Maintaining Matroid 3-Connectivity With Respect to a Fixed Basis

<p>We show that for any 3-connected matroid M on a ground set of at least four elements such that M does not contain any 4-element fans, and any basis B of M, there exists a set K [is a subset of] E(M) of four distinct elements such that for all k [is an element of the set] K, si(M=k) is 3-connected whenever k [is an element of the set] B, and co(M\k) is 3-connected whenever k [is an element of the set] E(M) - B. Moreover, we show that if no other elements of E(M) - K satisfy this property, then M necessarily has path-width 3.</p>

Maintaining Matroid 3-Connectivity With Respect to a Fixed Basis

<p>We show that for any 3-connected matroid M on a ground set of at least four elements such that M does not contain any 4-element fans, and any basis B of M, there exists a set K [is a subset of] E(M) of four distinct elements such that for all k [is an element of the set] K, si(M=k) is 3-connected whenever k [is an element of the set] B, and co(M\k) is 3-connected whenever k [is an element of the set] E(M) - B. Moreover, we show that if no other elements of E(M) - K satisfy this property, then M necessarily has path-width 3.</p>

Matrimonial Disputes

Following Marinos v Marinos in family disputes the courts apply the European rather than the domestic law definition of habitual residence and consider a party’s habitual residence to be the place where that person has established on a fixed basis her permanent or habitual centre of interest, with all of the relevant factors being taken into account for the purpose of determining such residence.

The accuracy investigation of point coordinates’ determination using a fixed basis for high-precision geodesy binding

Modern scanners can perform terrestrial topographic survey with resolution of 1 cm and accuracy of 2 mm in just a few minute‘s time, from the distance of up to 100 meters. However, for surface topographical surveying of large territories or complex industrial objects, it is necessary to conduct geodetic traverses and perform their binding to the points of the geodesic basis. One method of coordinate transferring during surveying is by using the method of inverse linear-angular intersection, which involves the measuring of the respective sides S1, S2 and the β angle between them. This method is more precise than the classical one, which usually contains centring and reduction errors. The linear-angular intersection method can also be used for many applications in engineering geodesy, for laying geodetic traverses, and for binding to the wall based points of ground-surveying.

Operational relevance of resource theories of quantum measurements

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourceful measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resourceful measurement offers in a class of minimal-error state discrimination (MESD) problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separable operators). For both of these scenarios we find, in the asymptotic setting in which the dimension or the number of particles increase to infinity, the maximal relative advantage that resourceful measurements offer for state discrimination tasks.

Almost inner derivations of Lie algebras

We study almost inner derivations of Lie algebras, which were introduced by Gordon and Wilson in their work on isospectral deformations of compact solvmanifolds. We compute all almost inner derivations for low-dimensional Lie algebras, and introduce the concept of fixed basis vectors for proving that all almost inner derivations are inner for [Formula: see text]-step nilpotent Lie algebras determined by graphs, free [Formula: see text] and [Formula: see text]-step nilpotent Lie algebras, free metabelian nilpotent Lie algebras on two generators, almost abelian Lie algebras and triangular Lie algebras. On the other hand, we also exhibit families of nilpotent Lie algebras having an arbitrary large space of non-inner almost inner derivations.

Bayesian feature learning for seismic compressive sensing and denoising

Extracting the maximum possible information from the available measurements is a challenging task but is required when sensing seismic signals in inaccessible locations. Compressive sensing (CS) is a framework that allows reconstruction of sparse signals from fewer measurements than conventional sampling rates. In seismic CS, the use of sparse transforms has some success; however, defining fixed basis functions is not trivial given the plethora of possibilities. Furthermore, the assumption that every instance of a seismic signal is sparse in any acquisition domain under the same transformation is limiting. We use beta process factor analysis (BPFA) to learn sparse transforms for seismic signals in the time slice and shot record domains from available data, and we use them as dictionaries for CS and denoising. Algorithms that use predefined basis functions are compared against BPFA, with BPFA obtaining state-of-the-art reconstructions, illustrating the importance of decomposing seismic signals into learned features.

Efecto del P sobre el rendimiento y extracción del NP de frijol cultivado en tres suelos.

Under controlled conditions and utilizing three soils of Red Ferralithic (Eutric Ferrasols) type with low, medium and high available P we studied the effect over the production of dry matter and the extraction of N and P performed by the bean plant (Phaseolus vulgaris L.), produced by the addition in increasing dosage of P, between 0 and 280 kg P2O5/ha, with fixed basis of 60 kg K2O/ha and 40kg N/ha and inoculation with bacteria from the Rhizobium genera. The experimental results showed a plant response differentiated by the availability of P in the soil. In soils with low P contents there was a positive response in the three evaluated indexes, while in the other two soil samples the higher availability of P produced a smaller or negative response. We also discuss the functional relationship found among the evaluated indexes.