily available comprehensive evaluation index system is analyzed to indicate its semantic concepts, and the document of index system is also pretreated. The concepts of indicators and the relationships among the indicators are all extracted. Based on these concepts and relationships, a basic ontology is constructed. Then a concept lattice on the basis ontology is obtained, and its concept description is further enriched. Finally, this concept lattice is converted into the domain ontology by using the methods and tools of formal concept analysis.
The readily available comprehensive evaluation index system is analyzed to indicate its semantic concepts, and the document of index system is also pretreated. The concepts of indicators and the relationships among the indicators are all extracted. Based on these concepts and relationships, a basic ontology is constructed. Then a concept lattice on the basis ontology is obtained, and its concept description is further enriched. Finally, this concept lattice is converted into the domain ontology by using the methods and tools of formal concept analysis.
2013, 45(4)
Abstract：
The recent progress in transition-metal catalyst synthesis of isoquinolines including Pa-, Ag-, Cu-, Rh- , Ru- and other catalysts is reviewed. In addition, the possible mechanisms of the cyclizations of forming isoquinolines were also discussed.
The recent progress in transition-metal catalyst synthesis of isoquinolines including Pa-, Ag-, Cu-, Rh- , Ru- and other catalysts is reviewed. In addition, the possible mechanisms of the cyclizations of forming isoquinolines were also discussed.
Abstract：
In order to explore the effect of high temperature stress on energy supply and photosynthetic rate in the leaves of Agrostis stolonifera L. “Yuexuan 1” and its parents, the plants were treated by heat stress with 35/30℃ (day/night) for 0, 12, 24, 36, and 48h. After the experiments, the fully expanded leaves were collected and measured. The results showed that the contents of ATP, ADP, AMP and the value of energy charge were higher in the leaves of "Yuexuan 1" than its parents during the whole treatment process. The activities of RuBPcase and chloroplast ATPase, the photosynthetic rate and the oxygen-evolving rate were also higher than those of its parents during the high temperature stress treatment. It could be concluded that "Yuexuan 1” had better heat stress tolerance and kept higher rate of photosynthesis than its parents, which may result from lager amount of ATP supply from its leaves.
In order to explore the effect of high temperature stress on energy supply and photosynthetic rate in the leaves of Agrostis stolonifera L. “Yuexuan 1” and its parents, the plants were treated by heat stress with 35/30℃ (day/night) for 0, 12, 24, 36, and 48h. After the experiments, the fully expanded leaves were collected and measured. The results showed that the contents of ATP, ADP, AMP and the value of energy charge were higher in the leaves of "Yuexuan 1" than its parents during the whole treatment process. The activities of RuBPcase and chloroplast ATPase, the photosynthetic rate and the oxygen-evolving rate were also higher than those of its parents during the high temperature stress treatment. It could be concluded that "Yuexuan 1” had better heat stress tolerance and kept higher rate of photosynthesis than its parents, which may result from lager amount of ATP supply from its leaves.
2013, 45(4)
Abstract：
Effects of thidiazuron (TDZ) on flowering of Dendrobium nobile were investigated, by spraying on leaves with a concentration of 20mg/L; and to further investigate the molecular mechanism of the process, theVRN1-like gene was cloned from protocorm-like bodies (PLBs) of Dendrobium nobile , the effects of cytokinins on its expression in axillary buds and PLBs were studied using semi-quantitative RT-PCR analysis. The results showed that flowering of D. nobile could be induced by application with TDZ instead of cold; the full-length cDNA of a VRN1-like gene named DnVRNA (GenBank accession No. EF535598) was cloned, which encodes a peptide with 63% and 62% similarity to the VRN1 protein from Festuca arundinacea and Triticum monococcum, respectively. Semi-quantitative RT-PCR analysis showed that the expression of DnVRNA in axillary buds was improved by TDZ, and those in PLBs were also up-regulated by cytokinins and cold, which suggesting that it would function in cytokinin-induced floral transition.
Effects of thidiazuron (TDZ) on flowering of Dendrobium nobile were investigated, by spraying on leaves with a concentration of 20mg/L; and to further investigate the molecular mechanism of the process, theVRN1-like gene was cloned from protocorm-like bodies (PLBs) of Dendrobium nobile , the effects of cytokinins on its expression in axillary buds and PLBs were studied using semi-quantitative RT-PCR analysis. The results showed that flowering of D. nobile could be induced by application with TDZ instead of cold; the full-length cDNA of a VRN1-like gene named DnVRNA (GenBank accession No. EF535598) was cloned, which encodes a peptide with 63% and 62% similarity to the VRN1 protein from Festuca arundinacea and Triticum monococcum, respectively. Semi-quantitative RT-PCR analysis showed that the expression of DnVRNA in axillary buds was improved by TDZ, and those in PLBs were also up-regulated by cytokinins and cold, which suggesting that it would function in cytokinin-induced floral transition.
Abstract：
According to point group transform theory, a general expression for the average integral function is derived. Based on this, the photonic orientation-dependent local density of states of Face-Center-Cubic (FCC) structure of photonic crystal is calculated. This approach makes the computation speed about 360 times faster than common methods.
According to point group transform theory, a general expression for the average integral function is derived. Based on this, the photonic orientation-dependent local density of states of Face-Center-Cubic (FCC) structure of photonic crystal is calculated. This approach makes the computation speed about 360 times faster than common methods.
2013, 45(4)
Abstract：
The extinction spectra and field distribution of the surface plasmon coupling of metallic nanorod dimmer structures in horizontal and vertical arrangements are calculated by the discrete dipole approximation. It is demonstrated that the peaks of extinction spectra will be red-shifted or blue-shifted due to the different arrangement and gap parameters. The appropriate separation gap has the stronger local electric field distribution for Au nanorod dimmers. The calculation results are expected to have potential applications in nano-scale probing device, nano-sized photocatalyst and biological sensors.
The extinction spectra and field distribution of the surface plasmon coupling of metallic nanorod dimmer structures in horizontal and vertical arrangements are calculated by the discrete dipole approximation. It is demonstrated that the peaks of extinction spectra will be red-shifted or blue-shifted due to the different arrangement and gap parameters. The appropriate separation gap has the stronger local electric field distribution for Au nanorod dimmers. The calculation results are expected to have potential applications in nano-scale probing device, nano-sized photocatalyst and biological sensors.
