Finally, the problem statement should frame how you intend to address the problem. Your goal here should not be to find a conclusive solution, but rather to propose more effective approaches to tackling or understanding it. The research aim is the overall purpose of your research. It is genera...
The Polymath 5 online collaboration project [15] devoted to the Erdős discrepancy problem was indeed able to reduce the proof of (1) to (an averaged version of) the completely multiplicative case (2), withfnow taking values on the unit circleof the complex plane. Tao established in [17]...
In this paper, we consider the stochastic recursive control problem under non-Lipschitz framework. More precisely, we assume that the generator of the backward stochastic differential equation that describes the cost functional is monotonic with respect to the first unknown variable and uniformly continuo...
However, the discretization and planning mechanism is designed conservatively to avoid bin overflow, which can lead to excessive wasted space in the solution and lowered consistency. Also, the performance of the algorithm largely depends on the chosen parameters. A more flexible mechanism may be ...
[48], through analysis and calculation in their study, found that greater air humidity reduces the density of the air and affects the output of the wind power generator, which is neglected in the wind farm calculation. With the development of the wind power generator, especially in wet ...
Let\rho \in (0,1], \alpha ,\beta ,k,r>0,Ais a closed linear operator mapping fromD(A)\subset Einto the Banach spaceE. OperatorAis said to be the generator of(\rho ,\alpha ,\beta ,k,r)-resolvent family, if there exist\omega \geq 0and a strongly continuous GEB operatorS_{\rh...
If the algorithm is allowed as many binary queries to the oracle as is the length of the solution/witness, then there is a trivial algorithm that solves the problem. Thus, this class of algorithms is looked at with the goal of minimizing the number of queries. The minimum number of ...
It has been reported the NSA pushed for the standardisation of a flawed pseudorandom number generator for use in cryptosystems known as the Dual EC Standard (Dual_EC_DRBG) as part of BULLRUN (Bern- stein et al., 2016; Menn, 2013, para. 2). During this period the 'arms race' was...
Solution of SAT problems with the adaptive-bias quantum approximate optimization algorithm. Phys. Rev. Res. 2023, 5, 023147. [Google Scholar] [CrossRef] Jansen, D.; Heightman, T.; Mortimer, L.; Perito, I.; Acín, A. Qudit inspired optimization for graph coloring. arXiv 2024, arXiv:...
Solving these scalarized functions will generate the Pareto optimal solution for the MOO problem. Assuming we have N scalar optimization subproblems and M objectives, our weight vector can be represented as 𝑤𝑖𝑗wij = [[𝑤11,𝑤12,𝑤1𝑀],…,[𝑤𝑁1,𝑤𝑁2,𝑤𝑁𝑀]].[...