SOME PERMUTING TRINOMIALS OVER FINITEFIELDS

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.

A Formula of General Solution for a Class of Homogeneous Trinomial Recurrence of Variable Coefficients with Two Indices

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.

Trinomial tree model of the real options approach used in mining investment price forecast and analysis

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.

Congruences involving generalized central trinomial coefficients

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.

A General Solution for Trinomial Linear Recurrence with Two Indices

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.

Application of UAV-Based Imaging and Deep Learning in Assessment of Rice Blast Resistance

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.

RESEARCH OF FAST MODULAR MULTIPLIER FOR A CLASS OF FINITE FIELDS

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.

Study on the investment value and investment opportunity of renewable energies under the carbon trading system

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.

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

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.