Discrete analogues of Wirtinger's inequality for a two-dimensional array
Discrete complex analysis – the medial graph approach
We discuss a new formulation of the linear theory of discrete complex analysis on planar quad-graphs based on their medial graphs. It generalizes the theory on rhombic quad-graphs developed by Duffin, Mercat, Kenyon, Chelkak and Smirnov and follows the approach on general quad-graphs proposed by Mercat. We provide discrete counterparts of the most fundamental objects in complex analysis such as holomorphic functions, differential forms, derivatives, and the Laplacian. Also, we discuss discrete versions...
Discrete differential operators in multidimensional Haar wavelet spaces.
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete fractional calculus with the nabla operator.
Discrete inequalities of Wirtinger's type for higher differences.
Discrete isothermic surfaces.
Discrete singular functionals
In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.
Discrete spectra criteria for singular difference operators
We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).
Discretized representations of harmonic variables by bilateral Jacobi operators.
Distribution of zeros and shared values of difference operators
We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that for n ≥ 2, and a is a small function with respect to f, then equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
Do nonsingular globally bounded positon solutions exist?
Dunkl operators
Dynamical behavior of a third-order rational difference equation.
Dynamical properties for a class of fourth-order nonlinear difference equations.
Dynamical properties in a fourth-order nonlinear difference equation.
Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls.
Dynamics for nonlinear difference equation .
Dynamics in a discrete predator-prey system with infected prey
In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.
Dynamics of a class of higher order difference equations.