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NONLIFT WEIGHT TWO PARAMODULAR EIGENFORM CONSTRUCTIONS
Poor, Cris,Shurman, Jerry,Yuen, David S. Korean Mathematical Society 2020 대한수학회지 Vol.57 No.2
We complete the construction of the nonlift weight two cusp paramodular Hecke eigenforms for prime levels N < 600, which arise in conformance with the paramodular conjecture of Brumer and Kramer.
THE CHIRAL SUPERSTRING SIEGEL FORM IN DEGREE TWO IS A LIFT
Poor, Cris,Yuen, David S. Korean Mathematical Society 2012 대한수학회지 Vol.49 No.2
We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group ${\Gamma}_1$(1, 2) to Siegel modular cusp forms over certain subgroups ${\Gamma}^{para}$(t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.
THE CUSP STRUCTURE OF THE PARAMODULAR GROUPS FOR DEGREE TWO
Poor, Cris,Yuen, David S. Korean Mathematical Society 2013 대한수학회지 Vol.50 No.2
We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.
The cusp structure of the paramodular groups for degree two
Cris Poor,David S. Yuen 대한수학회 2013 대한수학회지 Vol.50 No.2
We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.
The chiral superstring Siegel form in degree two is a lift
Cris Poor,David S. Yuen 대한수학회 2012 대한수학회지 Vol.49 No.2
We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t=2 over the theta group Γ1(1, 2) to Siegel modular cusp forms over certain subgroups Γpara(t, 1, 2) of paramodular groups. The theta group lift given here is a modication of the Gritsenko lift.
Computations of spaces of paramodular forms of general level
Cris Poor,David S. Yuen,Jeffery Breeding II 대한수학회 2016 대한수학회지 Vol.53 No.3
This article gives upper bounds on the number of Fourier-Jacobi coefficients that determine a paramodular cusp form in degree two. The level~N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.
Nonlift weight two paramodular eigenform constructions
Cris Poor,Jerry Shurman,David S. Yuen 대한수학회 2020 대한수학회지 Vol.57 No.2
We complete the construction of the nonlift weight two cusp para\-modular Hecke eigenforms for prime levels $N<600$, which arise in conformance with the paramodular conjecture of Brumer and Kramer.
Hamed Ziaei Poor,Hossain Ghorbani Menghari,Ricardo J. Alves De Sousa,Hassan Moosavi,Mahboubeh Parastarfeizabadi,Mahmoud Farzin,Hamed Sanei 한국정밀공학회 2014 International Journal of Precision Engineering and Vol. No.
Optimization of operating conditions is one of the most signicant issues concerning hydroforming the tubular components, includingstepped tubes, conical tubes, box shape tubes, and etc. Obtaining a sharp corner without any defects such as thinning and rupturingis one of the main goals in the production of these components. In order to manufacture tubes with filled corners, it is common toincrease the imposed pressure to the tubes. However, it may result in rupturing and thinning at the die corner radius, especially whenit is too small. In this paper, a new multistage die has been proposed for producing two stepped tubes. Numerical modeling has beenconducted using Abaqus/Explicit code. The results of simulation were afterwards checked against experiments in which it is shownthat a better thickness distribution could be obtained employing the proposed die set. There is no thinning in the final workpiece,particularly at the copper tube corners. Moreover, it could be possible to produce two stepped tubes with complete filled corners. Finally, comparing to other well-established methods, a lower pressure profile is required and a better thickness distribution can beachieved.
Reza Bakhshi,Sina Fard Moradinia,Rasool Jani,Ramin Vafaei Poor 대한토목학회 2022 KSCE JOURNAL OF CIVIL ENGINEERING Vol.26 No.8
A primary task to a project manager is to ensure that the project proceeds timely and on the budget. Earned value management (EVM) is the most common method to evaluate and further predict a project in terms of time and cost. Because of poor accuracy in forecasting different durations, the application of the EVM for schedule performance prediction has been limited. Therefore, in this paper, the Kalman filter was used to analyze the data and compare the results with those of a few hybrid machine learning (HML) techniques. The innovation of this study comes in the face of the prediction of the project time and cost by efficient machine learning algorithms based on some directly measurable variables. For this purpose, 398 data points from five different dam projects were used to predict two output variables by hybrid schemes of multilayer perceptron (MLP) algorithm combined with the genetic algorithm (GA) and particle swarm optimization (PSO), herein referred to as MLP-GA and MLP-PSO, respectively. Four input variables, namely earned schedule (month), earned value ($), actual progress (%), and actual cost (%), were considered for time prediction, and the time (month) was considered as an input variable for cost prediction. The results showed that early warnings for the risk of delay in project schedule and cost were generated in months 1 and 8 by the MLP-PSO, months 1 and 11 by the MLP-GA, and rather months 7 and NV (no value) for the Kalman filter, indicating the fast operation coupled with high accuracy of the HML algorithms, as compared to the Kalman filter. In addition, the two HML algorithms were compared based on statistical error indices to determine the best one. After reviewing the results, the MLP-PSO was found to outperform the MLP-GA in terms of convergence rate and accuracy. To the best of our knowledge, none of the previous studies have used the proposed hybrid algorithms (MELM-PSO and MELM-GA) for forecasting, simultaneously, the time and cost as two critical parameters in the project management, indicating the novelty of our research.