针对不确实海洋环境使声呐探测性能下降和宽容性差的问题,提出了环境参量和信号参量不确实性两嵌入的宽容波束形成贝叶斯方法.不确实环境参量的先验概率密度函数(probability density function,PDF)通过多项式混沌展开与传播模型相结合...针对不确实海洋环境使声呐探测性能下降和宽容性差的问题,提出了环境参量和信号参量不确实性两嵌入的宽容波束形成贝叶斯方法.不确实环境参量的先验概率密度函数(probability density function,PDF)通过多项式混沌展开与传播模型相结合嵌入到接收信号的概率建模中,导出信号参量的先验PDF;接收信号参量先验PDF通过贝叶斯波束形成嵌入到处理中,转化为后验PDF.导出的后验概率最大贝叶斯波束形成具有估计器和相关器相结合的GLRT结构.仿真和实验数据分析结果表明:不确实环境参量导致接收声场发生秩扩展,由秩1扩展为秩2或秩3,贝叶斯波束形成体现了相干匹配与非相干积累的结合,实现了浅海环境中目标的正确定位,增加了宽容性.展开更多
This paper discusses the repeatability and reproducibility of the international standard of ISO 5725:1994 Accuracy (trueness and precision) of Measurement Methods and Results, two concepts of "inter-laboratory var...This paper discusses the repeatability and reproducibility of the international standard of ISO 5725:1994 Accuracy (trueness and precision) of Measurement Methods and Results, two concepts of "inter-laboratory variance" and "reproducible variance" in the standard are questioned, the corresponding improvement idea is introduced, which aims to make this standard more rigorous, scientific and logical.展开更多
Similarity measure design on non-overlapped data was carried out and compared with the case of overlapped data.Unconsistant feature of similarity on overlapped data to non-overlapped data was provided by example.By th...Similarity measure design on non-overlapped data was carried out and compared with the case of overlapped data.Unconsistant feature of similarity on overlapped data to non-overlapped data was provided by example.By the artificial data illustration,it was proved that the conventional similarity measure was not proper to calculate the similarity measure of the non-overlapped case.To overcome the unbalance problem,similarity measure on non-overlapped data was obtained by considering neighbor information.Hence,different approaches to design similarity measure were proposed and proved by consideration of neighbor information.With the example of artificial data,similarity measure calculation was carried out.Similarity measure extension to intuitionistic fuzzy sets(IFSs)containing uncertainty named hesitance was also followed.展开更多
A new strategy is presented to solve robust multi-physics multi-objective optimization problem known as improved multi-objective collaborative optimization (IMOCO) and its extension improved multi-objective robust c...A new strategy is presented to solve robust multi-physics multi-objective optimization problem known as improved multi-objective collaborative optimization (IMOCO) and its extension improved multi-objective robust collaborative (IMORCO). In this work, the proposed IMORCO approach combined the IMOCO method, the worst possible point (WPP) constraint cuts and the Genetic algorithm NSGA-II type as an optimizer in order to solve the robust optimization problem of multi-physics of microstructures with uncertainties. The optimization problem is hierarchically decomposed into two levels: a microstructure level, and a disciplines levels, For validation purposes, two examples were selected: a numerical example, and an engineering example of capacitive micro machined ultrasonic transducers (CMUT) type. The obtained results are compared with those obtained from robust non-distributed and distributed optimization approach, non-distributed multi-objective robust optimization (NDMORO) and multi-objective collaborative robust optimization (McRO), respectively. Results obtained from the application of the IMOCO approach to an optimization problem of a CMUT cell have reduced the CPU time by 44% ensuring a Pareto front close to the reference non-distributed multi-objective optimization (NDMO) approach (mahalanobis distance, D2M =0.9503 and overall spread, So=0.2309). In addition, the consideration of robustness in IMORCO approach applied to a CMUT cell of optimization problem under interval uncertainty has reduced the CPU time by 23% keeping a robust Pareto front overlaps with that obtained by the robust NDMORO approach (D2M =10.3869 and So=0.0537).展开更多
Agriculture is a leading strategic sector in Turkey as it is in entire world. Despite this strategic significance, risks, and uncertainties, the dependence on natural conditions turns agriculture into a disadvantaged ...Agriculture is a leading strategic sector in Turkey as it is in entire world. Despite this strategic significance, risks, and uncertainties, the dependence on natural conditions turns agriculture into a disadvantaged sector. Just because of these disadvantages, agriculture is protected by various support policies throughout the world. Agricultural policies of Turkey have initiated with institutionalization policies of the Republican period and progressed through product supports, input supports, and low-interest credit implementations of the planned period. These policies experienced serious reforms at the beginning of 2000s. Within the scope of Agricultural supports and Reforms Implementation Project (ARIP), agricultural supports tried to be gathered under a single roof and Direct Income Support (DIS) implementations started. The DIS implementations lasted for eight years and terminated in 2008. The aim of this study is to examine agricultural supports in Turkey and their shares in the public budget. As material, macroeconomic data are used in this study. The data consist of transfers from the ministry of food, agriculture, and livestock to agriculture and budget numbers. The results of the study reveal that current agricultural policy tools are implemented as area-based supports, subsidiary payments, rural development, and agricultural insurance supports. The budget allocated to agriculture and the share of agricultural supports in Gross Domestic Product (GDP) of Turkey does not exhibit much change in years. Considering the policies and supports provided in developed countries and especially in European Union (EU) countries, it recommend for Turkey that the share of agricultural supports in total budget should be increased to levels in those countries.展开更多
This study deals with two novels of Eduar AI-Kharrat: Rama wal-Tinnin (Rama and the Dragon, 1979) and al-Zaman al-Akhar (The Other Time, 1985). The text in both novels is of the pluralist, polyphonic and modernis...This study deals with two novels of Eduar AI-Kharrat: Rama wal-Tinnin (Rama and the Dragon, 1979) and al-Zaman al-Akhar (The Other Time, 1985). The text in both novels is of the pluralist, polyphonic and modernistic type and the real and the imaginary are juxtaposed. The narrative imitates at its diverse levels the internal conflict, argument, and uncertainty of the protagonist Michael, who finally finds his self-realization in an imaginary time, "the other time", which is also the title of one of the novels. The present study focuses on the transformation and alternation of the perspectives and the narrative vision through the destruction of the narrator's identity and the text itself, the analysis of the narrative shift between the first and third person, the fragmentation of the self, the ambiguity of the signs, the severity of the crisis, and the psychological conflict at its diverse levels and multiplicities. Toward this plurality and shift, it is necessary to systematically depend upon what the theories of Bakhtin and Genette have to offer in order to cover the narrative levels and multiple voices prevailing in the texts.展开更多
The decrease of wind velocity (wake losses) in downstream area of wind turbine is generally quantified using wake models. The overall estimated power of wind farm varies according to reliability of wake model used, ...The decrease of wind velocity (wake losses) in downstream area of wind turbine is generally quantified using wake models. The overall estimated power of wind farm varies according to reliability of wake model used, however it's unclear which model is most appropriate and able to give a high performance in predicting wind velocity deficit. In this subject, a qualification of three analytical wake models (Jensen, lshihara and Frandsen) based on three principal criteria is presented in this paper: (i) the parsimony which characterizes the inverse of model complexity, (ii) the accuracy of estimation in which wake model is compared with the experimental data and (iii) imprecision that is related to assumptions and uncertainty on the value of variables considered in each model. This qualitative analysis shows the inability of wake models to predict wind velocity deficit due to the big uncertainty of variables considered and it sensitivity to wind farm characteristic.展开更多
Assessing probabilities for relevant and sometimes unique events in real-world decision situations can be problematic. This paper elucidates a 2-step process for assigning probabilities to relevant events enabling a r...Assessing probabilities for relevant and sometimes unique events in real-world decision situations can be problematic. This paper elucidates a 2-step process for assigning probabilities to relevant events enabling a rational decision process to supersede decision choices based only on a gut feeling. After assessing probabilities the decision maker can confirm or reverse a gut feeling choice using expected values for each available act and traditional decision theory methodology. A simple example involving a buy now or buy later situation with market uncertainty illustrates the process for typical yes or no decisions.展开更多
The inherent nonlinearities of the rudder servo system(RSS) and the unknown external disturbances bring great challenges to the practical application of fault detection technology. Modeling of whole rudder system is a...The inherent nonlinearities of the rudder servo system(RSS) and the unknown external disturbances bring great challenges to the practical application of fault detection technology. Modeling of whole rudder system is a challenging and difficult task. Quite often, models are too inaccurate, especially in transient stages. In model based fault detection, these inaccuracies might cause wrong actions. An effective approach, which combines nonlinear unknown input observer(NUIO) with an adaptive threshold, is proposed. NUIO can estimate the states of RSS asymptotically without any knowledge of external disturbance. An adaptive threshold is used for decision making which helps to reduce the influence of model uncertainty. Actuator and sensor faults that occur in RSS are considered both by simulation and experimental tests. The observer performance, robustness and fault detection capability are verified. Simulation and experimental results show that the proposed fault detection scheme is efficient and can be used for on-line fault detection.展开更多
By the mathematic models of flexible hinge,the accurate relationship between the phase-shifting and pressure acting on the hinge is deduced and verified by experimental results.Through the optimization of the geometri...By the mathematic models of flexible hinge,the accurate relationship between the phase-shifting and pressure acting on the hinge is deduced and verified by experimental results.Through the optimization of the geometric parameter of flexible hinge,a phase-shifting generator is developed to determine the length of an object precisely by interferometry.The experiments show that the triple phase-shifting produced using this generator is up to 1 m.With this generator,an example for the application in length measurement is introduced.The result shows the length uncertainty is 0.5 nm when the temperature uncertainty is limited in 2 mK.This paper provides a novel technique to measure the dimension of an object,especially to the diameter of a silicon sphere for Avogadro constant project.展开更多
The last two to three decades have seen significant advances in the mechanics of unsaturated soils.It is now widely recognized that the fundamental principles in soil mechanics must cover both saturated and unsaturate...The last two to three decades have seen significant advances in the mechanics of unsaturated soils.It is now widely recognized that the fundamental principles in soil mechanics must cover both saturated and unsaturated soils.Nevertheless,there is still a great deal of uncertainties in the geotechnical community about how soil mechanics principles well-established for saturated soils can be extended to unsaturated soils.There is even wide skepticism about the necessity of such extension in engineering practice.This paper discusses some common pitfalls related to the fundamental principles that govern the volume change,shear strength and hydromechanical behaviour of unsaturated soils.It also attempts to address the issue of engineering relevance of unsaturated soil mechanics.展开更多
Due to the dynamical character of electromagnetic exciter and the coupling between structure and exciter(s),the actual output force acting on the structure is usually not equal to the exact value that is supposed to b...Due to the dynamical character of electromagnetic exciter and the coupling between structure and exciter(s),the actual output force acting on the structure is usually not equal to the exact value that is supposed to be,especially when multi-exciters are used as actuators to precisely actuate large flexible structure.It is necessary to consider these effects to ensure the force generated by each exciter is the same as required.In this paper,a robust control method is proposed for the multi-input and multi-output(MIMO)structural vibration control system to trace the target actuating force of each exciter.A special signal is designed and put into the coupled mul-ti-exciter-structure system,and the input and output signals of the system are used to build a dynamic model involving both the dynamical characters of the exciters and the structure using the subspace identification method.Considering the uncertainty factors of the multi-exciter/structure system,an H-infinity robust controller is designed to decouple the coupling between structure and exciters based on the identified system model.A MIMO vibration control system combined with a flexible plate and three electromagnetic exciters is adopted to demonstrate the proposed method,both numerical simulation and model experiments showing that the output force of each exciter can trace its target force accurately within the requested frequency band.展开更多
Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics ...Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics and medicinal fields. In a pio-neering study, Luria and Delbruck exposed E. coli to T1 phage, to investigate whether the number of resistant colonies fol- lowed the Poisson distribution. They deduced that the development of resistant colonies is independent of phage presence. Similar results have since been obtained on solid medium containing antibacterial agents. Luria and Delbruck's conclusions were long considered a gold standard for analyzing drug resistance mutations. More recently, the concept of adaptive mutation has triggered controversy over this approach. Microbiological observation shows that, following exposure to drugs of various concentrations, drug-resistant cells emerge and multiply depending on the time course, and show a process function, incon-sistent with the definition of Poisson distribution (which assumes not only that resistance is independent of drug quantity but follows no specific time course). At the same time, since cells tend to aggregate after division rather than separating, colonies growing on drug plates arise from the multiplication of resistant bacteria cells of various initial population sizes. Thus, statisti-cal analysis based on equivalence of initial populations will yield erroneous results. In this paper, 310 data from the Lu- ria-DelbNck fluctuation experiment were reanalyzed from this perspective. In most cases, a high-end abnormal value, resulting from the non-synchronous variation of the two above-mentioned time variables, was observed. Therefore, the mean value cannot be regarded as an unbiased expectation estimate. The ratio between mean value and variance was similarly incompara-ble, because two different sampling methods were used. In fact, the Luria-Delbrtick data appear to follow an aggregated, rather than Poisson distribution. In stmnnary, the statistical analysis of Luria and Delbruck is insufficient to describe rules of resistant mutant development and multiplication. Correction of this historical misunderstanding will enable new insight into bacterial resistance mechanisms.展开更多
文摘针对不确实海洋环境使声呐探测性能下降和宽容性差的问题,提出了环境参量和信号参量不确实性两嵌入的宽容波束形成贝叶斯方法.不确实环境参量的先验概率密度函数(probability density function,PDF)通过多项式混沌展开与传播模型相结合嵌入到接收信号的概率建模中,导出信号参量的先验PDF;接收信号参量先验PDF通过贝叶斯波束形成嵌入到处理中,转化为后验PDF.导出的后验概率最大贝叶斯波束形成具有估计器和相关器相结合的GLRT结构.仿真和实验数据分析结果表明:不确实环境参量导致接收声场发生秩扩展,由秩1扩展为秩2或秩3,贝叶斯波束形成体现了相干匹配与非相干积累的结合,实现了浅海环境中目标的正确定位,增加了宽容性.
文摘This paper discusses the repeatability and reproducibility of the international standard of ISO 5725:1994 Accuracy (trueness and precision) of Measurement Methods and Results, two concepts of "inter-laboratory variance" and "reproducible variance" in the standard are questioned, the corresponding improvement idea is introduced, which aims to make this standard more rigorous, scientific and logical.
文摘Similarity measure design on non-overlapped data was carried out and compared with the case of overlapped data.Unconsistant feature of similarity on overlapped data to non-overlapped data was provided by example.By the artificial data illustration,it was proved that the conventional similarity measure was not proper to calculate the similarity measure of the non-overlapped case.To overcome the unbalance problem,similarity measure on non-overlapped data was obtained by considering neighbor information.Hence,different approaches to design similarity measure were proposed and proved by consideration of neighbor information.With the example of artificial data,similarity measure calculation was carried out.Similarity measure extension to intuitionistic fuzzy sets(IFSs)containing uncertainty named hesitance was also followed.
文摘A new strategy is presented to solve robust multi-physics multi-objective optimization problem known as improved multi-objective collaborative optimization (IMOCO) and its extension improved multi-objective robust collaborative (IMORCO). In this work, the proposed IMORCO approach combined the IMOCO method, the worst possible point (WPP) constraint cuts and the Genetic algorithm NSGA-II type as an optimizer in order to solve the robust optimization problem of multi-physics of microstructures with uncertainties. The optimization problem is hierarchically decomposed into two levels: a microstructure level, and a disciplines levels, For validation purposes, two examples were selected: a numerical example, and an engineering example of capacitive micro machined ultrasonic transducers (CMUT) type. The obtained results are compared with those obtained from robust non-distributed and distributed optimization approach, non-distributed multi-objective robust optimization (NDMORO) and multi-objective collaborative robust optimization (McRO), respectively. Results obtained from the application of the IMOCO approach to an optimization problem of a CMUT cell have reduced the CPU time by 44% ensuring a Pareto front close to the reference non-distributed multi-objective optimization (NDMO) approach (mahalanobis distance, D2M =0.9503 and overall spread, So=0.2309). In addition, the consideration of robustness in IMORCO approach applied to a CMUT cell of optimization problem under interval uncertainty has reduced the CPU time by 23% keeping a robust Pareto front overlaps with that obtained by the robust NDMORO approach (D2M =10.3869 and So=0.0537).
文摘Agriculture is a leading strategic sector in Turkey as it is in entire world. Despite this strategic significance, risks, and uncertainties, the dependence on natural conditions turns agriculture into a disadvantaged sector. Just because of these disadvantages, agriculture is protected by various support policies throughout the world. Agricultural policies of Turkey have initiated with institutionalization policies of the Republican period and progressed through product supports, input supports, and low-interest credit implementations of the planned period. These policies experienced serious reforms at the beginning of 2000s. Within the scope of Agricultural supports and Reforms Implementation Project (ARIP), agricultural supports tried to be gathered under a single roof and Direct Income Support (DIS) implementations started. The DIS implementations lasted for eight years and terminated in 2008. The aim of this study is to examine agricultural supports in Turkey and their shares in the public budget. As material, macroeconomic data are used in this study. The data consist of transfers from the ministry of food, agriculture, and livestock to agriculture and budget numbers. The results of the study reveal that current agricultural policy tools are implemented as area-based supports, subsidiary payments, rural development, and agricultural insurance supports. The budget allocated to agriculture and the share of agricultural supports in Gross Domestic Product (GDP) of Turkey does not exhibit much change in years. Considering the policies and supports provided in developed countries and especially in European Union (EU) countries, it recommend for Turkey that the share of agricultural supports in total budget should be increased to levels in those countries.
文摘This study deals with two novels of Eduar AI-Kharrat: Rama wal-Tinnin (Rama and the Dragon, 1979) and al-Zaman al-Akhar (The Other Time, 1985). The text in both novels is of the pluralist, polyphonic and modernistic type and the real and the imaginary are juxtaposed. The narrative imitates at its diverse levels the internal conflict, argument, and uncertainty of the protagonist Michael, who finally finds his self-realization in an imaginary time, "the other time", which is also the title of one of the novels. The present study focuses on the transformation and alternation of the perspectives and the narrative vision through the destruction of the narrator's identity and the text itself, the analysis of the narrative shift between the first and third person, the fragmentation of the self, the ambiguity of the signs, the severity of the crisis, and the psychological conflict at its diverse levels and multiplicities. Toward this plurality and shift, it is necessary to systematically depend upon what the theories of Bakhtin and Genette have to offer in order to cover the narrative levels and multiple voices prevailing in the texts.
文摘The decrease of wind velocity (wake losses) in downstream area of wind turbine is generally quantified using wake models. The overall estimated power of wind farm varies according to reliability of wake model used, however it's unclear which model is most appropriate and able to give a high performance in predicting wind velocity deficit. In this subject, a qualification of three analytical wake models (Jensen, lshihara and Frandsen) based on three principal criteria is presented in this paper: (i) the parsimony which characterizes the inverse of model complexity, (ii) the accuracy of estimation in which wake model is compared with the experimental data and (iii) imprecision that is related to assumptions and uncertainty on the value of variables considered in each model. This qualitative analysis shows the inability of wake models to predict wind velocity deficit due to the big uncertainty of variables considered and it sensitivity to wind farm characteristic.
文摘Assessing probabilities for relevant and sometimes unique events in real-world decision situations can be problematic. This paper elucidates a 2-step process for assigning probabilities to relevant events enabling a rational decision process to supersede decision choices based only on a gut feeling. After assessing probabilities the decision maker can confirm or reverse a gut feeling choice using expected values for each available act and traditional decision theory methodology. A simple example involving a buy now or buy later situation with market uncertainty illustrates the process for typical yes or no decisions.
基金Project(51221004)supported by the Science Fund for Creative Research Groups of National Natural Science Foundation of ChinaProject(51175453)supported by the National Natural Science Foundation of China
文摘The inherent nonlinearities of the rudder servo system(RSS) and the unknown external disturbances bring great challenges to the practical application of fault detection technology. Modeling of whole rudder system is a challenging and difficult task. Quite often, models are too inaccurate, especially in transient stages. In model based fault detection, these inaccuracies might cause wrong actions. An effective approach, which combines nonlinear unknown input observer(NUIO) with an adaptive threshold, is proposed. NUIO can estimate the states of RSS asymptotically without any knowledge of external disturbance. An adaptive threshold is used for decision making which helps to reduce the influence of model uncertainty. Actuator and sensor faults that occur in RSS are considered both by simulation and experimental tests. The observer performance, robustness and fault detection capability are verified. Simulation and experimental results show that the proposed fault detection scheme is efficient and can be used for on-line fault detection.
基金supported by the National Key Technology R&D Program of China (Grant No. 2006BAF06B06)
文摘By the mathematic models of flexible hinge,the accurate relationship between the phase-shifting and pressure acting on the hinge is deduced and verified by experimental results.Through the optimization of the geometric parameter of flexible hinge,a phase-shifting generator is developed to determine the length of an object precisely by interferometry.The experiments show that the triple phase-shifting produced using this generator is up to 1 m.With this generator,an example for the application in length measurement is introduced.The result shows the length uncertainty is 0.5 nm when the temperature uncertainty is limited in 2 mK.This paper provides a novel technique to measure the dimension of an object,especially to the diameter of a silicon sphere for Avogadro constant project.
基金supported by the National Natural Science Foundation of China(Grant No.51208519)
文摘The last two to three decades have seen significant advances in the mechanics of unsaturated soils.It is now widely recognized that the fundamental principles in soil mechanics must cover both saturated and unsaturated soils.Nevertheless,there is still a great deal of uncertainties in the geotechnical community about how soil mechanics principles well-established for saturated soils can be extended to unsaturated soils.There is even wide skepticism about the necessity of such extension in engineering practice.This paper discusses some common pitfalls related to the fundamental principles that govern the volume change,shear strength and hydromechanical behaviour of unsaturated soils.It also attempts to address the issue of engineering relevance of unsaturated soil mechanics.
基金supported by the National Natural Science Foundation of China(Grant Nos.11072198,11102162)111 Project of China(Grant No.B07050)
文摘Due to the dynamical character of electromagnetic exciter and the coupling between structure and exciter(s),the actual output force acting on the structure is usually not equal to the exact value that is supposed to be,especially when multi-exciters are used as actuators to precisely actuate large flexible structure.It is necessary to consider these effects to ensure the force generated by each exciter is the same as required.In this paper,a robust control method is proposed for the multi-input and multi-output(MIMO)structural vibration control system to trace the target actuating force of each exciter.A special signal is designed and put into the coupled mul-ti-exciter-structure system,and the input and output signals of the system are used to build a dynamic model involving both the dynamical characters of the exciters and the structure using the subspace identification method.Considering the uncertainty factors of the multi-exciter/structure system,an H-infinity robust controller is designed to decouple the coupling between structure and exciters based on the identified system model.A MIMO vibration control system combined with a flexible plate and three electromagnetic exciters is adopted to demonstrate the proposed method,both numerical simulation and model experiments showing that the output force of each exciter can trace its target force accurately within the requested frequency band.
文摘Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics and medicinal fields. In a pio-neering study, Luria and Delbruck exposed E. coli to T1 phage, to investigate whether the number of resistant colonies fol- lowed the Poisson distribution. They deduced that the development of resistant colonies is independent of phage presence. Similar results have since been obtained on solid medium containing antibacterial agents. Luria and Delbruck's conclusions were long considered a gold standard for analyzing drug resistance mutations. More recently, the concept of adaptive mutation has triggered controversy over this approach. Microbiological observation shows that, following exposure to drugs of various concentrations, drug-resistant cells emerge and multiply depending on the time course, and show a process function, incon-sistent with the definition of Poisson distribution (which assumes not only that resistance is independent of drug quantity but follows no specific time course). At the same time, since cells tend to aggregate after division rather than separating, colonies growing on drug plates arise from the multiplication of resistant bacteria cells of various initial population sizes. Thus, statisti-cal analysis based on equivalence of initial populations will yield erroneous results. In this paper, 310 data from the Lu- ria-DelbNck fluctuation experiment were reanalyzed from this perspective. In most cases, a high-end abnormal value, resulting from the non-synchronous variation of the two above-mentioned time variables, was observed. Therefore, the mean value cannot be regarded as an unbiased expectation estimate. The ratio between mean value and variance was similarly incompara-ble, because two different sampling methods were used. In fact, the Luria-Delbrtick data appear to follow an aggregated, rather than Poisson distribution. In stmnnary, the statistical analysis of Luria and Delbruck is insufficient to describe rules of resistant mutant development and multiplication. Correction of this historical misunderstanding will enable new insight into bacterial resistance mechanisms.