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In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the range of admissible pairs is improved. As an application, we show the global well-posedness of the semi-linear wave equation with inverse-square potential ... for power p being in some regime when the initial data are radial. This result extends the well-posedness result in Planchón, Stalker, and Tahvildar-Zadeh. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the restriction problem in harmonic analysis. Based on the spherical harmonics expansion and analyzing the asymptotic behavior of the Bessel function, we show that a modified linear adjoint restriction estimate holds for all Schwartz functions compactly supported on the cone, which generalizes Shao's result. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate a successful synthesis of highly ordered mesoporous carbons with large pores and tunable pore walls by using a home-designed ABC amphiphilic triblock copolymer poly(ethylene oxide)-block-poly(methyl methacrylate)-block-polystyrene (PEO-b-PMMA-b-PS) with gradient hydrophilicity as a template and resol as a carbon source via the solvent evaporation induced self-assembly (EISA) strategy. SAXS, TEM, HRSEM, and N2sorption characterizations show that the obtained carbon products possess ordered face-centered cubic (fcc) close-packed (Fm3̅m) mesostructure with large pores of about 20.0 nm. By simply adjusting the resol/template ratios, the wall thickness of products can easily be tuned in the range of 10−19 nm. For the first time, we observed numerous large micro/mesopores in the carbon pore walls, originating from the removal of PMMA segment during the pyrolysis. The obtained mesoporous carbons have an extra-large lattice constant of up to 55.0 nm, high surface areas of ∼ 900 m2/g, and pore volume of ∼ 0.6 cm3/g, as well as high stability even in concentrated KOH solution. The gradient hydrophilicity of the ABC triblock copolymer template facilitates the continuous invasion of resol precursor molecules along the PEO to PMMA segments of the spherical PEO-PMMA-PS micelles, tuning the pore wall thickness. The rationally designed ABC-type triblock copolymers make it possible to synthesize ordered mesoporous carbons with ultrathick pore walls as well as excellent chemical and thermal stability. [ABSTRACT FROM AUTHOR]

The aquation and subsequent reactions of the dinuclear Pt antitumor complexes [{ trans-PtCl(NH3)2}2(μ-NH2(CH2)6NH2)]2+ (1,1/t,t) and [{ cis-PtCl(NH3)2}2(μ-NH2(CH2)6NH2)]2+ (1,1/c,c) in 15 mM perchlorate, acetate or phosphate solutions were followed at 298 K by [1H,15N] HSQC 2D NMR spectroscopy. Rate and equilibrium constants for the initial reversible aquation and the subsequent reversible reaction with phosphate or acetate are reported. The rate constant for the first aquation step is two-fold lower for 1,1/c,c than 1,1/t,t but the anation rate constants are similar so that the equilibrium lies further towards the chloro form for the 1,1/c,c compound. A p K a value of 6.01±0.03 was determined for the diaquated species [{ cis-Pt(NH3)2(H2O)}2(μ-NH2(CH2)6NH2)]4+ (1,1/c,c- 3) which is 0.4 units higher than that of the 1,1/t,t compound. The rate constants for the binding of acetate and phosphate to 1,1/t,t are similar, but the rate constant for the reverse reaction is close to ten-fold higher in the case of phosphate so that equilibrium conditions are attained more rapidly (12 h compared with 64 h). On the other hand, for 1,1/c,c the rate constants for the forward and reverse reactions with acetate and phosphate are quite similar so that equilibrium conditions are reached very slowly (80–100 h) and a greater proportion of phosphate-bound species are present. The reduced lability of the bound phosphate for 1,1/c,c is attributed to the formation of a macrochelate phosphate-bridged species which was characterized by 31P NMR and ESI-MS. The speciation profiles of 1,1/t,t and 1,1/c,c under physiological conditions are explored. [ABSTRACT FROM AUTHOR]

Spatial light modulators are widely used in various fields such as light field control and beam shaping. It is necessary to calibrate the modulation curve of phase spatial light modulator (SLM) accurately so as to load the pattern correctly. Different from the calibration methods with interference fringes, a group of dynamic petal-like spots with different rotation angles can also be applied to calibrate the modulation curve. The number of petals is generated by a pair of conjugated vortex beams and increases as the increase of vortex topological charge. The calibration accuracy was then greatly improved by weighted algorithm based on the multiple rotated petals. The effectiveness of the proposed SLM calibration method was verified in experiments by four dynamic petals. Compared with the traditional fringe pattern calibration, this method has merit of simple structure, convenient operation and high precision. [ABSTRACT FROM AUTHOR]

To systematically evaluate the differences in therapeutic response to chemotherapy or immunotherapy between different molecular subtypes of bladder cancer (BC). A comprehensive literature search was performed up to December 2021. Consensus clusters 1 (CC1), CC2 and CC3 molecular subtypes were used to perform meta-analysis. Pooled odds ratios (ORs) with 95% confidence intervals (CIs) were used to assess the therapeutic response by fix-effect modeling. Eight studies involving 1,463 patients were included. For immunotherapy, CC3 showed the highest response rate (CC1 vs. CC3: OR=0.52, 95% CI=0.34-0.78, p=0.002; CC2 vs. CC3: OR=0.42, 95% CI=0.28-0.62, p<0.001), which was mainly reflected in the highest response rate to atezolizumab (CC1 vs. CC3: OR=0.47, 95% CI=0.29-0.75, p=0.002; CC2 vs. CC3: OR=0.38, 95% CI=0.24-0.59, p<0.001). For chemotherapy, CC3 had the lowest response rate to the overall chemotherapy (CC1 vs. CC3: OR=2.05, 95% CI=1.23-3.41, p=0.006; CC2 vs. CC3: OR=2.48, 95% CI=1.50-4.10, p<0.001). Compared with CC2, CC3 responded poorly to both neo-adjuvant chemotherapy (NAC) (OR=1.93, 95% CI=1.09-3.41, p=0.020) and chemoradiation therapy (CRT) (OR=6.07, 95% CI=1.87-19.71, p<0.001). Compared with CC1, CC3 only showed a poorer response to CRT (OR=4.53, 95% CI=1.26-16.27, p=0.020), and no difference in NAC. Our study suggested that molecular classifications are important predictors of cancer treatment outcomes of BC patients and could identify subgroup patients who are most likely to benefit from specific cancer treatments. [ABSTRACT FROM AUTHOR]

Three 15N-labelled trans-Pt(II) amine complexes with isopropylamine (15N-ipa), methylamine (15N-ma) and dimethylamine (15N-dma) have been prepared and characterized. 2D [1H,15N] HSQC NMR spectroscopy was used to obtain the rate and equilibrium constants for the aquation of trans-[PtCl2 (15N-ipa)(15N-ma)] (15N-1), trans-[PtCl2(15N-dma)(15N-ma)] (15N-2) and trans-[PtCl2(15N-dma)(15N-ipa)] (15N-3) in 100 mM NaClO4 solutions at 298 K. New 15N shift ranges for H2N-PtII-N and HN-PtII-N groups are reported. Formation of the diaqua complex was not observed for 3 and accounted for <2% of the species at equilibrium for 1 and 2. The first aquation step is significantly faster for 2 (k1 = 14 × 10-5 s-1) than for the two complexes with the bulkier ipa ligand (k1 = 5.5 × 10-5s-1(1), 6.1 × 10-5s-1(3)), but 2 is the least aquated of the three complexes at equilibrium. The pKa values for the monoaqua adducts of 1-3 are similar (5.98, 5.85 and 5.91, respectively) and 0.4 pH units lower than the related cis complex cis-[PtCl2(dma)2], indicating a smaller proportion of more reactive aqua species will exist at physiological pH. The pKa values for the diaqua adduct of 2 (4.59 and 7.98) are 0.3-0.6 pH units higher than those of 1 (4.31 and 7.30) and 3 (4.28 and 7.29), which have very similar values. The speciation profiles of 1-3, calculated on the basis of the calculated equilibrium and dissociation constants, indicate that <1% hydrolyzed species will exist under physiological conditions in cancer cells. The cytotoxicity of 1-3 (non-15N-labelled) was assessed in three cancer lines (SF268, MCF-7 and NCI-H460). The new trans-Pt(II) diamine complex 2 is more active than 1 and 3 in all cases and is more potent than cisplatin in the MCF-7 adenocarcinoma cell line. [ABSTRACT FROM AUTHOR]

Three 15N-labelled trans-Pt(ii) amine complexes with isopropylamine (15N-ipa), methylamine (15N-ma) and dimethylamine (15N-dma) have been prepared and characterized. 2D [1H,15N] HSQC NMR spectroscopy was used to obtain the rate and equilibrium constants for the aquation of trans-[PtCl2(15N-ipa)(15N-ma)] (15N-1), trans-[PtCl2(15N-dma)(15N-ma)] (15N-2) and trans-[PtCl2(15N-dma)(15N-ipa)] (15N-3) in 100 mM NaClO4solutions at 298 K. New 15N shift ranges for H2N–PtII–N and HN–PtII–N groups are reported. Formation of the diaqua complex was not observed for 3and accounted for <2% of the species at equilibrium for 1and 2. The first aquation step is significantly faster for 2(k1= 14 × 10−5s−1) than for the two complexes with the bulkier ipa ligand (k1= 5.5 × 10−5s−1(1), 6.1 × 10−5s−1(3)), but 2is the least aquated of the three complexes at equilibrium. The pKavalues for the monoaqua adducts of 1–3are similar (5.98, 5.85 and 5.91, respectively) and 0.4 pH units lower than the related ciscomplex cis-[PtCl2(dma)2], indicating a smaller proportion of more reactive aqua species will exist at physiological pH. The pKavalues for the diaqua adduct of 2(4.59 and 7.98) are 0.3–0.6 pH units higher than those of 1(4.31 and 7.30) and 3(4.28 and 7.29), which have very similar values. The speciation profiles of 1–3, calculated on the basis of the calculated equilibrium and dissociation constants, indicate that <1% hydrolyzed species will exist under physiological conditions in cancer cells. The cytotoxicity of 1–3(non-15N-labelled) was assessed in three cancer lines (SF268, MCF-7 and NCI-H460). The new trans-Pt(ii) diamine complex 2is more active than 1and 3in all cases and is more potent than cisplatin in the MCF-7 adenocarcinoma cell line. [ABSTRACT FROM AUTHOR]

Background: The platelet-to-lymphocyte ratio (PLR) and C-reactive protein (CRP) level are markers that have been reported to predict the histological type of various tumors, and here, we evaluated their utility in predicting colorectal polyp histological types.Methods: We retrospectively reviewed 172 patients with colorectal polyps who underwent endoscopic polypectomy. The associations between histological type and clinicopathologic parameters were assessed by multivariate analysis.Results: The optimal PLR and CRP cut-off values were 113.32 and 0.39, respectively. The PLR (P = 0.002) and CRP (P = 0.009) values were associated with the histological type according to the univariate analysis, whereas low PLR (P ≤ 0.001) and CRP (P = 0.017) values were independent risk factors in the multivariate analysis together with maximum tumor diameter (P ≤ 0.001) and tumor number (P = 0.0014).Conclusions: Preoperative PLR and CRP are correlated with the colorectal polyp histological type. [ABSTRACT FROM AUTHOR]

We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form (\Delta \lambda 2)u = N[u], where \Delta = \sum j \partial 2 j is the Laplacian on Rn, \lambda is a positive real number, and N[u] is a nonlinear operator depending polynomially on u and its derivatives of order up to order two. Nonlinear Helmholtz eigenfunctions with N[u] = \pm | u| p 1u were first considered by Guti\'errez [Math. Ann., 328 (2004), pp. 1--25]. We show that for suitable nonlinearities and for every f \in Hk+4(Sn 1) of sufficiently small norm, there is a nonlinear Helmholtz function taking the form u(r, \omega ) = r (n 1)/2(e i\lambda rf(\omega )+e+i\lambda rb(\omega )+O(r \epsilon )), as r \rightarrow \infty, \epsilon > 0, for some b \in Hk(Sn 1). Moreover, we prove the result in the general setting of asymptotically conic manifolds. The proof uses an elaboration of anisotropic Sobolev spaces defined by Vasy [A minicourse on microlocal analysis for wave propagation, in Asymptotic Analysis in General Relativity, London Math. Soc. Lecture Note Ser. 443, Cambridge University Press, Cambridge, 2018, pp. 219--374], between which the Helmholtz operator \Delta \lambda 2 acts invertibly. These spaces have a variable spatial weight \sansl \pm, varying in phase space and distinguishing between the two ``radial sets"" corresponding to incoming oscillations, e i\lambda r, and outgoing oscillations, e+i\lambda r. Our spaces have, in addition, module regularity with respect to two different ``test modules"" and have algebra (or pointwise multiplication) properties that allow us to treat nonlinearities N[u] of the form specified above. [ABSTRACT FROM AUTHOR]

On-surface synthesis has gradually become a prevalent approach to constructing two-dimensional functional monolayers on various substrates. In the present work, the synthesis of self-assembled monolayers (SAMs) of benzothiazole derivatives was conducted at the liquid/solid interface for the first time. Two kinds of nanostructures were achieved on the highly oriented pyrolytic graphite (HOPG) surface via the condensation reaction between aromatic aldehyde derivatives and 2-aminothiophenol (ATP). The formation of thiazole-based self-assemblies was revealed by scanning tunneling microscopy (STM) and further confirmed by X-ray photoelectron spectroscopy (XPS). The successful synthesis of the benzothiazole derivatives not only extends the scope of on-surface reactions but also can be applied in designing multifunctional SAMs at the interface. [ABSTRACT FROM AUTHOR]

Three new (R)-BINOL complexes havebeen prepared. 2D self-assemblyhas been observed in the system consisting of crystalline (R)-BINOLderivatives (guest) and 1,3,5-tris(10-carboxydecyloxy)-benzene (host)by means of the scanning tunneling microscopy (STM) technique. Densityfunctional theory (DFT) calculations help to reveal the assembly onthe HOPG surface. [ABSTRACT FROM AUTHOR]

The stability of high-speed spindle system affects the surface finish and tool life directly, which is an important factor to evaluate its performance. Meanwhile, the spindle dynamics and cutting stability are affected by the structure and dynamics of spindle-holder-tool joints significantly. The joints are simplified as the distribution-spring, and the FEM modeling process of spindle system is proposed based on the thought of parallel rotor system. Taking a vertical machining center as example, the effectiveness of the modeling method is verified. Starting from the stability evaluation criteria and different ways of getting FRF, the influence factors of unconditional and conditional stability regions are analyzed. Based on the proposed model, the influence laws of cutting stability on cutting force amplitude and speed are characterized by the three-dimensional lobes, limit cutting depths and lobe intersections, which provide the theoretical basis for optimizing the processing and improving the cutting stability. [ABSTRACT FROM AUTHOR]

When predicting the nonlinear stability of high-speed spindle system, it is necessary to create an accurate model that reflects the dynamic characteristics of the whole system, including the spindle-bearing joint and spindle-holder-tool joints. In this paper, the distribution spring model of spindle-holder-tool joints was built with the consideration of its dynamic characteristics; the five-DOF dynamic model of the angle contact ball bearing was also established to study the influence of speed and preload on the spindle-bearing joint, both of which were used in the general whole complete spindle system FEM model. The rationality of the model was verified by comparison with the FRF of traditional rigid model and experiments. At last, the influences of speed and cutting force on the nonlinear stability were analyzed by amplitude spectrum, bifurcation, and Poincaré mapping. The results provided a theoretical basis and an evaluating criterion for nonlinear stability prediction and product surface quality improvement. [ABSTRACT FROM AUTHOR]