The Nikola Tesla Constant and Its Relation to the Circumference Inscribed in a Square

This research work relates the surface of a square and the area circumscribed by a circle, resulting in a value called Nikola Tesla constant. This constant starts with the calculation of the areas of the square and the inscribed circle, giving a ratio of 9/40 and from which a residual area of the area proportions of the geometric figures described is obtained. Plotting smooth curves, particularly those in round shapes, can be represented efficiently with the use of Nikola Tesla constant, reducing complex mathematical calculus.

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch arrivals of fixed size a, and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time.

THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H^＊-ALGEBRA^＊

We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

Bayesian regularized quantile regression:A robust alternative for genome-based prediction of skewed data

Genomic prediction(GP)has become a valuable tool for predicting the performance of selection candidates for the next breeding cycle.A vast majority of statistical linear models on which GP is based rely on the assumption of normality of the residuals and therefore on the response variable itself.In this study,we propose to use Bayesian regularized quantile regression(BRQR)in the context of GP;the model has been successfully used in other research areas.We evaluated the prediction ability of the proposed model and compared it with the Bayesian ridge regression(BRR;equivalent to genomic best linear unbiased predictor,GBLUP).In addition,BLUP can be used with pedigree information obtained from the coefficient of coancestry(ABLUP).We have found that the prediction ability of BRQR is comparable to that of BRR and,in some cases,better;it also has the potential to efficiently deal with outliers.A program written in the R statistical package is available as Supplementary material.

Applications of Mogulskii, and Kurtz-Feng Large Deviation Results to Risk Reserve Processes with Aggregate Claims

In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions including (the non-super- exponential) exponential claims. We prove two large deviations principles: first, we obtain the LDP for risk processes on D∈[0,1] with the Skorohod topology. In this case, we provide an explicit form for the rate function, in which the safety loading condition appears naturally. The second theorem allows us to obtain the LDP for Aggregate Claims processes on D∈[0,∞) with a different time-scale modification. As an application of the first result we estimate the ruin probability, and for the second result we work explicit calculations for the case of exponential claims.

A generalization of the half-normal distribution

In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability.

A New Application of the Flux Approximation Method on Hyperbolic Conservation Systems

In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.

On Finite Rank Operators on Centrally Closed Semiprime Rings

We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for each , there exist and e an idempotent of C such that xz=eq.

Modeling and Simulation of Molecular Mechanism of Action of Dietary Polyphenols on the Inhibition of Anti-Apoptotic PI3K/AKT Pathway

In recent years, the role of dietary phenolic compounds in the regulation of cellular metabolism in normal and pathological conditions has become increasingly important in cancer research. In most cases, the molecular mechanism of action related to the anticarcinogenic effect of phenolic compounds has been studied in vitro and in animal models, but these studies are still not complete. It is precisely here where in silico approaches can be an invaluable tool for complementing in vitro and in vivo research. In this paper, we adopt a tuple space-based modeling and simulation approach, and show how it can be applied to the simulation of complex interaction patterns of intracellular signaling pathways. Specifically, we are working to explore and to understand the molecular mechanism of action of dietary phenolic compounds on the inhibition of the PI3K/AKT anti-apoptotic pathway. As a first approximation, using the tuple spaces- based in silico approach, we model and simulate the anti-apoptotic PI3K/AKT pathway in the absence and presence of phenolic compounds, in order to determine the effectiveness of our platform, to employ it in future prediction of experimentally non visualized interactions between the pathway components and phenolic compounds.

Hyperbolic Approximation on System of Elasticity in Lagrangian Coordinates

In this paper, we construct a sequence of hyperbolic systems (13) to approximate the general system of one-dimensional nonlinear elasticity in Lagrangian coordinates (2). For each fixed approximation parameter , we establish the existence of entropy solutions for the Cauchy problem (13) with bounded initial data (23).

Characterization of Natural Vuggy Fractured Porous Medium: Its Physicochemical Properties, Porosity and Permeability

The aim of this work was to obtain the physicochemical properties by SEM, XRD, FTIR analyses and the surface characteristics from carbonate outcrops cores such as pore diameter, surface area, porosity and permeability. The methods used to characterize them were Scanning Electron Microscopy, SEM;X Ray Diffraction, DRX;Fourier Transform Infrared Spectroscopy, FTIR. The porosity and permeability of natural vuggy fractured porous medium from core samples was determined obtained in the laboratory with conventional procedures. The cores have smooth and rough surfaces with porous with several sizes. Some crystals appear in preferential zones mainly composed by calcium, carbon and oxygen. Apparently into free spaces were found the organic materials, organic residues of crude oil. The cores have smooth and rough surfaces with porous with several sizes. Some crystals appear in preferential zones composed by calcium, carbon and oxygen. Apparently into free spaces were found the organic materials, organic residues of crude oil. The main inorganic compound in cores is calcite, (CaCO3). The porosity was for porous core 26% and for solid core 8.5%. The values obtained show that the cores have permeability where the fluid migrates through the particles at 2.23 × 10-4 cm/s.

Conditions for Singularity of Twist Grain Boundaries between Arbitrary 2-D Lattices

We have shown that the expression =2tan-1/ derived by Ranganathan to calculate the angles at which there exists a CSL for rotational interfaces in the cubic system can also be applied to general (oblique) two-dimensional lattices provided that the quantities 2 and /cos() are rational numbers, with =|b|/|a| and is the angle between the basis vectors a and b. In contrast with Ranganathan’s results, N;given by N=tan2() needs no longer be an integer. Specifically, vectors a and b must have the form a=(1,0);b=(r,tan) where r is an arbitrary rational number. We have also shown that the interfacial classification of cubic twist interfaces based on the recurrence properties of the O-lattice remains valid for arbitrary two-dimensional interfaces provided the above requirements on the lattice are met.

Nanocapacitor with a Cantor Multi-Layered Structure

We calculate numerically the quantum capacitance of a nanocapacitor formed of oxide-silicon layers deposited alternately with their widths following a Cantor set structure. We show that this configuration brings about a nano-hybrid capacitor which allows a classical and quantum behavior depending on the Cantor generation. In addition, we propose an approximate equivalent circuit representation for the nano-hybrid capacitor.

Any Hamiltonian System Is Locally Equivalent to a Free Particle

In this work we use the Hamilton-Jacobi theory to show that locally all the Hamiltonian systems with n degrees of freedom are equivalent. That is, there is a canonical transformation connecting two arbitrary Hamiltonian systems with the same number of degrees of freedom. This result in particular implies that locally all the Hamiltonian systems are equivalent to that of a free particle. We illustrate our result with two particular examples;first we show that the one-dimensional free particle is locally equivalent to the one-dimensional harmonic oscillator and second that the two-dimensional free particle is locally equivalent to the two-dimensional Kepler problem.

Gold Veins Location in Deposits Originated by a Slanting Magma Intrusion Dike

The location of gold veins, due to a slanting magma dike intrusion in a cold rock, considering earth surface effects is determined. The 400°C and 500°C isotherm evolution resulting from this magma intrusion are studied considering a 2-D model. In this analysis, it is shown that the isotherm envelopes are the most important surfaces. Analytic solutions have been found as a function of the angle a between the dike and the vertical planes. The present results are more general than previous ones in the contest of vertical dikes. Magma convection has been considered in a simplified way. The agreement found that the results in the work the actual vein sites at the gold mine, called Colombia, in the auriferous area of El Callao, located 180 Km south of Ciudad Guayana in Bolivar state, Venezuela, are much better than in previous works.

An Alternative Manifold for Cosmology Using Seifert Fibered and Hyperbolic Spaces

We propose a model with 3-dimensional spatial sections, constructed from hyperbolic cusp space glued to Seifert manifolds which are in this case homology spheres. The topological part of this research is based on Thurston’s conjecture which states that any 3-dimensional manifold has a canonical decomposition into parts, each of which has a particular geometric structure. In our case, each part is either a Seifert fibered or a cusp hyperbolic space. In our construction we remove tubular neighbourhoods of singular orbits in areas of Seifert fibered manifolds using a splice operation and replace each with a cusp hyperbolic space. We thus achieve elimination of all singularities, which appear in the standard-like cosmological models, replacing them by “a torus to infinity”. From this construction, we propose an alternative manifold for cosmology with finite volume and without Friedmann-like singularities. This manifold was used for calculating coupling constants. Obtaining in this way a theoretical explanation for fundamental forces is at least in the sense of the hierarchy.

Laws of Zipf and Benford, intermittency, and critical fluctuations

We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluctuations at criticality. The equivalences stem from a common statistical-mechanical structure that departs from the usual via a one-parameter deformation of the exponential and logarithmic functions. The generalized structure arises when configurational phase space is incompletely visited such that the accessible fraction has fractal properties. Thermodynamically, the common focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials. The theory is in quantitative agreement with real size-rank data and it naturally includes the bends or tails observed for small and large rank.

Type Ⅱ Blow-up in the 5-dimensional Energy Critical Heat Equation

We consider the Cauchy problem for the energy critical heat equation ■ in dimension n = 5. More precisely we find that for given points q_1, q_2,..., q_k and any sufficiently small T > 0 there is an initial condition u0 such that the solution u(x, t) of(0.1) blows-up at exactly those k points with rates type Ⅱ, namely with absolute size ～(T-t)^(-α) for α >3/4. The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin–Talenti bubbles.

A Maschke Type Theorem for Weak Hopf Algebras

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.

Severe Acute Hepatitis of Unknown Origin in Children: What Do We Know Today?

In May 2022, the UK International Health Regulations National Focal Point notified World Health Organization of 176 cases of severe acute hepatitis of unknown etiology in children under 10 years of age. From that moment on, cases of severe acute hepatitis of unknown origin in children began to be reported in several countries. As of June 17, 2022, a total of 991 cases had been reported in 35 countries worldwide, 50 children needed a liver transplant and 28 patients died. According to information published by ECDC, 449 cases have been detected in 21 EU countries. The children were between 1 month and 16 years of age. Adenovirus was detected in 62.2% of the analyzed samples. So far, the cause of these cases is unknown and many hypotheses remain open, but hepatitis A-E viruses and COVID-19 vaccines have been ruled out. A possible hypothesis has been published to explain the cause of these cases of severe hepatitis, according to which it could be a consequence of adenovirus infection in the intestine in healthy children previously infected with SARS-CoV-2. No other clear epidemiological risk factors have been identified to date. Thus, at this time, the etiology of the current cases of hepatitis remains under active investigation.