Intriguing Differences in the Gas-Phase Dissociation Behavior of Protonated and Deprotonated Gonyautoxin Epimers

The aim of this study was to investigate the unusual gas-phase dissociation behavior of two epimer pairs of protonated gonyautoxins (GTX) following electrospray ionization in comparison to their deprotonated counterparts. The chemical structures of the investigated GTX1-4 variants vary in their substitution pattern at N-1 and the stereochemical orientation of the hydroxysulfate group at C-11 (11α for GTX1/2 versus 11β for GTX3/4). The direct comparison of mass spectra in positive and negative ion modes illustrated two distinct features: first, an intriguing difference between protonated 11α and 11β species, where 11α conformations exhibited almost complete dissociation of [M + H]⁺ ions via facile SO₃ elimination, while 11β species remained mostly intact as [M + H]⁺; and second, the lack of such differences for the deprotonated counterparts. In this study, we propose an acid-catalyzed elimination mechanism from density functional theory calculations, initiated by a proton transfer of a guanidinium proton to the hydroxysulfate group with simultaneous SO₃ release, which is only possible for the 11α conformation based on intramolecular distances. The same mechanism explains the lack of a comparable SO₃ loss in the negative ion mode. CID experiments supported this proposed mechanism for GTX1 and GTX2. Computational modeling of product ions seen in the CID spectra of GTX3 and GTX4 established that the lowest energy dissociation pathway for the 11β epimers is elimination of water with the possibility for further SO₃ release from the intermediate product. Experimental data for structurally analogous decarbamoyl gonyautoxins confirmed the evidence for the GTX compounds as well as the proposed elimination mechanisms.     

Blow-up of solutions to critical semilinear wave equations with variable coefficients

We verify the critical case $p=p_0(n)$ of Strauss' conjecture [30] concerning the blow-up of solutions to semilinear wave equations with variable coefficients in ${\mathbf{R}}^n$, where $n\ge 2$. The perturbations of Laplace operator are assumed to be smooth and decay exponentially fast at infinity. We also obtain a sharp lifespan upper bound for solutions with compactly supported data when $p=p_0(n)$. The unified approach to blow-up problems in all dimensions combines several classical ideas in order to generalize and simplify the method of Zhou [43] and Zhou & Han [45]: exponential “eigenfunctions” of the Laplacian [37] are used to construct the test function ${?}_q$ for linear wave equation with variable coefficients and John's method of iterations [13] is augmented with the “slicing method” of Agemi, Kurokawa and Takamura [1] for lower bounds in the critical case.     

On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations

It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for B ?? 0 is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on e(4) with the standard Lie-Poisson bracket.     

Quadrature formula for computed tomography

We give a bivariate analog of the Micchelli–Rivlin quadrature for computing the integral of a function over the unit disk using its Radon projections.     

Mechanochemical Synthesis of Ternary Potassium Transition Metal Chlorides

Ternary halide systems KM^IICl₃ (M^II = Ti, Cr, Mn, Fe, Co, Ni, Cu, Zn) have been prepared by mechanochemical synthesis. Furthermore, TiCl₂ was converted to Ti₇Cl₁₆ by mechanochemical treatment. For most samples, the X‐ray powder diffraction patterns could either be assigned to isotypic structures or were found in accordance with reference data. The monochloride systems of Ti, Co and Zn were extended to their double chloride stoichiometry K₂M^IICl₄.     

Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator

Periodica Mathematica Hungarica - We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the supremum...     

Perfect splines of least uniform deviation

(v _k) ₁ ⁿ , 1v _kr, v₁+...+v_n r, p(;r) — =(x ₁,v ₁),...,(x _n,v _n), v _1+...+v _n-r ^(r(;·)=1. , (^*;t) [, ] (;t) _{x 1}<... n v ₁ ...,v _n. (^*;t) .