Global well-posedness of the 3D magneto-micropolar equations with damping

The 3D magneto-micropolar equations with damping are considered in this paper. We prove the existence and uniqueness of strong solution for 3D magneto-micropolar equations with damping for $\beta \ge 4$ with any $\alpha >0$.     

Extending partial representations of circle graphs

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph and a partial representation giving some predrawn chords that represent an induced subgraph of . The question is whether one can extend to a representation of the entire graph , that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of . Our main result is an time algorithm for partial representation extension of circle graphs, where is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.     

Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

We study an unsteady nonlinear fluid–structure interaction problem. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear wave equation or a linear beam equation. The fluid and the structure systems are coupled via interface conditions prescribing the continuity of the velocities at the fluid–structure interface and the action-reaction principle. Considering three different structure models, we prove existence of a unique local-in-time strong solution, for which there is no gap between the regularity of the initial data and the regularity of the solution enabling to obtain a blow up alternative. In the case of a damped beam this is an alternative proof (and a generalization to non zero initial displacement) of the result that can be found in [20]. In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added. The key points consist in studying the coupled system without decoupling the fluid from the structure and to use the fluid dissipation to control, in appropriate function spaces, the structure velocity.     

Amorphic association schemes from bent partitions

Bent partitions are partitions of an elementary abelian group, which have similarities to partitions from spreads. In fact, a spread partition is a special case of a bent partition. In particular, bent partitions give rise to a large number of (vectorial) bent functions. Examples of bent partitions, which generalize the Desarguesian spread, have been presented by Anbar, Meidl and Pirsic, 2021, 2022. Bent partitions, which generalize some other classes of (pre)semifield spreads, have been presented by Anbar, Kalaycı, Meidl 2023. In this article, it is shown that these bent partitions induce $(p^k+1)$-class amorphic associations schemes on ${\mathbb{F}}_{p^m}\times {\mathbb{F}}_{p^m}$, where k is a divisor of m with special properties. This implies a construction of amorphic association schemes from some classes of (pre)semifields.     

A note on imposing strong complementary slackness conditions in DEA

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems also that the basic matrices may be inherently ill-conditioned, leading to erroneous results. Numerical experiments have been carried out on two real datasets of medium size with 163 and 920 units. These experiments, using well known reliable software, show pervasive existence of ill-conditioned matrices leading to obviously wrong estimates of efficiency scores, and units declared as efficient reference units while actually being inefficient.     

Similarities in electronic properties of organic charge-transfer solids and layered cobaltates

The apparently counterintuitive carrier concentration-dependent electronic properties of layered cobaltates have attracted wide interest. Here we point out that very similar carrier-concentration dependence has previously been noted in strongly correlated quasi-one dimensional (quasi-1D) organic charge-transfer solids. The normal states of both families can be understood, over the entire range of carrier concentration of interest, within the extended Hubbard Hamiltonian with significant intersite Coulomb interaction. As with the charge-transfer solids, superconductivity in the cobaltates appears to be limited to bandfilling of one-quarter. We point out further that there exist other families of correlated superconductors, such as spinels, where too strong correlations, geometric lattice frustration and bandfilling of one-quarter seem to be the essential features of the unconventional superconductors.     

STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS

In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain ΩR3. We prove the local existence of unique strong solutions provided that the initial data μ0 and μ0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.     

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.