Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynom...Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.展开更多
In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of ho...In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.展开更多
In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete ...In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete and applicable model to solve the relevant problem with computer.展开更多
In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybde...In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybdenum ore as an example, a theoretical model for the hurdle price under the optimal investment timing is constructed. Based on the example data, the op- tion price model is simulated. By the model, mine investment price can be computed and forecast effectively. According to the characteristics of mine investment, cut-off grade, reserve estimation and mine life in different price also can be quantified. The result shows that it is reliable and practical to enhance the accuracy for mining investment decision.展开更多
The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coeffic...The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coefficient,which was conjectured by Z.-W.Sun.展开更多
For integers b and c the generalized central trinomial coefficient Tn(b,c)denotes the coefficient of xnin the expansion of(x2+bx+c)n.Those Tn=Tn(1,1)(n=0,1,2,...)are the usual central trinomial coefficients,and Tn(3,2...For integers b and c the generalized central trinomial coefficient Tn(b,c)denotes the coefficient of xnin the expansion of(x2+bx+c)n.Those Tn=Tn(1,1)(n=0,1,2,...)are the usual central trinomial coefficients,and Tn(3,2)coincides with the Delannoy number Dn=n k=0n k n+k k in combinatorics.We investigate congruences involving generalized central trinomial coefficients systematically.Here are some typical results:For each n=1,2,3,...,we have n-1k=0(2k+1)Tk(b,c)2(b2-4c)n-1-k≡0(mod n2)and in particular n2|n-1k=0(2k+1)D2k;if p is an odd prime then p-1k=0T2k≡-1p(mod p)and p-1k=0D2k≡2p(mod p),where(-)denotes the Legendre symbol.We also raise several conjectures some of which involve parameters in the representations of primes by certain binary quadratic forms.展开更多
Rice blast is regarded as one of the major diseases of rice.Screening rice genotypes with high resistance to rice blast is a key strategy for ensuring global food security.Unmanned aerial vehicles(UAV)-based imaging,c...Rice blast is regarded as one of the major diseases of rice.Screening rice genotypes with high resistance to rice blast is a key strategy for ensuring global food security.Unmanned aerial vehicles(UAV)-based imaging,coupled with deep learning,can acquire high-throughput imagery related to rice blast infection.In this study,we developed a segmented detection model(called RiceblastSegMask)for rice blast detection and resistance evaluation.The feasibility of different backbones and target detection models was further investigated.RiceblastSegMask is a two-stage instance segmentation model,comprising an image-denoising backbone network,a feature pyramid,a trinomial tree fine-grained feature extraction combination network,and an image pixel codec module.The results showed that the model combining the image-denoising and fine-grained feature extraction based on the Swin Transformer and the feature pixel matching feature labels with the trinomial tree recursive algorithm performed the best.The overall accuracy for instance segmentation of RiceblastSegMask reached 97.56%,and it demonstrated a satisfactory accuracy of 90.29%for grading unique resistance to rice blast.These results indicated that low-altitude remote sensing using UAV,in conjunction with the proposed RiceblastSegMask model,can efficiently calculate the extent of rice blast infection,offering a new phenotypic tool for evaluating rice blast resistance on a field scale in rice breeding programs.展开更多
A new structure of bit-parallel Polynomial Basis(PB)multiplier is proposed,which isbased on a fast modular reduction method.The method was recommended by the National Instituteof Standards and Technology(NIST).It take...A new structure of bit-parallel Polynomial Basis(PB)multiplier is proposed,which isbased on a fast modular reduction method.The method was recommended by the National Instituteof Standards and Technology(NIST).It takes advantage of the characteristics of irreducible polyno-mial,i.e.,the degree of the second item of irreducible polynomial is far less than the degree of thepolynomial in the finite fields GF(2m).Deductions are made for a class of finite field in which trino-mials are chosen as irreducible polynomials.Let the trinomial bex m +x k+1,where 1 ≤k≤?m/2?.??The proposed structure has shorter critical path than the best known one up to date,whilethe space requirement keeps the same.The structure is practical,especially in real time crypto-graphic applications.展开更多
China has promised to start the national carbon trading system in 2017.In the carbon trading system,the renewable energy projects may obtain additional benefits through the Certified Carbon Emission Reduction(CCER) tr...China has promised to start the national carbon trading system in 2017.In the carbon trading system,the renewable energy projects may obtain additional benefits through the Certified Carbon Emission Reduction(CCER) trade.As the carbon price fluctuates along with the market conditions,such fluctuation enables the renewable power projects to acquire the rights of an option,i.e.it may contain an even higher value due to the uncertainties in the future.While making an investment decision,the renewable power companies may choose to make the investment immediately,or postpone the investment and accumulate more information to increase the return of investment;and for immediate investments,the return must be sufficient to exceed the potential value of a waiting option.To study the investment in renewable power projects subject to the fluctuation of carbon price,this paper adopts the trinomial tree model of real options to estimate the net present value(NPV) and real option value(ROV) of three types of renewable power projects;according to the decision-making rules of real options to defer,all the three types of projects will exercise the option to postpone the investment decision.This thesis also calculates the benchmark prices of the three types of renewable projects at different times,in the two situations of having no government subsidy and having the government subsidy,so as to determine the investment opportunity of a project.The benchmark price decreases gradually along with the increase of government subsidy,indicating that the government subsidy will stimulate the investment in renewable projects.The benchmark price also increases gradually along with the lapse of time,indicating that the uncertainty will increase together with the time span and thus requires an even higher carbon price to determine the investment opportunity.This thesis also analyzes the sensitivity of factors affecting the investment in renewable projects and draws the conclusion that the fluctuation of carbon price is positively related with the benchmark price of renewable power projects,which indicates that the fluctuation of carbon price increases the option value of an investment but postpones the time of investment.As the China's carbon trading system improves gradually,the carbon price will reach a stable status,thus stimulate the power companies to invest in the renewable projects.展开更多
Accurate estimation of disease prevalence is crucial for effective public health intervention and resource allocation.Generating data by individual testing methods is often impractical and expensive for large populati...Accurate estimation of disease prevalence is crucial for effective public health intervention and resource allocation.Generating data by individual testing methods is often impractical and expensive for large populations,particularly when disease prevalence is low.Pool testing involves combining samples from multiple individuals into a pool and performing a single test,and offers a costeffective and efficient alternative.In pool testing strategy with retesting,if a pool tests negative,it is classified as non-defective,whereas if it is positive,then a retest is needed.The retesting strategy mitigates the effects of initial test errors,thereby enhancing the accuracy of the estimation of the prevalence rate.Evidence in the literature indicates that the traditional Wald method has been used to construct approximate confidence intervals for the prevalence rate.However,this interval estimation method is based on the normality ap-proximation and hence may not be accurate when the true prevalence rate is close to zero.In this paper,we propose a Bayesian interval estimation ap-proach which is not affected by extreme values of the prevalence rate and al-lows for incorporating prior information about the prevalence rate.We as-sumed that the prior distribution for the unknown prevalence rate p is a Beta distribution with parameters α_(0) and β_(0) and based on pool testing outcomes for the n pools each of size k,100(1-α)% credible intervals were constructed from the resulting posterior distribution.Simulation studies were carried out to compare the efficiencies of the Bayesian and Wald interval estimation methods for various values of p.展开更多
It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative ...It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.展开更多
文摘Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.
文摘In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.
基金Supported by the National Natural Science Foundation of China (70871094)
文摘In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete and applicable model to solve the relevant problem with computer.
文摘In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybdenum ore as an example, a theoretical model for the hurdle price under the optimal investment timing is constructed. Based on the example data, the op- tion price model is simulated. By the model, mine investment price can be computed and forecast effectively. According to the characteristics of mine investment, cut-off grade, reserve estimation and mine life in different price also can be quantified. The result shows that it is reliable and practical to enhance the accuracy for mining investment decision.
基金National Natural Science Foundation of China(11971222,12071208)Jiangsu Qinglan ProjectProject of Guangzhou Huashang College(2022HSDS27)。
文摘The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coefficient,which was conjectured by Z.-W.Sun.
基金supported by National Natural Science Foundation of China (Grant No.11171140)the PAPD of Jiangsu Higher Education Institutions
文摘For integers b and c the generalized central trinomial coefficient Tn(b,c)denotes the coefficient of xnin the expansion of(x2+bx+c)n.Those Tn=Tn(1,1)(n=0,1,2,...)are the usual central trinomial coefficients,and Tn(3,2)coincides with the Delannoy number Dn=n k=0n k n+k k in combinatorics.We investigate congruences involving generalized central trinomial coefficients systematically.Here are some typical results:For each n=1,2,3,...,we have n-1k=0(2k+1)Tk(b,c)2(b2-4c)n-1-k≡0(mod n2)and in particular n2|n-1k=0(2k+1)D2k;if p is an odd prime then p-1k=0T2k≡-1p(mod p)and p-1k=0D2k≡2p(mod p),where(-)denotes the Legendre symbol.We also raise several conjectures some of which involve parameters in the representations of primes by certain binary quadratic forms.
基金supported by the Natural Science Foundation of Fujian Province,China(Grant No.2022J01611).
文摘Rice blast is regarded as one of the major diseases of rice.Screening rice genotypes with high resistance to rice blast is a key strategy for ensuring global food security.Unmanned aerial vehicles(UAV)-based imaging,coupled with deep learning,can acquire high-throughput imagery related to rice blast infection.In this study,we developed a segmented detection model(called RiceblastSegMask)for rice blast detection and resistance evaluation.The feasibility of different backbones and target detection models was further investigated.RiceblastSegMask is a two-stage instance segmentation model,comprising an image-denoising backbone network,a feature pyramid,a trinomial tree fine-grained feature extraction combination network,and an image pixel codec module.The results showed that the model combining the image-denoising and fine-grained feature extraction based on the Swin Transformer and the feature pixel matching feature labels with the trinomial tree recursive algorithm performed the best.The overall accuracy for instance segmentation of RiceblastSegMask reached 97.56%,and it demonstrated a satisfactory accuracy of 90.29%for grading unique resistance to rice blast.These results indicated that low-altitude remote sensing using UAV,in conjunction with the proposed RiceblastSegMask model,can efficiently calculate the extent of rice blast infection,offering a new phenotypic tool for evaluating rice blast resistance on a field scale in rice breeding programs.
基金the Hi-Tech Research and DevelopmentProgram of China(863)(No.2003AA1Z1060).
文摘A new structure of bit-parallel Polynomial Basis(PB)multiplier is proposed,which isbased on a fast modular reduction method.The method was recommended by the National Instituteof Standards and Technology(NIST).It takes advantage of the characteristics of irreducible polyno-mial,i.e.,the degree of the second item of irreducible polynomial is far less than the degree of thepolynomial in the finite fields GF(2m).Deductions are made for a class of finite field in which trino-mials are chosen as irreducible polynomials.Let the trinomial bex m +x k+1,where 1 ≤k≤?m/2?.??The proposed structure has shorter critical path than the best known one up to date,whilethe space requirement keeps the same.The structure is practical,especially in real time crypto-graphic applications.
文摘China has promised to start the national carbon trading system in 2017.In the carbon trading system,the renewable energy projects may obtain additional benefits through the Certified Carbon Emission Reduction(CCER) trade.As the carbon price fluctuates along with the market conditions,such fluctuation enables the renewable power projects to acquire the rights of an option,i.e.it may contain an even higher value due to the uncertainties in the future.While making an investment decision,the renewable power companies may choose to make the investment immediately,or postpone the investment and accumulate more information to increase the return of investment;and for immediate investments,the return must be sufficient to exceed the potential value of a waiting option.To study the investment in renewable power projects subject to the fluctuation of carbon price,this paper adopts the trinomial tree model of real options to estimate the net present value(NPV) and real option value(ROV) of three types of renewable power projects;according to the decision-making rules of real options to defer,all the three types of projects will exercise the option to postpone the investment decision.This thesis also calculates the benchmark prices of the three types of renewable projects at different times,in the two situations of having no government subsidy and having the government subsidy,so as to determine the investment opportunity of a project.The benchmark price decreases gradually along with the increase of government subsidy,indicating that the government subsidy will stimulate the investment in renewable projects.The benchmark price also increases gradually along with the lapse of time,indicating that the uncertainty will increase together with the time span and thus requires an even higher carbon price to determine the investment opportunity.This thesis also analyzes the sensitivity of factors affecting the investment in renewable projects and draws the conclusion that the fluctuation of carbon price is positively related with the benchmark price of renewable power projects,which indicates that the fluctuation of carbon price increases the option value of an investment but postpones the time of investment.As the China's carbon trading system improves gradually,the carbon price will reach a stable status,thus stimulate the power companies to invest in the renewable projects.
文摘Accurate estimation of disease prevalence is crucial for effective public health intervention and resource allocation.Generating data by individual testing methods is often impractical and expensive for large populations,particularly when disease prevalence is low.Pool testing involves combining samples from multiple individuals into a pool and performing a single test,and offers a costeffective and efficient alternative.In pool testing strategy with retesting,if a pool tests negative,it is classified as non-defective,whereas if it is positive,then a retest is needed.The retesting strategy mitigates the effects of initial test errors,thereby enhancing the accuracy of the estimation of the prevalence rate.Evidence in the literature indicates that the traditional Wald method has been used to construct approximate confidence intervals for the prevalence rate.However,this interval estimation method is based on the normality ap-proximation and hence may not be accurate when the true prevalence rate is close to zero.In this paper,we propose a Bayesian interval estimation ap-proach which is not affected by extreme values of the prevalence rate and al-lows for incorporating prior information about the prevalence rate.We as-sumed that the prior distribution for the unknown prevalence rate p is a Beta distribution with parameters α_(0) and β_(0) and based on pool testing outcomes for the n pools each of size k,100(1-α)% credible intervals were constructed from the resulting posterior distribution.Simulation studies were carried out to compare the efficiencies of the Bayesian and Wald interval estimation methods for various values of p.
文摘It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.
