Highly edge-connected regular graphs without large factorizable subgraphs

We construct highly edge-connected $r$-regular graphs of even order which do not contain $r?2$ pairwise disjoint perfect matchings. When $r$ is a multiple of 4, the result solves a problem of Thomassen [4].     

Diborylated Magnesium Anthracene as Precursor for B2H5−‐Bridged 9,10‐Dihydroanthracene

9,10‐(Bpin)₂‐anthracene ( 3 , HBpin=pinacolborane) was synthesized from 9,10‐dibromoanthracene in a stepwise lithiation/borylation sequence. The reaction of 3 with highly activated magnesium furnished the diborylated magnesium anthracene 4 , which was quenched in situ with ethereal HCl to yield cis‐9,10‐(Bpin)₂‐DHA (cis‐ 5 , DHA=9,10‐dihydroanthracene). Compound cis‐ 5 , in turn, can be reduced with Li[AlH₄] in THF to give its diborate Li₂[cis‐9,10‐(BH₃)₂‐DHA] (Li₂[cis‐ 6 ]). In the crystal lattice, the THF solvate Li₂[cis‐ 6 ] ? 3 THF establishes a dimeric structure with Li‐(μ‐H)‐B coordination modes. Hydride abstraction from Li₂[cis‐ 6 ] with Me₃SiCl yields the B?H?B‐bridged DHA Li[ 7 ]. This product can also be viewed as a unique cyclic B₂H₇^? derivative with a hydrocarbon backbone. Treatment of Li₂[cis‐ 6 ] with the stronger hydride abstracting agent Me₃SiOTf (HOTf=trifluoromethanesulfonic acid) in THF affords the THF diadduct of cis‐9,10‐(BH(OTf))₂‐DHA.     

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

Experimental Evidence for the Incorporation of Two Metals at Equivalent Lattice Positions in Mixed-Metal Metal–Organic Frameworks

Metal–organic frameworks containing multiple metals distributed over crystallographically equivalent framework positions (mixed-metal MOFs) represent an interesting class of materials, since the close vicinity of isolated metal centers often gives rise to synergistic effects. However, appropriate characterization techniques for detailed investigations of these mixed-metal metal–organic framework materials, particularly addressing the distribution of metals within the lattice, are rarely available. The synthesis of mixed-metal FeCuBTC materials in direct syntheses proved to be difficult and only a thorough characterization using various techniques, like powder X-ray diffraction, X-ray absorption spectroscopy and electron paramagnetic resonance spectroscopy, unambiguously evidenced the formation of a mixed-metal FeCuBTC material with HKUST-1 structure, which contained bimetallic Fe−Cu paddlewheels as well as monometallic Cu−Cu and Fe−Fe units under optimized synthesis conditions. The in-depth characterization showed that other synthetic procedures led to impurities, which contained the majority of the applied iron and were impossible or difficult to identify using solely standard characterization techniques. Therefore, this study shows the necessity to characterize mixed-metal MOFs extensively to unambiguously prove the incorporation of both metals at the desired positions. The controlled positioning of metal centers in mixed-metal metal–organic framework materials and the thorough characterization thereof is particularly important to derive structure–property or structure–activity correlations.     

Reasoning about proof and knowledge

In previous work [15], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from Gödel's interpretation of IPC in S4, our modal systems contain IPC in the way established in [13]. The modal operator can be viewed as a predicate for intuitionistic truth, i.e. proof. Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [4]. In the present paper, we show that the S5-style systems of our hierarchy correspond to an extended Brouwer–Heyting–Kolmogorov interpretation and are complete w.r.t. a relational semantics based on intuitionistic general frames. In this sense, our S5-style logics are adequate and complete systems for the reasoning about proof combined with belief or knowledge. The proposed relational semantics is a uniform framework in which also IEL can be modeled. Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems.     

Convergence Rates for Fourier Partial Sums of Polygons and Periodic Splines

Journal of Fourier Analysis and Applications - Polygons can be seen as closed parameterized curves. Their parameterizations can be chosen as continuous, piecewise linear, periodic functions. Such...