New cubic rational basis with tension shape parameters

By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.

Spectral investigation of traveling ionospheric disturbances:IONOLAB-FFT

Ionosphere is an important layer of atmosphere which is under constant forcing from both below due to gravitational, geomagnetic and seismic activities, and above due to solar wind and galactic radiation. Spatio-temporal variability of ionosphere is made up of two major components that can be listed as spatio-temporal trends and secondary variabilities that are due to disturbances in the geomagnetic field, gravitational waves and coupling of seismic activities into the upper atmosphere and ionosphere. Some of these second order variabilities generate wave-like oscillations in the ionosphere which propagate at a certain frequency, duration and velocity. These oscillations cause major problems for navigation and guidance systems that utilize GNSS （Global Navigation Satellite Systems）. In this study, the frequency and duration of wave-like oscillations are determined using a DFT （Discrete Fourier Transform） based algo- rithm over the STEC （slant total electron content） values estimated from single GPS （Global Positioning System） station. The performance of the developed method, namely IONOLAB-FFT, is first determined using synthetic oscillations with known frequencies and durations. Then, IONOLAB-FFr is applied to STEC data from various midlatitude GPS stations for detection of frequency and duration of both medium and large scale TIDs （traveling ionospheric disturbances）. It is observed that IONOLAB-FFr can estimate TIDs with more than 80% accuracy for the following cases： frequencies from 0.6 mHz to 2.4 mHz and durations longer than 10 min; frequencies from 0.15 mHz to 0.6 mHz and durations longer than 50 min; fre- quencies higher than 0.29 mHz and durations longer than 50 rain.

CASE REPORT: TOTAL SUDDEN HEARING LOSS WITH BENIGN PAROXYSMAL POSITIONAL VERTIGO

Introduction Sudden sensorineural hearing loss(SSNHL)is defined as a hearing loss of at least 30 dB over three contiguous frequencies occurring in less than 3 days[1].Vertigo and profound hearing loss are considered poor prognostic factors in SSNHL[2-4].The most common diseases associated with vertigo in SSNHL include BPPV,vestibular neu-[3]

Total Positivity of UE Spline Basis

A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.

The influence of head-neck and implant position on the range of motion after total hip arthroplasty

To study the influence of head-neck ratio and implant position on the range of motion (ROM) after total hip arthroplasty (THA).Methods In this study the author established a three-dimensional computerized model of hip joint and tested the range of motion of three different head-neck ratio after total hip arthroplasty.Results Range of motion after total hip arthroplasty depended on design parameters such as head-neck ratio,but also on the implantation parameters such as the cup’s inclination and antevertion,the stem’s antevertion and their combination of each other.Optimal range of motion required compliant position of total hip components.The range of motion increased with the enlarging of head-hnck ratio.Conclusion Higher head-neck ratio leads to optimal range of motion and decreased the prevalence of prosthetic impingement within compliant,well-defined combination of cup’s inclination,cup’s antevertion and stem’s antevertion depending on the intended ROM.Domestic magnesium-silicon jade total hip prosthesis has too low head-neck ratio to result in enough range of motion that fulfilled daily living after total hip arthroplasty.14 refs,4 figs,3 tabs.

NEW TRIGONOMETRIC BASIS POSSESSING EXPONENTIAL SHAPE PARAMETERS

Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．

Novel passive localization algorithm based on double side matrix-restricted total least squares

In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares （DSMRTLS） is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.

Hamburger Moment Sequences in Combinatorics

We show that many well-known counting coefficients in combinatorics are Hamburger moment sequences in certain unified approaches and that Hamburger moment sequences are infinitely convex. We introduce the concept of the q-Hamburger moment sequence of polynomials and present some examples of such sequences of polynomials. We also suggest some problems and conjectures.

DEVELOPMENTS ON MTP_2 PROPERTIES OF ABSOLUTE VALUE MULTINORMAL VARIABLES WITH NONZERO MEANS

et X=(X1,...,Xn )' have a multivariate normal distribution with mean μ and covariance matrix Σ. In the case μ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X1|,...,|Xn|)' to be MTP2. In this paper we consider the case μ≠0, and give some conditions under which |X| is MTP2. A necessary and sufficient condition is given for |X| to be TP2 when n=2 and μ≠0. Some results about the TP2 stochastic ordering are also given. The results are applied to obtain positive dependence and associated inequalities for multinormal and related distributions.