Fourth order evolution equations which describe pseudospherical surfaces

Differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K=−1$K=-1$. They can also be described as the compatibility condition of an associated linear problem also referred to as a zero curvature representation. A complete and explicit classification of a class of fourth order evolution equations is given. The classification provides four huge classes (referred to as Types I–IV) of fourth order evolution equations that describe pseudospherical surfaces, together with the associated one (or more) parameter linear problems. The differential equations of each type are determined by choosing certain arbitrary differentiable functions. Fourth-order member of the Burgers hierarchy and a modified Kuramoto–Sivashinsky equation are examples of equations described by Types I and IV, respectively. Many other explicit examples are presented.     

Algebraic functions in quasiprimal algebras

A function is algebraic on an algebra if it can be implicitly defined by a system of equations on . In this note we give a semantic characterization for algebraic functions on quasiprimal algebras. This characterization is applied to obtain necessary and sufficient conditions for a quasiprimal algebra to have every one of its algebraic functions be a term function. We also apply our results to particular algebras such as finite fields and monadic algebras.     

On the hyperbolic order

We define the hyperbolic order of any locally injective holomorphic function between arbitrary hyperbolic domains of the complex plane and study the relation between the hyperbolic order and the Schwarzian derivative for locally injective holomorphic functions from the unit disk into itself.     

A Randomized Homotopy for the Hermitian Eigenpair Problem

Foundations of Computational Mathematics - We describe and analyze a randomized homotopy algorithm for the Hermitian eigenvalue problem. Given an $$ntimes n$$ Hermitian matrix $$A$$ , the...     

Long time behavior of heat kernels of operators with unbounded drift terms

Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L²(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.     

Spectrum comparison on free boundary minimal submanifolds of Euclidean domains

In this paper, using ideas of Simons, Ros, and Savo, we prove a comparison between the spectrums of the stability operator and the Hodge–Laplacian acting on differential 1-forms on a compact minimal submanifold immersed into a Euclidean domain.     

The interaction of biliverdin and its dimethyl ester with superoxide ion

Bilin-1,19(21H,24H)-diones interact with O₂·- in DMSO giving rise to adducts showing charge-transfer character. This reaction can be reversed by addition of O₂·- consuming compounds. The O₂·-biliverdin dimethyl ester adduct collapses partially to 10-oxobilirubin dimethyl ester when treated with thiourea and 2-mercaptoethanol.     

Microwave-assisted alkaline digestion combined with microwave-assisted distillation for the determination of iodide and total iodine in edible seaweed by catalytic spectrophotometry

Microwave energy has been novelty applied to speed up a tetramethylammonium hydroxide (TMAH) alkaline digestion of seaweed samples and to assist distillation of iodine from seaweed alkaline digests. Iodide in the alkaline digests from seaweed and distilled iodine, reduced back to iodine in a hydroxylamine hydrochloride solution, was determined by a catalytic spectrophotometric method based on the catalytic effect of iodide on the oxidation of As(III) by Ce(IV) in H₂SO₄/HCl medium (Sandell-Kolthoff reaction). The determination of iodide was directly performed in the alkaline digests, while total iodine was assessed by analyzing the hydroxylamine hydrochloride solution after the distillation process. Microwave-assisted alkaline digestion was performed using 7.5 mL of TMAH and irradiating samples at 670 W for two 5.5 min steps. Microwave-assisted distillation was carried out using 4.0 mL of the alkaline digest and 3 mL of a 2.2 M hydrochloric acid and 0.05% (m/v) sodium nitrite solution, with a microwave power at 670 W for two 90 s steps. The distillate (iodine vapor) was bubbled in 10 mL of a 500 μg mL⁻¹ hydroxylamine hydrochloride solution (accepting solution). The linear calibration ranges were 0.30-20.0 and 0.40-20.0 μg L⁻¹ for iodide determination and total iodine determination, respectively. The limit of detection was 9.2 μg g⁻¹ for iodide and 28.5 μg g⁻¹ for total iodine. Repeatability of the overall procedures, expressed as R.S.D. for 11 determinations, was 2.6% for 196.3 μg g⁻¹ of iodide measured after microwave-assisted alkaline digestion, and 5.8% for 954.3 μg g⁻¹ of total iodine by microwave-assisted alkaline digestion followed by microwave-assisted distillation. Finally, accuracy of the methods was assessed by analyzing the NIST-09 (Sargasso) certified reference material and the methods were applied to the determination of iodide and total iodine in different Atlantic edible seaweed samples with satisfactory results.