Search results for "Additive function"
showing 10 items of 26 documents
On the additivity of block designs
2016
We show that symmetric block designs $${\mathcal {D}}=({\mathcal {P}},{\mathcal {B}})$$D=(P,B) can be embedded in a suitable commutative group $${\mathfrak {G}}_{\mathcal {D}}$$GD in such a way that the sum of the elements in each block is zero, whereas the only Steiner triple systems with this property are the point-line designs of $${\mathrm {PG}}(d,2)$$PG(d,2) and $${\mathrm {AG}}(d,3)$$AG(d,3). In both cases, the blocks can be characterized as the only k-subsets of $$\mathcal {P}$$P whose elements sum to zero. It follows that the group of automorphisms of any such design $$\mathcal {D}$$D is the group of automorphisms of $${\mathfrak {G}}_\mathcal {D}$$GD that leave $$\mathcal {P}$$P in…
Uncertainty measures—Problems concerning additivity
2009
Additivity of an uncertainty measure on an MV-algebra has a clear meaning. If the divisibility is dropped, we come up to a so-called Girard algebra. There we discuss strong resp. weak additivity based on so-called divisible disjoint unions resp. on additivity for all sub-MV-algebras. We obtain a description of those extensions from additive measures on an MV-algebra to the canonical Girard algebra extension of pairs which are strongly additive and valuation measures. Finally, we prove the non-existence of strongly additive measure extensions, if the underlying MV-algebra is a finite chain with more than two non-trivial elements.
Measure-free conditioning and extensions of additive measures on finite MV-algebras
2010
Using the well known representation of any finite MV-algebra as a product of finite MV-chains as factors, we obtain a representation of its canonical extension as a Girard algebra product of the canonical extensions of the MV-chain factors. Based on this representation and using the results from our last paper, we characterize the additive measures on any finite MV-algebra resp. the weakly and the strongly additive measures on its canonical Girard algebra extension, and that as convex combinations of the corresponding measures on the respective factors. After that we apply the results to measure-free defined conditional events which for this reason are considered as elements of the canonica…
Axiomatic characterization of the weighted solidarity values
2014
Abstract We define and characterize the class of all weighted solidarity values . Our first characterization employs the classical axioms determining the solidarity value (except symmetry ), that is, efficiency , additivity and the A-null player axiom , and two new axioms called proportionality and strong individual rationality . In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality .
Three-page encoding and complexity theory for spatial graphs
2004
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.
Electron correlation effects on the calculated 13C NMR spectra of vinyl cations
1997
Abstract A study of calculated 13C NMR chemical shifts in vinyl cations is presented. The sensitivity of predicted isotropic shifts to correlation, basis set and geometry effects is explored. In order to obtain accurate estimates that are reasonably well converged with respect to further improvements in theory, it appears that the CCSD(T) method must be used with a basis of triple-zeta plus polarization quality on the carbon atoms. Second-order many-body perturbation theory performs adequately for all carbons except for that bearing the formal positive charge, while the self-consistent field approximation cannot be relied upon to predict even the correct qualitative ordering in the spectrum…
The semi-experimental equilibrium structures of AlCCH and AlNC
2015
Abstract Based on experimental rotational constants available in the literature (Walker and Gerry, Chem. Phys. Lett. 278, 9 (1997); Walker et al., J. Mol. Spectrosc. 209, 178 (2001); Sun et al., Chem. Phys. Lett. 553, 11 (2012)) [14,17,19] for five isotopologues of AlCCH and three isotopologues of AlNC as well as quantum-chemical computations for the vibrational corrections to rotational constants, the semi-experimental structures of these two aluminum compounds are determined. These empirical equilibrium structures (AlCCH: r e (Al C) = 1.957 A, r e (C C) = 1.222 A, r e (C H) = 1.065 A; AlNC: r e (Al N) = 1.850 A, r e (N C) = 1.181 A) compare favorably with theoretical best-estimate structu…
Additivity of effective quadrupole moments and angular momentum alignments in the A~130 nuclei
2007
The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and angular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.
Deformation of rotational structures inKr73andRb74: Probing the additivity principle at triaxial shapes
2008
Lifetimes have been deduced in the intermediate/high-spin range for the three known rotational bands in $^{73}\mathrm{Kr}$ and the $T=0$ band in $^{74}\mathrm{Rb}$ using the residual Doppler shift method. This has enabled relative transition quadrupole moments to be studied for the first time in triaxial nuclei as a function of spin. The data suggest that the additivity principle for transition quadrupole moments is violated, a result that is in disagreement with predictions from cranked Nilsson-Strutinsky and cranked relativistic mean-field theory calculations. The reasons for the discrepancy are not understood but may indicate that important correlations are missing from the models.
Silicon Oxysulfide, OSiS: Rotational Spectrum, Quantum-Chemical Calculations, and Equilibrium Structure.
2011
Silicon oxysulfide, OSiS, and seven of its minor isotopic species have been characterized for the first time in the gas phase at high spectral resolution by means of Fourier transform microwave spectroscopy. The equilibrium structure of OSiS has been determined from the experimental data using calculated vibration-rotation interaction constants. The structural parameters (rO-Si = 1.5064 A and rSi-S = 1.9133 A) are in very good agreement with values from high-level quantum chemical calculations using coupled-cluster techniques together with sophisticated additivity and extrapolation schemes. The bond distances in OSiS are very short in comparison with those in SiO and SiS. This unexpected fi…