Dirac-K\"ahler particle in Riemann spherical space: boson interpretation

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed

Using neural networks to obtain indirect information about the state variables in an alcoholic fermentation process

This work provides a manual design space exploration regarding the structure, type, and inputs of a multilayer neural network (NN) to obtain indirect information about the state variables in the alcoholic fermentation process. The main benefit of our application is to help experts reduce the time needed for making the relevant measurements and to increase the lifecycles of sensors in bioreactors. The novelty of this research is the flexibility of the developed application, the use of a great number of variables, and the comparative presentation of the results obtained with different NNs (feedback vs. feed-forward) and different learning algorithms (Back-Propagation vs. Levenberg–Marquardt). The simulation results show that the feedback neural network outperformed the feed-forward neural network. The NN configuration is relatively flexible (with hidden layers and a number of nodes on each of them), but the number of input and output nodes depends on the fermentation process parameters. After laborious simulations, we determined that using pH and CO2 as inputs reduces the prediction errors of the NN. Thus, besides the most commonly used process parameters like fermentation temperature, time, the initial concentration of the substrate, the substrate concentration, and the biomass concentration, by adding pH and CO2, we obtained the optimum number of input nodes for the network. The optimal configuration in our case was obtained after 1500 iterations using a NN with one hidden layer and 12 neurons on it, seven neurons on the input layer, and one neuron as the output. If properly trained and validated, this model can be used in future research to accurately predict steady-state and dynamic alcoholic fermentation process behaviour and thereby improve process control performance

Hilbert transforms and the equidistribution of zeros of polynomials

We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connection between this inequality and an extremal problem in Fourier analysis involving the maxima of Hilbert transforms, for which we provide a complete solution. Prior to Soundararajan (2019), refinements of the discrepancy inequality of Erdős and Turán had been obtained by Ganelius (1954) and Mignotte (1992)

Hydrogeology and geochemistry of the sulfur karst springs at Santa Cesarea Terme (Apulia, southern Italy)

This work describes the geochemical and hydrogeological characteristics of Santa Cesarea Terme, an active sulfuric acid speleogenetic system located along the Adriatic coastline (Apulia, southern Italy). It represents a very peculiar site, where rising thermal and acidic waters mix with seawater creating undersaturated solutions with respect to CaCO3, able to dissolve and corrode limestone and create caves. The Santa Cesarea Terme system is composed of four caves: Fetida, Sulfurea, Gattulla, and Solfatara. Hypogene morphologies and abundant deposits of native sulfur (especially in Gattulla Cave) and sulfate minerals are present in these caves. Fetida and Gattulla caves were investigated primarily because they are easily accessible throughout the whole year through artificial entrances, the other caves being reachable only from the sea. Geochemical analysis of water, monitoring of cave atmosphere, and measurement of the stable isotopes of S, O, and H helped to identify the main processes occurring in this complex cave system. In particular, changes in Ba2+ and Sr2+ concentration allowed for the identification of two main domains of influence, characterized by marine and rising acidic waters

Spontaneous intracranial hemorrhage in children – ruptured lobar arteriovenous malformations: Report of two cases

Brain arteriovenous malformations (AVMs) are lesions thought to be primarily congenital in origin, consisting of fistulous connections of abnormal arteries and veins, without normal intervening capillary beds and no cerebral parenchyma between vessels. In the pediatric population, AVMs represent the most common cause of spontaneous intracranial hemorrhage (ICH), with a high recurrent bleeding risk. The aim of this paper is to report 2 cases of ruptured lobar AVMs in children, presenting with spontaneous ICH. Due to the patients’ neurological status, the only imaging examination performed preoperatively was a CT scan, showing intraparenchymal hemorrhage. Thus, there was no MRI/angiographic examination to prove the existence of a brain AVM prior to the surgical interventions. Also, the cerebral angiography performed after the surgery showed, in both patients, no signs of residual vascular malformations. Therefore, the diagnosis of AVM was certified by macroscopic and microscopic pathological findings, with no brain imaging suggestive of a vascular malformation

The Ruled Vertex and Nontoric del Pezzo Surfaces

We construct the topological partition function of local nontoric del Pezzo surfaces using the ruled vertex formalism.Comment: 16 pages, 4 figure

Next frontiers in cleaner synthesis: 3D printed graphene-supported CeZrLa mixed-oxide nanocatalyst for CO2 utilisation and direct propylene carbonate production

A rapidly-growing 3D printing technology is innovatively employed for the manufacture of a new class of heterogenous catalysts for the conversion of CO2 into industrially relevant chemicals such as cyclic carbonates. For the first time, directly printed graphene-based 3D structured nanocatalysts have been developed combining the exceptional properties of graphene and active CeZrLa mixed-oxide nanoparticles. It constitutes a significant advance on previous attempts at 3D printing graphene inks in that it does not merely explore the printability itself, but enhances the efficiency of industrially relevant reactions, such as CO2 utilisation for direct propylene carbonate (PC) production in the absence of organic solvents. In comparison to the starting powder, 3D printed GO-supported CeZeLa catalysts showed improved activity with higher conversion and no noticeable change in selectivity. This can be attributed to the spatially uniform distribution of nanoparticles over the 2D and 3D surfaces, and the larger surface area and pore volume of the printed structures. 3D printed GO-supported CeZeLa catalysts compared to unsupported 3D printed samples exhibited higher selectivity and yield owing to the great number of new weak acid sites appearing in the supported sample, as observed by NH3-TPD analysis. In addition, the catalyst's facile separation from the product has the capacity to massively reduce materials and operating costs resulting in increased sustainability. It convincingly shows the potential of these printing technologies in revolutionising the way catalysts and catalytic reactors are designed in the general quest for clean technologies and greener chemistry

Allogeneic Mesenchymal Stem Cells as a Treatment for Aging Frailty

As life expectancy is projected to increase in the ensuing decades, individuals of older age continue to exceed the previous generation’s lifespan. Advancing age is associated with a reduction in physical and mental functional capacity, and chronic inflammation is a major factor contributing to this decline. A heightened inflammatory state can lead to exhaustion, weakness, weight loss, slow gate speed, and an overall decrease in activity level. These phenotypes define the onset of the disease process known as frailty. Frailty is a growing epidemic, which severely undermines a person’s ability to deal with outside stressors, and increases their rate of hospitalization, institutionalization, and mortality. Current interventions focus on preventative care by improving exercise capacity, strength, nutritional supplementation, diet, and mobility. However, a biological cure has heretofore remained elusive. Here, we introduce the novel therapeutic principle that mesenchymal stem cell (MSC) therapy may represent a safe, practical, and efficacious both the treatment and prevention of frailty in individuals of advancing age. To date, a phase I safety trial reveals an excellent safety profile and suggests that mesenchymal stem cells can ameliorate signs and symptoms of frailty. These early studies lay the groundwork for future large-scale clinical trials of this exciting and novel therapeutic concept that has the potential to expand health span in the aging population

D-brane Instantons on the T^6/Z_3 orientifold

We give a detailed microscopic derivation of gauge and stringy instanton generated superpotentials for gauge theories living on D3-branes at Z_3-orientifold singularities. Gauge instantons are generated by D(-1)-branes and lead to Affleck, Dine and Seiberg (ADS) like superpotentials in the effective N=1 gauge theories with three generations of bifundamental and anti/symmetric matter. Stringy instanton effects are generated by Euclidean ED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana masses in one case and non-renormalizable superpotentials for the other cases. Finally we determine the conditions under which ADS like superpotentials are generated in N=1 gauge theories with adjoints, fundamentals, symmetric and antisymmetric chiral matter.Comment: 31 pages, no figure

Non-Perturbative Effects on a Fractional D3-Brane

In this note we study the N=1 abelian gauge theory on the world volume of a single fractional D3-brane. In the limit where gravitational interactions are not completely decoupled we find that a superpotential and a fermionic bilinear condensate are generated by a D-brane instanton effect. A related situation arises for an isolated cycle invariant under an orientifold projection, even in the absence of any gauge theory brane. Moreover, in presence of supersymmetry breaking background fluxes, such instanton configurations induce new couplings in the 4-dimensional effective action, including non-perturbative contributions to the cosmological constant and non-supersymmetric mass terms.Comment: 18 pages, v3: refs adde