The Krein-Rutman theorem is vital in partial differential equations that are non-linear and provides evidence of the presence of several significant eigenvalues useful in topological degree calculations, stability ana...The Krein-Rutman theorem is vital in partial differential equations that are non-linear and provides evidence of the presence of several significant eigenvalues useful in topological degree calculations, stability analysis, and bifurcation theory. Schr?der’s equation which has been used extensively in studies of turbulence is an equation with a single independent variable suitable for encoding self-similarity. The concept of Hilbert spaces has been an inner product space frequently used due to its convenience in countless dimensional vector analysis. This paper is aimed at proving a number of solutions through the Krein-Rutman theorem in unitary spaces especially in Hilbert spaces. It has been certainly observed that the whole Krein-Rutman theorem system has a fairly stable scope, and has strong regular features, and many non-linear elliptic operators need the most ethical principles to satisfy the comparison policy.展开更多
The main concern of this paper is with a bijective approach to various classes ofincreasing trees. We discover an increasing tree counterpart of the decomposition algorithmfor Schroder trees. This bijection has probab...The main concern of this paper is with a bijective approach to various classes ofincreasing trees. We discover an increasing tree counterpart of the decomposition algorithmfor Schroder trees. This bijection has probably reached its full generality for decomposingincreasing trees. As a special case of our algorithm, we provide a solution to a problemconcerning the enumeration of plane trees by the net number of inversions.展开更多
基金Supported by National Natural Science Foundation of China(10471048)Research Foundation of Hubei Education Committee(B20092809)Research Foundation of Xianning University(Bk0714)
文摘The Krein-Rutman theorem is vital in partial differential equations that are non-linear and provides evidence of the presence of several significant eigenvalues useful in topological degree calculations, stability analysis, and bifurcation theory. Schr?der’s equation which has been used extensively in studies of turbulence is an equation with a single independent variable suitable for encoding self-similarity. The concept of Hilbert spaces has been an inner product space frequently used due to its convenience in countless dimensional vector analysis. This paper is aimed at proving a number of solutions through the Krein-Rutman theorem in unitary spaces especially in Hilbert spaces. It has been certainly observed that the whole Krein-Rutman theorem system has a fairly stable scope, and has strong regular features, and many non-linear elliptic operators need the most ethical principles to satisfy the comparison policy.
文摘The main concern of this paper is with a bijective approach to various classes ofincreasing trees. We discover an increasing tree counterpart of the decomposition algorithmfor Schroder trees. This bijection has probably reached its full generality for decomposingincreasing trees. As a special case of our algorithm, we provide a solution to a problemconcerning the enumeration of plane trees by the net number of inversions.
