On the solutions of a class of difference equations

AbstractIn this note we investigate the solutions of a class of difference equations and prove that Conjectures 4.8.2, 4.8.3, 5.4.6 and 6.10.3 proposed by M. Kulenovic and G. Ladas in [M. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, Chapman & Hall/CRC Press, 2002] are true

Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales

We establish some new oscillation criteria for nonlinear dynamic equation of the form on an arbitrary time scale with , where are positive rd-continuous functions. An example illustrating the importance of our result is included

Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales

We investigate the asymptotic behavior of solutions of the following higher-order dynamic equation , on an arbitrary time scale , where the function is defined on . We give sufficient conditions under which every solution of this equation satisfies one of the following conditions: (1) ; (2) there exist constants with , such that , where are as in Main Results.</p

Global Behavior of the Difference Equation x

We study the following difference equation xn+1=(p+xn-1)/(qxn+xn-1), n=0,1,…, where p,q∈(0,+∞) and the initial conditions x-1,x0∈(0,+∞). We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true

Soil Labile Organic Carbon Fractions and Soil Enzyme Activities After 10 Years of Continuous Fertilization and Wheat Residue Incorporation

Labile organic carbon (LOC) fractions and related enzyme activities in soils are considered to be early and sensitive indicators of soil quality changes. We investigated the influences of fertilization and residue incorporation on LOC fractions, enzyme activities, and the carbon pool management index (CPMI) in a 10-year field experiment. The experiment was composed of three treatments: (1) no fertilization (control), (2) chemical fertilizer application alone (F), and (3) chemical fertilizer application combined with incorporation of wheat straw residues (F + R). Generally, the F + R treatment led to the highest concentrations of the LOC fractions. Compared to the control treatment, the F + R treatment markedly enhanced potential activities of cellulase (CL), β-glucosidase (BG), lignin peroxidase (LiP), and manganese peroxidase (MnP), but decreased laccase (LA) potential activity. Partial least squares regression analysis suggested that BG and MnP activities had a positive impact on the light-fraction organic carbon (LFOC), permanganate-oxidizable carbon (POXC), and dissolved organic carbon (DOC) fractions, whereas laccase activity had a negative correlation with those fractions. In addition, the F + R treatment significantly increased the CPMI compared to the F and control treatments. These results indicated that combining fertilization with crop residues stimulates production of LOC and could be a useful approach for maintaining sustainable production capacity in lime concretion black soils along the Huai River region of China

Blockchain Smart Contracts for Grid Connection Management in Achieving Net Zero Energy Systems

Energy systems are transitioning towards a decentralized and decarbonized paradigm with the integration of distributed renewable energy sources. Blockchain smart contracts have the increasing potential to facilitate the transition of energy systems due to the natures of automation, standardization, and selfenforcement. This paper proposes a Blockchain smart contracts based platform to manage the grid connection for both large scale generation companies and individual prosumers (both producers and consumers). Through evaluating the capacity margin and carbon intensity for each substation or feeder in power networks, the incurred connection fee and low carbon incentive are formulated for incentivizing the local energy balance and connection of renewable energy sources. Case studies testify the effectiveness for encouraging the low carbon grid connection. Energy systems are transitioning towards a decentralized and decarbonized paradigm with the integration of distributed renewable energy sources. Blockchain smart contracts have the increasing potential to facilitate the transition of energy systems due to the natures of automation, standardization, and selfenforcement. This paper proposes a Blockchain smart contracts based platform to manage the grid connection for both large scale generation companies and individual prosumers (both producers and consumers). Through evaluating the capacity margin and carbon intensity for each substation or feeder in power networks, the incurred connection fee and low carbon incentive are formulated for incentivizing the local energy balance and connection of renewable energy sources. Case studies testify the effectiveness for encouraging the low carbon grid connection

The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1)

In this paper, we consider the nonlinear difference equation xn+1=f(xn−l+1,xn−2k+1), n=0,1,…, where k,l∈{1,2,…} with 2k≠l and gcd(2k,l)=1 and the initial values x−α,x−α+1,…,x0∈(0,+∞) with α=max{l−1,2k−1}. We give sufficient conditions under which every positive solution of this equation converges to a ( not necessarily prime ) 2-periodic solution, which extends and includes corresponding results obtained in the recent literature