Characterizations of ( m,n )-Jordan Derivations and ( m,n )-Jordan Derivable Mappings on Some Algebras

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A~2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters.     

Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

Measurement of integrated luminosities at BESIII for data samples at center-of-mass energies between 4.0 and 4.6 GeV

The integrated luminosities of data samples collected in the BESIII experiment in 2016–2017 at center-of-mass energies between 4.19 and 4.28 GeV are measured with a precision better than 1% by analyzing large-angle Bhabha scattering events. The integrated luminosities of old datasets collected in 2010–2014 are updated by considering corrections related to detector performance, offsetting the effect of newly discovered readout errors in the electromagnetic calorimeter, which can haphazardly occur.     

Tuning the properties of a black TiO2-Ag visible light photocatalyst produced by a rapid one-pot chemical reduction

A highly efficient black TiO₂-Ag photocatalytic nanocomposite, active under both UV and visible light illumination, was synthesized by decorating the surface of 25 nm TiO₂ particles with Ag nanoparticles. The material was obtained via a rapid, one-pot, simple (surfactant and complexing agent free) chemical reduction method using silver nitrate and formaldehyde as a metal salt and reducing agent, respectively. The nanocomposite shows an increase of over 800% in the rate of photocatalytic methylene blue dye degradation, compared to commercial unmodified TiO_2, under UV-VIS illumination. Unlike pure TiO₂, the nanocomposite exhibits visible light activation, with a corresponding drop in optical reflectance from 100% to less than 10%. The photocatalytic properties were shown to be strongly enhanced by post-reduction annealing heat treatments in air, which were observed to decrease, rather than coarsen, silver particle size, and increase particle distribution. This, accompanied by a variation in the silver surface oxidation states, appear to dramatically affect the photocatalytic efficiency under both UV and visible light. This highly active photocatalyst could have wide ranging applications in water and air pollution remediation and solar fuel production.     

Computational analysis for the determination of deleterious nsSNPs in human MTHFD1 gene

Single nucleotide polymorphisms (SNPs) are the most common genetic polymorphisms and play a major role in many inherited diseases. Methylenetetrahydrofolate dehydrogenase 1 (MTHFD1) is one of the enzymes involved in folate metabolism. In the present study, the functional and structural consequences of nsSNPs of human MTHFD1 gene was analyzed using various computational tools like SIFT, PolyPhen2, PANTHER, PROVEAN, SNAP2, nsSNPAnalyzer, PhD-SNP, SNPs&GO, I-Mutant, MuPro, ConSurf, InterPro, NCBI Conserved Domain Search tool, ModPred, SPARKS-X, RAMPAGE, FT Site and PyMol. Out of 327 nsSNPs form human MTHFD1 gene, total 45 SNPs were predicted as functionally most significant SNPs, among which 17 were highly conserved and functional, 17 were highly conserved and structural residues. Among 45 most significant SNPs, 15 were predicted to be involved in post translational modifications. The p.Gly165Arg may interfere in homodimer interface formation. The p.Asn439Lys and p.Asp445Asn may interfere in binding interactions of MTHFD1 protein with cesium cation and potassium. The two SNPs (p.Asp562Gly and p.Gly637Cys) might interfere in interactions of MTHFD1 with ligand.     

Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

局部上循环的3-Hom李双代数和3-李经典Hom-杨巴克斯方程

本文介绍了局部上循环的3-Hom李双代数,它的乘法和余乘两种运算的相容条件由局部上循环条件给出.作者研究了扭的3元版本的杨巴克斯方程,称为3-李Hom-杨巴克斯方程,它是文献[1]中3- 李杨巴克斯方程的一种广义化.文章证明由3-李Hom-杨巴克斯方程的解所诱导的双代数,可得到上边缘的局部上循环的3-Hom 李双代数.     

代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.