A 1D numerical model of Nonlinear Shallow Water Equations (NSWEs) coupled to an advection equation for suspended sediment and a bed evolution equation is developed. The moving boundary at the shore- line is treated by a **coordinate** **transformation** **method** (**CTM**). An absorbing-generating seaward boundary condition in the transformed variables is also developed. The purely hydrodynamic component (NSWEs) is verified against analytical results. The NSWEs plus advection equation is verified quasi-analytical re- sults. The fully-coupled model with bed change due to bed-load is verified against a single swash event and long-term numerical simulation. Excellent agreement is observed in all verifications.

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The form-invariant, spatial **coordinate** **transformation** **method** [1– 3] provides a conceptually simple approach to the design of complex electromagnetic structures. Following this **method**, the invisibility cloaks have received much attention [4–12]. Apart from invisibility cloaks, other interesting metamaterial devices [13] such as rotators [14, 15], concentrators [16–19], illusion devices [20, 21], superscatterers [22, 23], equiscatterers [24], invisible tunnels [25], and beam shifters [26] were investigated.

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When the CMA is used to equalize 16QAM signal, the error function is written as ( is a specific module value). Even if the channels are equal- ized completely, the error is not zero. This affects equalization results. So, **coordinate** **transformation** **method** is used to make 16QAM signal points in differ- ent circles turn into A, B, C, D four points in the same circle. In other words, after multi-modulus 16QAM sig- nals is become constant modulus 4QAM signals, the er- ror is zero under the condition that the channels are equalized completely. The performance of the algorithm based on **coordinate** **transformation** **method** (T/2-FSE-

**Coordinate** **transformation** **method** [11]-[15] is a commonly-used **method** to achieve computation on physical nonuniform grids. This **method** needs to transform the nonuniform grids in the physical domain to the uniform grids in the computational domain by using reversible **coordinate** **transformation** functions. After computation, it returns the computed results back to the physical domain by the inverse **transformation**. The **method** has its ad- vantages. Firstly, it can be used to construct HOC schemes more easily on uniform grids than on nonuniform grids by discretizing the derivative terms directly; secondly, such transformations are also used to reflect many interior/boundary layer phenomena without refining the mesh near to the interior/boundary layers in the compu- tational domain. A few researchers have used this **method** to deal with convection diffusion equations or Navier- Stokes equations. For instance, Choo and Schultz [11] used the **transformation** **method** and developed a fourth order compact difference scheme to solve the steady Navier-Stokes equations. The results show that the **method** is accurate and stable. Spotz [12] developed a class of HOC finite difference schemes for steady convection dif- fusion equation on uniform grids. And then he extended them to nonuniform grids by using the **coordinate** **transformation** **method**. Ge and Zhang [13] also solved the 2D convection diffusion equations with boundary layers using the **coordinate** **transformation** **method** and a fourth order scheme was applied on the uniform com- putational grids. The authors extended the **coordinate** **transformation** **method** to the three-dimensional (3D) case [14] to resolve 3D boundary layer problems. Liu C. and Liu Z. [15] employed the **coordinate** **transformation** and combined it with a fourth order finite difference scheme and multigrid **method** to simulate the whole process of flow transition in 3D boundary layers. If we fix our attention on elliptic equations, we notice that the coefficients of the first or second order derivatives in the original model equations considered in the literature are constant [11]-[14]. Although after **coordinate** **transformation**, the coefficients turn to be variable, the high order differ- ence schemes, which are developed based on it, could not be used to compute the solutions of original model equations in which the coefficients of the first or second order derivatives are variable. So, the potential advan- tages of applying **coordinate** **transformation** **method** and HOC schemes to solve variable coefficients elliptic problems have not been fully investigated.

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Many eﬀorts have been made to simplify these material parameters [31, 32]. There are some major approaches for yielding simple constitutive parameters. The ﬁrst and most straightforward **method** is to make approximation to the obtained design to achieve material simplicity [31]; the second **method** is to apply numerical optimization techniques that begins with **transformation** design, to ﬁnd realizable material parameters [33]. The third procedure uses the degrees of freedom associated with the **transformation** itself which is applied in this paper.

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model for all regions except the tropical boundary layer where the **CTM** uniformly underestimates the observed CO by about 12 ppb. In **CTM** sensitivity tests with a range of CO-like tracers (not shown here), we find that much of the observed variance (e.g., as measured by M - Q), including fine-scale features, is driven by large and synoptic-scale systems acting on the global-scale latitudinal gradients in CO, rather than by the nearby east Asian emissions. Thus we take this agreement to mean that the large-scale CO gradients and meteorological systems are well simulated. Above the 75th percentile, however, the simulations are uniformly much smaller than observed. One cause might be the failure of the **CTM** to resolve urban plumes, for example, the intense, small-scale pollution events such as the Shanghai plume [Russo et al., 2003; Simpson et al., 2003; Talbot et al., 2003]. However, for the distributions shown in the figure (CO < 300 ppb), the observed proba- bility distributions are unaffected by spatial filtering at the **CTM** resolution, and hence these probability distributions should be resolved by the model. Thus the uniform under- prediction of the CO probabilities at the upper end of the distribution as shown are likely due to an underestimate of CO emissions from east Asian sources [Palmer et al., 2003] or possibly to chemical influences rather than lack of model Table 1. Number of Data Points (N) for CO and O 3 From DC-8

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variable corresponding to angles θ, φ. We name the transformations from (1) to (5) as the positive **transformation**. The scattering ﬁeld from an ellipse target irradiating by the incident wave with arbitrary polarization and propagation will be presented by the contradictorily **transformation** in the following. We know from [7] the following relation of electromagnetic ﬁeld between two coordinates and coordinates m

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We use D-H parameters to describe the vibration behavior of the system “platform-arm”. It is proposed to model the platform as a single degree-of-freedom rigid body, with its parameters: – mass and inertia tensor, correspondingly. As the main source of the vibration in the manipulator is from the irregularities in the wheels contact points, we introduce one degree-of-freedom for the platform – its vertical displacement Figure 1 shows a sketch of the platform with assigned **coordinate** frames. We introduce several **coordinate** transformations:

necessarily entail that the velocity of this light is in each direction the same. That is, even though the averaged, round trip velocity agrees with the empirically determined velocity of light in vacuo, its one-way velocity need not be in agreement with the empirically determined value. Franzel also noted that a kind of "practical" absolute simultaneity is possible as an alternative to the relativity of simultaneity developed by Einstein. The point missed by such adherents to these other positions is the theoretical simplicity and yet fundamental and far reaching ramifications of the argument on the relativity of simultaneity as regards the special theory. It is not difficult to show that it is the relativity of simultaneity, as opposed to the absolute simultaneity of the kinematics underlying Newtonian mechanics, that distinguishes the results of the special theory from the results of Newtonian mechanics. It has been shown, for example, in the present paper how the relativity of simultaneity is central to the Lorentz **coordinate** **transformation** equations and the spatiotemporal relations that underlie the other results of the special theory. It should be emphasized that the concern in the present paper is not with attempting to refute the significance of the relativity of simultaneity in the special theory. The concern is with investigating certain implications of the relativity of simultaneity in the special theory.

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Aiming at solving problems of pose angle singularity in the initial alignment of SINS, a quaternion alignment **method** is proposed. The calculation amount of quaternion **method** is small and there is no singularity. The initial alignment **method** of quaternion is obtained directly by quaternion attitude **transformation** matrix, which can improve both the efficiency of initial alignment and apply larger attitude angle range.

Three-dimensional (3D) **coordinate** **transformation** is the most common issue in geodesy, photogrammetry, geographical information science (GIS), computer vision and other research areas. It involves transforming spatial data (locations, images, maps, etc.) from an original **coordinate** system to a target **coordinate** system by means of mathematical **transformation** model. Presently, the most frequently model is the similarity **transformation** model with seven parameters (namely, one scale factor, three translation parameter, and three rotation angles.), also known as Helmert or conformal group C 7 (3)

The main insight. We show that the parallelization potential of Hydra, that is, its ability to accelerate as τ is increased, depends on two data-dependent quantities: i) the spectral norm of the data (σ) and ii) a partition-induced norm of the data (σ 0 ). The first quantity completely describes the behavior of the **method** in the c = 1 case. If σ is small, then utilization of more processors (i.e., increasing τ ) leads to nearly linear speedup. If σ is large, speedup may be negligible, or there may be no speedup whatsoever. Hence, the size of σ suggests whether it is worth to use more processors or not. The second quantity, σ 0 , characterizes the effect of the initial partition on the algorithm, and as such is relevant in the c > 1 case. Partitions with small σ 0 are preferable. We show that, surprisingly, that as long as τ ≥ 2, the effect of a bad partitioning is that it most doubles the number of iterations of Hydra. Hence, data partitioning can be used to optimize for different aspects of the **method**, such as reducing communication complexity, if needed.

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Abstract. An accurate characterisation of the complex and heterogeneous forest architecture is necessary to parame- terise physically-based hydrologic models that simulate pre- cipitation interception, energy fluxes and water dynamics. While hemispherical photography has become a popular **method** to obtain a number of forest canopy structure met- rics relevant to these processes, image acquisition is field- intensive and, therefore, difficult to apply across the land- scape. In contrast, airborne laser scanning (ALS) is a remote- sensing technique increasingly used to acquire detailed in- formation on the spatial structure of forest canopies over large, continuous areas. This study presents a novel **method**- ology to calibrate ALS data with in situ optical hemispher- ical camera images to obtain traditional forest structure and solar radiation metrics. The approach minimises geometrical differences between these two techniques by transforming the Cartesian coordinates of ALS data to generate synthetic images with a polar projection directly comparable to opti- cal photography. We demonstrate how these new **coordinate**- transformed ALS metrics, along with additional standard ALS variables, can be used as predictors in multiple linear regression approaches to estimate forest structure and solar radiation indices at any individual location within the extent of an ALS transect. We expect this approach to substantially reduce fieldwork costs, broaden sampling design possibili- ties, and improve the spatial representation of forest structure metrics directly relevant to parameterising fully-distributed hydrologic models.

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For multi distances assessment, eight (8) targets were distributed at the slope located at Faculty of Electrical Engineering, Universiti Teknologi Malaysia. The aim of this experiment was to investigate the scale effect in TLS datum **transformation** with respect to various distance, especially when the scanner was far away from the targets. As illustrated in Figure 7, the measurement was started roughly 60m from targets, the procedure was continue by moving the scanner at 10m interval until maximum distance 140m. Registration process was made using pairwise approach and targets extracted from 60m distance were employed as reference for other configurations. All eight (8) scale factors obtained from the experiment then were analysed in term of significance in TLS datum **transformation**.

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Lesson plans and formative assessment developed with the help of multimedia strategy to carry out teaching learning process on experimental group for nine weeks only. At the end of the experiment, learning outcome per-test, post-test and mean gain score was computed. Then, data were subjected to analyzed by using ANOVA and t-test to determine the performance by comparing the mean scores. Results revealed that prospective teachers taught through multimedia package showed significant improvement in their learning outcome than the prospective teachers taught through conventional **method**. Further, high, average and low intelligence prospective teachers taught through multimedia package performed better than counter parts. There was no significant interaction effect of instructional treatment and levels of intelligence on mean gain learning outcome scores. In conclusion, this study had proven that teaching through multimedia instructional package enhance the prospective teachers’ learning performance.

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The purpose of an optimal **coordinate** being multivalued and the difference from the conventional description can be illustrated as follows. Consider a system that stochastically transits between two states 1 and 2 (illustrative example 2). Let an ensemble of such systems be initially in state 1. With time some systems will transit to state 2 and then some of them will return to state 1. State 1 now contains two sets of systems: the systems which came back there from state 2 and the systems which never left state 1. The future dynamics of the two sets are described by the same set of equations and, conventionally, one considers them identical and counts them together. However, after such mixing, the information about the past dynamics (which was different) is lost; one cannot reconstruct dynamics back in time. The multivaluedness (of an optimal **coordinate**) is used to distinguish the two sets.

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Previous studies about blockage effect on capacity signalized intersections have been vey limited. They generally focused on examining the capacity of signalized intersections by considering geometric properties of intersections, traffic flow properties, lane and driver charactaristics etc. But this study aims to investigate the relation between blockage of traffic flow and signalized intersection capacity. For this purpose a macroscopic model called the Cell Transmission Model (**CTM**) was implemented in analysis to design an alternative **method** for predicting the the blockage effect of traffic flow caused by a bus stop or a road surface deformation at a signalized intersection. To reach focused aim, different methods for the prediction of bus or deformation blockage effect due to a stoppage were investigated and compared under different conditions.

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**transformation** properties of the individual terms, will be referred to as manifestly covariant. In the field of numerical relativity, Einstein’s theory is interpreted as an initial value problem. With the Einstein field equations being written in 3+1 format, rather than spacetime **coordinate** transformations we focus our attention on achieving general covariance under another class of **coordinate** transformations. This new family of **coordinate** transformations breaks time and space symmetry in the same sense as the 3 + 1 decomposition. General covariance of various numerical formulations under this set of **coordinate** transformations is discussed in the next section.

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The performance about two of those points in 500 tests by MSV **method** are presented in Figure 5. Clearly, The No. 68 point (red) is more seriously corrupted by noise than the No. 28 point (black). In order to present some good properties of our new **method**, the results of the No. 68 point by MSV, TSVD, and Tikhovon regularization with L-curve are drawn in Figures 6(a)-(c), respectively. Table 2 summarizes mean of RMSE and their corre- sponding standard deviations of No. 68 points through using different methods. Clearly, when the point has poor precision, our MSV **method** can balance the point preci- sion and robustness well.

on the computational domain. Since the **transformation** is invertible between the computational domain and the practical domain, by using the equivalent norm property (Lemma 2.2 in [4]), we get the same conclusion for the corresponding approximation solution U and the exact solution u of (2.1) on the practical domain Ω(t).