760 research outputs found
Evidence for Factorization in Three-body Decays
Motivated by experimental results on , we use a
factorization approach to study these decays. Two mechanisms concerning kaon
pair production arise: current-produced (from vacuum) and transition (from the
meson). The kaon pair in the decays can be
produced only by the vector current (current-produced), whose matrix element
can be extracted from processes via isospin relations. The
decay rates obtained this way are in good agreement with experiment. The
decays involve both current-produced and transition
processes. By using QCD counting rules and the measured decay rates, the measured decay spectra can be understood.Comment: 3 pages, 6 figures. Talk presented at EPS2003 Conference, Aachen,
Germany, July 200
Thermal microwave emissions from vegetated fields: A comparison between theory and experiment
The radiometric measurements over bare field and fields covered with grass, soybean, corn, and alfalfa were made with 1.4 GHz and 5 GHz microwave radiometers during August - October 1978. The measured results are compared with radiative transfer theory treating the vegetated fields as a two layer random medium. It is found that the presence of a vegetation cover generally gives a higher brightness temperature T(B) than that expected from a bare soil. The amount of this T(B) excess increases in the vegetation biomass and in the frequency of the observed radiation. The results of radiative transfer calculations generally match well with the experimental data, however, a detailed analysis also strongly suggests the need of incorporating soil surface roughness effect into the radiative transfer theory in order to better interpret the experimental data
On a Class of Combinatorial Sums Involving Generalized Factorials
The object of this paper is to show that generalized Stirling numbers can be effectively used to evaluate a class of combinatorial sums involving generalized factorials
On the Solutions of Three Variable Frobenius Related Problems Using Order Reduction Approach
This paper presents a new approach to determine the number of solutions of
three variable Frobenius related problems and to find their solutions by using
order reducing methods. Here, the order of a Frobenius related problem means
the number of variables appearing in the problem. We present two types of order
reduction methods that can be applied to the problem of finding all nonnegative
solutions of three variable Frobenius related problems. The first method is
used to reduce the equation of order three from a three variable Frobenius
related problem to be a system of equations with two fixed variables. The
second method reduces the equation of order three into three equations of order
two, for which an algorithm is designed with an interesting open problem on
solutions left as a conjecture
Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials
Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of the Fibonacci, the Lucas, the Pell, and the Jacobsthal numbers in terms of the generalized Gegenbauer-Humbert polynomial values are given. The applications of the relationship to the construction of identities of number and polynomial value sequences defined by linear recurrence relations are also discussed
A Note on Eulerian Numbers and Toeplitz Matrices
This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach
On the Solutions of Three-Variable Frobenius-Related Problems Using Order Reduction Approach
This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture
Some identities of Gaussian binomial coefficients
In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their relationships
Enumeration Problems for a Linear Congruence Equation
Abstract Let m ≥ 2 and r ≥ 1 be integers and let c ∈ Z m = {0, 1, . . . , m − 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x 1 , . . . , x n ∈ Z m of the congruence x 1 + x 2 + · · · + x r ≡ c mod m. Exact formulae are also given when m or r is prime. This solution number involves the Catalan number or generalized Catalan number in some special cases. Moreover, the enumeration problem has interrelationship with the restricted integer partition
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