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).     

Ultrametric skeletons

We prove that for every ε∈(0,1) there exists C_ε∈(0,∞) with the following property. If (X,d) is a compact metric space and μ is a Borel probability measure on X then there exists a compact subset S⊆X that embeds into an ultrametric space with distortion O(1/ε), and a probability measure ν supported on S satisfying ν(B_d(x,r))⩽(μ(B_d(x,C_εr))^1-ε for all x∈X and r∈(0,∞). The dependence of the distortion on ε is sharp. We discuss an extension of this statement to multiple measures, as well as how it implies Talagrand’s majorizing measure theorem.     

Reinforced 3D Composite Structures of γ-, α-Al2O3 with Carbon Nanotubes and Reduced GO Ribbons Printed from Boehmite Gels

The ability of boehmite to form printable inks has sparked interest in the manufacturing of 3D alumina (Al₂O₃) and composite structures by enabling direct ink writing methods while avoiding the use of printing additives. These materials may exhibit high porosity due to the printing and sintering procedures, depending on the intended application. The 3D-printed porous composite structures of γ-Al₂O₃ and α-Al₂O₃ containing 2 wt.% of carbon nanotubes or reduced graphene oxide ribbons were fabricated from boehmite gels, followed by different heat treatments. The reinforcing effect of these carbon nanostructures was evidenced by compression tests carried out on the different alumina structures. A maximum relative increase of 50% in compressive strength was achieved for the γ-Al₂O₃ composite structure reinforced with reduced graphene oxide ribbons, which was also accompanied by an increase in the specific surface area.     

Conversion of Bivalve Shells to Monocalcium and Tricalcium Phosphates: An Approach to Recycle Seafood Wastes

The search for sustainable resources remains a subject of global interest and the conversion of the abundantly available bivalve shell wastes to advanced materials is an intriguing method. By grinding, calcium carbonate (CaCO₃) powder was obtained from each shell of bivalves (cockle, mussel, and oyster) as revealed by FTIR and XRD results. Each individual shell powder was reacted with H₃PO₄ and H₂O to prepare Ca(H₂PO₄)₂·H₂O giving an anorthic crystal structure. The calcination of the mixture of each shell powder and its produced Ca(H₂PO₄)₂·H₂O, at 900 °C for 3 h, resulted in rhombohedral crystal β-Ca₃(PO₄)₂ powder. The FTIR and XRD data of the CaCO₃, Ca(H₂PO₄)₂·H₂O, and Ca₃(PO₄)₂ prepared from each shell powder are quite similar, showing no impurities. The thermal behaviors of CaCO₃ and Ca(H₂PO₄)₂·H₂O produced from each shell were slightly different. However, particle sizes and morphologies of the same products obtained from different shells were slightly different—but those are significantly different for the kind of the obtained products. Overall, the products (CaCO₃, Ca(H₂PO₄)₂·H₂O, and Ca₃(PO₄)₂) were obtained from the bivalve shell wastes by a rapidly simple, environmentally benign, and low-cost approach, which shows huge potential in many industries providing both economic and ecological benefits.     

Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions

The paper deals with strict solutions u(x,t) = u(x₁,x₂,x₃,t) of an equation [Formula: see text] where Du is the set of four first derivatives of u. For given initial values u(x,0) = εF(x), u_t(x,0) = εG(x), the life span T(ε) is defined as the supremum of all t to which the local solution can be extended for all x. Blowup in finite time corresponds to T(ε) < ∞. Examples show that this can occur for arbitrarily small ε. On the other hand, T(ε) must at least be very large for small ε. By assuming that a_ik,F,G [unk] C^∞, that a_ik(0) = 0, and that F,G have compact support, it is shown that [Formula: see text] for every N. This result had been established previously only for N < 4.     

Subordinate quadratic forms and their complementary forms

Theorem 1. For α, β on the range 1,..., μ, let Q(z) = ^*aαβzαzβ be a real valued, nonsingular, symmetric quadratic form. For positive integers r and s such that μ = r + s set (z₁,..., z_μ) = (u₁,..., u_r:S₁,..., S_n), Q(z) = P(u, s) and [Formula: see text] Let B = (z⁽¹⁾,..., z^(r)) be a base “over R” for points z ε π_r. For an arbitrary r-tuple ω₁,..., ω_r set [Formula: see text] index H_B(ω) = κ and nullity H_B(ω) = ν. Then [Formula: see text]     

Selenite Substituted Calcium Phosphates: Preparation,Characterization, and Cytotoxic Activity

The aim of this study was to prepare a biomimetic selenium substituted calcium phosphate system for potential application in osteosarcoma therapy. Calcium phosphate (CaP) systems substituted with selenite ions were prepared by the wet precipitation method, using biogenic CaCO₃ (derived from cuttlefish bone), CO(NH₂)₂-H₃PO₄, and Na₂SeO₃·5H₂O as reagents. Starting reaction mixtures were prepared based on the formula for selenite-substituted hydroxyapatite, Ca₁₀(PO₄)_6-x(SeO₃)_x(OH)₂, with Ca/(P + Se) molar ratio of 1.67 and Se/(P + Se) molar ratio of: 0, 0.01, 0.05, and 0.10, respectively. The prepared CaP powders were characterized by Fourier transform infrared spectrometry, elemental analysis, scanning electron microscopy, X-ray powder diffraction analysis and Rietveld refinement studies. Phase transformation and ion release were analyzed during 7 days of incubation in simulated body fluid at 37 °C. The metabolic activity of healthy and osteosarcoma cell lines was assessed by cell cytotoxicity and viability test. The as-prepared powders were composed of calcium-deficient carbonated hydroxyapatite (HAp), octacalcium phosphate (OCP), and amorphous calcium phosphate (ACP). Along with the selenite substitution, the presence of Sr²⁺, Na⁺, and Mg²⁺ was detected as a result of using cuttlefish bone as a precursor for Ca²⁺ ions. Inductively coupled plasma mass spectrometry analysis showed that the Se/(P + Se) molar ratios of selenite substituted powders are lower than the nominal ratios. Heat treated powders were composed of HAp, α-tricalcium phosphate (α-TCP) and β-tricalcium phosphate (β-TCP). Doping CaP structure with selenite ions improves the thermal stability of HAp. The powder with the Se/(P + Se) molar ratio of 0.007 showed selective toxicity to cancer cells.     

Copper-Doped Biphasic Calcium Phosphate Powders: Dopant Release,Cytotoxicity and Antibacterial Properties

Cytotoxicity and antibacterial properties associated with the dopant release of Cu-doped Biphasic Calcium Phosphate (BCP) powders, mainly composed of hydroxyapatite mixed with β-tricalcium phosphate powders, were investigated. Twelve BCP ceramics were synthesized at three different sintering temperatures (600 °C, 900 °C and 1200 °C) and four copper doping rates (x = 0.0, 0.05, 0.10 and 0.20, corresponding to the stoichiometric amount of copper in Ca₁₀Cu_x(PO₄)₆(OH)_2-2xO_2x). Cytotoxicity assessments of Cu-doped BCP powders, using MTT assay with human-Mesenchymal Stem Cells (h-MSCs), indicated no cytotoxicity and the release of less than 12 ppm of copper into the biological medium. The antibacterial activity of the powders was determined against both Gram-positive (methicillin-sensitive (MS) and methicillin resistant (MR) Staphylococcus aureus) and Gram-negative (Escherichia coli and Pseudomonas aeruginosa) bacteria. The Cu-doped biomaterials exhibited a strong antibacterial activity against MSSA, MRSA and E. coli, releasing approximatively 2.5 ppm after 24 h, whereas 10 ppm were required to induce an antibacterial effect against P. aeruginosa. This study also demonstrated that the culture medium used during experiments can directly impact the antibacterial effect observed; only 4 ppm of Cu²⁺ were effective for killing all the bacteria in a 1:500 diluted TS medium, whereas 20 ppm were necessary to achieve the same result in a rich, non-diluted standard marrow cell culture medium.     

High-κ oxide nanoribbons as gate dielectrics for high mobility top-gated graphene transistors

Deposition of high-κ dielectrics onto graphene is of significant challenge due to the difficulties of nucleating high quality oxide on pristine graphene without introducing defects into the monolayer of carbon lattice. Previous efforts to deposit high-κ dielectrics on graphene often resulted in significant degradation in carrier mobility. Here we report an entirely new strategy to integrate high quality high-κ dielectrics with graphene by first synthesizing freestanding high-κ oxide nanoribbons at high temperature and then transferring them onto graphene at room temperature. We show that single crystalline Al₂O₃ nanoribbons can be synthesized with excellent dielectric properties. Using such nanoribbons as the gate dielectrics, we have demonstrated top-gated graphene transistors with the highest carrier mobility (up to 23,600 cm²/V·s) reported to date, and a more than 10-fold increase in transconductance compared to the back-gated devices. This method opens a new avenue to integrate high-κ dielectrics on graphene with the preservation of the pristine nature of graphene and high carrier mobility, representing an important step forward to high-performance graphene electronics.     

Immersions of manifolds

This paper outlines a proof of the conjecture that every compact, differentiable, n-dimensional manifold immerses in Euclidean space of dimension 2n - α(n), where α(n) is the number of ones in the dyadic expansion of n.     

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.     

Effects of Sodium Hexametaphosphate Addition on the Dispersion and Hydration of Pure Calcium Aluminate Cement

The effects of sodium hexametaphosphate (SHMP) addition on the dispersion and hydration of calcium aluminate cement were investigated, and the relevant mechanisms discussed. The content of SHMP and the adsorption capacity of SHMP on the surface of cement particles were estimated using plasma adsorption spectroscopy and the residual concentration method. The rheological behavior of hydrate, ζ-potential value of cement particles, phase transformation and the microstructure of the samples were determined by coaxial cylinder rheometer, zeta probe, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The results indicate that SHMP readily reacted with Ca²⁺, forming complexes [Ca₂(PO₃)₆]²⁻ ions which were subsequently adsorbed onto the surfaces of cement particles. When the content of SHMP was 0.05%, the adsorption ratio reached 99%. However, it decreased to 89% upon further increasing the addition of SHMP to 0.4%. The complexes [Ca₂(PO₃)₆]²⁻ adsorbed onto the surfaces of cement particles inhibited the concentration of Ca²⁺ and changed ζ-potential, resulting in enhanced electrostatic repulsive force between the cement particles and reduced viscosity of cement-water slurry. The experimental results indicate that the complexes [Ca₂(PO₃)₆]²⁻ covering the surfaces of cement particles led to a delayed hydration reaction, i.e., they extended the hydration time of the cement particles, and that the optimal addition of SHMP was found to be about 0.2%.     

Transformation of Tri-Titanium(IV)-Substituted α-Keggin Polyoxometalate (POM) into Tetra-Titanium(IV)-Substituted POMs : Reaction Products of Titanium(IV) Sulfate with the Dimeric Keggin POM Precursor under Acidic Conditions

Reaction products of titanium(IV) sulfate in HCl-acidic aqueous solution with the dimeric species linked through three intermolecular Ti-O-Ti bonds of the two tri-titanium(IV)-substituted α-Keggin polyoxometalate (POM) subunits are described. Two novel titanium(IV)-containing α-Keggin POMs were obtained under different conditions. One product was a dimeric species through two intermolecular Ti-O-Ti bonds of the two tetra-titanium(IV)-substituted α-Keggin POM subunits, i.e., [[{Ti(H₂O)₃}₂(μ-O)](α-PW₉Ti₂O₃₈)]₂^6- (1). The other product was a monomeric α-Keggin species containing the tetra-titanium(IV) oxide cluster and two coordinated sulfate ions, i.e., [{Ti₄(μ-O)₃(SO₄)₂(H₂O)₈}(α-PW₉O₃₄)]^3- (2). Molecular structures of 1 and 2 were also discussed based on host (lacunary site)-guest (titanium atom) chemistry.     

Locality principle in wave mechanics

This paper proves a locality principle for a wave-mechanical particle governed by the Schrödinger equation. It is shown that ρ(r,β), the Laplace transform of the local density of states n(r,E), depends significantly only on the potential V(r′) at points r′ near r. The effect of changes of V(r′) at distant points r′ (|x_i′ - x_i| > a) on ρ(r,β) decay in a Gaussian fashion with a. This result sheds some light on the locality of physical properties of extended systems and provides general support for various local methods of calculation.     

The power of the optimal asymptotic tests of composite statistical hypotheses

The easily computable asymptotic power of the locally asymptotically optimal test of a composite hypothesis, known as the optimal C(α) test, is obtained through a “double” passage to the limit: the number n of observations is indefinitely increased while the conventional measure ξ of the error in the hypothesis tested tends to zero so that ξ_nn^½ → τ ≠ 0. Contrary to this, practical problems require information on power, say β(ξ,n), for a fixed ξ and for a fixed n. The present paper gives the upper and the lower bounds for β(ξ,n). These bounds can be used to estimate the rate of convergence of β(ξ,n) to unity as n → ∞. The results obtained can be extended to test criteria other than those labeled C(α). The study revealed a difference between situations in which the C(α) test criterion is used to test a simple or a composite hypothesis. This difference affects the rate of convergence of the actual probability of type I error to the preassigned level α. In the case of a simple hypothesis, the rate is of the order of n^-½. In the case of a composite hypothesis, the best that it was possible to show is that the rate of convergence cannot be slower than that of the order of n^-½ ln n.     

Worldwide data sets constrain the water vapor uptake coefficient in cloud formation

Cloud droplet formation depends on the condensation of water vapor on ambient aerosols, the rate of which is strongly affected by the kinetics of water uptake as expressed by the condensation (or mass accommodation) coefficient, α_c. Estimates of α_c for droplet growth from activation of ambient particles vary considerably and represent a critical source of uncertainty in estimates of global cloud droplet distributions and the aerosol indirect forcing of climate. We present an analysis of 10 globally relevant data sets of cloud condensation nuclei to constrain the value of α_c for ambient aerosol. We find that rapid activation kinetics (α_c > 0.1) is uniformly prevalent. This finding resolves a long-standing issue in cloud physics, as the uncertainty in water vapor accommodation on droplets is considerably less than previously thought.     

omega-Theorems for Quotients of Zeta-Functions at Combinations of Points

Theorem A. Let q ≥ O and r ≥ O be integers. Let s = σ + it, let ζ(s) be the Riemann zeta-function, let G_o(s) = 1, and [Formula: see text] and let F(s) = G_q(s)/H_r(s). Then as t → ∞ lim sup [unk]F(1 + it)[unk]/(log log t)^q+r+1 ≥ (6/π)²)^r+1 exp {(q + r + 1)γ}, where γ is Euler's constant.     

Recycling of Coal Fly Ash for the Fabrication of Porous Mullite/Alumina Composites

Coal fly ash with the addition of Al₂O₃ was recycled to produce mullite/alumina composites and the camphene-based freeze casting technique was processed to develop a controlled porous structure with improved mechanical strength. Many rod-shaped mullite crystals, formed by the mullitization of coal fly ash in the presence of enough silicate, melt. After sintering at 1300–1500 °C with the initial solid loadings of 30–50 wt.%, interconnected macro-sized pore channels with nearly circular-shaped cross-sections developed along the macroscopic solidification direction of camphene solvent used in freeze casting and a few micron-sized pores formed in the walls of the pore channels. The macro-pore size of the mullite/alumina composites was in the range 20–25 μm, 18–20 μm and 15–17 μm with reverse dependence on the sintering temperature at 30, 40 and 50 wt.% solid loading, respectively. By increasing initial solid loading and the sintering temperature, the sintered porosity was reduced from 79.8% to 31.2%, resulting in an increase in the compressive strength from 8.2 to 80.4 MPa.     

β2 Adrenergic receptors mediate important electrophysiological effects in human ventricular myocardium

OBJECTIVE—To define the effects of β₂ adrenergic receptor stimulation on ventricular repolarisation in vivo.
DESIGN—Prospective study.
SETTING—Tertiary referral centre.
PATIENTS—85 patients with coronary artery disease and 22 normal controls.
INTERVENTIONS—Intravenous and intracoronary salbutamol (a β₂ adrenergic receptor selective agonist; 10-30 µg/min and 1-10 µg/min), and intravenous isoprenaline (a mixed β₁/β₂ adrenergic receptor agonist; 1-5 µg/min), infused during fixed atrial pacing.
MAIN OUTCOME MEASURES—QT intervals, QT dispersion, monophasic action potential duration.
RESULTS—In patients with coronary artery disease, salbutamol decreased QT_onset and QT_peak but increased QT_end duration; QT_onset-QT_peak and QT_peak-QT_end intervals increased, resulting in T wave prolongation (mean (SEM): 201 (2) ms to 233 (2) ms; p < 0.01). There was a large increase in dispersion of QT_onset, QT_peak, and QT_end which was more pronounced in patients with coronary artery disease—for example, QT_end dispersion: 50 (2) ms baseline v 98 (4) ms salbutamol (controls), and 70 (1) ms baseline v 108 (3) ms salbutamol (coronary artery disease); p < 0.001. Similar responses were obtained with isoprenaline. Monophasic action potential duration at 90% repolarisation shortened during intracoronary infusion of salbutamol, from 278 (4.1) ms to 257 (3.8) ms (p < 0.05).
CONCLUSIONS—β₂ adrenergic receptors mediate important electrophysiological effects in human ventricular myocardium. The increase in dispersion of repolarisation provides a mechanism whereby catecholamines acting through this receptor subtype may trigger ventricular arrhythmias.


Keywords: β₂ adrenergic receptors; ventricular repolarisation; QT dispersion; salbutamol; isoprenaline     

Adaptive design in regression and control

When y = M(x) + ε, where M may be nonlinear, adaptive regression designs of the levels x₁, x₂,... at which y₁, y₂,... are observed lead to asymptotically efficient estimates of the value θ of x for which M(θ) is equal to any desired value y^*. More importantly, these designs also make the “cost” of the observations, defined at the nth stage to be Σ₁ⁿ (x_i — θ)², to be of the order of log n instead of n, an obvious advantage in medical and other applications.