The precise interpretation of environmental sulfur isotope records requires a quantitative understanding of the biochemical controls on sulfur isotope fractionation by the principle isotope-fractionating process within the S cycle, microbial sulfate reduction (MSR). Here we provide the only direct observation of the major ((34)S/(32)S) and minor ((33)S/(32)S, (36)S/(32)S) sulfur isotope fractio...

Lanczos and Ortiz placed the canonical polynomials (c.p.’s) in a central position in the Tau Method. In addition, Ortiz devised a recursive process for determining c.p.’s consisting of a generating formula and a complementary algorithm coupled to the formula. In this paper a) We extend the theory so as to include in the formalism also the ordinary linear differential operators with polynomial c...

A question is proposed whether or not set theory is consistent. We consider a formal set theory S, where we can develop a number theory. As no generality is lost, in the following we consider a number theory that can be regarded as a subsystem of S, and will call it S. Definition 1. 1) We assume that a Gödel numbering of the system S is given, and denote a formula with the Gödel number n by An....

objective(s): in spect, the sinogram contains scatter and lack of attenuated counts that degrade the reconstructed image quality and quantity. many techniques for attenuation and scatter correction have been proposed. an acceptable method of correction is to incorporate effects into an iterative statistical reconstruction. here, we propose new maximum likelihood expectation maximization (mlem) ...

The single-breath diffusing capacities for singly and doubly 18O-labeled CO2,[Formula: see text]and[Formula: see text], as well as for NO, were determined in seven anesthetized rabbits to investigate whether the theoretically predicted ratio of specific blood uptake rates of both isotopic CO2species,[Formula: see text]/[Formula: see text]= 2.0, can be derived from the measured values of[Formula...

We establish a Kronecker limit formula for the zeta function ζF (s,A) of a wide ideal class A of a totally real number field F of degree n. This formula relates the constant term in the Laurent expansion of ζF (s,A) at s = 1 to a toric integral of a SLn(Z)-invariant function logG(Z) along a Heegner cycle in the symmetric space of GLn(R). We give several applications of this formula to algebraic...

Let $R=\Bbbk[x_1,\dots,x_n]$ be a polynomial ring over field $\Bbbk$ and let $I\subset R$ monomial ideal preserved by the natural action of symmetric group $\mathfrak S_n$ on $R$. We give combinatorial method to determine S_n$-module structure $\mathrm{Tor}_i(I,\Bbbk)$. Our formula shows that $\mathrm{Tor}_i(I,\Bbbk)$ is built from induced representations tensor products Specht modules associat...

We show a connection between the deMorgan formula size of a Boolean function and the noise stability of the function. Using this connection, we show that the Fourier spectrum of any balanced Boolean function computed by a deMorgan formula of size s is concentrated on coefficients of degree up to O( √ s). These results have several applications that apply to any function f that can be computed b...

Optical eigenvalue transmission is a promising technique to overcome Kerr nonlinear limits in optical communication systems. The associated with the Schrödinger equation invariant during fiber-based dispersive transmission. However, effect of carrier frequency offset (CFO) induces an shift presence CFO for digitally coherent receivers. estimation method using eigenvalues capable achieving highl...