Oxidative dehydrogenation of n-butenes: Product effect in the reactions over tin-antimony mixed oxides

The addition of possible oxidation and/or isomerization products (butadiene, water, isomeric n-butenes) resulted in neither promotion nor inhibition in the oxidative dehydrogenation of n-butenes over tin-antimony mixed oxide catalysts. On the basis of these and other information on the influence of products an interpretation has been given to complete the reaction mechanism more realistic than those based on previous experimental results.

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Determination of <Superscript>93</Superscript>Zr in nuclear power plant wastes

A radioanalytical method (based on separation using UTEVA columns and ICP-MS measurement) has been used for determination of ⁹³Zr in 37 nuclear power plant samples. As ⁹³Nb might affect the detection of ⁹³Zr, Monte Carlo activation model was used to calculate the expected ⁹³Zr/^natZr mass ratio, which was compared to measured ones. It was found, that a decontamination factor of 10³ is sufficient to get a measurement uncertainty of less than 10%.     

Using Stepanov's method for exponential sums involving rational functions

For any additive character ψ and multiplicative character χ on a finite field F_q, and rational functions f,g in F_q(x), we show that the elementary Stepanov-Schmidt method can be used to obtain the corresponding Weil bound for the sum ∑_x∈Fq?Sχ(g(x))ψ(f(x)) where S is the set of the poles of f and g. We also determine precisely the number of characteristic values ω_i of modulus q^1/2 and the number of modulus 1.     

Upper bounds on a two-term exponential sum*

We obtain upper bounds for mixed exponential sums of the type where p^m is a prime power with m⩾ 2 and X is a multiplicative character (mod p^m). If X is primitive or p⫮(a, b) then we obtain |S(χ,f,p ^m)| ⩽2np ^{2/3 m}. If X is of conductor p and p⫮( a, b) then we get the stronger bound |S(χ,f,p ^m)|⩽np ^m/2. This paper is dedicated to Prof. Wang Yuan on the occasion of his 70th birthday.     

Small solutions of the congruencea1x12 +a2x22 +a3x32 +a4x42 ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ₂ a ₃ a ₄≢0(modp), this paper shows that there exists a solutionX=(x ₁,x ₂,x ₃,x ₄) ∈Z ⁴ of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp) such that

The interaction of an osmium-carbon triple bond with copper(I), silver(I) and gold(I) to give mixed dimetallocyclopropene species and the structures of Os(AgCl) (CR) Cl(CO) (PPh3)2

The osmium carbyne complex, Os(CR)Cl(CO)(PPh₃)₂, (R  p-tolyl) reacts with Group I halides to form the mixed dimetallocyclopropene species, $\text{Os(Cul)(C}$R)Cl(CO)(PPh₃)₂, $\text{Os(AgCl)(C}$R)Cl(CO)(PPh₃)₂, $\text{Os(AuCl)(C}$R)Cl(CO)(PPh₃)₂, and [$\text{Os[Ag(OClO}{}_3\text{)](C}$R)Cl(CO)(MeCN)(PPh₃)₂] ClO₄ X-ray crystal structure determination of $\text{Os(AgCl)(C}$R)Cl(CO)(PPh₃)₂ confirms the presence of a three-membered ring and the structure can be viewed as the “acetylene-like” interaction of an osmium—carbon triple bond with AgCl. In acid solution AgCl is precipitated and an alkylidene complex results from proton addition to the carbyne ligand.     

An improved Mordell type bound for exponential sums

For a sparse polynomial , with and , we show that

thus improving upon a bound of Mordell. Analogous results are obtained for Laurent polynomials and for mixed exponential sums.

     

Sensitivity analysis of discrete Markov chains via matrix calculus

Markov chains are often used as mathematical models of natural phenomena, with transition probabilities defined in terms of parameters that are of interest in the scientific question at hand. Sensitivity analysis is an important way to quantify the effects of changes in these parameters on the behavior of the chain. Many properties of Markov chains can be written as simple matrix expressions, and hence matrix calculus is a powerful approach to sensitivity analysis. Using matrix calculus, we derive the sensitivity and elasticity of a variety of properties of absorbing and ergodic finite-state chains. For absorbing chains, we present the sensitivities of the moments of the number of visits to each transient state, the moments of the time to absorption, the mean number of states visited before absorption, the quasistationary distribution, and the probabilities of absorption in each of several absorbing states. For ergodic chains, we present the sensitivity of the stationary distribution, the mean first passage time matrix, the fundamental matrix, and the Kemeny constant. We include two examples of application of the results to demographic and ecological problems.