The influence of matrix concentration and solvent composition on the results of MALDI MSI,with the aid of wet-interface matrix deposition

Imaging mass spectrometry is a powerful technique for the molecular analysis of tissue sections. As in many analytical methods, sample preparation is one of the main and most important steps to obtain results of good quality. Usually, the matrix concentration and solvent composition in different studies are taken for granted without any further consideration. In our studies, we aimed to find how matrix concentration and a type of solvent influence the signal. Moreover, we also aimed to find the relationship between these parameters, how they influence the spectra, and how they influence obtained ion maps. In our experiments, we used SunCollect®, which is a commercially available wet-interface system for matrix deposition. We decided to choose two matrix concentrations (2,5-dihydroxybenzoic acid [DHB]: 15 and 25 mg/mL; 9-aminoacridine [9AA]: 7 and 5 mg/mL) and two different water solutions of solvents in two different percentages for the matrices (DHB: 50% and 70% of methanol [MeOH] and acetonitrile [ACN]; 9AA 70% and 50% of ethanol [EtOH] and MeOH). In the end, the influence of these parameters on obtained spectra and ion maps was assessed.     

Evaluating the potential and limitations of double-spiking species-specific isotope dilution analysis for the accurate quantification of mercury species in different environmental matrices

A new double-spiking approach, based on a multiple-spiking numerical methodology, has been developed and applied for the accurate quantification of inorganic mercury (IHg) and methylmercury (MeHg) by GC–ICPMS in different environmental matrices such as water, sediments and a wide range of biological tissues. For this purpose, two enriched mercury species (²⁰¹MeHg and ¹⁹⁹IHg) were added to the samples before sample preparation in order to quantify the extents of the methylation and demethylation processes, and thereby correct the final species concentrations. A critical evaluation of the applicability of this methodology was performed for each type of matrix, highlighting its main advantages and limitations when correcting for the conversion reactions of the species throughout the whole sample preparation procedure. The double-spike isotope dilution (DSIDA) methodology was evaluated by comparing it with conventional species specific isotope dilution (IDA) when analysing both certified reference materials and environmental samples (water, biotissues and sediment). The results demonstrate that this methodology is able to provide both accurate and precise results for IHg and MeHg when their relative concentrations are not too different (ratio MeHg/IHg > 0.05), a condition that holds for most natural waters and biotissues. Significant limitations on the accurate and precise determination of the demethylation factor are however observed, especially for real sediment samples in which the relative concentrations of the species are substantially different (ratio MeHg/IHg < 0.05). A determination of the sources of uncertainty in the methylation/demethylation factors has demonstrated that the accurate and precise measurement of the isotope ratios in the species involved in the transformations is crucial when quantifying the extents of these reactions. Although the double-spike methodology is established as a reference approach that permits the correction of most analytical biases and the accurate quantification of Hg species, some limitations have been identified for the first time in this work.     

A note on Browder spectrum of operator matrices

When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the Hilbert space H⊕K of the form . In this note, it is shown that the following results in [Hai-Yan Zhang, Hong-Ke Du, Browder spectra of upper-triangular operator matrices, J. Math. Anal. Appl. 323 (2006) 700-707]

     

Inclusion matrices and chains

Given integers t, k, and v such that 0?t?k?v, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset ²[v] into symmetric skipless chains is given. Based on this decomposition, we construct an inclusion matrix, denoted by , which is row-equivalent to Wtk(v). Its Smith normal form is determined. As applications, Wilson's diagonal form of Wtk(v) is obtained as well as a new proof of the well-known theorem on the necessary and sufficient conditions for existence of integral solutions of the system Wtkx=b due to Wilson. Finally we present another inclusion matrix with similar properties to those of which is in some way equivalent to Wtk(v).     

循环矩阵的两种特性的判定

揭示几类矩阵之间的紧密联系.借助于群的子群的判定以及循环布尔矩阵是本原矩阵的判定方法,得到循环模糊矩阵成为幂等矩阵的充要条件,反循环布尔矩阵成为本原矩阵的充要条件.并给出了循环模糊矩阵成为幂等矩阵的判定方法,反循环布尔矩阵成为本原矩阵的判定方法.     

On kaonic deuterium. Quantum field-theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field-theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances (1405), (1750) and a smooth elastic background, and the inelastic channels K^-d NY and K^-d NY, where Y = ^±,^{0} and ^{0}, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_Kd NY and experimental data on the rates of the NY pair production in the reactions K^-d NY. We obtain _{1s} = (630±100)eV. For the shift of the energy level of the ground state of kaonic deuterium we predict _{1s} = (325±60)eV.     

On the Diaconis-Shahshahani Method in Random Matrix Theory

If Γ is a random variable with values in a compact matrix group K, then the traces Tr(Γ^j) (j ∊ N) are real or complex valued random variables. As a crucial step in their approach to random matrix eigenvalues, Diaconis and Shahshahani computed the joint moments of any fixed number of these traces if Γ is distributed according to Haar measure and if K is one of U_n, O_n or Sp_n, where n is large enough. In the orthogonal and symplectic cases, their proof is based on work of Ram on the characters of Brauer algebras. The present paper contains an alternative proof of these moment formulae. It invokes classical invariant theory (specifically, the tensor forms of the First Fundamental Theorems in the sense of Weyl) to reduce the computation of matrix integrals to a counting problem, which can be solved by elementary means.     

Some estimates of norms of random matrices

We show that for any random matrix with independent mean zero entries

where is some universal constant.

     

Fuglede's conjecture fails in dimension 4

In this note we modify a recent example of Tao and give an example of a set such that admits an orthonormal basis of exponentials for some set , but which does not tile by translations. This shows that one direction of Fuglede's conjecture fails already in dimension 4. Some common properties of translational tiles and spectral sets are also proved.

     

Invariants and nonequilibrium density matrices

A new method of calculating nonequilibrium density matrices with the aid of the quantum integrals of motion is proposed. The method is shown to be very effective in the case of systems described by means of quadratic Hamiltonians. The possibility of constructing phenomenological nonstationary Hamiltonians for a wide class of dissipative systems is discussed. The exact formulas for nonequilibrium density matrices of arbitrary quadratic systems are obtained. The quantum problem of the motion of a charged particle in uniform electric and magnetic fields in the presence of a frictional force proportional to the velocity is solved exactly by means of introducing the new phenomenological Hamiltonian.