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In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity: (−Δ)su=λu|x|2s+μuγ+fin Ω,u>0in Ω,u=0in (RN∖Ω). Here 00, γ>0, and Ω⊂RN (N>2s) is a bounded smooth domain such that 0∈Ω. Moreover, 0≤μ,f∈L1(Ω). For 0<λ≤ΛN,s, ΛN,s being the best constant in the fractional Hardy inequality, we find a necessary and sufficient condition for the existence of a positive weak solution to the problem with respect to the data μ and f. Also, for a regular datum of f, under suitable assumptions, we obtain some existence and uniqueness results and calculate the rate of growth of solutions. Moreover, we mention a nonexistence and a complete blowup result for the case λ>ΛN,s. Besides, we consider the parabolic equivalence of the above problem in the case μ≡1 and some suitable f(x,t), that is, ut+(−Δ)su=λu|x|2s+1uγ+f(x,t)in Ω×(0,T),u>0in Ω×(0,T),u=0in (RN∖Ω)×(0,T),u(x,0)=u0in RN, where u0∈X0s(Ω) satisfies an appropriate cone condition. In the case 0<γ≤1 or γ>1 with 2s(γ−1)<(γ+1), we show the existence of a unique solution for any 0<λ<ΛN,s and prove a stabilization result for certain range of λ.

Nomlabofusp is a recombinant, cell‐penetrating human frataxin (hFXN) fusion protein in development for the treatment of Friedreich's ataxia (FRDA). This study evaluated whether nomlabofusp‐derived hFXN concentrations covary across accessible peripheral matrices and FRDA‐relevant tissues, supporting the feasibility of surrogate tissue sampling to monitor drug‐derived hFXN exposure. Following subcutaneous administration in mice, rats, non‐human primates, and patients with FRDA, we quantified nomlabofusp‐derived hFXN and assessed cross‐tissue correlations across target tissues (brain, heart, skeletal muscle, dorsal root ganglia) and accessible peripheral matrices (skin, buccal cells, platelets). We observed significant and consistent cross‐tissue correlations, with concordant relationships among heart, skeletal muscle, dorsal root ganglia, skin, buccal cells, liver, and mitochondrial fractions, indicating coordinated distribution and/or retention of nomlabofusp‐derived hFXN across these matrices. Correlation patterns were maintained across species, supporting the robustness and translational relevance of the observed relationships. Collectively, these data support the use of peripheral tissues—particularly skin and buccal cells—for cross‐sectional and longitudinal monitoring of hFXN supplementation in FRDA. Study Highlights What is the current knowledge on the topic? Friedreich's ataxia (FRDA) is caused by frataxin (FXN) deficiency with prominent involvement of dorsal root ganglia, heart, and skeletal muscle, but repeated FXN measurement in these target tissues is invasive and impractical for longitudinal trials. Nomlabofusp is a subcutaneously administered recombinant human FXN (hFXN) fusion protein intended for mitochondrial delivery, and early clinical studies show dose‐dependent hFXN increases in accessible matrices (skin, buccal cells, platelets). However, key translational uncertainties persisted: whether peripheral tissues consistently mirror hFXN in FRDA target organs across species and clinical dosing schedules, and whether whole‐tissue measures capture mitochondrial delivery—both prerequisites for using surrogate tissues in longitudinal trials. What question did this study address? Do nomlabofusp‐derived hFXN concentrations in minimally invasive peripheral tissues (skin biopsy, buccal swab, platelets) correlate with hFXN in FRDA‐relevant tissues (brain, heart, skeletal muscle, dorsal root ganglia) across species and dosing regimens? What does this study add to our knowledge? Across mice, rats, non‐human primates, and FRDA patients, nomlabofusp produced increases in hFXN and showed significant, directionally consistent cross‐tissue associations linking peripheral matrices—especially skin and buccal epithelium—with FRDA‐relevant organs. Mouse whole‐liver and liver‐mitochondrial hFXN were strongly concordant (r = 0.88–1.00 early), supporting mitochondrial uptake and interpretability of whole‐tissue measurements. In patients, skin–buccal correlations were strongest with consistent daily dosing (Spearman r = 0.73 in Phase 2). How might this change clinical pharmacology or translational science? Skin and buccal epithelium are supported as practical surrogate tissues for monitoring hFXN and tissue exposure when target‐organ sampling is infeasible. This enables serial assessment to inform dose/regimen optimization and sampling windows while reducing participant burden and strengthening translational bridging for FXN supplementation strategies.

Textile wastewater containing toxic dyes needs efficient treatment before being released into the environment. Certain dyes are known or presumed to have carcinogenic potential for humans. In this work, hybrid electrochemical processes including electrocoagulation (EC) alone and combined with electro Fenton (EF), anodic oxidation (AO) and peroxi-coagulation (PC) were tested to treat real textile wastewater using a batch reactor. A sequential EC and EF (EC-EF) process was found to be more effective. The experimental results indicated that the effectiveness of the treatment decreases in the following order: EC-EF > EC-AO > EC-PC > EC. EC-EF results showed a decrease in chemical oxygen demand (COD, 97%), total organic carbon (98%), total suspended solids (98%), and the concentration of metal species; showing that the treatment of such wastewater type can be achieved by combined EC-EF process in a one-pot bench-scale reactor. The electrical energy consumption, the iron dissolution, and the biological oxygen demand/COD ratios of EC and EC-EF processes were evaluated. Characterization of the sludge generated during EC treatment at current density of 20 mA cm − 2 was carried out. Precipitation, adsorption, and electrochemical oxidation/reduction of organic dyes and metallic ions occurred during the treatment. This investigation shows the efficiency of combined EC-EF to treat textile wastewater.

In the present manuscript, we focus on a novel tri-nonlocal Kirchhoff problem, which involves the$ p(x) $ -fractional Laplacian equations of variable order. The problem is stated as follows: $ \\begin{eqnarray*} \\left\\{ \\begin{array}{ll} M\\Big(\\sigma_{p(x, y)}(u)\\Big)(-\\Delta)^{s(\\cdot)}_{p(\\cdot)}u(x) = \\lambda |u|^{q(x)-2}u\\left(\\int_{\\Omega}\\frac{1}{q(x)} |u|^{q(x)}dx \\right)^{k_1}+\\beta|u|^{r(x)-2}u\\left(\\int_{\\Omega}\\frac{1}{r(x)} |u|^{r(x)}dx \\right)^{k_2} \\quad \\mbox{in }\\Omega, \\\ \\ u = 0 \\quad \\mbox{on }\\partial\\Omega, \\end{array} \\right. \\end{eqnarray*} $ where the nonlocal term is defined as $ \\sigma_{p(x, y)}(u) = \\int_{\\Omega\\times \\Omega}\\frac{1}{p(x, y)}\\frac{|u(x)-u(y)|^{p(x, y)}}{|x-y|^{N+s(x, y)p(x, y)}} \\, dx\\, dy. $ Here,$ \\Omega\\subset\\mathbb{R}^{N} $represents a bounded smooth domain with at least$ N\\geq2 $ . The function$ M(s) $is given by$ M(s) = a - bs^\\gamma $ , where$ a\\geq 0 $ ,$ b > 0 $ , and$ \\gamma > 0 $ . The parameters$ k_1 $ ,$ k_2 $ ,$ \\lambda $and$ \\beta $are real parameters, while the variables$ p(x) $ ,$ s(\\cdot) $ ,$ q(x) $ , and$ r(x) $are continuous and can change with respect to$ x $ . To tackle this problem, we employ some new methods and variational approaches along with two specific methods, namely the Fountain theorem and the symmetric Mountain Pass theorem. By utilizing these techniques, we establish the existence and multiplicity of solutions for this problem separately in two distinct cases: when$ a > 0 $and when$ a = 0 $ . To the best of our knowledge, these results are the first contributions to research on the variable-order$ p(x) $ -fractional Laplacian operator.

In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.

Objective Current treatments for Friedreich's ataxia, a neurodegenerative disorder characterized by decreased intramitochondrial frataxin, do not address low frataxin concentrations. Nomlabofusp (previously CTI‐1601) is a frataxin replacement therapy with a unique mechanism of action that directly addresses this underlying frataxin deficiency. Phase 1 studies assessed the safety, pharmacokinetic, and pharmacodynamic profiles of subcutaneously administered nomlabofusp in adults with Friedreich's ataxia. Methods Patients were enrolled in two Phase 1, double‐blind, placebo‐controlled studies. The single ascending‐dose (SAD) study (NCT04176991) evaluated single doses of nomlabofusp (25, 50, 75, or 100 mg) or placebo. The multiple ascending‐dose (MAD) study (NCT04519567) evaluated nomlabofusp (25 mg daily for 4 days then every third day, 50 mg daily for 7 days then every 2 days, or 100 mg daily) or placebo for 13 days. Results Patients aged 19–69 years were enrolled (SAD, N = 28; MAD, N = 27). Nomlabofusp was generally well tolerated through 13 days. Most adverse events were mild and resolved quickly. No serious adverse events or deaths were reported. Peak nomlabofusp plasma concentrations occurred 15 min after subcutaneous administration. Nomlabofusp plasma exposures increased with increasing doses and daily administration and decreased with reduced dosing frequency. Increased frataxin concentrations were observed in buccal cells, skin, and platelets with higher and more frequent nomlabofusp administration. Interpretation Results from this study support a favorable safety profile for nomlabofusp. Subcutaneous nomlabofusp injections were quickly absorbed; higher doses and daily administration resulted in increased tissue frataxin concentrations. Future studies will evaluate longer‐term safety and possible efficacy of nomlabofusp.

To evaluate ocular comfort of lifitegrast ophthalmic solution 5.0% among patients with dry eye disease (DED) in the OPUS-3 trial. OPUS-3 was a multicenter, randomized, double-masked, placebo-controlled study. Adults with DED and recent artificial tear use were randomized 1:1 (lifitegrast:placebo) to ophthalmic drops twice daily for 84 days. On days 0 (baseline), 14, 42, and 84, drop comfort score (scale, 0-10; 0 = very comfortable, 10 = very uncomfortable) was measured at 0, 1, 2, and 3 minutes postinstillation. If the score was >3 at 3 minutes, assessment was repeated at 5, 10, and 15 minutes until score ≤3. Ocular treatment-emergent adverse events (TEAEs) were assessed. Overall, 711 participants were randomized (n=357 received lifitegrast; n=354 received placebo). Drop comfort scores for lifitegrast-treated participants improved within 3 minutes of instillation (mean scores on day 84 for both study and fellow eyes: instillation: lifitegrast, 3.4, placebo, 1.0; 3 minutes: lifitegrast, 1.5, placebo, 0.7). The majority (64%-66%) of participants had scores <3 within 3 minutes postinstillation on days 14, 42, and 84. In participants with scores >3 at 3 minutes, the mean score in the lifitegrast group was similar to or better than that in the placebo group at 5, 10, or 15 minutes postinstillation. Lifitegrast appeared to be well tolerated, with ocular TEAEs rarely leading to discontinuation. In OPUS-3, lifitegrast appeared to be well tolerated and drop comfort scores approached placebo levels by 3 minutes postinstillation.

This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional px-operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak solution. This is our first attempt to study this kind of system, in the case of variable-order fractional variable exponents. Our main theorem extends in several directions previous results.

Anemia associated with PNH is caused by hemolysis. The C5 inhibitor eculizumab blocks intravascular hemolysis, but anemia often persists owing to extravascular hemolysis. Pegcetacoplan, an inhibitor of C3, prevents extravascular hemolysis. After 16 weeks of treatment, hemoglobin increased nearly 4 g per deciliter in 41 patients treated with pegcetacoplan, and 85% no longer needed transfusion.