In order to determine various traits which need to be improved for improving the productive life span and longevity, purebred Sahiwal cows available at bull mother experimental farm and cattle breeding farm located at...In order to determine various traits which need to be improved for improving the productive life span and longevity, purebred Sahiwal cows available at bull mother experimental farm and cattle breeding farm located at Veterinary College, Durg, Chhattisgarh, India were used. For present investigation, 17 linear type traits were measured, scaled and scored as per the guidelines of International Committee for Animal Recording （2001）. The average score point （ASP） under 1-9 point scale score system along with respective observed group for different linear type traits were stature （6.88; taller）, chest width （5.30; intermediate）, body depth （4.11; intermediate）, rump angle （4.27; intermediate）, rump width （5.09; intermediate）, rear leg set-side view （4.55; intermediate）, rear leg set-rear view （5.95; intermediate）, foot angle （5.66; intermediate）, udder depth （5.71; intermediate）, rear udder height （4.90; intermediate）, udder balance （5.27; intermediate）, udder cleft （3.75; intermediate）, fore udder attachment （5.55; intermediate）, teat length （3.54; intermediate）, fore teat placement （5.33; intermediate）, rear teat placement （6.37; intermediate） and teat thickness （2.76; narrow）. For most of the traits, ASP which lies near midpoint （i.e. near five） is known to be ideal for dairy type cattle. Moreover, some traits also showed the presence of undesirable ASP. Hence, the traits such as body depth, rump angle, foot angle, udder depth, rear udder height, udder cleft, fore udder attachment, teat length, and teat thickness needs to be improved for improving the production sustainability and herd life of Sahiwal cattle. Thus, present investigation gives explicit clue to incorporate these conformation traits in selection program of this valuable germplasm commonly found in Southern part of Asia （India, Pakistan, Srilanka, etc.）.展开更多
Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of l...Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of linear type.展开更多
The Puziwan gold deposit is a special linear cryptoexplosive breccia type deposit found in northeastern Shanxi, China, in recent years. The deposit is located in a secondary metallogenic belt of the most famous Au-Ag ...The Puziwan gold deposit is a special linear cryptoexplosive breccia type deposit found in northeastern Shanxi, China, in recent years. The deposit is located in a secondary metallogenic belt of the most famous Au-Ag polymetallic metallogenic belt along the north margin of the North China platform. The secondary metallogenic belt is a synmagmatic tension-shear fault-fracture belt of ENE linear trend. The Indosinian cryptoexplosive breccia body, quartz monzonitic porphyry (beschtauite breccia), quartz monzonite (243.7 Ma, K-Ar), Yanshanian granite-porphyry (105±6 Ma, Rb-Sr) and orebodies mostly occur as dykes or veins and short lenses along the structural fracture belt. The orebodies are emplaced in the fractured cryptoexplosive breccia body in the tectonomagmatic belt and their attitude is consistent with that of the breccia body. The orebodies have two types: one is shallow-seated thick and big ones, which are short-lenticular in plan and wedge-shaped in cross section, shallow buried, large in size and high-grade; the other is lean orebodies, which occur as parallel veins at depths. The ores are mainly of Au-Ag polymetallic sulphide-rich breccia type. Pyrite (limonite) is the dominant metallic mineral, with subordinate chal-copyrite, galena, sphalerite, tenantite, native gold, electrum, native silver and argentite. The gangue minerals consist mainly of quartz and plagioclase, with subordinate carbonate minerals, alunite chalcedony and kaolin. Kaolinization is the characteristic alteration type. Sulphide minerals contain abundant trace minerals such as Cu, Pb, Ag, Sb and Hg, while in the ores Ag, Cu, Pb, Zn, As and Sb are the best indicator element assemblage of Au. The δ34S(%o) values of the ores rane from ?3.2%o to 5.3%o, with average ?0.102%o. The δO H2O(%o) and δ(%o) values are in the ranges from ?3.1%o to 7.73%o and from ?64%o to ?90%o respectively. The Pb isotopic compositions of the rocks and ores in this region indicate that Pb comes from three tectonic sources—upper mantle, lower crust and orogenic belt. The inclusion homogenization temperature are in the ranges of 110 to 220°C and 230 to 310°C, which suggests that the deposit formed under meso-epithermal conditions. The ore-forming pressures range from 6 to 32 MPa and the depths are 230 to 1200 m. In view of the above, the Puziwan gold deposit is genetically ascribed to a high-sulphur (alunite-kaolin) meso-epithermal gold deposit related to subvolcanic rocks. This gold deposit formed during the Indosinian stage (245.9±0.3 Ma) and then was influenced by a thermal event in the Yanshanian stage (142.9±0.5 Ma).展开更多
We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the...We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.展开更多
To take advantage of merits of higher output-power and efficiency of bolt-clamped transducer,a T-type linear ultrasonic motor was proposed in this paper.The proposed motor contained a horizontal transducer and a verti...To take advantage of merits of higher output-power and efficiency of bolt-clamped transducer,a T-type linear ultrasonic motor was proposed in this paper.The proposed motor contained a horizontal transducer and a vertical transducer.The horizontal transducer included two exponential shape horns,and the vertical transducer contained one exponential shape horn.And the horns intersected at tip ends where a driving foot was located.The longitudinal vibrations of transducers were excited by the stretching vibration of PZT ceramics.Longitudinal vibrations were superimposed in the motor and generated elliptical trajectory at the driving foot.The actuating mechanism of the proposed motor was analyzed.The two working modals of the motor were gained with FEM.The resonant frequencies of two working modals were degenerated by adjusting the structural parameters.The motion trajectory of nodes on the driving foot was gained by transient analysis.The vibration amplitude of node on the driving foot indicates that the proposed motor has potential good output characteristics.The results verify the feasibility of the proposed design and provide instructions for the development of the new ultrasonic motor.展开更多
The paper presents a two-stage method for estimating the parameters in the censored linear model Y-i = max(0, alpha(o) + X-i'beta(o)), 1 less than or equal to i less than or equal to n. In the first stage the data...The paper presents a two-stage method for estimating the parameters in the censored linear model Y-i = max(0, alpha(o) + X-i'beta(o)), 1 less than or equal to i less than or equal to n. In the first stage the data are grouped in some groups and then some adjustments are made, the results are used in the latter stage to form a Tobin-type estimate. The asymptotic normality of the estimate is proved and some simulations are made.展开更多
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Bo...For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with pad6 approximation.展开更多
This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
Mehrotra-type predictor-corrector algorithm, as one of most efficient interior point methods, has become the backbones of most optimization packages. Salahi et al. proposed a cut strategy based algorithm for linear op...Mehrotra-type predictor-corrector algorithm, as one of most efficient interior point methods, has become the backbones of most optimization packages. Salahi et al. proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice. We extend their algorithm to P. （~） linear complementar- ity problems. The way of choosing corrector direction for our algorithm is different from theirs： The new algorithm has been proved to have an O（（1 ＋ 4k）（17 ＋ 19k）√1＋2kn 3/2 log（x0）Ts0/ε） worst case iteration complexity bound. An numerical experiment verifies the feasibility of the new algorithm.展开更多
In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we ob...In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.展开更多
A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law re...A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field øand scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.展开更多
In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-know...In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.展开更多
In this paper, we extend our previous study of addressing the important problem of automatically identifying question and non-question segments in Arabic monologues using prosodic features. We propose here two novel c...In this paper, we extend our previous study of addressing the important problem of automatically identifying question and non-question segments in Arabic monologues using prosodic features. We propose here two novel classification approaches to this problem: one based on the use of the powerful type-2 fuzzy logic systems (type-2 FLS) and the other on the use of the discriminative sensitivity-based linear learning method (SBLLM). The use of prosodic features has been used in a plethora of practical applications, including speech-related applications, such as speaker and word recognition, emotion and accent identification, topic and sentence segmentation, and text-to-speech applications. In this paper, we continue to specifically focus on the Arabic language, as other languages have received a lot of attention in this regard. Moreover, we aim to improve the performance of our previously-used techniques, of which the support vector machine (SVM) method was the best performing, by applying the two above-mentioned powerful classification approaches. The recorded continuous speech is first segmented into sentences using both energy and time duration parameters. The prosodic features are then extracted from each sentence and fed into each of the two proposed classifiers so as to classify each sentence as a Question or a Non-Question sentence. Our extensive simulation work, based on a moderately-sized database, showed the two proposed classifiers outperform SVM in all of the experiments carried out, with the type-2 FLS classifier consistently exhibiting the best performance, because of its ability to handle all forms of uncertainties.展开更多
In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory...In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.展开更多
文摘In order to determine various traits which need to be improved for improving the productive life span and longevity, purebred Sahiwal cows available at bull mother experimental farm and cattle breeding farm located at Veterinary College, Durg, Chhattisgarh, India were used. For present investigation, 17 linear type traits were measured, scaled and scored as per the guidelines of International Committee for Animal Recording （2001）. The average score point （ASP） under 1-9 point scale score system along with respective observed group for different linear type traits were stature （6.88; taller）, chest width （5.30; intermediate）, body depth （4.11; intermediate）, rump angle （4.27; intermediate）, rump width （5.09; intermediate）, rear leg set-side view （4.55; intermediate）, rear leg set-rear view （5.95; intermediate）, foot angle （5.66; intermediate）, udder depth （5.71; intermediate）, rear udder height （4.90; intermediate）, udder balance （5.27; intermediate）, udder cleft （3.75; intermediate）, fore udder attachment （5.55; intermediate）, teat length （3.54; intermediate）, fore teat placement （5.33; intermediate）, rear teat placement （6.37; intermediate） and teat thickness （2.76; narrow）. For most of the traits, ASP which lies near midpoint （i.e. near five） is known to be ideal for dairy type cattle. Moreover, some traits also showed the presence of undesirable ASP. Hence, the traits such as body depth, rump angle, foot angle, udder depth, rear udder height, udder cleft, fore udder attachment, teat length, and teat thickness needs to be improved for improving the production sustainability and herd life of Sahiwal cattle. Thus, present investigation gives explicit clue to incorporate these conformation traits in selection program of this valuable germplasm commonly found in Southern part of Asia （India, Pakistan, Srilanka, etc.）.
文摘Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of linear type.
文摘The Puziwan gold deposit is a special linear cryptoexplosive breccia type deposit found in northeastern Shanxi, China, in recent years. The deposit is located in a secondary metallogenic belt of the most famous Au-Ag polymetallic metallogenic belt along the north margin of the North China platform. The secondary metallogenic belt is a synmagmatic tension-shear fault-fracture belt of ENE linear trend. The Indosinian cryptoexplosive breccia body, quartz monzonitic porphyry (beschtauite breccia), quartz monzonite (243.7 Ma, K-Ar), Yanshanian granite-porphyry (105±6 Ma, Rb-Sr) and orebodies mostly occur as dykes or veins and short lenses along the structural fracture belt. The orebodies are emplaced in the fractured cryptoexplosive breccia body in the tectonomagmatic belt and their attitude is consistent with that of the breccia body. The orebodies have two types: one is shallow-seated thick and big ones, which are short-lenticular in plan and wedge-shaped in cross section, shallow buried, large in size and high-grade; the other is lean orebodies, which occur as parallel veins at depths. The ores are mainly of Au-Ag polymetallic sulphide-rich breccia type. Pyrite (limonite) is the dominant metallic mineral, with subordinate chal-copyrite, galena, sphalerite, tenantite, native gold, electrum, native silver and argentite. The gangue minerals consist mainly of quartz and plagioclase, with subordinate carbonate minerals, alunite chalcedony and kaolin. Kaolinization is the characteristic alteration type. Sulphide minerals contain abundant trace minerals such as Cu, Pb, Ag, Sb and Hg, while in the ores Ag, Cu, Pb, Zn, As and Sb are the best indicator element assemblage of Au. The δ34S(%o) values of the ores rane from ?3.2%o to 5.3%o, with average ?0.102%o. The δO H2O(%o) and δ(%o) values are in the ranges from ?3.1%o to 7.73%o and from ?64%o to ?90%o respectively. The Pb isotopic compositions of the rocks and ores in this region indicate that Pb comes from three tectonic sources—upper mantle, lower crust and orogenic belt. The inclusion homogenization temperature are in the ranges of 110 to 220°C and 230 to 310°C, which suggests that the deposit formed under meso-epithermal conditions. The ore-forming pressures range from 6 to 32 MPa and the depths are 230 to 1200 m. In view of the above, the Puziwan gold deposit is genetically ascribed to a high-sulphur (alunite-kaolin) meso-epithermal gold deposit related to subvolcanic rocks. This gold deposit formed during the Indosinian stage (245.9±0.3 Ma) and then was influenced by a thermal event in the Yanshanian stage (142.9±0.5 Ma).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774377 and 11574343)。
文摘We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.
基金Sponsored by the National Natural Science Foundation of China(Grant No. 50875057 and 51075082)the State Key Laboratory of Robotics and Systems(HIT No. SKLRS200901A04)
文摘To take advantage of merits of higher output-power and efficiency of bolt-clamped transducer,a T-type linear ultrasonic motor was proposed in this paper.The proposed motor contained a horizontal transducer and a vertical transducer.The horizontal transducer included two exponential shape horns,and the vertical transducer contained one exponential shape horn.And the horns intersected at tip ends where a driving foot was located.The longitudinal vibrations of transducers were excited by the stretching vibration of PZT ceramics.Longitudinal vibrations were superimposed in the motor and generated elliptical trajectory at the driving foot.The actuating mechanism of the proposed motor was analyzed.The two working modals of the motor were gained with FEM.The resonant frequencies of two working modals were degenerated by adjusting the structural parameters.The motion trajectory of nodes on the driving foot was gained by transient analysis.The vibration amplitude of node on the driving foot indicates that the proposed motor has potential good output characteristics.The results verify the feasibility of the proposed design and provide instructions for the development of the new ultrasonic motor.
文摘The paper presents a two-stage method for estimating the parameters in the censored linear model Y-i = max(0, alpha(o) + X-i'beta(o)), 1 less than or equal to i less than or equal to n. In the first stage the data are grouped in some groups and then some adjustments are made, the results are used in the latter stage to form a Tobin-type estimate. The asymptotic normality of the estimate is proved and some simulations are made.
基金financially supported by the National Science and Technology Support Program of China(Grant No.2010BAC68B04)
文摘For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with pad6 approximation.
基金supported by the NNSF of China(Grant No.41405083)Hunan Provincial Natural Science Foundation of China(Grant No.2015JJ3098)
文摘This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
基金Supported by the Natural Science Foundation of Hubei Province(Grant No.2008CDZ047)
文摘Mehrotra-type predictor-corrector algorithm, as one of most efficient interior point methods, has become the backbones of most optimization packages. Salahi et al. proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice. We extend their algorithm to P. （~） linear complementar- ity problems. The way of choosing corrector direction for our algorithm is different from theirs： The new algorithm has been proved to have an O（（1 ＋ 4k）（17 ＋ 19k）√1＋2kn 3/2 log（x0）Ts0/ε） worst case iteration complexity bound. An numerical experiment verifies the feasibility of the new algorithm.
文摘In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.
文摘A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field øand scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.
基金Project supported by National Natural Science Foundation of China (Grant No .10271074)
文摘In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
文摘In this paper, we extend our previous study of addressing the important problem of automatically identifying question and non-question segments in Arabic monologues using prosodic features. We propose here two novel classification approaches to this problem: one based on the use of the powerful type-2 fuzzy logic systems (type-2 FLS) and the other on the use of the discriminative sensitivity-based linear learning method (SBLLM). The use of prosodic features has been used in a plethora of practical applications, including speech-related applications, such as speaker and word recognition, emotion and accent identification, topic and sentence segmentation, and text-to-speech applications. In this paper, we continue to specifically focus on the Arabic language, as other languages have received a lot of attention in this regard. Moreover, we aim to improve the performance of our previously-used techniques, of which the support vector machine (SVM) method was the best performing, by applying the two above-mentioned powerful classification approaches. The recorded continuous speech is first segmented into sentences using both energy and time duration parameters. The prosodic features are then extracted from each sentence and fed into each of the two proposed classifiers so as to classify each sentence as a Question or a Non-Question sentence. Our extensive simulation work, based on a moderately-sized database, showed the two proposed classifiers outperform SVM in all of the experiments carried out, with the type-2 FLS classifier consistently exhibiting the best performance, because of its ability to handle all forms of uncertainties.
基金Partially supported by NFS of China (11071127, 10621101)973 Program of STM (2011CB808002)
文摘In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.
