AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.

Rheological properties and concentration evolution of thickened tailings under the coupling effect of compression and shear

Cemented paste backfill(CPB)is a key technology for green mining in metal mines,in which tailings thickening comprises the primary link of CPB technology.However,difficult flocculation and substandard concentrations of thickened tailings often occur.The rheological properties and concentration evolution in the thickened tailings remain unclear.Moreover,traditional indoor thickening experiments have yet to quantitatively characterize their rheological properties.An experiment of flocculation condition optimization based on the Box-Behnken design(BBD)was performed in the study,and the two response values were investigated:concentration and the mean weighted chord length(MWCL)of flocs.Thus,optimal flocculation conditions were obtained.In addition,the rheological properties and concentration evolution of different flocculant dosages and ultrafine tailing contents under shear,compression,and compression-shear coupling experimental conditions were tested and compared.The results show that the shear yield stress under compression and compression-shear coupling increases with the growth of compressive yield stress,while the shear yield stress increases slightly under shear.The order of shear yield stress from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Under compression and compression-shear coupling,the concentration first rapidly increases with the growth of compressive yield stress and then slowly increases,while concentration increases slightly under shear.The order of concentration from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Finally,the evolution mechanism of the flocs and drainage channels during the thickening of the thickened tailings under different experimental conditions was revealed.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Optimizing nutrition in hepatic cirrhosis:A comprehensive assessment and care approach

Cirrhosis is considered a growing cause of morbidity and mortality,which represents a significant public health problem.Currently,there is no effective treatment to reverse cirrhosis.Treatment primarily centers on addressing the underlying liver condition,monitoring,and managing portal hypertension-related complications,and evaluating the potential for liver transplantation in cases of decompensated cirrhosis,marked by rapid progression and the emer-gence of complications like variceal bleeding,hepatic encephalopathy,ascites,malnutrition,and more.Malnutrition,a prevalent complication across all disease stages,is often underdiagnosed in cirrhosis due to the complexities of nutritional assessment in patients with fluid retention and/or obesity,despite its crucial impact on prognosis.Increasing emphasis has been placed on the collaboration of nutritionists within hepatology and Liver transplant teams to deliver compre-hensive care,a practice that has shown to improve outcomes.This review covers appropriate screening and assessment methods for evaluating the nutritional status of this population,diagnostic approaches for malnutrition,and context-specific nutrition treatments.It also discusses evidence-based recommendations for supplementation and physical exercise,both essential elements of the standard care provided to cirrhotic patients.

增材制造Ti6Al4V合金的闪速等离子体电解氧化与在生理介质中的电化学行为

研究激光粉末床熔融增材制造(AM)(又称直接金属激光烧结)技术制备的Ti6Al4V合金等离子体电解氧化(PEO)处理及其电化学行为。通过短时间(<120 s)PEO处理(也称闪速PEO),在AM合金和传统合金表面制备了3~10μm厚、含Ca和P的涂层。然后在改良的α-MEM溶液中,通过动电位极化曲线和电化学阻抗谱(EIS)评估了合金的电化学行为。与传统合金相比,AM合金中形成了细小的层片状α显微组织和层间小尺寸的β相颗粒,这促使了火花的产生,从而促进了PEO涂层的生长。闪速PEO涂层提高了传统合金和AM合金的耐腐蚀性,最薄的涂层(<3μm)提供了高达3倍的保护。AM Ti6Al4V由于其高的晶界密度,易受局部缝隙腐蚀的影响。而即使短至35 s的闪速PEO处理也足以成功避免这种情况。

Exploring multifaceted factors in chronic kidney disease risk: A comprehensive analysis of biochemistry, lifestyle, and inflammation in elderly Chinese individuals

This letter praises a recent article in the World Journal of Clinical Cases(Roles of biochemistry data,lifestyle,and inflammation in identifying abnormal renal function in old Chinese),examining factors affecting abnormal renal function in elderly Chinese using advanced machine learning.It highlights the importance of uric acid,age,hemoglobin,body mass index,sport hours,and systolic blood pressure.The study's holistic approach,integrating lifestyle and inflammation,offers a nuanced understanding of chronic kidney disease risk factors.The letter suggests exploring mechanistic pathways of hyperuricemia,the link between anemia and renal function,and the connection between body mass index and estimated glomerular filtration rate.It advocates investigating physical activity's impact on renal health and the independent effects of blood pressure.The study significantly contributes to chronic kidney disease understanding,proposing avenues for further exploration and interventions.Commendations are extended to the authors and the journal.

Cosmological Model in Four Time and Four Space Dimensions

We develop a cosmological model in a physical background scenario of four time and four space dimensions ((4+4)-dimensions or (4+4)-universe). We show that in this framework the (1+3)-universe is deeply connected with the (3+1)-universe. We argue that this means that in the (4+4)-universe there exists a duality relation between the (1+3)-universe and the (3+1)-universe.

A Probabilistic Description of the Impact of Vaccine-Induced Immunity in the Dynamics of COVID-19 Transmission

The recent outbreak of COVID-19 has caused millions of deaths worldwide and a huge societal and economic impact in virtually all countries. A large variety of mathematical models to describe the dynamics of COVID-19 transmission have been reported. Among them, Bayesian probabilistic models of COVID-19 transmission dynamics have been very efficient in the interpretation of early data from the beginning of the pandemic, helping to estimate the impact of non-pharmacological measures in each country, and forecasting the evolution of the pandemic in different potential scenarios. These models use probability distribution curves to describe key dynamic aspects of the transmission, like the probability for every infected person of infecting other individuals, dying or recovering, with parameters obtained from experimental epidemiological data. However, the impact of vaccine-induced immunity, which has been key for controlling the public health emergency caused by the pandemic, has been more challenging to describe in these models, due to the complexity of experimental data. Here we report different probability distribution curves to model the acquisition and decay of immunity after vaccination. We discuss the mathematical background and how these models can be integrated in existing Bayesian probabilistic models to provide a good estimation of the dynamics of COVID-19 transmission during the entire pandemic period.

Floristic composition and edaphic relationships in ferruginous campo rupestre reference ecosystems

Land use change and occupation have led to modifications in the environment causing loss of biodiversity and ecosystem services throughout the planet.Some environments with high economic relevance,such as the ferruginous campo rupestre(rupestrian grassland known as Canga in Brazil),are even more susceptible to severe impacts due to their extreme habitat conditions and low resilience.The determination of reference ecosystems based on the intrinsic characteristics of the ecosystem is essential for conservation as well as to the implementation of ecological restoration.We proposed the reference ecosystem of the three main types of habitats of the ferruginous campo rupestre based on their floristic composition.We described the floristic composition of each habitat and evaluated the physicochemical properties of the soils and the relationship between plants and soils.All three habitats showed high diversity of plant species and many endemic species,such as Chamaecrista choriophylla,Cuphea pseudovaccinium,Lychnophora pinaster,and Vellozia subalata.The distribution of vegetation was strongly related with the edaphic characteristics,with a set of species more adapted to high concentration of base saturation,fine sand,organic carbon,and iron,while another set of species succeeded in more acidic soils with higher S and silt concentration.We provide support for the contention that the ferruginous campo rupestre is a mosaic of different habitats shaped by intrinsic local conditions.Failure to recognize the floristic composition of each particular habitat can lead to inappropriate restoration,increased habitat homogenization and increased loss of biodiversity and ecosystem services.This study also advances the knowledge base for building the reference ecosystem for the different types of ferruginous campo rupestre habitats,as well as a key database for highlighting those species contribute most to community assembly in this diverse and threatened tropical mountain ecosystem.

Environmental changes affect picoplanktonic composition in Antarctic Peninsula ponds

Antarctic Peninsula is experiencing one of the largest global warming events worldwide.Shallow water bodies generated by the melting of snow in summer are numerous,and they might act as sentinels of climate change due to their rapid response and ability to integrate catchment information.Shifts in climate can influence the structure of microbial communities which dominate these freshwaters ecosystems.Here,we characterize three ponds at Cierva Point(Antarctic Peninsula)by examining their physico-chemical and morphological characteristics and we explored how different factors modify the structure of the microbial community.We studied the abundance and biomass of heterotrophic bacteria,picocyanobacteria and picoeukaryote algae during January and February of two consecutive summers(2017 and 2018).We found that ponds had different limnological characteristics,due to their location,geomorphological features and presence of the surrounding flora and fauna.Physico-chemical parameters as well as microbial community differed between ponds,months and years.In 2017,most ponds were oligo to mesotrophic states.The larger accumulated rainfall(as a result of environmental changes on the Antarctic Peninsula)during 2018,particularly in February,causes nutrient runoff into water bodies.This affects those ponds with the highest seabird circulation,such as gentoo penguin,increasing eutrophication.As a result,picoplanktonic abundances were higher,and the community structure shifts to a largely heterotrophic bacteria dominated one.These results suggest that these communities could act as sentinels to environmental changes,anticipating a future with mostly hypertrophic ponds.

Insight into endoplasmic reticulum-mitochondria contacts in human amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis(ALS) is a fastprogressing fatal neurodegenerative disease and the most common form of motor neuron disease.There is currently no cure and approximately 90% of cases are sporadic.ALS shares genetic causes,clinical and neuropathological features with frontotemporal dementia,the second most common form of presenile dementia.ALS and frontotemporal dementia are therefore considered a disease spectrum(Abramzon et al.,2020).

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.

Distribution and Relation of Primes with Tesla Numbers 3, 6, and 9

This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.

Designing Pair of Nonlinear Components of a Block Cipher over Gaussian Integers

In block ciphers,the nonlinear components,also known as sub-stitution boxes(S-boxes),are used with the purpose of inducing confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Gaussian integers(GI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.But the prime field dependent on the Elliptic curve(EC)provides one S-box at a time by fixing three parameters a,b,and p.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.

Application of the extended Fourier amplitude sensitivity testing(FAST)method to inflated,axial stretched,and residually stressed cylinders

This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Air Quality Estimation Using Nonhomogeneous Markov Chains: A Case Study Comparing Two Rules Applied to Mexico City Data

A nonhomogeneous Markov chain is applied to the study of the air quality classification in Mexico City when the so-called criterion pollutants are used. We consider the indices associated with air quality using two regulations where different ways of classification are taken into account. Parameters of the model are the initial and transition probabilities of the chain. They are estimated under the Bayesian point of view through samples generated directly from the corresponding posterior distributions. Using the estimated parameters, the probability of having an air quality index in a given hour of the day is obtained.

A Class of Potentials for Hyperbolic Transcendental Entire Maps

We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.