CONVERGENCE ON RANDOMLY TRIMMED SUMS WITH A DEPENDENT SAMPLE

§１．ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＲｅｓｕｌｔｓＬｅｔ｛Ｘｎ，ｎ１｝ｂｅａｓｅｑｕｅｎｃｅｏｆｒａｎｄｏｍｖａｒｉａｂｌｅｓｗｉｔｈａｃｏｍｍｏｎｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎＦ（ｘ）ａｎｄｌｅｔＸｎ１Ｘｎ２…Ｘｎｎｂｅｔｈｅｏｒ...     

Optical current transducer with bulk type Bi12SiO20 faraday sensor for power systems

Two types of optical current transducers (OCTs) have a bulk Faraday sensor inserted into the gap of an iron core and a porcelain insulator with optical fiber. The sensor consists of Bi₁₂SiO₂₀ (BSO) single crystal, a polarizer, and an analyzer. The OCTs satisfied the target performance requirement for fault location and metering and demonstrated maintained performance at some power utilities in Japan and the US. We have developed a fault location system that immediately detects the fault current with the OCTs, there by locating the fault section. The OCT can easily replace the existing support insulators for the disconnecting switch without any modifications to structure height or bus-bar. For metering requiring 0.3% class accuracy, use of a BSO with right optical rotatory power combined with BSO with left optical rotatory power results in a Faraday sensor with improved temperature characteristics. The OCT demonstrated 0.3% class accuracy for metering described in the current transformer Specifications of IEEE C57–13, 1993.     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

On solving energy-dependent partitioned eigenvalue problem by genetic algorithm: The case of real symmetric Hamiltonian matrices

An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin’s strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed     

Dielectric properties of KDP-type ferroelectric crystals in the presence of external electric field

Considering external electric field as well as third- and fourth-order phonon anharmonic interaction terms in the pseudospin-lattice coupled mode (PLCM) model Hamiltonian for KDP-type ferroelectrics, expressions for field-dependent shift, width, renormalized soft mode frequency, Curie temperature, dielectric constant and dielectric loss are evaluated. For the calculation, method of statistical double-time temperature-dependent Green’s function has been used. By fitting model values of physical quantities, temperature and electric field dependences of soft mode frequency, dielectric constant and loss have been calculated which compare well with experimental results of Baumgartner [8] and Choi and Lockwood [9]. Both dielectric constant and loss decrease with electric field.     

Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.     

The hydrogen molecule in an arbitrarily oriented magnetic field

Summary The modifications induced by a magnetic field of arbitrary direction and intermediate strength (i.e not larger than 2.35·10⁵ tesla, the ?atomic tesla?) on the lowest singlet and triplet energy states of the hydrogen molecule are studied. Using a linear combination of products of field-modified atomic orbitals, it is found that increasing the field strength the depth of the singlet energy well increases and the equilibrium internuclear distance decreases, yielding more rigid and localized nuclear vibrations. For sufficiently strong fields perpendicular to the internuclear axis, the triplet state exhibits a bonding behaviour. An explanation of the above results is given in terms of the field-modified electronic-charge distributions in the internuclear region. Based on the thesis submitted by S. Basile to the University of Palermo for graduation in Physics.     

On a generalization of Pólya’s theorem

We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points.     

Fourier Analysis of Semistable Distributions

We consider the generalized convolution powers G _α ^*u (x) of an arbitrary semistable distribution function G _α (x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G _α ^(k,j)(x;u)=∂ ^k+j G _α ^*u (x)/∂ x ^k ∂ u ^j , x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in merge theorems from the domain of geometric partial attraction of semistable laws. An erratum to this article can be found at