A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In ...A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.展开更多
The technique of fitting a response surface design is useful in modelling of experimental designs.Response surface is used in situations where the response of interest is influenced by several experimental variables.T...The technique of fitting a response surface design is useful in modelling of experimental designs.Response surface is used in situations where the response of interest is influenced by several experimental variables.The objective of fitting a response surface design is to reduce cost of experimentation and to obtain optimal designs.The property of rotatability is a desirable quantity of experimental design and requires the variance of the fitted design to be constant on circles or spheres about the centre of the design.In this article,a construction technique of fitting modified non-sequential third order rotatable design(TORD)using Pairwise Balanced Design(PBD)is presented.The variance function of a third order response surface design and the properties of Pairwise Balanced Design are utilised for the construction.展开更多
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical ind...The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).展开更多
An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB ...An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.展开更多
Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatmen...Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatments.Also,the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units.However,balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case.In this paper,several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed.The proposed construction of designs has high efficiency and,therefore,can save the cost of experimentations due to a fewer exper-imental subjects.Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters.A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.展开更多
By use of partially balanced t-designs (v,b, k;λ,0) that is constructed by the rational normal curves given by [5] and the Cartesian product given by [4],an authentication code with arbitration is constructed and its...By use of partially balanced t-designs (v,b, k;λ,0) that is constructed by the rational normal curves given by [5] and the Cartesian product given by [4],an authentication code with arbitration is constructed and its probability of success of attacks by the transmitter, the receiver and the opponent is obtained in this paper.展开更多
文摘A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.
文摘The technique of fitting a response surface design is useful in modelling of experimental designs.Response surface is used in situations where the response of interest is influenced by several experimental variables.The objective of fitting a response surface design is to reduce cost of experimentation and to obtain optimal designs.The property of rotatability is a desirable quantity of experimental design and requires the variance of the fitted design to be constant on circles or spheres about the centre of the design.In this article,a construction technique of fitting modified non-sequential third order rotatable design(TORD)using Pairwise Balanced Design(PBD)is presented.The variance function of a third order response surface design and the properties of Pairwise Balanced Design are utilised for the construction.
文摘The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).
文摘An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.
文摘Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatments.Also,the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units.However,balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case.In this paper,several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed.The proposed construction of designs has high efficiency and,therefore,can save the cost of experimentations due to a fewer exper-imental subjects.Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters.A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.
文摘By use of partially balanced t-designs (v,b, k;λ,0) that is constructed by the rational normal curves given by [5] and the Cartesian product given by [4],an authentication code with arbitration is constructed and its probability of success of attacks by the transmitter, the receiver and the opponent is obtained in this paper.
