THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the evolution of the analytic radius is the same as the heat equations.

Mitochondrial aberrations in systemic lupus erythematosus pathogenesis:Insights and therapeutic implications

Systemic lupus erythematosus(SLE),a chronic autoimmune disease,is marked by impaired immune tolerance and heightened activity in both innate and adaptive immune systems.Hallmarks of SLE include elevated type I interferons and autoantibody production,though the exact causes of SLE remain elusive despite advances in research techniques.Crucial to SLE research is understanding its pathogenesis and developing effective diagnostic and therapeutic methods.Recent studies have highlighted a significant link between mitochondrial abnormalities and SLE's development and progression.Mitochondrial dysfunction plays a key role in SLE pathogenesis through various mechanisms such as mitochondrial DNA mutations,oxidative stress,immune metabolic reprogramming,and cellular death.These factors collectively contribute to the loss of self-tolerance,increased autoantibody production,and impaired clearance of immune complexes,leading to their deposition.This triggers sustained inflammatory responses and damages multiple organs.This review focuses on the diagnostic and therapeutic approaches related to mitochondrial abnormalities in SLE.Targeting mitochondrial pathways presents a promising strategy for treating SLE,potentially improving prognosis and quality of life for those affected.Future research should further investigate the role of mitochondria in the onset and progression of SLE,providing new avenues for understanding and managing this complex disease.

SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL

In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.

Telitacicept as a novel treatment for refractory lupus nephritis complicated by podocytic infolding glomerulopathy

To the Editor,Lupus nephritis(LN),a renal symptom of systemic lupus erythematosus(SLE),frequently causes severe organ damage in SLE patients.1 There is no consensus on the definition of refractory LN,which has been suggested to occur when remission is not achieved after 3–12 months of combined glucocorticoids and immunosuppressive therapy.2 Podocytic infolding glomerulopathy(PIG),a rare type of glomerular morphological alteration,is primarily characterized by the presence of microspheres,microtubular structures,or a combination of the two,which are associated with podocyte infolding into the glomerular basement membrane(GBM).3,4 The exact pathogenesis of PIG remains unclear,but it may be associated with autoimmune diseases like SLE and Sjögren's syndrome.The occurrence of refractory LN complicated by PIG is rare and poses significant challenges in management.Here,we endeavor to provide the patient with benefits by employing a novel treatment,Telitacicept,which has demonstrated the potential to achieve complete renal remission in such cases.