The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ ...The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(Ω) ∩ L∞(Ω) and f : R2n→R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).展开更多
We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the...We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.展开更多
An efficient computer algorithm for minimisation of exclusive-OR logic function is presented. The algorithm is n/(1 + (n-1)2-n) times faster than fast Reed-Muller transform algorithm for minimizing an exclusive-OR fun...An efficient computer algorithm for minimisation of exclusive-OR logic function is presented. The algorithm is n/(1 + (n-1)2-n) times faster than fast Reed-Muller transform algorithm for minimizing an exclusive-OR function with n input variables.展开更多
Due to their exceptional programmability,DNA molecules are widely employed in the design of molecular circuits for applications such as DNA computing,DNA storage and cancer diagnosis and treatment.The quality of DNA s...Due to their exceptional programmability,DNA molecules are widely employed in the design of molecular circuits for applications such as DNA computing,DNA storage and cancer diagnosis and treatment.The quality of DNA sequences directly determines the reliability of these molecular circuits.However,existing DNA encoding algorithms suffer from limitations such as reliance on Hamming distance and conflicts among multiple objectives,resulting in insufficient stability of the generated sequences.To address these issues,this paper proposes a thermodynamics-based multi-objective evolutionary optimisation algorithm(TEMOA).The core innovations of the proposed algorithm are as follows:First,a thermodynamics-based DNA encoding modelling strategy(TDEMS)is introduced,which simplifies the encoding process and significantly improves the sequence quality by incorporating thermodynamic stability constraints.Second,two diversity optimisation strategies—the diversity assessment strategy(DAS)and the front equalisation nondominated sorting(FENS)strategy—are designed to enhance the algorithm's global search capability.Finally,a flexible fitness function design is incorporated to accommodate diverse user requirements.Experimental results demonstrate that TEMOA is more effective than state-of-the-art methods on challenging multi-objective optimisation problems,whereas the DNA sequences generated by TEMOA exhibit greater reliability compared to those produced by traditional DNA encoding algorithms.展开更多
Surgical electrodes are frequently associated with disadvantages such as high surface adhesion and severe thermal damage to adjacent normal tissues,which threaten operation quality and patient safety.In this study,by ...Surgical electrodes are frequently associated with disadvantages such as high surface adhesion and severe thermal damage to adjacent normal tissues,which threaten operation quality and patient safety.In this study,by mimicking the micromorphology and bio-anti-adhesion of shark skin,we proposed a strategy that utilized nanoscale aluminium oxide(Al_(2)O_(3))films deposited on bioinspired shark skin(BSS)microstructures to design a composite surface(Al_(2)O_(3)@BSS)and integrated it into both flat sides of the surgical electrodes.Micro/nano-manufacturing of the Al_(2)O_(3)@BSS surface was sequentially accomplished using nanosecond laser texturing,atomic layer deposition,and low-temperature annealing,endowing it with excellent blood-repellent properties.Visualisation experiments revealed that the tensile stress gradient of the blood coagulum with increasing thickness under a thermal field prompted it to separate from the Al_(2)O_(3)@BSS surface,resulting in anti-adhesion.Furthermore,it was observed for the first time that Al_(2)O_(3) films could transiently excite discharge along a dielectric surface(DADS)to ablate tissues while suppressing Joule heat,thereby minimising thermal damage.A combination of ex vivo tissue and living mouse experiments demonstrated that the Al_(2)O_(3)@BSS electrodes exhibited optimal comprehensive performance in terms of anti-adhesion,damage minimisation,and drag reduction.In addition,the Al_(2)O_(3)@BSS electrodes possessed remarkable antibacterial efficacy against E.coli and S.aureus.The proposed strategy can meet the extreme application requirements of surgical electrodes to improve operation quality and offer valuable insights for future studies.展开更多
Operating an Agilent 7700X ICP-MS spectrometer under robust plasma conditions (1550 W) with a He-filled octopole collision cell and analysing solutions (?1 total dissolved solids) still suffered analyte peak suppressi...Operating an Agilent 7700X ICP-MS spectrometer under robust plasma conditions (1550 W) with a He-filled octopole collision cell and analysing solutions (?1 total dissolved solids) still suffered analyte peak suppression due to matrix effects. International reference rocks BCR-1, BHVO-1, AGV-1, G-2 and BCR-2 all showed count rate reductions for 36 elements (mass range 7Li to 238U) averaging ~10% but with no dependence on isotope mass. Use of an internal standard (103Rh) and/or using a ten-fold dilution of sample solutions reduced these effects but problems with reduced count rates combined with larger errors for some elements introduced other problems. The best approach was to normalise the count rates for each element in the other samples against those for BCR-1 as an external standard;thus the count suppression due to the matrix effect is corrected for each individual element. This approach provides standardization “traceability” in line with the ERM ISO/IEC requirement. Experiments are also reported on quantifying the proportions of Ba and selected REE oxide/hydroxide components versus parent isotopes (XO/X and XOH/X). This information is essential for correcting peak interferences on higher mass number REE for the rock samples, and equations are developed to use measured CeO/Ce and CeOH/Ce ratios to predict such values for any other member of the REE suite. Concentrations obtained show excellent agreement with recommended values for the international reference materials especially for the REE. Robust data are also provided for two other standard rocks: nepheline syenite STM-1 and quartz syenite CAAS-1;the latter shows exceptional enrichments of Zr, REE, Th, and U.展开更多
Human epidermal growth factor receptor-2 over expression has been reported in 23% - 37.3% of Malaysian breast cancer patients. Trastuzumab is a recommended adjuvant therapy for patients with early breast cancer. Curre...Human epidermal growth factor receptor-2 over expression has been reported in 23% - 37.3% of Malaysian breast cancer patients. Trastuzumab is a recommended adjuvant therapy for patients with early breast cancer. Currently, trastuzumab is administered intravenously but a new subcutaneous formulation could save time and costs. In Malaysia, the Ministry of Health funds most of the costs of secondary care, including cancer treatment. We performed a cost-minimisation analysis from the Ministry of Health and societal perspectives by adapting an excel-based mathematical model. Model inputs comprised of drug, consumables and personnel costs. Data sources were government statistics, price lists, government salary scales and estimated personnel time costs. Doctors, nurses and pharmacists at four hospitals estimated the time to perform necessary tasks following their usual practice. Results showed that subcutaneous trastuzumab could, on average, save an estimated 43.5 minutes of pharmacists’ time and 11.6 minutes and 4.9 minutes of nurses’ time administering loading dose and subsequent doses, respectively. Total cost savings were RM7561 (8.7%) per patient per year, consisting of RM6496 (7.6%) reduction in drug cost and RM1065 (66.2%) reduction in non-drug costs. Similarly, cost savings from the societal perspective were RM7820 per patient per year, comprising RM6496 (7.6%) and RM1325 (63.7%) of drug and non-drug costs savings, respectively. Sensitivity analyses showed that cost savings on subcutaneous formulation ranged from RM3715 to RM11408 to the Ministry of Health. Overall, subcutaneous trastuzumab is estimated to be cost-saving from Ministry of Health and societal perspectives. Other benefits from saving patients’ and carers’ time and convenience could not be taken into account. This study was a first to investigate cost-savings from subcutaneous trastuzumab in a middle-income Asian country and the findings were consistent with findings of earlier studies. Given the favourable impact on time and costs, subcutaneous trastuzumab should be considered a viable option for Malaysian patients.展开更多
The large-scale optimization problem requires some optimization techniques, and the Metaheuristics approach is highly useful for solving difficult optimization problems in practice. The purpose of the research is to o...The large-scale optimization problem requires some optimization techniques, and the Metaheuristics approach is highly useful for solving difficult optimization problems in practice. The purpose of the research is to optimize the transportation system with the help of this approach. We selected forest vehicle routing data as the case study to minimize the total cost and the distance of the forest transportation system. Matlab software helps us find the best solution for this case by applying three algorithms of Metaheuristics: Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Extended Great Deluge (EGD). The results show that GA, compared to ACO and EGD, provides the best solution for the cost and the length of our case study. EGD is the second preferred approach, and ACO offers the last solution.展开更多
Effective maintenance is a key for infrastructuresr high operational reliability.The integration of corrective repairs and schedule-based failure preventions has been a mainstream of modern maintenance,and an associat...Effective maintenance is a key for infrastructuresr high operational reliability.The integration of corrective repairs and schedule-based failure preventions has been a mainstream of modern maintenance,and an associated policy-making technique,delay-time modelling,is overviewedin this paper for optimising the maintenance cost-efficiency in different practical scenarios,including imperfect,opportunistic and nested maintenance.A few typical examples of its applications in minimising maintenance operating expenses are discussed in this paper and their results are explained to better demonstrate the benefits of the technique.This work aims to prepare for the future applications of the delay-time modelling in railway maintenance policy making.展开更多
基金This work is supported by NNSF(10471063), Hunan NSF(03JJY4002) & Hunan Education Administration Item(03A011)
文摘The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(Ω) ∩ L∞(Ω) and f : R2n→R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).
文摘We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.
文摘An efficient computer algorithm for minimisation of exclusive-OR logic function is presented. The algorithm is n/(1 + (n-1)2-n) times faster than fast Reed-Muller transform algorithm for minimizing an exclusive-OR function with n input variables.
基金supported by the National Major Scientific Instrument and Equipment Development Project of National Natural Science Foundation of China(62427811,62272115).
文摘Due to their exceptional programmability,DNA molecules are widely employed in the design of molecular circuits for applications such as DNA computing,DNA storage and cancer diagnosis and treatment.The quality of DNA sequences directly determines the reliability of these molecular circuits.However,existing DNA encoding algorithms suffer from limitations such as reliance on Hamming distance and conflicts among multiple objectives,resulting in insufficient stability of the generated sequences.To address these issues,this paper proposes a thermodynamics-based multi-objective evolutionary optimisation algorithm(TEMOA).The core innovations of the proposed algorithm are as follows:First,a thermodynamics-based DNA encoding modelling strategy(TDEMS)is introduced,which simplifies the encoding process and significantly improves the sequence quality by incorporating thermodynamic stability constraints.Second,two diversity optimisation strategies—the diversity assessment strategy(DAS)and the front equalisation nondominated sorting(FENS)strategy—are designed to enhance the algorithm's global search capability.Finally,a flexible fitness function design is incorporated to accommodate diverse user requirements.Experimental results demonstrate that TEMOA is more effective than state-of-the-art methods on challenging multi-objective optimisation problems,whereas the DNA sequences generated by TEMOA exhibit greater reliability compared to those produced by traditional DNA encoding algorithms.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52275425,52405473,and 52405472)the Natural Science Foundation of Guangdong Province(Grant No.2024A1515010993)。
文摘Surgical electrodes are frequently associated with disadvantages such as high surface adhesion and severe thermal damage to adjacent normal tissues,which threaten operation quality and patient safety.In this study,by mimicking the micromorphology and bio-anti-adhesion of shark skin,we proposed a strategy that utilized nanoscale aluminium oxide(Al_(2)O_(3))films deposited on bioinspired shark skin(BSS)microstructures to design a composite surface(Al_(2)O_(3)@BSS)and integrated it into both flat sides of the surgical electrodes.Micro/nano-manufacturing of the Al_(2)O_(3)@BSS surface was sequentially accomplished using nanosecond laser texturing,atomic layer deposition,and low-temperature annealing,endowing it with excellent blood-repellent properties.Visualisation experiments revealed that the tensile stress gradient of the blood coagulum with increasing thickness under a thermal field prompted it to separate from the Al_(2)O_(3)@BSS surface,resulting in anti-adhesion.Furthermore,it was observed for the first time that Al_(2)O_(3) films could transiently excite discharge along a dielectric surface(DADS)to ablate tissues while suppressing Joule heat,thereby minimising thermal damage.A combination of ex vivo tissue and living mouse experiments demonstrated that the Al_(2)O_(3)@BSS electrodes exhibited optimal comprehensive performance in terms of anti-adhesion,damage minimisation,and drag reduction.In addition,the Al_(2)O_(3)@BSS electrodes possessed remarkable antibacterial efficacy against E.coli and S.aureus.The proposed strategy can meet the extreme application requirements of surgical electrodes to improve operation quality and offer valuable insights for future studies.
文摘Operating an Agilent 7700X ICP-MS spectrometer under robust plasma conditions (1550 W) with a He-filled octopole collision cell and analysing solutions (?1 total dissolved solids) still suffered analyte peak suppression due to matrix effects. International reference rocks BCR-1, BHVO-1, AGV-1, G-2 and BCR-2 all showed count rate reductions for 36 elements (mass range 7Li to 238U) averaging ~10% but with no dependence on isotope mass. Use of an internal standard (103Rh) and/or using a ten-fold dilution of sample solutions reduced these effects but problems with reduced count rates combined with larger errors for some elements introduced other problems. The best approach was to normalise the count rates for each element in the other samples against those for BCR-1 as an external standard;thus the count suppression due to the matrix effect is corrected for each individual element. This approach provides standardization “traceability” in line with the ERM ISO/IEC requirement. Experiments are also reported on quantifying the proportions of Ba and selected REE oxide/hydroxide components versus parent isotopes (XO/X and XOH/X). This information is essential for correcting peak interferences on higher mass number REE for the rock samples, and equations are developed to use measured CeO/Ce and CeOH/Ce ratios to predict such values for any other member of the REE suite. Concentrations obtained show excellent agreement with recommended values for the international reference materials especially for the REE. Robust data are also provided for two other standard rocks: nepheline syenite STM-1 and quartz syenite CAAS-1;the latter shows exceptional enrichments of Zr, REE, Th, and U.
文摘Human epidermal growth factor receptor-2 over expression has been reported in 23% - 37.3% of Malaysian breast cancer patients. Trastuzumab is a recommended adjuvant therapy for patients with early breast cancer. Currently, trastuzumab is administered intravenously but a new subcutaneous formulation could save time and costs. In Malaysia, the Ministry of Health funds most of the costs of secondary care, including cancer treatment. We performed a cost-minimisation analysis from the Ministry of Health and societal perspectives by adapting an excel-based mathematical model. Model inputs comprised of drug, consumables and personnel costs. Data sources were government statistics, price lists, government salary scales and estimated personnel time costs. Doctors, nurses and pharmacists at four hospitals estimated the time to perform necessary tasks following their usual practice. Results showed that subcutaneous trastuzumab could, on average, save an estimated 43.5 minutes of pharmacists’ time and 11.6 minutes and 4.9 minutes of nurses’ time administering loading dose and subsequent doses, respectively. Total cost savings were RM7561 (8.7%) per patient per year, consisting of RM6496 (7.6%) reduction in drug cost and RM1065 (66.2%) reduction in non-drug costs. Similarly, cost savings from the societal perspective were RM7820 per patient per year, comprising RM6496 (7.6%) and RM1325 (63.7%) of drug and non-drug costs savings, respectively. Sensitivity analyses showed that cost savings on subcutaneous formulation ranged from RM3715 to RM11408 to the Ministry of Health. Overall, subcutaneous trastuzumab is estimated to be cost-saving from Ministry of Health and societal perspectives. Other benefits from saving patients’ and carers’ time and convenience could not be taken into account. This study was a first to investigate cost-savings from subcutaneous trastuzumab in a middle-income Asian country and the findings were consistent with findings of earlier studies. Given the favourable impact on time and costs, subcutaneous trastuzumab should be considered a viable option for Malaysian patients.
文摘The large-scale optimization problem requires some optimization techniques, and the Metaheuristics approach is highly useful for solving difficult optimization problems in practice. The purpose of the research is to optimize the transportation system with the help of this approach. We selected forest vehicle routing data as the case study to minimize the total cost and the distance of the forest transportation system. Matlab software helps us find the best solution for this case by applying three algorithms of Metaheuristics: Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Extended Great Deluge (EGD). The results show that GA, compared to ACO and EGD, provides the best solution for the cost and the length of our case study. EGD is the second preferred approach, and ACO offers the last solution.
文摘Effective maintenance is a key for infrastructuresr high operational reliability.The integration of corrective repairs and schedule-based failure preventions has been a mainstream of modern maintenance,and an associated policy-making technique,delay-time modelling,is overviewedin this paper for optimising the maintenance cost-efficiency in different practical scenarios,including imperfect,opportunistic and nested maintenance.A few typical examples of its applications in minimising maintenance operating expenses are discussed in this paper and their results are explained to better demonstrate the benefits of the technique.This work aims to prepare for the future applications of the delay-time modelling in railway maintenance policy making.
