Graded polynomial identities for matrices with the transpose involution over an infinite field

Let F be an infinite field and let M_n(F) be the algebra of n×n matrices over F endowed with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of M_n(F) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature, which were obtained for the field of complex numbers and for a particular class of elementary G-gradings.     

Description of the viscosity of honeys in the supercooled regime

For several honeys from different countries, we study the dependence of the Logarithmic Shift Factor (LSF$LSF$) with temperature that obeys the Williams–Landel–Ferry equation. We find that the LSF$LSF$ may be expressed in terms of a linear equation. On the other hand, the viscosities of different honeys present a corresponding state behavior through a master plot in terms of an adimensional temperature. This kind of behavior has been reported for other glass formers.     

p-Hub approach for the optimal park-and-ride facility location problem

Park and Ride facilities (P&R) are car parks at which users can transfer to public transportation to reach their final destination. We propose a mixed linear programming formulation to determine the location of a fixed number of P&R facilities so that their usage is maximized. The facilities are modeled as hubs. Commuters can use one of the P&R facilities or choose to travel by car to their destinations, and their behavior follows a logit model. We apply a p-hub approach considering that users incur in a known generalized cost of using each P&R facility as input for the logit model. For small instances of the problem, we propose a novel linearization of the logit model, which allows transforming the binary nonlinear programming problem into a mixed linear programming formulation. A modification of the Heuristic Concentration Integer (HCI) procedure is applied to solve larger instances of the problem. Numerical experiments are performed, including a case in Queens, NY. Further research is proposed.     

An Elliptic Non Distributive Algebra

In this paper we extend the results of hyperbolic scator algebra introduced in [5], to consider an elliptic product in a subset of ${\mathbb{R}^{1 + n}}$ which recovers the field of complex numbers when only one director component is present. The product of this algebra, that we call elliptic scator algebra in ${\mathbb{E}^{1 + n}}$ , is associative and commutative provided that divisors of zero are excluded. However, as with the hyperbolic case, the elliptic product is not distributive over addition. We explore the geometry of this algebra by considering some interesting objects, such as spheres.     

A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra ${\mathbb{H}_2}$ . The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.     

Rheological behavior in the transient state of PP/EPDM blends with carbon nanofillers

The rheological properties in the transient state of PP/EPDM blends with carbon nanofillers had been studied. The carbon nanofillers were incorporated into molten EPDM in an internal mixer at 150 °C. The rheological variables were determined in rotational rheometry at constant temperature of 200 °C. The results suggest that the magnitude of the difference of the normal stress differences (N₁-N₂) of PP/EPDM blends through the time, with and without nanofillers, and has a transition cycle from positive to negative values and vice versa, at constant and at zero shear rate in previously sheared samples. At constant shear rate, the transition cycle is random; meanwhile, it is constant at zero shear rate. This behavior is attributed to the polymeric chain movement, considering that the sheared samples have two molecular reorder processes: an immediate mechanism and another one slower. The fastest reorder process is attributed to the polymeric chains entanglement forming non-stable and stressed molecular structures. In the other hand, the second process is referred to the molecular mobility that takes place inside the stressed entangled polymer, in such a way that its structure tends to molecular stability as the rest time increases.     

The structure of 2,4,6-tris(1<Emphasis Type="Italic">H</Emphasis>–pyrazol-1-yl)-1,3,5-triazine in the solid state: on polymorphs,pseudopolymorphs and co-crystals

Three structures of 2,4,6-tris(1H–pyrazol-1-yl)-1,3,5-triazine (TPT) have been determined at 193 K: the isolated molecule (2a), a solvate containing molecules of water and acetonitrile (2b) and a complex of two molecules of TPT and three molecules of water (2c). To discuss the structures, B3LYP/6–311++G(d,p) calculations have been carried out, in particular, in what concerns hydrogen bonds.     

The role of cardiac tissue structure in defibrillation

The purpose of this paper is to investigate the relationship between cardiac tissue structure, applied electric field, and the transmembrane potential induced in the process of defibrillation. It outlines a general understanding of the structural mechanisms that contribute to the outcome of a defibrillation shock. Electric shocks defibrillate by changing the transmembrane potential throughout the myocardium. In this process first and foremost the shock current must access the bulk of myocardial mass. The exogenous current traverses the myocardium along convoluted intracellular and extracellular pathways channeled by the tissue structure. Since individual fibers follow curved pathways in the heart, and the fiber direction rotates across the ventricular wall, the applied current perpetually engages in redistribution between the intra- and extracellular domains. This redistribution results in changes in transmembrane potential (membrane polarization): regions of membrane hyper- and depolarization of extent larger than a single cell are induced in the myocardium by the defibrillation shock. Tissue inhomogeneities also contribute to local membrane polarization in the myocardium which is superimposed over the large-scale polarization associated with the fibrous organization of the myocardium. The paper presents simulation results that illustrate various mechanisms by which cardiac tissue structure assists the changes in transmembrane potential throughout the myocardium. (c) 1998 American Institute of Physics.     

Diazatetraester 1H-pyrazole crowns as fluorescent chemosensors for AMPH, METH, MDMA (ecstasy), and dopamine

The synthesis and steady-state fluorescence studies on the interaction with AMPH, METH, MDMA, and DA of two diazatetraester pyrazole crowns containing appended N-(9H-fluoren-9-yl) and N-(naphth-2-ylmethyl) functions, in a water/ethanol 70:30 mixture at physiological pH, are described.     

Temperature-Controlled Mechanochemistry Unlocks the Nickel-Catalyzed Suzuki–Miyaura-Type Coupling of Aryl Sulfamates at Different Scales

Several mechanochemically heated processes have been published in recent years. However, precise control over the mechanochemical catalysed coupling reactions remained elusive. A recent report from Leitch, Browne and co-workers demonstrated how a programmable jar heater manifold delivers an efficient methodology for the Suzuki–Miyaura-type cross coupling reaction of aryl sulfamates and aryl boronic acid species. This methodology can be readily upscaled 200-fold using twin-screw extrusion methodologies.