CHANGES IN REAL ESTATE VALUE DYNAMICS DURING SERVICE CYCLES AS A SOURCE OF NEGATIVE PERIODIC PROPERTY DEPRECIATION

Main methodological principles of mathematically describing the patterns of changes in the asset’s value/depreciation dynamics are studied in cases when economic measurements are performed by independent expert evaluation. The basic hypothesis suggests that for all tangible assets, which are characterized by redeemable depreciation, there is a possibility of negative periodic depreciation during short-term service periods when remedial and repair work to eliminate depreciation signs is carried out. The most influential price-forming factors that determine the asset’s depreciation indexes and indicators of value dynamics over long periods are identified and analysed. It is shown that when this period is comparable to the asset’s service life, most of tangible assets are characterized by both positive and negative periodic depreciation indexes at separate times. It is noted that the models used in accounting documents do not describe the actual changes in the value dynamics, and amortization in particular, since they do not take into account the possibility of increasing asset value and periodic negative depreciation. A new kind of mathematical model is proposed that takes into account the opposite signs of periodic depreciation in the operation and service periods. It is proved that the actual indicators of fair market value and periodic depreciation indexes of these types of assets can be determined by performing periodic independent expert evaluation (revaluation).

Periodic Property and Instability of a Rotating Pendulum System

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

Periodic solution of fractal Phi-4 equation

This paper focuses on a fractal Phi-4 equation with time-space fractal derivatives, though its solitary solutions have been deeply studied, its periodic solution was rarely revealed due to its strong nonlinearity. Now the condition is completely changed, He?s frequency formulation provides with a universal tool to having a deep insight into the periodic property of the fractal Phi-4 equation. The two-scale transform is used to convert approximately the fractal Phi-4 equation to a differential model, and a criterion is suggested for the existence of a periodic solution of the equation, the effect of fractal orders on the periodic property is also elucidated.

Design of microwave lowpass filter based on log periodic zigzag DGS

This contribution presents, for the first time, the design of microwave lowpass filter with ultrawide stopband and low insertion loss based on the log-periodic zig-zag defected ground structure (DGS); the design is specifically evolved from the principle of the log-periodic line antenna and the slotline based DGS. Based on the log-periodic property, studies show that ultra-wideband suppression can be realized by increasing the flare angle or the angle subtended by each element of the slotline DGS. The developed filter therefore shows low insertion loss of 0.7 dB within the passband, sharp transition between the passband and the stopband and ultra-wide suppression band from 2.61-26.5 GHz with a 20 dB suppression level. The DGS architecture is simple and easy to realize, and the design is thus useful in many microwave applications. The fabricated prototype filter validates the study, both from simulations and from measurements.

CHANGES IN REAL ESTATE VALUE DYNAMICS DURING SERVICE CYCLES AS A SOURCE OF NEGATIVE PERIODIC PROPERTY DEPRECIATION

Main methodological principles of mathematically describing the patterns of changes in the asset’s value/depreciation dynamics are studied in cases when economic measurements are performed by independent expert evaluation. The basic hypothesis suggests that for all tangible assets, which are characterized by redeemable depreciation, there is a possibility of negative periodic depreciation during short-term service periods when remedial and repair work to eliminate depreciation signs is carried out. The most influential price-forming factors that determine the asset’s depreciation indexes and indicators of value dynamics over long periods are identified and analysed. It is shown that when this period is comparable to the asset’s service life, most of tangible assets are characterized by both positive and negative periodic depreciation indexes at separate times. It is noted that the models used in accounting documents do not describe the actual changes in the value dynamics, and amortization in particular, since they do not take into account the possibility of increasing asset value and periodic negative depreciation. A new kind of mathematical model is proposed that takes into account the opposite signs of periodic depreciation in the operation and service periods. It is proved that the actual indicators of fair market value and periodic depreciation indexes of these types of assets can be determined by performing periodic independent expert evaluation (revaluation).

Periodic Property and Asymptotic Behavior for a Discrete Ratio-Dependent Food-Chain System with Delays

In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established.

A fractional nonlinear system for release oscillation of silver ions from hollow fibers

A fractional nonlinear differential system is studied to search for its periodic solution near the equilibrium. The release oscillation of silver ions from hollow fibers is used as an example to illustrate the importance of fractional order to the release frequency. The criterion for the periodic solution is obtained and it shows that the fractional order will greatly affect its periodic property.