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This paper is devoted to studying the weighted boundedness and compactness of commutators of Marcinkiewicz integral related to Schrödinger operators. We show that the commutators of Marcinkiewicz integral related to Schrödinger operators with pointwise multiplication with functions in BMO (σ) space are weighted L p (p > 1) bounded and with functions in CMO (σ) space are compact operators when acting on weighted Lebesgue spaces. As a byproduct, the weighted compactness of commutators of maximal operator associated with Schrödinger operators is given. Here BMO (σ) is a function space which is larger than the classical BMO space and CMO (σ) denotes the closure of C c ∞ (R d) in the BMO (σ) topology. [ABSTRACT FROM AUTHOR]

Hydrogen molecule (H2) exhibits broad-spectrum but microenvironment-dependent biomedical effects in varied oxidation stress-related diseases, but its molecular mechanism is unclear and its targeting molecule is unknown so far. Herein, we originally reveal that Fe-porphyrin is a H2-targeted molecule. We have demonstrated that the oxidized Fe-porphyrin in both free and protein-confining states can self-catalyze the hydrogenation/reduction by reacting with H2 to catalytically scavenge ·OH, and can also catalytically hydrogenate to reduce CO2 into CO in the hypoxic microenvironment of in vitro simulation and in vivo tumor, confirming that Fe-porphyrin is a redox-related biosensor of H2 and H2 is an upstream signaling molecule of CO. These discoveries are favorable for deep understanding and exploration of profound biomedical effects of H2, and helpful for development of innovative drugs and hydrogen energy/agricultural materials. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the parabolic off-diagonal Muckenhoupt Ap,q+ weights. We reveal the properties of these weights, and our main results characterize them through weak-type and strong-type weighted norm inequalities for the fractional forward-in-time maximal operator. Moreover, our results cover some well-known results. [ABSTRACT FROM AUTHOR]

Let L = - Δ + V be a Schrödinger operator with the potential V belonging to the reverse Hölder class B q , q > n / 2 . Denote by CMO θ (ρ) the vanishing mean oscillation type space associated with L. By the aid of the regularity estimates of the fractional heat kernel related with L, we investigate the weighted boundedness and compactness of the commutators of operators generated by fractional heat semigroups related to L and functions belonging to CMO θ (ρ) . [ABSTRACT FROM AUTHOR]

High-glucose microenvironment in the diabetic foot ulcer (DFU) causes excessive glycation and induces chronic inflammation, leading to the difficulty of DFU healing. Hydrogen-rich water bath can promote the healing of DFU in clinic by virtue of the anti-inflammatory effect of hydrogen molecules, but the long-term daily soaking counts against the formation of a scab and cannot change the high-glucose microenvironment, limiting the outcome of DFU therapy. In this work, photocatalytic therapy of diabetic wound is proposed for sustainable hydrogen generation and local glucose depletion by utilizing glucose in the high-glucose microenvironment as a sacrificial agent. Hydrogen-incorporated titanium oxide nanorods are developed to realize efficient visible light (VIS)-responsive photocatalysis for glucose depletion and hydrogen generation, achieving a high efficacy of diabetic wound healing. Mechanistically, local glucose depletion and hydrogen generation jointly attenuate the apoptosis of skin cells and promote their proliferation and migration by inhibiting the synthesis of advanced glycation end products and the expression of their receptors, respectively. The proposed VIS-photocatalytic strategy provides a solution for facile, safe and efficient treatment of DFU. Hydrogenation is a treatment for chronic inflammation caused by high glucose levels in diabetic ulcers, However, current therapies have limitations. Here, the authors report on the creation of a visible light photocatalytic agent which depletes glucose in the wound and generates hydrogen to aid in diabetic wound healing. [ABSTRACT FROM AUTHOR]

Purpose: Strongyloidiasis is mainly prevalent in developing countries with poor economic and sanitary conditions. The clinical manifestations of Strongyloides stercoralis infection are complex and diverse, lacking specificity, which can easily lead to misdiagnosis and delayed treatment. Methods: An elderly male patient, repeated cough and expectoration for 4 years, with exacerbation and dyspnea for 10 days, was admitted to hospital. Sputum culture and smear were taken for examination. Nematode larvae were found under the microscope. Nematodes were also found in feces. Results: Upon confirmation, the patient was diagnosed with a pulmonary infection caused by Strongyloides stercoralis. After treatment with albendazole, the symptoms improved, and the patient was discharged. Conclusion: In this case report, combination of microscopic examination of sputum and alveolar lavage fluid and CT scan were used to quickly identify the cause of the patient, it provides a diagnostic basis and method for clinical treatment. [ABSTRACT FROM AUTHOR]

Let E ⊂ R be a closed set, which has nonzero Hausdorff dimension and some other properties. For some t > 0 , we proved the three- point patterns x , x + t , x + γ (t) belong to E, where γ (t) is a convex curve with some curvature constraints. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the weighted boundedness for the local multi(sub)linear Hardy–Littlewood maximal operators and local multilinear fractional integral operators associated with the local Muckenhoupt weights on Gaussian measure spaces. We deal with these problems by introducing a new pointwise equivalent "radial" definitions of these local operators. Moreover, using a similar approach, we also get the weighted boundedness for the local fractional maximal operators with rough kernel and local fractional integral operators with rough kernel on Gaussian measure spaces. [ABSTRACT FROM AUTHOR]

We prove a plethora of the boundedness property of Adams type for bilinear fractional integral operators of the form B α (f , g) (x) = ∫ R n f (x - y) g (x + y) | y | n - α d y , 0 < α < n. For 1 < t ≤ s < ∞ , we prove the non-weighted case through the known Adams type result. And we show that these results of Adams type is optimal. For 0 < t ≤ s < ∞ and 0 < t ≤ 1 , we obtain new result of a weighted theory describing Morrey boundedness of above form operators if two weights (v , w →) satisfy [ v , w → ] t , q → / a r , a s = sup Q , Q ′ ∈ D Q ⊂ Q ′ | Q | | Q ′ | 1 - s as | Q ′ | 1 r ⨍ Q v t 1 - t 1 - t t ∏ i = 1 2 ⨍ Q ′ w i - (q i / a) ′ 1 (q i / a) ′ < ∞ , 0 < t < s < 1 and [ v , w → ] t , q → / a r , a s : = sup Q , Q ′ ∈ D Q ⊂ Q ′ | Q | | Q ′ | 1 - a s as | Q ′ | 1 r ⨍ Q v t 1 - t 1 - t t ∏ i = 1 2 ⨍ Q ′ w i - (q i / a) ′ 1 (q i / a) ′ < ∞ , s ≥ 1 where ‖ v ‖ L ∞ (Q) = sup Q v when t = 1 , a, r, s, t and q → satisfy proper conditions. As some applications we formulate a bilinear version of the Olsen inequality, the Fefferman–Stein type dual inequality and the Stein–Weiss inequality on Morrey spaces for fractional integrals. [ABSTRACT FROM AUTHOR]

In this paper, we derive an incompressible Oldroyd-B model with hybrid dissipation and partial damping on stress tensor τ via the velocity equations and the generalized constitutive law so that global well-posedness of the model is established in the Sobolev space framework. Precisely speaking, the proof is based on the curl-div free property of τ - ∇ 1 Δ P div τ - (∇ 1 Δ P div τ) T , the low frequency dissipation and high frequency damping of τ and the dissipation of u. [ABSTRACT FROM AUTHOR]

Drug therapy unavoidably brings toxic side effects and drug content-limited therapeutic efficacy although many nanocarriers have been developed to improve them to a certain extent. In this work, a concept of drug-free therapeutics is proposed and defined as a therapeutic methodology without the use of traditional toxic drugs, without the consumption of therapeutic agents during treatment but with the inexhaustible therapeutic capability to maximize the benefit of treatment, and a Z-scheme SnS1.68-WO2.41 nanocatalyst is developed to achieve near infrared (NIR)-photocatalytic generation of oxidative holes and hydrogen molecules for realizing combined hole/hydrogen therapy by the drug-free therapeutic strategy. Without the need of any drug and other therapeutic agent assistance, the nanocatalyst oxidizes/consumes intratumoral over-expressed glutathione (GSH) by holes and simultaneously generates hydrogen molecules in a lasting and controllable way under NIR irradiation. Mechanistically, generated hydrogen molecules and GSH consumption inhibit cancer cell energy and destroy intratumoral redox balance, respectively, to synergistically damage DNA and induce tumor cell apoptosis. High efficacy and biosafety of combined hole/hydrogen therapy of tumors are achieved by the nanocatalyst. The proposed catalysis-based drug-free therapeutic strategy breaks a pathway to realize high efficacy and low toxicity of cancer treatment. Nanoparticles have been used to reduce the toxicity associated with chemotherapeutic agents. Here, the authors report a Z-scheme SnS1.68-WO2.41 nanocatalyst for photocatalytic generation of oxidative holes and hydrogen molecules for drug-free therapeutic strategy. [ABSTRACT FROM AUTHOR]

We will prove that for 1 < p < ∞ and 0 < λ < n, the central Morrey norm of the truncated centered Hardy-Littlewood maximal operator Mγc equals that of the centered Hardy-Littlewood maximal operator for all 0 < γ < +∞. When p = 1 and 0 < λ < n, it turns out that the weak central Morrey norm of the truncated centered Hardy-Littlewood maximal operator Mγc equals that of the centered Hardy-Littlewood maximal operator for all 0 < γ < +∞. Moreover, the same results are true for the truncated uncentered Hardy-Littlewood maximal operator. Our work extends the previous results of Lebesgue spaces to Morrey spaces. [ABSTRACT FROM AUTHOR]

We investigate a class of fractional Hardy type operators Hβ1,β2,...,βm defined on higher-dimensional product spaces ℝn1×ℝn2×⋯×ℝnm and use novel methods to obtain their sharp bounds. In particular, we optimize the result due to S. M. Wang, S. Z. Lu, and D. Y. Yan [Sci. China Math., 2012, 55(12): 2469-2480]. [ABSTRACT FROM AUTHOR]

Regular spherical mesoporous bioactive glass microspheres (MBG-MSs) with tunable SiO-CaO-PO composition and adjustable mesoporous structure have been synthesized by a new approach of emulsification and solvent evaporation-induced self-assembly. Less ordered mesostructure and enhanced bioactivity resulting from the addition of CaO are investigated through scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, and X-ray diffraction characterizations. The MBG-MSs have high storage capacities and sustained release patterns of anti-osteoporosis (alendronate sodium, NaAL) drugs which are hardly absorbed via oral administration. Furthermore, to some extent the dosage and release rate could also be controlled by CaO content. Cell viability and proliferation assay with rabbit bone marrow stromal cells indicates a positive effect of the CaO/PO components on improving the cell growth cumulatively in about 2 weeks. [ABSTRACT FROM AUTHOR]

By delivering the concept of clean hydrogen energy and green catalysis to the biomedical field, engineering of hydrogen-generating nanomaterials for treatment of major diseases holds great promise. Leveraging virtue of versatile abilities of Pd hydride nanomaterials in high/stable hydrogen storage, self-catalytic hydrogenation, near-infrared (NIR) light absorption and photothermal conversion, here we utilize the cubic PdH0.2 nanocrystals for tumour-targeted and photoacoustic imaging (PAI)-guided hydrogenothermal therapy of cancer. The synthesized PdH0.2 nanocrystals have exhibited high intratumoural accumulation capability, clear NIR-controlled hydrogen release behaviours, NIR-enhanced self-catalysis bio-reductivity, high NIR-photothermal effect and PAI performance. With these unique properties of PdH0.2 nanocrystals, synergetic hydrogenothermal therapy with limited systematic toxicity has been achieved by tumour-targeted delivery and PAI-guided NIR-controlled release of bio-reductive hydrogen as well as generation of heat. This hydrogenothermal approach has presented a cancer-selective strategy for synergistic cancer treatment. The tracking and targeted release of multi-agents to cooperatively treat cancer is a developing and evolving field. Here, the authors demonstrate the anticancer effects of cubic Pd hydride nanocrystals with photoacoustic imaging properties that can release hydrogen under an NIR trigger and have photothermal effects. [ABSTRACT FROM AUTHOR]