On set theoretic complete intersections in P k 3

We prove that smooth monomial curves of degree greater than three are not set theoretic complete intersections on a wide class of surfaces, called bihonogeneous surfaces.     

Quenching of hadron spectra due to the collisional energy loss of partons in the quark-gluon plasma

We estimate the energy loss distribution and investigate the quenching of hadron spectra in ultrarelativistic heavy-ion collisions due to the collisional energy loss of energetic partons from hard parton collisions in the initial stage.     

The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method

The Linear Complementarity Problem (LCP), with an H₊?matrix coefficient, is solved by using the new “(Projected) Matrix Analogue of the AOR (MAAOR)” iterative method; this new method constitutes an extension of the “Generalized AOR (GAOR)” iterative method. In this work two sets of convergence intervals of the parameters involved are determined by the theories of “Perron-Frobenius” and of “Regular Splittings”. It is shown that the intervals in question are better than any similar convergence intervals found so far by similar iterative methods. A deeper analysis reveals that the “best” values of the parameters involved are those of the (projected) scalar Gauss-Seidel iterative method. A theoretical comparison of the “best” (projected) Gauss-Seidel and the “best” modulus-based splitting Gauss-Seidel method is in favor of the former method. A number of numerical examples support most of our theoretical findings.     

Ab initio study of the electronic structure and bonding of aluminum nitride

For the diatomic aluminum nitride (AlN), we have constructed potential energy curves for 45 states employing multi-reference variational methods and quantitative basis sets. Thirty-six states are relatively strongly bound, five present local minima, and four are of repulsive nature. Almost all states are of intense multi-reference character rendering their calculation and interpretation quite problematic. Our tentative assignment of the ground state is 3Pi, while a 3Sigma- state is above by less than 1 kcal/mol. Our best estimate for the binding energy of the X3Pi state is D0 = 56.0 +/- 0.5 kcal/mol at re = 1.783 A, in good agreement with the experimental values of D = 66 +/- 9 kcal/mol and re = 1.7864 A. The binding energy of the A3Sigma- state is very similar to the X state because they both correlate to the ground-state atoms, but the bond distance of the former is 0.13 A longer. The first seven states can be tagged as follows: X3Pi, A3Sigma-, a1Sigma+, b1Pi, c1Delta, B3Sigma+, and d1Sigma+, a rather definitive order with the exception of X and A states.     

Rotational properties of annulus dusty plasma in a strong magnetic field

The collective dynamics of an annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radiofrequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In the absence of the magnetic field, the dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in the anticlockwise direction with increasing magnetic field (B > 0.02 T ), and the constant value of the angular frequency at various strengths of the magnetic field confirms the rigid body rotation. The angular frequency of dust grains linearly increases up to a threshold magnetic field (B > 0.6 T ) and after that its value remains nearly constant in a certain range of magnetic field. Further increase in magnetic field (B > 1 T ) lowers the angular frequency. Low value of the angular frequency is expected by reducing the width of the annulus dusty plasma or the input rf power. The azimuthal ion drag force due to the magnetic field is assumed to be the energy source which drives the rotational motion. The resultant radial electric field in the presence of a magnetic field determines the direction of rotation. The variation of floating (plasma) potential across the annular region at given magnetic field explains the rotational properties of the annulus dusty plasma in the presence of a magnetic field.     

On the average volume of sections of convex bodies

The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: \(as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|} d\sigma \left( \xi \right)\). We study the question whether there exists an absolute constantC > 0 such that for every n, for every centered convex body K in R ⁿ and for every 1 ≤ k ≤ n ? 2,

$$as\left( K \right) \leqslant {C^k}{\left| K \right|^{\frac{k}{n}}}\mathop {\max }\limits_{|E \in G{r_{n - k}}} {\kern 1pt} as\left( {K \cap E} \right)$$

. We observe that the case k = 1 is equivalent to the hyperplane conjecture. We show that this inequality holds true in full generality if one replaces C by CL _K orCd_ovr(K, BP _k ⁿ ), where L _K is the isotropic constant of K and dovr(K, BP _k ⁿ ) is the outer volume ratio distance of K to the class BP _k ⁿ of generalized k-intersection bodies. We also compare as(K) to the average of as(K ∩ E) over all k-codimensional sections of K. We examine separately the dependence of the constants on the dimension when K is in some classical position. Moreover, we study the natural lower dimensional analogue of the average section functional.

     

Minimal systems of binomial generators and the indispensable complex of a toric ideal

Let be a vector configuration and its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of different minimal systems of binomial generators of . In the second part we associate to a simplicial complex . We show that the vertices of correspond to the indispensable monomials of the toric ideal , while one dimensional facets of with minimal binomial -degree correspond to the indispensable binomials of .

     

Ultrasensitive Determination of Vitamin B12 Using Disposable Graphite Screen‐Printed Electrodes and Anodic Adsorptive Voltammetry

A facile, rapid and ultra‐sensitive method for the determination of vitamin B₁₂ (cyanocobalamin) at the sub‐nanomolar concentration range by using low‐cost, disposable graphite screen‐printed electrodes is described. The method is based on the cathodic preconcentration of square planar vitamin B_12s, as occurred due to the electro reduction of Co(III) center in vitamin B_12a to Co(I), at ?1.3 V versus Ag/AgCl/3 M KCl for 40 s. Then, an anodic square wave scan was applied and the height of the peak appeared at ca. ?0.73 V versus Ag/AgCl/3 M KCl, due to the oxidation of Co(I) to Co(II) in the adsorbed molecule, was related to the concentration of the vitamin B₁₂ in the sample. EDTA was found to serve as a key‐component of the electrolyte by eliminating the background signal caused by metal cations impurities contained in the electrolyte (0.1 M phosphate buffer in 0.1 M KCl, pH 3). It also blocks trace metals contained in real samples, thus eliminating their interference effect. The method was optimized to various working parameters and under the selected conditions the calibration curve was linear over the range 1×10^?10–8×10^?9 mol L^?1 vitamin B₁₂ (R²=0.994), while the limit of detection for a signal‐to‐noise ratio of 3 (7×10^?11 mol L^?1 vitamin B₁₂) is the lowest value of any reported in the literature for the electrochemical determination of vitamin B₁₂. The sensors were successfully applied to the determination of vitamin B₁₂ in pharmaceutical products.