Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Comparative Characterization of Maxillary Expansion and Alternate Maxillary Expansions and Constrictions in Rats

The purpose of this study was to evaluate whether the cranial and circumaxillary sutures react differently to maxillary expansion （ME） and alternate maxillary expansions and constrictions （Alt-MEC） in a rat model. Twenty-two male Sprague-Dawley rats （6 weeks old） were used and divided into three groups. In ME group （n=9）, an expander was activated for 5 days. In Alt-MEC group （9 animals）, an al- ternate expansion and constriction protocol （5-day expansion and 5-day constriction for one cycle） was conducted for 2.5 cycles （25 days total）. The control group comprised 4 animals with no appliances used, each of two sacrificed on day 5 and day 25 respectively. Midpalatal suture expansion or constriction levels were assessed qualitatively and quantitatively by bite-wing X-rays and cast models. Distances between two central incisors and two maxillary first molars were measured on cast models after each activation. Circumaxillary sutures （midpalatal, maxillopalatine, premaxillary, zygomaticotemporal and frontonasal suture） in each group were characterized histologically. Results showed that midpalatal suture was wid- ened and restored after each expansion and constriction. At the end of activation, the widths between both central incisors and first molars in Alt-MEC group were significantly larger than those in ME group （P〈0.05）. Histologically, all five circumaxillary sutures studied were widened in multiple zones in Alt- MEC group. However, only midpalatal suture was expanded with cellular fibrous tissue filling in ME group. Significant osteoclast hyperplasia was observed in all circumaxillary sutures after alternate expan- sions and constrictions, but osteoclast count increase was only observed in midpalatal suture in ME group. These results suggested that cranial and circumaxillary sutures were actively reconstructed after Alt-MEC, while only midpalatal suture had active reaction after ME.

The Factorizational Theory of Finite Asymptotic Expansions in the Real Domain: A Survey of the Main Results

After studying finite asymptotic expansions in real powers, we have developed a general theory for expansions of type (*) ,x → x0 where the ordered n-tuple forms an asymptotic scale at x0 , i.e. as x → x0, 1 ≤ i ≤ n – 1, and is practically assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x o. As in previous papers by the author concerning polynomial, real-power and two-term theory, the locution “factorizational theory” refers to the special approach based on various types of factorizations of a differential operator associated to . Moreover, the guiding thread of our theory is the property of formal differentiation and we aim at characterizing some n-tuples of asymptotic expansions formed by (*) and n -1 expansions obtained by formal applications of suitable linear differential operators of orders 1,2,…,n-1. Some considerations lead to restrict the attention to two sets of operators naturally associated to “canonical factorizations”. This gives rise to conjectures whose proofs build an analytic theory of finite asymptotic expansions in the real domain which, though not elementary, parallels the familiar results about Taylor’s formula. One of the results states that to each scale of the type under consideration it remains associated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion(*), if valid, is automatically formally differentiable n-1 times in two special senses.

GENERALIZED EXPANSIONS IN HILBERT SPACE

In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to all abstract Hilbert space. Then in the case L-2(-infinity + infinity) they discussed extensively the generalized expansion problem by Hermite functions, and applied to a non-strictly nonlinear hyperbolic system.

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-A: The Factorizational Theory for Chebyshev Asymptotic Scales

This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)?, , , where the asymptotic scale?, , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of . It follows two pre-viously published papers: the first, labelled as Part I, contains the complete (elementary but non-trivial) theory for;the second is a survey highlighting only the main results without proofs. All the material appearing in §2 of the survey is here reproduced in an expanded form, as it contains all the preliminary formulas necessary to understand and prove the results. The remaining part of the survey—especially the heuristical considerations and consequent conjectures in §3—may serve as a good introduction to the complete theory.

NECESSARY AND SUFFICIENT CONDITIONS FOR EXPANSIONS OF GABOR TYPE

In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

Ex vivo expansions and transplantations of mouse bone marrow－derived hematopoietic stem／progenitor cells

To examine the effects of co-culture with bone marrow mesenchymal stem cells on expansion of hematopoietic stem/progenitor cells and the capacities of rapid neutrophil engraftment and hematopoietic reconstitution of the expanded cells, we expanded mononuclear cells (MNCs) and CD34+/c-kit+ cells from mouse bone marrow and transplanted the ex-panded cells into the irradiated mice. MNCs were isolated from mouse bone marrow and CD34+/c-kit+ cells were selected from MNCs by using MoFlo Cell Sorter. MNCs and CD34+/c-kit+ cells were co-cultured with mouse bone marrow-derived mesenchymal stem cells (MSCs) under a two-step expansion. The expanded cells were then transplanted into sublethally irradiated BDF1 mice. Results showed that the co-culture with MSCs resulted in expansions of median total nucleated cells, CD34+ cells, GM-CFC and HPP-CFC respectively by 10.8-, 4.8-, 65.9- and 38.8-fold for the mononuclear cell culture, and respectively by 76.1-, 2.9-, 71.7- and 51.8-fold for the CD34+/c-kit+ cell culture. The expanded cells could rapidly engraft in the sublethally irradiated mice and reconstitute their hematopoiesis. Co-cultures with MSCs in conjunction with two-step expansion increased expansions of total nucleated cells, GM-CFC and HPP-CFC, which led us to conclude MSCs may create favorable environment for expansions of hematopoietic stem/progenitor cells. The availability of increased numbers of ex-panded cells by the co-culture with MSCs may result in more rapid engraftment of neutrophils following infusion to transplant recipients.

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-B: Solutions of Differential Inequalities and Asymptotic Admissibility of Standard Derivatives

Part II-B of our work continues the factorizational theory of asymptotic expansions of type (*) , , where the asymptotic scale , , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x0. The main result states that to each scale of this type it remains as-sociated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion (*), if valid, is automatically formally differentiable n ? 1 times in the two special senses characterized in Part II-A. A second result shows that formal applications of ordinary derivatives to an asymptotic expansion are rarely admissible and that they may also yield skew results even for scales of powers.

Magnetoresistances and magnetic entropy changes associated with negative lattice expansions in NaZn13-type compounds LaFeCoSi

Magnetoresistances and magnetic entropy changes in NaZn13-type compounds La（Fel-xCox）11.9Si1.1 （x=0.04, 0.06, and 0.08） with Curie temperatures of 243 K, 274 K, and 301 K, respectively, are studied. The ferromagnetic ordering is accompanied by a negative lattice expansion. Large magnetic entropy changes in a wide temperature range from ～230 K to ～320 K are achieved. Raising Co content increases the Curie temperature but weakens the magnetovolume effect, thereby causing a decrease in magnetic entropy change. These materials exhibit a metallic character below Tc, whereas the electrical resistance decreases abruptly and then recovers the metal-like behaviour above Tc. Application of a magnetic field retains the transitions via increasing the ferromagnetic ordering temperature. An isothermal increase in magnetic field leads to an increase in electrical resistance at temperatures near but above Tc, which is a consequence of the field-induced metamagnetic transition from a paramagnetic state to a ferromagnetic state.

The Limiting Case of Blending Differences for Bivariate Blending Continued Fraction Expansions

For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.

SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α IN SEVERAL COMPLEX VARIABLES

In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.

Dealing with Asymmetrical Abel Inversion Using Fourier-Bessel Expansions

A new method is presented for dealing with asymmetrical Abel inversion in this paper.We separate the integrated quantity into odd and even parts using Yasutomo's method. The asymmetric local value is expressed as the product of a weight function and a symmetric local value. The symmetric distribution is expanded into Fourier-Bessel series. The coefficients of the series are determined by the use of a least-square-fitting method.

Hydrogenation and Anisotropic Expansions in R_3Fe_(29-x)T_x (R=Y, Ce, Nd, Sm, Gd, Tb and Dy; T=V and Cr)

A systematic study of the phase formation, structure and magnetic properties of the R3Fe29-xTxcompounds (R=Y, Ce, Nd, Sm, Gd, Tb, and Dy; T=V and Cr) has been performed uponhydrogenation. The lattice constants and the unit cell volume of R3Fe29-xTxHy decrease withincreasing R atomic number from Nd to Dy, except for Ce, reflecting the lanthanide contraction.Regular anisotropic expansions mainly along the a- and b-axis rather than along the c-axis areobserved for all of the compounds upon hydrogenation. Hydrogenation leads to an increase inthe Curie temperature and a corresponding increase in the saturation magnetization at roomtemperature for each compound. First order magnetization processes (FOMP) occur in theexternal magnetic fields for Nd3Fe24.5Cr4.5H5.0, Tb3Fe27.0Cr2.0H2.8, and Gd3Fe28.0Cr1.0H4.2compounds

PERIODICITY OF THE UNIVOQUE β-EXPANSIONS

Let m ≥ 1 be an integer,1 〈 β ≤ m ＋ 1.A sequence ε1ε2ε3 … with εi ∈{0,1,…,m} is called a β-expansion of a real number x if x = Σi εi/βi.It is known that when the base β is smaller than the generalized golden ration,any number has uncountably many expansions,while when β is larger,there are numbers which has unique expansion.In this paper,we consider the bases such that there is some number whose unique expansion is purely periodic with the given smallest period.We prove that such bases form an open interval,moreover,any two such open intervals have inclusion relationship according to the Sharkovskii ordering between the given minimal periods.We remark that our result answers an open question posed by Baker,and the proof for the case m = 1 is due to Allouche,Clarke and Sidorov.

HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES

In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.

ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS

Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence

We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of Xn. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of Xn.

The Role of Asymptotic Mean in the Geometric Theory of Asymptotic Expansions in the Real Domain

We call “asymptotic mean” (at +∞) of a real-valued function the number, supposed to exist, , and highlight its role in the geometric theory of asymptotic expansions in the real domain of type (*) where the comparison functions , forming an asymptotic scale at +∞, belong to one of the three classes having a definite “type of variation” at +∞, slow, regular or rapid. For regularly varying comparison functions we can characterize the existence of an asymptotic expansion (*) by the nice property that a certain quantity F(t) has an asymptotic mean at +∞. This quantity is defined via a linear differential operator in f and admits of a remarkable geometric interpretation as it measures the ordinate of the point wherein that special curve , which has a contact of order n - 1 with the graph of f at the generic point t, intersects a fixed vertical line, say x = T. Sufficient or necessary conditions hold true for the other two classes. In this article we give results for two types of expansions already studied in our current development of a general theory of asymptotic expansions in the real domain, namely polynomial and two-term expansions.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.