The constraints are listed as follows: sum_{k=1}^{K} {x_{k}^{n}}(t)= 1, nin lbrace1,2,ldots,Nrbrace. (8).
If φ is strongly time consistent, then we also have that φ 0(X n )=φ 0(X 1), (nin mathbb {N}).
We speculate that NIN, in our report, is not a sporadic familial occurrence based on the following observations: (1) NIN is an extremely uncommon neuralgia and the co-existence in two members of one family is, therefore, unlikely to be a sporadic event.
When applying probes to guide the transition of macro-state, the determination of macro-state at step (b) in the original algorithm is revised as pleft({s}_n=jright)=left{begin{array}{l}{alpha}_{ij}, nnotin p and i,jin S 1, nin p, jne i, and i,jin S 0, nin p, j=i, and i,jin Send{array}right.
Let begin{aligned}& A=biggl{ biggl 0,frac{1}{ninmathbb{N}biggrhbb{N}biggr} cupbigl{ (0,0 bigr}, & B=biggl{ biggl(1,frac{1}{niniggr) : nin mathbb{N}biggr} cupbigl{ (1,0 bigr}.
Two separate loci were observed on chromosome 14q21 near SOS2, L2HGDH, ATP5S, CDKL1, MAP4K5, ATL1, SAV1, and NIN genes, and on chromosome 14q31, near SEL1L.
In order to treat asymptotically cubic or super-cubic nonlinearities in a unified way, we use a weaker condition (F3) instead of (F3′) where (Nin(2alpha,4alpha)) with (alphain 0,1)).
(mugeq0 ) represents the amount of the pulse input of toxicant concentration at (t=(n+l tau), (0< l<1), (nin Z_) in patch 1.
μ ((0< mu < 1)) is the proportion of the successful vaccination which is called pulse vaccination rate, at (t=(n+l tau), (0< l<1), (nin Z_).
Under these conditions, for each constant s the numbers (lambda_{sjn}=ialpha_{n} ( omega_{j}-omega_{s} ) ^{-1}), (nin mathbb{N}), (j=1,2,ldots,m), (jneq s), are located on the (m-1) rays from the origin.
Indeed, assume that (q_{n}>1), (nin {mathbb {N}}_{0}), is an decreasing sequence such that the sequence Q_{n}:=prod_{j=0}^{n-1}q_{j},quad nin {mathbb {N}}_{0}, converges to (Q>1) as (nto+infty), and that there are some numbers l and L such that (13) holds.
