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

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

Evidence for Factorization in Three-body B --> D(*) K- K0 Decays

Motivated by recent experimental results, we use a factorization approach to study the three-body B --> D(*) K- K0 decay modes. Two mechanisms are proposed for kaon pair production: current-produced (from vacuum) and transition (from B meson). The Bbar0 --> D(*)+ K- K0 decay is governed solely by the current-produced mechanism. As the kaon pair can be produced only by the vector current, the matrix element can be extracted from e+ e- --> K Kbar processes via isospin relations. The decay rates obtained this way are in good agreement with experiment. Both current-produced and transition processes contribute to B- --> D(*)0 K- K0 decays. By using QCD counting rules and the measured B- --> D(*)0 K- K0 decay rates, the measured decay spectra can be understood.Comment: 17 pages, 6 figure