Regular ternary triangular forms

An integer of the form $T_x=\frac{x(x+1)}2$ for some positive integer $x$ is called a triangular number. A ternary triangular form $aT_{x}+bT_{y}+cT_{z}$ for positive integers $a,b$ and $c$ is called regular if it represents every positive integer that is locally represented. In this article, we prove that there are exactly 49 primitive regular ternary triangular forms.Comment: 28 page

Tight universal triangular forms

For a subset $S$ of nonnegative integers and a vector $\mathbf{a}=(a_1,\dots,a_k)$ of positive integers, let $V'_S(\mathbf{a})=\{ a_1s_1+\cdots+a_ks_k : s_i\in S\} \setminus \{0\}$. For a positive integer $n$, let $\mathcal T(n)$ be the set of integers greater than or equal to $n$. In this paper, we consider the problem of finding all vectors $\mathbf{a}$ satisfying $V'_S(\mathbf{a})=\mathcal T(n)$, when $S$ is the set of (generalized) $m$-gonal numbers and $n$ is a positive integer. In particular, we completely resolve the case when $S$ is the set of triangular numbers

Prime-universal diagonal quadratic forms

A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all prime-universal diagonal quaternary quadratic forms under two conjectures proposed by themselves. In this article, we classify all prime-universal diagonal quadratic forms regardless of ranks. Furthermore, we prove, so called, $67$-Theorem for a diagonal quadratic form to be prime-universal.Comment: 14 page

GA-ARMA Model for Predicting IGS RTS Corrections

The global navigation satellite system (GNSS) is widely used to estimate user positions. For precise positioning, users should correct for GNSS error components such as satellite orbit and clock errors as well as ionospheric delay. The international GNSS service (IGS) real-time service (RTS) can be used to correct orbit and clock errors in real-time. Since the IGS RTS provides real-time corrections via the Internet, intermittent data loss can occur due to software or hardware failures. We propose applying a genetic algorithm autoregressive moving average (GA-ARMA) model to predict the IGS RTS corrections during data loss periods. The RTS orbit and clock corrections are predicted up to 900 s via the GA-ARMA model, and the prediction accuracies are compared with the results from a generic ARMA model. The orbit prediction performance of the GA-ARMA is nearly equivalent to that of ARMA, but GA-ARMA’s clock prediction performance is clearly better than that of ARMA, achieving a 32% error reduction. Predicted RTS corrections are applied to the broadcast ephemeris, and precise point positioning accuracies are compared. GA-ARMA shows a significant accuracy improvement over ARMA, particularly in terms of vertical positioning

Numerical studies on added resistance and motions of KVLCC2 in head seas for various ship speeds

In this study, numerical simulations for the prediction of added resistance and ship motions at various ship speeds and wave steepnesses for the KVLCC2 are presented. These are calculated using URANS CFD and 3-D potential methods, both in regular head seas. Numerical analysis is focused on the added resistance and the vertical ship motions for a wide range of wave conditions at stationary, operating and design speeds. Firstly, the characteristics of the CFD and the 3-D potential method are presented. Simulations of various wave conditions at design speed are used as a validation study, and then simulations are carried out at stationary and operating speed. Secondly, unsteady wave patterns and time history results of the added resistance and the ship motions are simulated and analysed at each ship speed using the CFD tool. Finally, the relationship between the added resistance and the vertical ship motions is studied in detail and the non-linearity of the added resistance and ship motions with the varying wave steepness are investigated. Systematic studies of the numerical computations at various ship speeds are conducted as well as the grid convergence tests, to show that the numerical results have a reasonable agreement with the available EFD results