Morrey Spaces on Domains: Different Approaches and Growth Envelopes

We deal with Morrey spaces on bounded domains \(\Omega \) obtained by different approaches. In particular, we consider three settings \(\mathcal {M}_{u,p}(\Omega )\), \(\mathbb {M}_{u,p}(\Omega )\) and \(\mathfrak {M}_{u,p}(\Omega )\), where \(0<p\le u<\infty \), commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes \(\mathfrak {E}_{\mathsf {G}}(\mathcal {M}_{u,p}(\Omega ))\) as well as \(\mathfrak {E}_{\mathsf {G}}(\mathfrak {M}_{u,p}(\Omega ))\), and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether \(\frac{n}{u}\ge \frac{1}{p}\) or \(\frac{n}{u} < \frac{1}{p}\) plays a decisive role when it comes to the behaviour of these spaces.     

Nonsmooth generalized guiding functions for periodic differential inclusions

We consider the periodic problem for differential inclusions in $$ \user2{\mathbb{R}}^{\rm N} $$ with a nonconvex-valued orientor field F(t, ζ), which is lower semicontinuous in $$ \zeta \in \user2{\mathbb{R}}^{\rm N} $$ Using the notion of a nonsmooth, locally Lipschitz generalized guiding function, we prove that the inclusion has periodic solutions. We have two such existence theorems. We also study the “convex” periodic problem and prove an existence result under upper semicontinuity hypothesis on F(t, ·) and using a nonsmooth guiding function. Our work was motivated by the recent paper of Mawhin-Ward [23] and extends the single-valued results of Mawhin [19] and the multivalued results of De Blasi-Górniewicz-Pianigiani [4], where either the guiding function is C¹ or the conditions on F are more restrictive and more difficult to verify.     

Existence and multiplicity of solutions for second order periodic systems with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

Fast broadcasting and gossiping in radio networks

We establish an O(nlog²n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of Ω(nlogn). The fastest previously known algorithm for this problem works in time O(n^3/2). Using our broadcasting algorithm, we develop an O(n^3/2log²n) algorithm for gossiping in the same network model.     

Phase diagram of the TbBr(3)-RbBr binary system: thermodynamic and transport properties of the Rb(3)TbBr(6) compound

Phase equilibria in the TbBr3-RbBr binary system were established from differential scanning calorimetry (DSC) measurements. This binary system is characterized by two compounds, namely Rb3TbBr6 and RbTb2Br7, and two eutectics located at the TbBr3 mole fractions, x = 0.117 (728 K) and x = 0.449 (718 K), respectively. Rb3TbBr6 undergoes a solid-solid phase transition at 728 K and melts congruently at 1047 K with the related enthalpies 7.8 and 58.7 kJ mol(-1), respectively. RbTb2Br7 melts incongruently at 803 K. It undergoes also a solid-solid phase transition at 712 K, a temperature very close to that (718 K) of the second eutectic, and much attention was paid in evidencing and separating these transition and eutectic effects. Separate investigations of the thermodynamic and transport properties were performed on the Rb3TbBr6 compound. These heat capacity and electrical conductivity experimental results suggest an order-disorder mechanism in the alkali-metal cation sublattice whereas the TbBr6 octahedra, forming the anionic sublattice, retain their normal lattice positions.     

Catalytic activity of Pd/CN systems in hydrogenation of styrene

Hydrogenation of styrene was applied as a test reaction to study the catalytic activity of Pd deposited on the surface of carbonaceous materials enriched with nitrogen (C_N). The nitrogen content in the support material was found to have a great influence on the degree of styrene conversion to ethylbenzene. In addition, the reaction was carried out in the presence of modified carbonaceous materials acting as catalysts.     

Molecular applications of the intermediate Hamiltonian Fock-space coupled-cluster method for calculation of excitation energies

The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.