A class of bounded pseudo-differential operators

Pseudo-differential operators of order -M and type ρ, δ₁, δ₂ are shown to be bounded in L² provided that 0 ≤ ρ ≤ δ₁ < 1, 0 ≤ ρ ≤ δ₂ < 1, and [Formula: see text].     

Existence of nonarithmetic monodromy groups

In an 1885 paper, E. Picard defined a subgroup Τ(Λ) of PU(2,1) generated by monodromies and depending on parameters Λ = (λ₁,λ₂,λ₃,λ₄), 0 < λ_i < 1, < λ_i < 3, λ_i + λ_j ≥ 1, 1 ≤ i < j ≤ 4. The family Τ(Λ) resembles the family of groups Τ([unk]) defined in 1978 but is a different family. In common with the groups Τ([unk]), (i) Τ(Λ) is discrete for a finite number of Λ, (ii) Τ(Λ) is a nonarithmetic lattice for some Λ, and (iii) for all Λ [unk]⁴, there is a compact complex surface S(Λ) with π₁ [S(Λ)] of finite index in Τ(Λ).     

Study on Concrete Deterioration in Different NaCl-Na2SO4 Solutions and the Mechanism of Cl− Diffusion

The diffusion of sulfate (SO₄²⁻) and chloride (Cl⁻) ions from rivers, salt lakes and saline soil into reinforced concrete is one of the main factors that contributes to the corrosion of steel reinforcing bars, thus reducing their mechanical properties. This work experimentally investigated the corrosion process involving various concentrations of NaCl-Na₂SO₄ leading to the coupled erosion of concrete. The appearance, weight, and mechanical properties of the concrete were measured throughout the erosion process, and the Cl⁻ and SO₄²⁻ contents in concrete were determined using Cl⁻ rapid testing and spectrophotometry, respectively. Scanning electron microscopy, energy spectrometry, X-ray diffractometry, and mercury porosimetry were also employed to analyze microstructural changes and complex mineral combinations in these samples. The results showed that with higher Na₂SO₄ concentration and longer exposure time, the mass, compressive strength, and relative dynamic elastic modulus gradually increased and large pores gradually transitioned to medium and small pores. When the Na₂SO₄ mass fraction in the salt solution was ≥10 wt%, there was a downward trend in the mechanical properties after exposure for a certain period of time. The Cl⁻ diffusion rate was thus related to Na₂SO₄ concentration. When the Na₂SO₄ mass fraction in solution was ≤5 wt% and exposure time short, SO₄²⁻ and cement hydration/corrosion products hindered Cl⁻ migration. In a concentrated Na₂SO₄ environment (≥10 wt%), the Cl⁻ diffusion rate was accelerated in the later stages of exposure. These experiments further revealed that the Cl⁻ migration rate was higher than that of SO₄²⁻.     

Potassium secretion in rat distal colon during dietary potassium loading: role of pH regulated apical potassium channels

Background—Chronicdietary K⁺ loading increases the abundance of largeconductance (210 pS) apical K⁺ channels in surface cells ofrat distal colon, resulting in enhanced K⁺ secretion inthis epithelium. However, the factors involved in the regulation ofthese K⁺ channels are at present unclear.
Aims—To evaluate theeffect of dietary K⁺ loading on intracellular pH and itsrelation to large conductance apical K⁺ channel activity insurface cells of rat distal colon.
Methods/Results—Asassessed by fluorescent imaging, intracellular pH was higher inK⁺ loaded animals (7.48 (0.09)) than in controls (7.07 (0.04); p<0.01) when surface cells were bathed in NaCl solution, and asimilar difference in intracellular pH was observed when cells werebathed in Na₂SO₄ solution (7.67 (0.09) and 6.92 (0.05) respectively; p<0.001). Ethylisopropylamiloride (EIPA; aninhibitor of Na⁺-H⁺ exchange; 1 µM) decreasedintracellular pH when surface cells from K⁺ loaded animalswere bathed in either solution, although the decrease was greater whenthe solution contained NaCl (ΔpH 0.50 (0.03)) rather thanNa₂SO₄ (ΔpH 0.18 (0.02); p<0.05). Incontrast, EIPA had no effect in cells from control animals. As assessedby patch clamp recording techniques, the activity of large conductance K⁺ channels in excised inside-out membrane patches fromdistal colonic surface cells of K⁺ loaded animals increasedtwofold when the bath pH was raised from 7.40 to 7.60. As assessed bycell attached patches in distal colonic surface cells fromK⁺ loaded animals, the addition of 1 µM EIPA decreasedK⁺ channel activity by 50%, consistent with reversal ofNa⁺-H⁺ exchange mediated intracellular alkalinisation.
Conclusion—Intracellularalkalinisation stimulates pH sensitive large conductance apicalK⁺ channels in rat distal colonic surface cells as part ofthe K⁺ secretory response to chronic dietary K⁺loading. Intracellular alkalinisation seems to reflect an increase inEIPA sensitive Na⁺-H⁺ exchange, which may be amanifestation of the secondary hyperaldosteronism associated with thismodel of colonic K⁺ adaptation.

     

Generalized random fields related to self-intersections of the Brownian motion

Let T_k^ε(λ; t₁,..., t_k) = ρ(X_t1)q^ε(X_t2 - X_t1)... q^ε(X_tk - X_tk-1), where X_t is a Brownian motion in R², λ(dx) = ρ(x)dx, and q^ε converges to Dirac's δ function as ε ↓ 0. The self-intersection local times of order k are described by a generalized random field T_k(λ; t₁,..., t_k) = lim_ε↓0T_k^ε(λ; t₁,..., t_k) for 0 < t₁ <... < t_k. The field “blows up” as t_i - t_j → 0 for some i ≠ j. I show that with a proper choice of the coefficients B_k^l(ε), a generalized random field [unk] _k(λ; t₁,..., t_k) = lim_ε↓0 [T_k^ε(λ; t₁,..., t_k) + Σ_l=1^k-1 [B_k^l(ε)T_l^ε](λ; t₁,..., t_k)] is well defined for all 0 ≤ t₁ ≤... ≤ t_k and it coincides with T_k(λ; t₁,..., t_k) for t₁ <... < t_k.     

Maximal functions associated to smooth curves

Let t → γ(t), 0 ≤ t ≤ 1, be a smooth curve in IRⁿ. Define the maximal function [unk](f) by [unk](f)(x) = sup_0<h≤1 (1/h) ʃ₀^h | f(x - γ(t))| dt. We state conditions under which [unk](f)_p ≤ A_p f_p, for 1 < p ≤ ∞.     

Blow-up of solutions of nonlinear wave equations in three space dimensions

Solutions u(x, t) of the inequality □u ≥ A|u|^p for x ε R₃, t ≥ 0 are considered, where □ is the d'Alembertian, and A,p are constants with A > 0, 1 < p < 1 + √2. It is shown that the support of u is compact and contained in the cone 0 ≤ t ≤ t₀ -|x - x⁰|, if the “initial data” u(x, 0), u_t(x, 0) have their support in the ball|x - x⁰| ≤ t₀. In particular, “global” solutions of □u = A|u|^p with initial data of compact support vanish identically. On the other hand, for A > 0, p > 1 + √2, global solutions of □u = A|u|^p exist, if the initial data are of compact support and “sufficiently” small.     

Isotropic probability measures in infinite-dimensional spaces

Every isotropic probability measure on the space R^∞ of real sequences x = (x₁, x₂,...) is a convex combination of the measure concentrated at 0 and a member of I₀(R^∞), the set of all isotropic probability measures p_∞ on R^∞ with p_∞({0}) = 0. Each p_∞ [unk] I₀(R^∞) is completely determined by any one of its finite-dimensional marginal distributions p_n. Each p_n has a density function f_n with dp_n(x₁,..., x_n) = dx₁... dx_nf_n(x₁² +... + x_n²). Each f_n is completely monotone in 0 < ξ < ∞ (hence analytic in the right complex ξ half-plane), and π^n/2Γ(n/2)^-1 ʃ₀^∞dξ ξ^n/2-1f_n(ξ) = 1. Every f that satisfies these two conditions is f_n for a unique p_∞ [unk] I₀(R^∞). Hence the equation πʃ_ξ^∞dζ f₂(ζ) = ʃ₀^∞dμ (t)e^-tξ defines a bijection between I₀(R^∞) and the set of all probability measures μ on 0 ≤ t < ∞. If p_∞ [unk] I₀(R^∞) then p_∞({x: Σ_i=1^∞x_i² < ∞}) = 0, so p_∞ is not a “softened” or “fuzzy” version of the inequality Σ_i=1^∞x_i² ≤ 1. If the prior information in a linear inverse problem consists of this inequality and nothing else, stochastic inversion and Bayesian inference are both unsuitable inversion techniques.     

Polar Order Evolutions near the Rhombohedral to Pseudocubic and Tetragonal to Pseudocubic Phase Boundaries of the BiFeO3-BaTiO3 System

Solid solutions of (1-x)BiFeO₃-xBaTiO₃ (BF-BT, 0.05 ≤ x ≤ 0.98) were prepared and characterized. It was found that the dielectric constant ε_m, remnant polarization P_r and piezoelectric coefficient d₃₃ reach their maximum values near the rhombohedral–pseudocubic phase boundary. In particular, the 0.7BF-0.3BT composition shows large polarization (P_r > 20 μC/cm²) and a temperature-stable piezoelectric property (d₃₃ > 100 pC/N when the annealing temperature is lower than ~400 °C). Near the tetragonal–pseudocubic phase boundary, ε_m and P_r decrease, and the piezoelectric property vanishes when the BF content reaches 4 mol %.     

Increased stray gas abundance in a subset of drinking water wells near Marcellus shale gas extraction

Horizontal drilling and hydraulic fracturing are transforming energy production, but their potential environmental effects remain controversial. We analyzed 141 drinking water wells across the Appalachian Plateaus physiographic province of northeastern Pennsylvania, examining natural gas concentrations and isotopic signatures with proximity to shale gas wells. Methane was detected in 82% of drinking water samples, with average concentrations six times higher for homes <1 km from natural gas wells (P = 0.0006). Ethane was 23 times higher in homes <1 km from gas wells (P = 0.0013); propane was detected in 10 water wells, all within approximately 1 km distance (P = 0.01). Of three factors previously proposed to influence gas concentrations in shallow groundwater (distances to gas wells, valley bottoms, and the Appalachian Structural Front, a proxy for tectonic deformation), distance to gas wells was highly significant for methane concentrations (P = 0.007; multiple regression), whereas distances to valley bottoms and the Appalachian Structural Front were not significant (P = 0.27 and P = 0.11, respectively). Distance to gas wells was also the most significant factor for Pearson and Spearman correlation analyses (P < 0.01). For ethane concentrations, distance to gas wells was the only statistically significant factor (P < 0.005). Isotopic signatures (δ¹³C-CH₄, δ¹³C-C₂H₆, and δ²H-CH₄), hydrocarbon ratios (methane to ethane and propane), and the ratio of the noble gas ⁴He to CH₄ in groundwater were characteristic of a thermally postmature Marcellus-like source in some cases. Overall, our data suggest that some homeowners living <1 km from gas wells have drinking water contaminated with stray gases.     

Research on Three-Dimensional Porous Composite Nano-Assembled α-MnO2/Reduced Graphene Oxides and Their Super-Capacitive Performance

A series of three-dimensional porous composite α-MnO₂/reduced graphene oxides (α-MnO₂/RGO) were prepared by nano-assembly in a hydrothermal environment at pH 9.0–13.0 using graphene oxide as the precursor, KMnO₄ and MnCl₂ as the manganese sources and F⁻ as the control agent of the α-MnO₂ crystal form. The α-MnO₂/RGO composites prepared at different hydrothermal pH levels presented porous network structures but there were significant differences in these structures. The special pore structure promoted the migration of ions in the electrolyte in the electrode material, and the larger specific surface area promoted the contact between the electrode material and the electrolyte ions. The introduction of graphene solved the problem of poor conductivity of MnO₂, facilitated the rapid transfer of electrons, and significantly improved the electrochemical performance of materials. When the pH was 12.0, the specific surface area of the 3D porous composite material αMGs-12.0 was 264 m²·g⁻¹, and it displayed the best super-capacitive performance; in Na₂SO₄ solution with 1.0 mol·L⁻¹ electrolyte, the specific capacitance was 504 F·g⁻¹ when the current density was 0.5 A·g⁻¹ and the specific capacitance retention rate after 5000 cycles was 88.27%, showing that the composite had excellent electrochemical performance.     

Rational approximations to linear forms of exponentials and binomials

Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: |Σ_i=0ⁿC_ie^ri| > H^-n-ε for any distinct rational numbers r₀,r₁,..., r_n and rational integers C₀,C₁,...,C_n with H = max_0≤i≤n |C_i|. We improve Mahler's estimate by replacing exponentials e^ri by linearly independent linear forms L_i = Σ L_ije^sij with rational L_ij,s_iji = 0,1,...,n. Similar results are obtained for binomials (a/b)^ri or Σ L_ij(a/b)^sij with integers a,b and log|b|/log|a| > 1 - ε. The simplest examples of new numbers with the irrationality exponent “2 + ε” are sinh 1 or sin 1.     

Picosecond kinetics of fluorescence and absorbance changes in photosystem II particles excited at low photon density

Oxygen-evolving photosystem II particles (from Synechococcus) with about 80 chlorophyll molecules per primary electron donor (P₆₈₀) were used for a correlated study of picosecond kinetics of fluorescence and absorbance changes, detected by the single-photon-timing technique and by a pump-probe apparatus, respectively. Chlorophyll fluorescence decays were biexponential with lifetimes τ₁ = 80 ± 20 ps and τ₂ = 520 ± 120 ps in open reaction centers and τ₁ = 220 ± 30 ps and τ₂ = 1.3 ± 0.15 ns in closed reaction centers. The corresponding fluorescence yield ratio F_max/F_o was 3-4. Absorbance changes were monitored in the spectral range of 620-700 nm after excitation at 675 nm with 10-ps pulses sufficiently weak (<7 × 10¹² photons/cm² per pulse) to avoid singlet-singlet annihilation. With open reaction centers, the absorbance changes could be fit to the sum of three exponentials. The associated absorbance difference spectra were attributed to (i) exciton trapping and charge separation (τ = 100 ± 20 ps), (ii) the electron-transfer step P₆₈₀⁺ I^- Q_A → P₆₈₀⁺ I Q_A^- (where I is the primary electron acceptor and Q_A is the first quinone acceptor) (τ = 510 ± 50 ps), and (iii) the reduction of P₆₈₀⁺ by the intact donor side (τ > 10 ns). With closed reaction centers, the absorbance changes were biexponential with lifetimes τ₁ = 170-260 ps and τ₂ = 1.6-1.75 ns. The results are explained in terms of a kinetic model that assumes P₆₈₀ to constitute a shallow trap. The results show that Q_A reduction in these photosystem II particles decreases both the apparent rate and the yield of the primary charge separation by a factor of 2-3 and increases the mean lifetime of excitons in the antenna by a factor of 3-4. Thus, we conclude that the long-lived, nanosecond chlorophyll fluorescence is not charge-recombination luminescence but rather emission from equilibrated excited states of antenna chlorophylls.     

Removal of Cr(VI) from Wastewater Using Graphene Oxide Chitosan Microspheres Modified with α–FeO(OH)

Graphene oxide and chitosan microspheres modified with α–FeO(OH) (α–FeO(OH)/GOCS) are prepared and utilized to investigate the performance and mechanism for Cr(VI) removal from aqueous solutions and the possibility of Fe secondary pollution. Batch experiments were carried out to identify the effects of pH, mass, and volume ratio (m/v), coexisting ions, time (t), temperature (T), and Cr(VI) initial concentration (C₀) on Cr(VI) removal, and to evaluate adsorption kinetics, equilibrium isotherm, and thermodynamics, as well as the possibility of Fe secondary pollution. The results showed that Cr(VI) adsorption increased with C₀, t, and T but decreased with increasing pH and m/v. Coexisting ions inhibited Cr(VI) adsorption, and this inhibition increased with increasing concentration. The influence degrees of anions and cations on the Cr(VI) adsorption in descending order were SO₄²⁻ > PO₄²⁻ > NO₃⁻ > Cl⁻ and Ca²⁺ > Mg²⁺ > Mn²⁺, respectively. The equilibrium adsorption capacity of Cr(VI) was the highest at 24.16 mg/g, and the removal rate was 97.69% under pH = 3, m/v = 1.0 g/L, T = 298.15 K, and C₀ = 25 mg/L. Cr(VI) adsorption was well fitted to a pseudo-second-order kinetic model and was spontaneous and endothermic. The best fit of Cr(VI) adsorption with the Langmuir and Sips models indicated that it was a monolayer and heterogeneous adsorption. The fitted maximum adsorption capacity was 63.19 mg/g using the Sips model under 308.15 K. Cr(VI) removal mainly included electrostatic attraction between Cr(VI) oxyanions with surface Fe–OH₂⁺, and the adsorbed Cr(VI) was partially reduced to Cr(III) and then precipitated on the surface. In addition, there was no Fe secondary pollution during Cr(VI) adsorption.     

Fatty acids suppress voltage-gated Na+ currents in HEK293t cells transfected with the α-subunit of the human cardiac Na+ channel

Studies have shown that fish oils, containing n-3 fatty acids, have protective effects against ischemia-induced, fatal cardiac arrhythmias in animals and perhaps in humans. In this study we used the whole-cell voltage-clamp technique to assess the effects of dietary, free long-chain fatty acids on the Na⁺ current (I_Na,α) in human embryonic kidney (HEK293t) cells transfected with the α-subunit of the human cardiac Na⁺ channel (hH1_α). Extracellular application of 0.01 to 30 μM eicosapentaenoic acid (EPA, C20:5n-3) significantly reduced I_Na,α with an IC₅₀ of 0.51 ± 0.06 μM. The EPA-induced suppression of I_Na,α was concentration- and voltage-dependent. EPA at 5 μM significantly shifted the steady-state inactivation relationship by −27.8 ± 1.2 mV (n = 6, P < 0.0001) at the V_1/2 point. In addition, EPA blocked I_Na,α with a higher “binding affinity” to hH1_α channels in the inactivated state than in the resting state. The transition from the resting state to the inactivated state was markedly accelerated in the presence of 5 μM EPA. The time for 50% recovery from the inactivation state was significantly slower in the presence of 5 μM EPA, from 2.1 ± 0.8 ms for control to 34.8 ± 2.1 ms (n = 5, P < 0.001). The effects of EPA on I_Na,α were reversible. Furthermore, docosahexaenoic acid (C22:6n-3), α-linolenic acid (C18:3n-3), conjugated linoleic acid (C18:2n-7), and oleic acid (C18:1n-9) at 5 μM and all-trans-retinoic acid at 10 μM had similar effects on I_Na,α as EPA. Even 5 μM of stearic acid (C18:0) or palmitic acid (C16:0) also significantly inhibited I_Na,α. In contrast, 5 μM EPA ethyl ester did not alter I_Na,α (8 ± 4%, n = 8, P > 0.05). The present data demonstrate that free fatty acids suppress I_Na,α with high “binding affinity” to hH1_α channels in the inactivated state and prolong the duration of recovery from inactivation.     

Athermal ω Phase and Lattice Modulation in Binary Zr-Nb Alloys

To further explore the potential of Zr-based alloys as a biomaterial that will not interfere with magnetic resonance imaging (MRI), the microstructural characteristics of Zr-xat.% Nb alloys (10 ≤ x ≤ 18), particularly the athermal ω phase and lattice modulation, were investigated by conducting electrical resistivity and magnetic susceptibility measurements and transmission electron microscopy observations. The 10 Nb alloy and 12 Nb alloys had a positive temperature coefficient of electrical resistivity. The athermal ω phase existed in 10 Nb and 12 Nb alloys at room temperature. Alternatively, the 14 Nb and 18 Nb alloys had an anomalous negative temperature coefficient of the resistivity. The selected area diffraction pattern of the 14 Nb alloy revealed the co-occurrence of ω phase diffraction and diffuse satellites. These diffuse satellites were represented by g_β + q when the zone axis was [001] or [113], but not [110]. These results imply that these diffuse satellites appeared because the transverse waves consistent with the propagation and displacement vectors were q = <ζ ζ¯ 0>* for the ζ~1/2 and <110> directions. It is possible that the resistivity anomaly was caused by the formation of the athermal ω phase and transverse wave. Moreover, control of the athermal ω-phase transformation and occurrence of lattice modulation led to reduced magnetic susceptibility, superior deformation properties, and a low Young’s modulus in the Zr-Nb alloys. Thus, Zr-Nb alloys are promising MRI-compatible metallic biomaterials.     

Maximal functions: Homogeneous curves

Let t → γ(t) be a homogeneous curve in Rⁿ. For suitable f, define [unk](f)(x) = sup_{h > 0}|(1/h) [unk]₀^hf(x - γ(t)) dt|. Then [unk](f)_p ≤ A_p f_p, 1 < p ≤ ∞.     

Gravitational field of a charged mass point

Adopting, with Schwarzschild, the Einstein gauge (|_μν| = -1), a solution of Einstein's field equations for a charged mass point of mass M and charge Q is derived, which differs from the Reissner-Nordstrøm solution only in that the variable r is replaced by R = (r³ + a³)^⅓, where a is a constant. The Newtonian gravitational potential ψ (2/c²)(1 - g₀₀) obeys exactly the Poisson equation (in the R variable), with the mass density equal to (E²/4πc²), E denoting the electric field. ψ also obeys a second linear equation in which the operator on ψ is the square root of the Laplacian operator. The electrostatic potential Φ (= Q/R), ψ, and all the components of the curvature tensor remain finite at the origin of coordinates. The electromagnetic energy of the point charge is finite and equal to (Q²/a). The charge Q defines a pivotal mass M^* = (Q/G^½). If M < M^*, then the whole mass is electromagnetic. If M > M^*, the electromagnetic part of the mass M_em equals [M - (M² - M^*2)^½], whereas the material part of the mass M_mat equals (M² - M^*2)^½. When M > M^*, the constant a is determined, following Schwarzschild, by shrinking the “Schwarzschild radius” to zero. When M < M^*, a is determined so as to make the gravitational acceleration vanish at the origin.     

Chaotic motion of a weakly nonlinear, modulated oscillator

A weakly nonlinear oscillator of natural frequency ω₀ and damping ratio δ is driven by an amplitude-modulated force of dimensionless amplitude ε, carrier frequency ω, and modulation frequency ω₁. Each of (ω - ω₀)/ω₀, ω₁/ω₀, and δ is O(ε^2/3) as ε → 0. The response in this resonant neighborhood is a slowly modulated sine wave, the envelope of which is described by three first-order, autonomous, ordinary differential equations. This envelope, which is periodic for δ >> ε^2/3, is chaotic in certain ranges of (ω - ω₀)/ω₀ and ω₁/ω₀ if δ/ε^2/3 is sufficiently small.     

Impact of Age on Stent Strut Coverage and Neointimal Remodeling as Assessed by Optical Coherence Tomography

While older age associates with adverse percutaneous coronary intervention (PCI) outcomes, detailed information relating age to stent strut coverage and neointimal characteristics is lacking.One hundred nineteen patients with 123 sirolimus-eluting stents (SESs) were divided into 3 groups: group A (≤55 years), group B (56–65 years), and group C (>65 years). At 6 and 12 months of follow-up, optical coherence tomography was performed to assess strut coverage and neointimal remodeling.At 6 months, the proportion of uncovered struts increased with age: 6.1% in group A versus 7.3% in group B versus 11.7% in group C (P < 0.001) while the proportion of embedded struts decreased: 72.1% versus 57.0% vs. 55.0%, respectively (P < 0.001). Mean neointimal thicknesses were 90 μm versus 60 μm versus 60 μm, respectively (P < 0.001), and neointimal areas were 0.82 mm² versus 0.52 mm² versus 0.57 mm² (P < 0.001). At 12 months, the proportion of uncovered struts increased with age (3.9% vs. 3.3% vs. 4.9 %; P < 0.001), while mean neointimal thicknesses were 100 versus 70 versus 80 μm (P < 0.001) and neointimal areas were 0.87 versus 0.60 versus 0.67 mm² (P < 0.001).Patients ≤55 years receiving SES showed highest strut coverage and neointimal repair rate compared with the other 2 groups. A “catch-up phenomenon” appeared to occur in the oldest patients, as in the first 6 months the neointima showed lowest endothelial cell coverage and lowest neointimal proliferation rate, whereas from 6 to 12 months, the highest neointimal proliferation rate was seen in the oldest patients.