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Let q be a Lie algebra over field k and p,p˜∈k[t] two different normalised polynomials of degree n⩾2. As vector spaces, both quotient algebras q[t]/(p) q[t]/(p˜) can identified with W=q⋅1⊕qt¯⊕…⊕qt¯n−1. If deg⁡(p−p˜)⩽1, then the brackets [,]p, [,]p˜ induced on W by p p˜, respectively, are compatible. Making use Lenard–Magri scheme, we construct subalgebra Z=Z(p,p˜)⊂S(W)q⋅1 such that {Z,Z}p={Z,Z}...

It is straightforward to show that the steady state price with full commitment is p(z) = θ θ − 1 S, where variables without subscripts denote steady state values. Notice furthermore that equation (1) in the paper implies that C = (1 − γ)c(z) and equation (2) in the paper implies that (1 − γβ)P = p(z). A second order Taylor series approximation of the value of the firm around the steady state of...

We investigate various aspects of the modular representation theory of Z/p × Z/p with particular focus on modules of constant Jordan type. The special modules we consider and the constructions we introduce not only reveal some of the structure of (Z/p× Z/p)-modules but also provide a guide to further study of the representation theory of finite group schemes.

and Applied Analysis 3 We make the following assumptions. A1 W t, z ∈ C1 R × R2N,R is 1-periodic in t. W t, 0 0 for all t ∈ R. There exist constants c1 > 0 and μ > 2 such that Wz t, z z ≥ c1|z| for t, z ∈ R × R2N. A2 there exist c2, r > 0 such that |Wz t, z | ≤ c2|z|μ−1 for t ∈ R and |z| ≤ r. A3 there exist c3, R ≥ r and p ≥ μ such that |Wz t, z | ≤ c3|z|p−1 for t ∈ R and |z| ≥ R. A4 there exis...

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

and Applied Analysis 3 Theorem 4. Assume that (H 1 )–(H 6 ) and (7) hold. If there exists a function ξ(t) ∈ C rd(T , (0,∞)) such that for any positive numberM, lim t→∞ ∫ t t0 (ξ (s) p (s) − Q (s)) Δs = ∞, (12) where p (s) = q (s) [1 − p (δ (s))] β , Q (s) = αM(R (σ (s))) α−β r (δ (s)) ((ξ Δ (s)) + ) α+1 (α + 1) α+1 βξ (s) (δ (s)) α , (ξ Δ (s)) + := max {ξΔ (s) , 0} , (13) then (1) is oscillator...