We first prove the local existence and uniqueness of mild solutions for IVP (1.1) on interval ([0,a_{1}]) for an appropriately small constant (a_{1}>0), which will be given later.
The approximate size, convection velocity, and circulation time of unconfined burning-cloud releases scale with the cloud mass at powers 1/3, 1/6, and 1/6, respectively, multiplied by an appropriately dimensional constant; the influence of cross flow can only be important if its velocity exceeds that of internal convection.
with appropriately chosen constants.
Using a concave lower bound (assuming appropriately chosen constants) to the user rates, given by R ~ ijb m : = α ijb m log ( F ijb m ) + β ijb m ≤ R ijb m, (27).
Specifically, (R_i^1 t)=1-A_isin ^2(a(t+b_i))+B_i, ~forall i,) for class (m=1), where (a>0) determines the period of users' interests and (A_i,~b_i,~B_i) are appropriately defined constants.
σ and μ are the appropriately chosen constants, P EH,i is the harvesting power rate for each node i, E S,i and E M,i are the stored energy in the node i's battery and the maximum battery capacity, respectively.
Doward ably clarifies the financial context and keeps the momentum constant – appropriately, given how concerned Toxic is with running and the telltale properties of smart watches.
where ε is an appropriately small positive constant.
Not honestly assessing a situation and handling it appropriately leads to constant low-grade anxiety, which, as we know from all the research on the effects of stress, can result in sleeping problems, being short-tempered, and feeling overwhelmed by once "easy" situations.
It is proved that the proposed design approach is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system, with arbitrary small error by appropriately choosing design constants.
