A Refined Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation Related to the Vortex Filament

The Cauchy problem of one dimensional fourth-order nonlinear Schrödinger equation related to the vortex filament is studied. Local well-posedness for initial data in H ^s (?) (s > 1/2) is obtained without conditions ν < 0 and μ ? ν/2 = 0 by the Fourier restriction norm method. The result is a refinement of our previous paper (Huo and Jia, 2005 Huo , Z. , Jia , Y. ( 2005 ). The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament . J. Diff. Eq. 214 : 1 – 35 . [Google Scholar]).     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

Topologically-Interlocked Minicircles as Probes of DNA Topology and DNA-Protein Interactions

DNA minicircles exist in biological contexts, such as kinetoplast DNA, and are promising components for creating functional nanodevices. They have been used to mimic the topological features of nucleosomal DNA and to probe DNA-protein interactions such as HIV-1 and PFV integrases, and DNA gyrase. Here, we synthesized the topologically-interlocked minicircle rotaxane and catenane inside a frame-shaped DNA origami. These minicircles are 183 bp in length, constitute six individual single-stranded DNAs that are ligated to realize duplex interlocking, and adopt temporary base pairing of single strands for interlocking. To probe the DNA-protein interactions, restriction reactions were carried out on DNAs with different topologies such as free linear duplex or duplex constrained inside origami and free or topologically-interlocked minicircles. Except the free linear duplex, all tested structures were resistant to restriction digestion, indicating that the topological features of DNA, such as flexibility, curvature, and groove orientation, play a major role in DNA-protein interactions.     

Relationships Between Various Outer Measures Induced by Lattice Measures

In this paper, we work with lattice spaces. (A lattice space is an ordered pair consisting of a set X and a lattice on X). As is known, each lattice measure µ induces six outer measures on P(X), one of which is the well-known "induced outer measure" µ^*(in case µ is countably additive); the others are µ, µ, µ,, and .In the first part of the paper, we consider an arbitrary lattice measure and discover various relationships involving two or more of the seven set functions under consideration, on P(X) and on various special subsets of P(X), under various conditions on the measure or on the lattice.In the second part of the paper, we consider two lattice measures related by "domination" and obtain similar results.In the third part of the paper, we consider two lattice measures related by "restriction" and obtain similar results.     

Small solutions of the congruencea1x12 +a2x22 +a3x32 +a4x42 ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ₂ a ₃ a ₄≢0(modp), this paper shows that there exists a solutionX=(x ₁,x ₂,x ₃,x ₄) ∈Z ⁴ of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp) such that

Signal modelization for improved precision of assessment of minimum and mean telomere lengths

Telomere length is an important measure of cell and tissue regenerative capacities. The mean telomere length is classically used as global indicator of a tissue telomere length. In skeletal muscle, which is made of postmitotic myonuclei and satellite cells (muscle stem cells), minimum telomere length is also used to assess the telomere length of satellite cells and newly incorporated myonuclei. At present, the estimation of the method reproducibility during the assessment of mean and minimum telomere length using Southern blot analysis has never been documented. The aim of this report is to describe a signal modelization for improved precision of assessment of minimum and mean telomere lengths and to document the method reproducibility. Telomeres are assessed using a Southern technique where the gel is directly hybridized with the specific probe without the membrane-transferring step in order to prevent telomeric low signal loss. We found that the improved signal analysis for determination of telomere length is associated with coefficients of variation ranging from 1.37 to 4.29% for the mean telomeric restriction fragment (TRF) length and from 2.04 to 4.95% for the minimum TRF length. Improved method reproducibility would allow saving time and biological material as duplicate and triplicate measurement of the same sample is no longer required.     

分段函数与初等函数关系及表达的讨论与进展

依据历史的延革、认知的进展,提出了关于初等函数的一个比较系统的概念;给出的限制域、存在域、定义域的概念,使函数的表达、相关的判断得以扩展,给出了分段函数初等性的一个简明的充分性判断;对于分段函数初等性主要的、广传的文献作了综述与评析,指出了存在的与需要研讨的问题.