In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the degrees and heights of its elements. In addition to that, we propose two algorithms to effectively compute this parametrization.
Abstract Hydrodynamic cavitation poses a significant challenge to the durability and performance of hydraulic machinery, such as hydrofoils, necessitating high-fidelity predictive models. This study addresses the critical need for accurately simulating three-dimensional cavitation dynamics in complex flows. We develop a novel 3D multiphase model (SC-CS) by integrating the Shan-Chen pseudopotential method with the Carnahan-Starling equation of state within the Lattice Boltzmann framework. This coupled approach successfully captures the complete lifecycle of both heterogeneous and homogeneous cavitation, including inception, development, and collapse around a hydrofoil. To validate the numerical model, experimental investigations were conducted in a high-speed water tunnel using high-speed photography, providing empirical evidence for the simulated cavitation behavior. The SC-CS model demonstrates an exceptional capability for handling high density ratios, providing a robust mesoscopic tool for fundamental cavitation research and engineering design optimization.
Using Hahn series, one can attach to any linear Mahler equation a basis of solutions at 0 reminiscent of the solutions of linear differential equations at a regular singularity. We show that such a basis of solutions can be produced by using a variant of Frobenius method.
Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty matrix formats.
The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a supercomputer with distributed memory and dynamic decentralized control.
In this short article I introduce the frab package which provides an alternative interpretation of named vectors in the R programming language; it is available on CRAN. The underlying mathematical object is the free Abelian group.
Production of cotton is faced with a number of challenges and amongst these are a lot of pests including aphids, mealybugs, and bollworms. Cotton bollworms namely heliothis, red, spiny, and pink can cause a yield reduction of 67 percent if they are not properly controlled. A study to evaluate the efficacy of Vantex 60 CS, Dynamo 1.15% WP and Blanket 150 SC, new insecticides intended for use in cotton was carried out at CRI, Tokwane and Matikwa in 2020 – 21 and 2021-22 seasons. Vantex 60 CS levels were 50ml, 100ml and 150ml. Dynamo 1.15% was tested at 1250g, 2500g and 3000g. Blanket 150 SC levels were 125ml, 250ml and 300ml. Decis Forte rate was 50ml/ha. There was a no control treatment. Bollworm counts and predator counts were measured. Data analysis was done using Genstat 14th Edition. Data that did not follow the normal distribution was transformed using the square root transformation of (x + 3/8). Means were separated using Duncan’s Multiple Range Test in ascending order.Vantex at 150ml/ha, Blanket at both 250ml/ha and 300ml/ha were comparable to Decis Forte for Red, Heliothis and spiny bollworms as well as predator preservation. Dynamo was comparable to Decis Forte in preserving predators at all its levels as shown by Matikwa for both seasons but was outcompeted by Decis Forte in Heliothis bollworm control. Its 2500g and 3000g/ha were comparable to Decis Forte for RBWL and spiny bollworm control
Here I present the 'clifford' package for working with Clifford algebras in the R programming language. The algebra is described and package idiom is given.
We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p (x). Our methods rely on specific tools arising in positive characteristic: p-curvature, structure of simple central algebras and p-Riccati equations.
We present an algorithm for computing limits of quotients of real analytic functions. The algorithm is based on computation of a bound on the Lojasiewicz exponent and requires the denominator to have an isolated zero at the limit point.
Here we present some revised arguments to a randomized algorithm proposed by Sudan to find the polynomials of bounded degree agreeing on a dense fraction of a set of points in $\mathbb{F}^{2}$ for some field $\mathbb{F}$.
Claudia Daiane Trentin Lampert, Silvana Alba Scortegagna
O uso de instrumentos de autoexpressão pode trazer contribuições na apreensão do trabalho mental. Este estudo propõe avaliar a autopercepção no Rorschach-SC de idosos com depressão em uma perspectiva idiográfica. Foram analisados 31 protocolos de idosos entre 60 e 86 anos de idade, 29 mulheres e dois homens. A análise qualitativa contemplou respostas codificadas com conteúdo mórbido (MOR), Sombreado Vista (SumV), Representação Humana de Má qualidade (PHR) com qualidade formal distorcida (FQ-), e codificadas com PHR, Códigos Especiais (Sum6) e Códigos Especiais Críticos (WSum6). Os resultados demonstraram: a) respostas com MOR sugestivas de uma autoimagem negativa e desqualificada; b) respostas SumV indicando para autocritica e autoaversão; c) respostas PHR com FQ- sugerindo uma autopercepção distorcida e inadequada; e d) respostas de PHR com Sum6 e WSum6 reportando para alterações cognitivas e autoperceptivas. Os achados do Rorschach permitiram analisar configurações típicas de idosos com depressão e indicam perspectivas para o seguimento psicoterapêutico.
We present an algorithm for computing asymptotic approximations of roots of polynomials with exp-log function coefficients. The real and imaginary parts of the approximations are given as explicit exp-log expressions. We provide a method for deciding which approximations correspond to real roots. We report on implementation of the algorithm and present empirical data.
Mohan Penumala, Raveendra Babu Zinka, Jeelan Basha Shaik
et al.
Cooccurrence of Diabetes Mellitus and Alzheimer’s disease in elder people prompts scientists to develop multitarget agents that combat causes and symptoms of both diseases simultaneously. In line with this modern paradigm and as a follow-up to our previous studies, the present study is designed to investigate the crude methanolic extracts and subsequent CHCl3,n-BuOH, and H2O fractions ofAcalypha alnifolia,Pavetta indica,andOchna obtusatafor their inhibitory activities towards specific targets involved in AD and DM, namely, acetylcholinesterase, butyrylcholinesterase, andα-glucosidase (α-Glc). The methanolic extract and its derived chloroform fractions exhibited remarkable inhibitory capacities with IC50values being found at theμg/mL level. Further studies on most active chloroform fractions presented a prominent ability to scavenge DPPH and ABTS reactive species and highest neuroprotective effect against H2O2induced cell injury. Phytochemical analysis showed a large amount of phenolics, flavonoids, and terpenoids in active fractions. In conclusion,A. alnifolia,P. indica,andO. obtusatacould be promising sources for the treatment of AD and DM since these fractions induced significant anticholinesterase, antidiabetic, antioxidant, and neuroprotection effects attributable to phenolic, flavonoid, and terpenoid contents and encourage further studies for development of multifunctional therapeutic agent for AD and DM dual therapy.
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
We present a new open source implementation in the SageMath computer algebra system of algorithms for the numerical solution of linear ODEs with polynomial coefficients. Our code supports regular singular connection problems and provides rigorous error bounds.
Variations at the ITGAM gene, which encodes for the CD11b chain of the Mac-1 (alphaMbeta2; CD11b/CD18; complement receptor-3) integrin, is one of the strongest genetic risk factors for systemic lupus erythematosus (SLE). More specifically, a genetic variant (rs1143679) which results in an arginine to histidine substitution at position 77 in the extracellular portion of the integrin is associated with disease. It has recently been shown that this amino acid substitution results in a dysfunctional integrin, which is deficient in mediating cell adhesion to integrin ligands, phagocytosis and in addition cannot restrict inflammatory cytokine production in macrophages. In this review, we discuss immunological functions of the Mac-1 integrin and how defects in the genetic variant of Mac-1 may relate to SLE development.