Search results for "algebra"
showing 10 items of 4129 documents
Comparison of different theory models and basis sets in the calculation of 13C NMR chemical shifts of natural products.
2004
The influence of the calculation method in mimicking experimental 13C NMR chemical shifts of 15 low-polarity natural products singularly containing 10–20 carbon atoms was investigated by employing different quantum chemistry approaches and basis sets, both in the preliminary geometry optimizations and in the following single-point 13C GIAO calculations of the NMR chemical shifts. The geometries of the involved species were optimized at the PM3, HF, B3LYP and mPW1PW91 levels whereas the 13C NMR parameters were determined at the HF, B3LYP and mPW1PW91 levels. Different combinations of basis sets were also tested. The consistency and efficiency of the considered combinations of geometry optimi…
Natural Addition of Ordinals
2019
Summary In [3] the existence of the Cantor normal form of ordinals was proven in the Mizar system [6]. In this article its uniqueness is proven and then used to formalize the natural sum of ordinals.
Vibrational Spectrum of HXeSH revisited : Combined computational and experimental study
2020
Vibrational spectrum of HXeSH embedded in low-temperature matrix is experimentally studied. To support the spectrum interpretation, anharmonic vibrational analysis is performed using different models and basis sets and the data is compared with previous experimental and theoretical analyses. Computations of overtones and combination modes allowed for new band assignments. The HXeSH molecule exhibits high anharmonicity similarly as other molecules from the noble-gas hydride family. Comparison of the employed computational methods shows once again that the modelling of the noble-gas compounds faces theoretical challenges to yield quantitatively reliable results. peerReviewed
On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups
2002
Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.
The Bishop-Phelps-Bollobás property for bilinear forms and polynomials
2014
For a $\sigma$-finite measure $\mu$ and a Banach space $Y$ we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on $L_1(\mu)\times Y$, that is, a (continuous) bilinear form on $L_1(\mu)\times Y$ almost attaining its norm at $(f_0,y_0)$ can be approximated by bilinear forms attaining their norms at unit vectors close to $(f_0,y_0)$. In case that $Y$ is an Asplund space we characterize the Banach spaces $Y$ satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.
Matriisin Hessenbergin muoto
2013
Modeling epidemics through ladder operators
2020
Highlights • We propose an operatorial model to describe epidemics. • The model describes well the asymptotic numbers of the epidemics. • Ladder operators are used to model exchanges between the “actors” of the system.
An evolutionary Haar-Rado type theorem
2021
AbstractIn this paper, we study variational solutions to parabolic equations of the type $$\partial _t u - \mathrm {div}_x (D_\xi f(Du)) + D_ug(x,u) = 0$$ ∂ t u - div x ( D ξ f ( D u ) ) + D u g ( x , u ) = 0 , where u attains time-independent boundary values $$u_0$$ u 0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values $$u_0$$ u 0 admit a modulus of continuity $$\omega $$ ω and the estimate $$|u(x,t)-u_0(\gamma )| \le \omega (|x-\gamma |)$$ | u ( x , t ) - u 0 ( γ ) | ≤ ω ( | x - γ | ) holds, then u admits the same modulus of continuity in the spatial variable.
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
2022
AbstractWe present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of…