Optimizing UV laser focus profiles for improved MALDI performance

Matrix assisted laser desorption/ionization (MALDI) applications, such as proteomics, genomics, clinical profiling and MALDI imaging, have created a growing demand for faster instrumentation. Since the commonly used nitrogen lasers have throughput and life span limitations, diode-pumped solid-state lasers are an alternative. Unfortunately this type of laser shows clear performance limitations in MALDI in terms of sensitivity, resolution and ease of use, for applications such as thin-layer sample preparations, acceptance of various matrices (e.g. DHB for glycopeptides) and MALDI imaging. While it is obvious that the MALDI process has some dependence on the characteristics of the laser used, it is unclear which features are the most critical in determining laser performance for MALDI. In this paper we show, for the first time, that a spatially structured laser beam profile in lieu of a Gaussian profile is of striking importance. This result enabled us to design diode-pumped Nd : YAG lasers that on various critical applications perform as well for MALDI as the nitrogen lasers and in some respects even better. The modulation of the beam profile appears to be a new parameter for optimizing the MALDI process. In addition, the results trigger new questions directing us to a better understanding of the MALDI process.     

The border rank of the multiplication of matrices is seven

We prove that the bilinear map corresponding to matrix multiplication of matrices is not the limit of a sequence of bilinear maps that can be executed by performing six multiplications. This solves a longstanding problem dating back to Strassen's discovery in 1968 that the map could be executed by performing seven multiplications.

     

On operators which commute with analytic Toeplitz operators modulo the finite rank operators

It is shown that an operator on the Hardy space (or ) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if . Here is a finite rank operator, and in the case , is a sum of a rational function and a bounded analytic function, and in the case , is a bounded analytic function.

     

Quasi-finite modules for Lie superalgebras of infinite rank

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras , and , and determine the necessary and sufficient conditions for such modules to be unitarizable. The unitarizable irreducible modules are constructed in terms of Fock spaces of free quantum fields, and explicit formulae for their formal characters are also obtained by investigating Howe dualities between the infinite rank Lie superalgebras and classical Lie groups.

     

Finite rank operators in Jacobson radical \mathcal{R}_{\mathcal{N} \otimes \mathcal{M}}

In this paper we investigate finite rank operators in the Jacobson radical of Alg( ), where are nests. Based on the concrete characterizations of rank one operators in Alg( ) and , we obtain that each finite rank operator in can be written as a finite sum of rank one operators in and the weak closure of equals Alg( ) if and only if at least one of is continuous.     

Boron diffusion and activation in polysilicon multilayer films for P MOS structure: Characterization and modeling

This work deals with in situ boron diffusion and activation in multilayer films: polysilicon (Poly1)/amorphous silicon (Poly2). These films are deposited by LPCVD technique. However, several heat treatments were carried in order to determine the optimal annealing conditions to suppress boron penetration from the gate to the substrate through the gate oxide in MOS structure. The boron concentration is monitored by secondary ion mass spectrometry (SIMS). To investigate SIMS profiles we proposed a model of boron diffusion into these multilayer structures. It is important to note that the parameter values of the studied films such as the diffusion coefficient, the activation percentage of boron as well as the acceleration rate of boron diffusion are deduced from adjustment of simulated profiles with experimental profiles. From these results, we inferred that the boron is electrically active and its distribution does not reach the oxide layer and consequently, the Poly2 may reduce the boron diffusion in optimal annealing conditions.     

On minimum rank and zero forcing sets of a graph

For a graph G on n vertices and a field F, the minimum rank of G over F, written as mr^F(G), is the smallest possible rank over all n×n symmetric matrices over F whose (i,j)th entry (for ) is nonzero whenever ij is an edge in G and is zero otherwise. The maximum nullity of G over F is M^F(G)=n-mr^F(G). The minimum rank problem of a graph G is to determine mr^F(G) (or equivalently, M^F(G)). This problem has received considerable attention over the years. In [F. Barioli, W. Barrett, S. Butler, S.M. Cioab?, D. Cvetkovi?, S.M. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanovi?, H. van der Holst, K.V. Meulen, A.W. Wehe, AIM Minimum Rank-Special Graphs Work Group, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008) 1628-1648], a new graph parameter Z(G), the zero forcing number, was introduced to bound M^F(G) from above. The authors posted an attractive question: What is the class of graphs G for which Z(G)=M^F(G) for some field F? This paper focuses on exploring the above question.     

Exact travelling wave solutions for the dissipative (2 + 1)-dimensional AKNS equation

This paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions of the dissipative (2 + 1)-dimensional AKNS equation. By qualitative analysis, global phase portraits of the dynamic system corresponding to the equation are obtained under different parameter conditions. Furthermore, the relations between the properties of travelling wave solutions and the dissipation coefficient r of the equation are investigated. In addition, the possible bell profile solitary wave solution, kink profile solitary wave solutions and approximate damped oscillatory solutions of the equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. Based on above studies, a main contribution in this paper is to reveal the dissipation effect on travelling wave solutions of the dissipative (2 + 1)-dimensional AKNS equation.     

用CF_4等离子体处理来剪裁AlGaN/GaN异质结能带

自洽求解薛定谔方程和泊松方程研究了CF4等离子体处理对AlGaN/GaN异质结能带的影响。证实了强F离子注入和势垒层的腐蚀是导致沟道电子气耗尽和夹断电压正移的根源。建立了夹断电压移动与异质结构间的关联,为精确的能带剪裁奠定了基础。针对GaN HFET对肖特基势垒、欧姆接触和沟道电场分布的要求,提出了用CF4等离子体剪裁能带的方案。     

Perturbation of Yamabe equation on Iwasawa N groups in presence of symmetry

Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU ＋ （1 ＋ ∈K（x, z））u2＊-1 = 0 on N, which generalizes the result of Malchiodi and Uguzzoni to the Kohn＇s subelliptic context on N in presence of symmetry.