Nonexistence of Global Solutions of Systems of Time Fractional Differential equations posed on the Heisenberg group

We first consider the nonlinear time fractional diffusion equation D^{1+α}u+D^β u−∆_{H} u=|u|^p posed on the Heisenberg group H, where 1 < p is a positive real nimber to be specified later; D^δ_{0|t} is the Liouville-Caputo derivative of order δ. For 0 < α < 1,0 < β ≤ 1. This equation interpolates the heat equation and the wave equation with the linear damping D^β_{0|t}u. We present the Fujita exponent for blow-up. Then establish sufficient conditions ensuring non-existence of local solutions. We extend the analysis to the case of the system D^{1+α}u+D^β u−∆_{H} u=|v|^q D^{1+δ}v+D^γ v−∆_{H} v=|u|^p. Our method of proof is based on the nonlinear capacity method.

Production Capacity Requirements Planning Using The Capacity Method Requirement Planning

PT. ABC is a company engaged in the manufacture of Dolomite Fertilizer. The number of requests is greater than the amount of production. Due to fluctuations in the number of requests that tend to increase, this occurs due to a lack of capacity at the workstation. Therefore, it is necessary to calculate the capacity requirements planning analysis for each work station to know the company's capacity needs. The research aims to identify the shortage/excess production capacity and provide proposals for the balance of production capacity at PT. A B C. Production capacity research was conducted using the Capacity Requirement Planning (CRP) method. Results and Discussion, comparison of available capacity and required capacity (load) are as follows, work station jaw crusher available capacity 36.74 hours/week while required capacity (load) 36 hours/week, work station bucket elevator available capacity 36, 74 hours/week while the required capacity (load) is 14.4 hours/week, work station ball mill available capacity is 36.74 hours/week while the required capacity (load) is 45.6 hours/week, and work station silo flour the available capacity is 36.74 hours/week while the required capacity (load) is 51.59 hours/week. In conclusion, two stations experience excess capacity, namely the jaw crusher work station with an excess capacity of 0.74 hours/week and the bucket elevator work station with an excess capacity of 22.34 hours/week. The other two work stations experienced a lack of capacity, namely the ball mill work station with a capacity shortage of 22.34 hours/week and the silo flour work station with a capacity shortage of 14.85 hours/week. Efforts to balance capacity by scheduling overtime and adding equipment (machinery) to work centers that lack capacity, so that the company's production targets are achieved.

Antioxidant Capacity Assessment of Plant Extracts for Green Synthesis of Nanoparticles

In this work, water extracts from different bio-based products of plant origin were studied to evaluate their antioxidant capacity and their potential to form metal nanoparticles from aqueous solutions. Two traditional tests, the Folin–Ciocalteu assay and the DPPH radical scavenging capacity method were compared with a more recent one, SNPAC, based on the formation of silver nanoparticles. The silver nanoparticle antioxidant capacity method (SNPAC) was optimized for its application in the characterization of the extracts selected in this work; kinetic studies and extract concentration were also evaluated. The extracts were obtained from leaves of oak, eucalyptus, green tea, white and common thyme, white cedar, mint, rosemary, bay, lemon, and the seaweed Sargassum muticum. The results demonstrate that any of these three methods can be used as a quick test to identify an extract to be employed for nanoparticle formation. Additionally, we studied the synthesis of Cu, Fe, Pb, Ni, and Ag nanoparticles using eucalyptus extracts demonstrating the efficiency of this plant extract to form metallic nanoparticles from aqueous metal salt solutions. Metal nanoparticles were characterized by transmission electron microscopy and dynamic light scattering techniques.

APPLICATION OF A RISK-BASED APPROACH IN THE OCCUPATIONAL HEALTH MANAGEMENT SYSTEM

The economic efficiency of the application of the risk-oriented approach is considered, the use of the risk capacity method allows justifying the costs of labor protection as an investment in the development of the organization itself.

Economic technology analysis of LTE advanced pro dual spectrum licensed and unlicensed access using discounted cash flow methods

<p>Since implementing the long term evolution (LTE) technology, the surge in data service traffic has increased, causing an increase in demand spectrum, which has resulted in gaps in capacity requirements. Wireless service providers can respond to LTE technology updates. With LTE advanced pro technology that utilizes unlicensed spectrum technology can provide solutions to increase capacity and throughput. In this study, LTE advanced pro planning by capacity method to find the number of eNodeB and using the discounted cash flow method to analyze the feasibility of the costs to be invested in the implementation of the LTE. The results of the four simulated scenarios concluded that the number of eNodeB from the IV scenario with 20 MHz bandwidth at 1800 MHz frequency and 20 MHz bandwidth at 5 GHz frequency amounted to 23 sites, with a positive NPV value of $ 271,936.96, IRR of 14.91%, and for payback period occurred in the 3rd year. Thus the fourth scenario is feasible to be implemented.</p>

Using the capacity method to analyze historical events

The use of the capacity method of rare events analysis [1,2] for the historical events analysis is demonstrated using the example of the Russian-Turkish wars. Modeling rare events as events of overflow of a certain capacity, for example, a cup of patience, it turns out to recover from these rare events the resulting function of the difference between incoming and outgoing disturbance flows. For different variants of representing the effect of an event, different functions were obtained, which were given an interesting interpretation, as example the speed of preparation for the next war.