Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy

The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.

PARAMETRIZATION OF BALANCED MULTIWAVELET

This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.

Parametrization of Transfer Matrix:for One-Dimensional Anderson Model with Diagonal Disorder

In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.

Parametrization to Improve the Solution Accuracy of Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function

The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.

Cosmological test of dark energy parametrizations within the framework of Horava-Lifshitz gravity via baryon acoustic oscillation

We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations(Wettrich,Efstathiou,and Ma-Zhang)within the Horava-Lifshitz gravity framework.As an alternative to general relativity,this theory introduces anisotropic scaling at ultraviolet scales.Our primary objective is to constrain the key cosmic parameters and baryon acoustic oscillation(BAO)scale,specifically the sound horizon(rd),by utilizing 24 uncorrelated measurements of BAOs derived from recent galaxy surveys spanning a redshift range from z=0.106 to z=2.33.Additionally,we integrate the most recent Hubble constant measurement by Riess in 2022(denoted as R22)as an extra prior.For the parametrizations of Wettrich,Efstathiou,and Ma-Zhang,our analysis of BAO data yields sound horizon results of r_(d)=148.1560±2.7688 Mpc,r_(d)=148.6168±10.2469 Mpc,and r_(d)=147.9737±10.6096 Mpc,respectively.Incorporating the R22 prior into the BAO dataset results in r_(d)=139.5806±3.8522 Mpc,r_(d)=139.728025±2.7858 Mpc,and r_(d)=139.6001±2.7441 Mpc.These outcomes highlight a distinct inconsistency between early and late observational measurements,analogous to the H_(0) tension.A notable observation is that,when we do not include the R22 prior,the outcomes for rd tend to be in agreement with Planck and SDSS results.Following this,we conducted a cosmography test and comparative study of each parametrization within the Lambda Cold Dark Matter paradigm.Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region.All dark energy parametrizations predict an equation of state parameter close ω=-1,indicating a behavior similar to that of a cosmological constant.The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.

On the Base Point Locus of Surface Parametrizations:Formulas and Consequences

This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant.As a consequence,we get a new proof of the degree formula relating the degree of the surface,the degree of the parametrization,the base point multiplicity and the degree of the rational map induced by the parametrization.In addition,we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related.As an application of these results,we explore how the degree of a surface reparametrization is affected by the presence of base points.

Determination and(Re)Parametrization of Rational Developable Surfaces

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.

Boundary-Mapping Parametrization in Isogeometric Analysis

In isogeometric analysis(IGA),parametrization is an important and difficultissue that greatly influences the numerical accuracy and efficiency of the numericalsolution.One of the problems facing the parametrization in IGA is the existence ofthe singular points in the parametrization domain.To avoid producing singular points,boundary-mapping parametrization is given by mapping the computational domainto a polygon domain which may not be a square domain and mapping each segmentof the boundary in computational domain to a corresponding boundary edge of thepolygon.Two numerical examples in finite element analysis are presented to show thenovel parametrization is efficient.

THE PROPER PARAMETRIZATION OF A SPECIAL CLASS OF RATIONAL PARAMETRIC EQUATIONS

We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.

Boundary parametrization of planar self-affine tiles with collinear digit set

We consider a class of planar self-affine tiles T = M-1 a∈D(T + a) generated by an expanding integral matrix M and a collinear digit set D as follows:M =(0-B 1-A),D = {(00),...,(|B|0-1)}.We give a parametrization S1 →T of the boundary of T with the following standard properties.It is H¨older continuous and associated with a sequence of simple closed polygonal approximations whose vertices lie on T and have algebraic preimages.We derive a new proof that T is homeomorphic to a disk if and only if 2|A| |B + 2|.

PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONAL VARIETIES

In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.

Three dimensional parametrization of electromagnetic shower in Alpha Magnetic Spectrometer Ⅱ ECAL

We develop an empirical formula to parameterize the 3-dimension （3D） distribution of electromagnetic showers in the Alpha Magnetic Spectrometer Ⅱ electromagnetic calorimeter（ECAL）. The formula was verified by ECAL test beam data in 2002 and found to perform well. The distribution of electron showers in the ECAL are well described by the formula, which has parameters that allow one to determine the 3D shape of electromagnetic showers in the ECAL. We use this formula to correct for lateral energy leakage and dead channels in the ECAL; good results are obtained.

The Parametrization of Orthonormal Compactly Supported Wavelets and Wave Digital Filter

In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.

Casas-Ibarra parametrization and leptogenesis

The Casas-Ibarra parametrization is a description of the Dirac neutrino mass matrix MD in terms of the neutrino mixing matrix V , an orthogonal matrix O and the diagonal mass matrices of light and heavy Majorana neutrinos in the type-I seesaw mechanism. Because MDMD is apparently independent of V but dependent on O in this parametrization, a number of authors have claimed that unflavored leptogenesis has nothing to do with CP violation at low energies. Here we question this logic by clarifying the physical meaning of O. We establish a clear relationship between O and the observable quantities, and find that O does depend on V . We show that both unflavored leptogenesis and flavored leptogenesis have no direct connection with low-energy CP violation.

Decentralized Bezout Identity and a Parametrization of Decentralized Controllers for Singular Systems

In this paper, the construction problem of the decentralized Bezout identity for singular decentralized control systems is considered. A state space realization of the decentralized Bezout identity for singular decentralized control systems is developed. What is more, the parametrization of all normal decentralized properly stabilizing controllers is characterized and interpreted on the basis of the decentralized Bezout identity presented here. In fact, the work done in this paper is an extension of which was derived for normal decentralized control systems in the references by Date (1991) and Date and Chow (1994).

General one-loop reduction in generalized Feynman parametrization form

The search for an effective reduction method is one of the main topics in higher loop computation.Recently,an alternative reduction method was proposed by Chen in[1,2].In this paper,we test the power of Chen’s new method using one-loop scalar integrals with propagators of higher power.More explicitly,with the improved version of the method,we can cancel the dimension shift and terms with unwanted power shifting.Thus,the obtained integrating-by-parts relations are significantly simpler and can be solved easily.Using this method,we present explicit examples of a bubble,triangle,box,and pentagon with one doubled propagator.With these results,we complete our previous computations in[3]with the missing tadpole coefficients and show the potential of Chen’s method for efficient reduction in higher loop integrals.

Parametrization of Mean Radiative Properties of Optically Thin Steady-State Plasmas and Applications

Plasma radiative properties play a pivotal role both in nuclear fusion and astrophysics.They are essential to analyze and explain experiments or observations and also in radiative-hydrodynamics simulations.Their computation requires the generation of large atomic databases and the calculation,by solving a set of rate equations,of a huge number of atomic level populations in wide ranges of plasma conditions.These facts make that,for example,radiative-hydrodynamics in-line simulations be almost infeasible.This has lead to develop analytical expressions based on the parametrization of radiative properties.However,most of them are accurate only for coronal or local thermodynamic equilibrium.In this work we present a code for the parametrization of plasma radiative properties of mono-component plasmas,in terms of plasma density and temperature,such as radiative power loss,the Planck and Rosseland mean opacities and the average ionization,which is valid for steady-state optically thin plasmas in wide ranges of plasma densities and temperatures.Furthermore,we also present some applications of this parametrization such as the analysis of the optical depth and radiative character of plasmas,the use to perform diagnostics of the electron temperature,the determination of mean radiative properties for multicomponent plasmas and the analysis of radiative cooling instabilities in some kind of experiments on high-energy density laboratory astrophysics.Finally,to ease the use of the code for the parametrization,this one has been integrated in a user interface and brief comments about it are presented.

Differences between lower extremity joint running kinetics captured by marker-based and markerless systems were speed dependent

Background:The development of computer vision technology has enabled the use of markerless movement tracking for biomechanical analysis.Recent research has reported the feasibility of markerless systems in motion analysis but has yet to fully explore their utility for capturing faster movements,such as running.Applied studies using markerless systems in clinical and sports settings are still lacking.Thus,the present study compared running biomechanics estimated by marker-based and markerless systems.Given running speed not only affects sports performance but is also associated with clinical injury prevention,diagnosis,and rehabilitation,we aimed to investigate the effects of speed on the comparison of estimated lower extremity joint moments and powers between markerless and marker-based technologies during treadmill running as a concurrent validating study.Methods:Kinematic data from marker-based/markerless technologies were collected,along with ground reaction force data,from 16 young adults running on an instrumented treadmill at 3 speeds:2.24 m/s,2.91 m/s,and 3.58 m/s(5.0 miles/h,6.5 miles/h,and 8.0 miles/h).Sagittal plane moments and powers of the hip,knee,and ankle were calculated by inverse dynamic methods.Time series analysis and statistical parametric mapping were used to determine system differences.Results:Compared to the marker-based system,the markerless system estimated increased lower extremity joint kinetics with faster speed during the swing phase in most cases.Conclusion:Despite the promising application of markerless technology in clinical settings,systematic markerless overestimation requires focused attention.Based on segment pose estimations,the centers of mass estimated by markerless technologies were farther away from the relevant distal joint centers,which led to greater joint moments and powers estimates by markerless vs.marker-based systems.The differences were amplified by running speed.

Tunable topological interface states via a parametric system in composite lattices with/without symmetric elements

Over the past decades, topological interface states have attracted significant attention in classical wave systems. Generally, research on the topological interface states of elastic waves is conducted in the lattices with symmetric elements. This paper proposes composite lattices with/without symmetric elements, and demonstrates the realization of tunable topological interface states of elastic waves via parametric systems.To quantize the topological characteristics of the bands, a modified Zak phase is defined to calculate the topological invariant by the eigenstates for the lattices with/without symmetric elements. The numerical results show that the tunable frequencies of topological interface states can be realized in composite lattices with/without symmetric elements through the modulation of the parametric excitation frequency. The tunable topological interface states can be introduced into the vibration energy harvesting to design efficient and steady energy harvesting systems.

Enhanced picosecond terahertz wave generation based on cascade effects in a terahertz parametric generator

Enhanced terahertz wave generation via a Stokes cascade process has been demonstrated using picosecond pulse pumped terahertz parametric generation at 1 kHz repetition rate.Clear cascade saturation of terahertz output was observed,and the corresponding cascade-Stokes spectra were analyzed.The maximum terahertz wave average power was 22μW under a pump power of 30 W,whereas the maximum power conversion efficiency was 8×10^(-7)under a pump power of 21 W.The THz power fluctuation was measured to be about 1%in 20 min.This THz parametric source with a relatively stable output is suitable for a variety of practical applications.