Noncommutative Versions of the Singer-Wermer Conjecture with Linear Left θ-derivations

The noncommutative Singer-Wermer conjecture states that every linear （possibly unbounded） derivation on a （possibly noncommutative） Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left θ-derivations.

ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE(α, β)-DERIVATIONS OR GENERALIZED(α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS

Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.

A lean-zinc anode battery based on metal-organic framework-derived carbon

Improving zinc metal(Zn^(0))reversibility and minimizing the N/P ratio are critical to boosting the energy density of Zn^(0) batteries.However,in reality,an excess Zn source is usually adopted to offset the irreversible zinc loss and guarantee sufficient zinc cycling,which sacrifices the energy density and leads to poor practicability of Zn^(0) batteries.To address the above conundrum,here,we report a lean-Zn and hierarchical anode based on metal-organic framework(MOF)-derived carbon,where trace Zn^(0) is pre-reserved within the anode structure to make up for any irreversible zinc source loss.This allows us to construct low N/P ratio Zn^(0) full cells when coupling the lean-Zn anode with Zn-containing cathodes.Impressively,high Zn^(0) reversibility(average Coulombic efficiency of 99.4% for 3000 cycles)and long full-cell lifetime(92% capacity retention after 900 cycles)were realized even under the harsh lean-Zn condition(N/P ratio:1.34).The excellent Zn reversibility is attributed to the hierarchy structure that homogenizes zinc ion flux and electric field distribution,as confirmed by theoretical simulations,which therefore stabilizes Zn^(0) evolution.The lean-Zn anode design strategy will provide new insights into construction of high-energy Zn^(0) batteries for practical applications.

LIE IDEALS, MORITA CONTEXT AND GENERALIZED (α, β)-DERIVATIONS

A classical problem in ring theory is to study conditions under which a ring is forced to become commutative. Stimulated from Jacobson＇s famous result, several tech- niques are developed to achieve this goal. In the present note, we use a pair of rings, which are the ingredients of a Morita context, and obtain that if one of the ring is prime with the generalized （α β）-derivations that satisfy certain conditions on the trace ideal of the ring, which by default is a Lie ideal, and the other ring is reduced, then the trace ideal of the reduced ring is contained in the center of the ring. As an outcome, in case of a semi-projective Morita context, the reduced ring becomes commutative.

LINEAR *-DERIVATIONS ON JB*-ALGEBRAS

It is shown that for a derivation on a JB* -algebra B, there exists a unique C-linear *-derivation D:B→B near the derivation.

A Perturbation of Jensen *-Derivations from K(H)into K(H)

Let＇s take H as an infinite-dimensional Hilbert space and K（H） be the set of all compact operators on H. Using Spectral theorem for compact self-adjoint operators, we prove the Hyers-Ulam stability of Jensen z-derivations from K（H） into K（H）.

The Commutativity of a *-Ring with Generalized Left *-α-Derivation

In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R in [1] are extended by using generalized left *-α-derivation. The commutativity of a *-ring with generalized left *-α-derivation is investigated and some results are given for generalized *-α-derivation.

Jordan Γ*-Derivation on Semiprime Γ-Ring M with Involution

Let M be a 2-torsion free semiprime G-ring with involution satisfying the condition that ( and ). In this paper, we will prove that if a non-zero Jordan G*-derivation d on M satisfies for all and , then .

Omni-functional simultaneous interfacial treatment for enhancing stability and outgassing suppression of lithium-ion batteries

Ni-rich layered oxides in lithium-ion batteries have problems with gas generation and electrochemical performance reduction due to residual lithium's reaction on the surface with the electrolyte.To address this issue,in this study,the Acid solvent evaporation(AsE)method has been proposed as a potential method to remove residual lithium while promoting the formation of a new LiNO_(3)-derived coating layer on the cathode surface.The reduction of residual lithium using the ASE method and the construction of a LiNO_(3)-derived coating layer suppresses gas evolution caused by the side effects of the electrolyte,improves electrochemical performance,and improves thermal stability by facilitating the smooth movement of lithium ions.Furthermore,the structural stability and resistance change due to the LiNO_(3)-derived coating layer effects is guaranteed through cycling and DCIR of the pouch cell.As a result,compared to Pristine,the capacity retention of coin cells increased by 8%after 100 cycles,and pouch cells increased by 25%after 160 cycles.In addition,after cycling the pouch cell,CO_(2) gas has significantly reduced by about 30%compared to Pristine using gas chromatography.The ASE method effectively forms a robust LiNO_(3)-derived coating layer on the cathode active material,which helps minimize electrolyte reactivity,suppress ,CO_(2) emissions,enhance surface structure stability,improve thermal stability,and improveoverallbatteryperformance.

THE(p,q)-ANALOG OF MULTIVALENT BAZILEVIC FUNCTIONS ASSOCIATED WITH A LIMACON

This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions.

Experimental Research on Ectopic Osteogenesis of BMP2-derived Peptide P24 Combined with PLGA Copolymers

To experimentally evaluate the ectopic osteogenetic capacity of synthesized BMP2-derived peptide P24 combined with poly lactic-co-glycolic acid （PLGA）, Wistar rats were divided into two groups： group A, in which BMP2-derived peptide P24/PLGA complex was implanted, and group B which received simple PLGA implant. The complex was respectively implanted into the back muscles of rats. Samples were taken the 1st, 4th, 8th, and the 12th week after the implantation. Their bone formation was detected by X-ray examination, and tissue response was histologically observed. Western blotting was used for the detection of the expression of collagen Ⅰ （Col- Ⅰ ） and osteopontin （OPN）. There was acute inflammation in the tissue around both types of implants at early stage. The cartilage was found around implant areas 4 weeks after the implantation of BMP2-derived peptide p24/PLGA complex, 8 weeks after the implantation, osteoblasts were found, and 12 weeks after the implantation, typical trabecular bone structure was observed. In group B, after 12 weeks, no osteoblasts were found. It is concluded that PLGA is an ideal scaffold material for bone tissue engineering. BMP2-derived peptide can start endochondral ossification and is more effective in inducing ectopic osteogenesis.

带有对合的素环的微分恒等式

Let R be a prime ring of characteristic different from two with the second involution∗andαan automorphism of R.An additive mapping F of R is called a generalized(α,α)-derivation on R if there exists an(α,α)-derivation d of R such that F(xy)=F(x)α(y)+α(x)d(y)holds for all x,y∈R.The paper deals with the study of some commutativity criteria for prime rings with involution.Precisely,we describe the structure of R admitting a generalized(α,α)-derivation F satisfying any one of the following properties:(i)F(xx∗)−α(xx∗)∈Z(R),(ii)F(xx∗)+α(xx∗)∈Z(R),(iii)F(x)F(x∗)−α(xx∗)∈Z(R),(iv)F(x)F(x∗)+α(xx∗)∈Z(R),(v)F(xx∗)−F(x)F(x∗)∈Z(R),(vi)F(xx∗)−F(x∗)F(x)=0 for all x∈R.Also,some examples are given to demonstrate that the restriction of the various results is not superfluous.In fact,our results unify and extend several well known theorems in literature.

Cannabidiol-Mediated Sequestration of Alzheimer’s Amyloid-β Peptides in ADDL Oligomers

Cannabidiol (CBD), one of the most studied phytocannabinoids, is non-psychotropic and can induce protective effects on the central nervous system against acute and chronic brain injury. Interestingly, CBD inhibits processes relating to amyloid beta (Aβ)-induced neurotoxicity in mouse models of Alzheimer’s disease, though the detailed molecular mechanism underlying the CBD neurotoxicity modulation is not fully understood. In this study, using atomic force microscopy, we find that CBD promotes the aggregation of Aβ peptides, enhancing the formation of Aβ oligomers, also known as Aβ-derived diffusible ligands (ADDLs). The CBD-mediated sequestration of Aβ monomers in soluble ADDLs could reduce neurotoxicity. This study highlights a possible role of CBD in modulating the formation of ADDL aggregates and provides insight into potentially neuroprotective properties of CBD in Alzheimer’s disease.

Transfer RNA-derived fragment tRF-23-Q99P9P9NDD promotes progression of gastric cancer by targeting ACADSB

Gastric cancer(GC)is one of the most common gastrointestinal tumors.As a newly discovered type of non-coding RNAs,transfer RNA(tRNA)-derived small RNAs(tsRNAs)play a dual biological role in cancer.Our previous studies have demonstrated the potential of tRF-23-Q99P9P9NDD as a diagnostic and prognostic biomarker for GC.In this work,we confirmed for the first time that tRF-23-Q99P9P9NDD can promote the proliferation,migration,and invasion of GC cells in vitro.The dual luciferase reporter gene assay confirmed that tRF-23-Q99P9P9NDD could bind to the 3'untranslated region(UTR)site of acyl-coenzyme A dehydrogenase short/branched chain(ACADSB).In addition,ACADSB could rescue the effect of tRF-23-Q99P9P9NDD on GC cells.Next,we used Gene Ontology(GO),the Kyoto Encyclopedia of Genes and Genomes(KEGG),and Gene Set Enrichment Analysis(GSEA)to find that downregulated ACADSB in GC may promote lipid accumulation by inhibiting fatty acid catabolism and ferroptosis.Finally,we verified the correlation between ACADSB and 12 ferroptosis genes at the transcriptional level,as well as the changes in reactive oxygen species(ROS)levels by flow cytometry.In summary,this study proposes that tRF-23-Q99P9P9NDD may affect GC lipid metabolism and ferroptosis by targeting ACADSB,thereby promoting GC progression.It provides a theoretical basis for the diagnostic and prognostic monitoring value of GC and opens upnew possibilities for treatment.

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.

Design and synthesis of novel cytotoxic podophyllotoxin derivatives

In order to investigate the effect of different C4 linkage moieties on the cytotoxicity of podophyllotoxin derivatives, novel 4-N- and 4-C-substituted 4＇-O-demethylepipodophyllotoxin derivatives were designed and synthesized. All the compounds were tested against A549 and MCF-7 tumor cells in vitro, and six compounds showed significant cytotoxicity. The most active compound 9f was superior to GL-331, and exhibited potent cytotoxicity with IC50 value at 10^-7 mol/L level.

The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

On Generalized （m, n）-Derivations and Generalized （m, n）-Jordan Derivations in Rings

The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.

Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales

This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).

On ε-Derivations and Local ε-Derivations

In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded algebras.