On the Smoothness of a Class of Weak Solutions to the Navier--Stokes equations

We improve regularity criteria for weak solutions to the Navier-Stokes equations stated in references [1], [3] and [12], by using in the proof given in [3], a new idea introduced by H. O. Bae and H. J. Choe in [1]. This idea allows us, in one of the main hypothesis (see eq. (1.7)), to replace the velocity u by its projection [`(u)] \bar u into an arbitrary hyperplane of \Bbb Rⁿ {\Bbb R}^n ; see Theorem A. For simplicity, we state our results for space dimension n ￡ 4 n \le 4 , since if n 3 5 n \ge 5 the proofs become more technical and additional hypotheses are needed. However, for the interested reader, we will present the formal calculations for arbitrary dimension n.     

Summability of multilinear mappings: Littlewood, Orlicz and beyond

In this paper we prove new results concerning summability properties of multilinear mappings between Banach spaces, such as an extension of Littlewood’s 4/3 Theorem. The role of the Littlewood–Orlicz property in the theory is established, especially in the question of determining when multilinear mappings are (1; 2, . . . , 2)-summing.     

Smooth driving of M?ssbauer electromechanical transducers

Quality of Mössbauer spectra is strongly related to the performance of source velocity modulator. Traditional electromechanical driving techniques demand hard-edged square or triangular velocity waveforms that introduce long settling times and demand careful driver tuning. For this work, the behavior of commercial velocity transducers and drive units was studied under different working conditions. Different velocity reference waveforms in constant-acceleration, constant-velocity and programmable-velocity techniques were tested. Significant improvement in spectrometer efficiency and accuracy was achieved by replacing triangular and square hard edges with continuous smooth-shaped transitions. A criterion for best waveform selection and synchronization is presented and attainable enhancements are evaluated. In order to fully exploit this driving technique, a compact microprocessor-based architecture is proposed and a suitable data acquisition system implementation is presented. System linearity and efficiency characterization are also shown.     

An edge-swap heuristic for generating spanning trees with minimum number of branch vertices

This paper presents a new edge-swap heuristic for generating spanning trees with a minimum number of branch vertices, i.e. vertices of degree greater than two. This problem was introduced in Gargano et al. (Lect Notes Comput Sci 2380:355–365, 2002) and has been called the minimum branch vertices problem by Cerulli et al. (Comput Optim Appl 42:353–370, 2009). The heuristic starts with a random spanning tree and iteratively reduces the number of branch vertices by swapping tree edges with edges not currently in the tree. It can be easily implemented as a multi-start heuristic. We report on extensive computational experiments comparing single-start and multi-start variants on our heuristic with other heuristics previously proposed in the literature.     

On a family of results concerning direction of vorticity and regularity for the Navier–Stokes equations

These notes concern existence, and suitable formulation, of meaningful conditions on the direction of the vorticity which guarantee the regularity of the solutions to the evolution Navier–Stokes equations. A main concern here is to compare the different situations which appear in considering slip and no-slip boundary conditions. The paper reviews mainly results obtained in some of the references cited.     

Mucuna pruriens Administration Minimizes Neuroinflammation and Shows Anxiolytic,Antidepressant and Slimming Effects in Obese Rats

This study evaluated the effect of Mucuna pruriens (MP) administration on neuroinflammation and behavioral and murinometric parameters in obese rats. Proximate composition, oligosaccharide and phenolic compound profile of MP were determined. Wistar adult male rats were randomized into healthy (HG) and obese group (OG). The HG consumed a control chow diet while OG consumed a cafeteria diet for eight weeks. Then, they were subdivided into: Healthy (HG); Healthy with MP administration (HGMP); Obese (OG); Obese with MP administration (OGMP), with the consumption of the respective diets remaining for another eight weeks, in addition to gavage with MP extract to supplemented groups (750 mg/kg weight). MP presented a composition rich in proteins and phenolic compounds, especially catechin, in addition to 1-kestose and levodopa. Supplementation reduced food intake, body weight, and thoracic and abdominal circumferences in obese rats. MP showed anxiolytic and antidepressant effects and reduced morphological damage and expression of interleukin 6 in the hippocampus of obese rats. MP treatment showed satietogenic, slimming, anxiolytic and antidepressant effects, besides to minimizing hippocampal neuroinflammation in obese rats. Our results demonstrated the potential anti-obesity of MP which are probably related to the high content of bioactive compounds present in this plant extract.     

Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.     

On the sharp singular limit for slightly compressible fluids

We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well-specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.