ON THE MANAGEMENT OF INTERCONNECTED WILDLIFE POPULATIONS

Abstract Economic interdependency of wildlife or fish stocks is usually attributed to ecological interdependency, such as predator–prey and competitive relationships, or to density‐dependent migration of species between different areas. This paper provides another channel for economic interdependency of wildlife where density‐independent migration and market price interaction affect the management strategies among different landowners. Management is studied under three market conditions for selling hunting licenses: price taking behavior, monopoly market, and duopoly market. Harvesting of the Scandinavian moose is used as an example. The paper provides several results on how economic interdependency works through the migration pattern. When a duopoly market is introduced, hunting license price interaction among the landowners plays an additional role in determining the optimal harvesting strategy.     

ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract

We study the efficient set X _E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X _E ) of X _E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X _E ). Application to optimization over the efficient set for a multiple objective linear program is considered.     

ENSS' Theory in Long Range Scattering: Second Order Hyperbolic and Parabolic Operators

We prove asymptotic completeness using ENSS' method for h₀(P) + W_S(Q) + W_L(Q) where h₀: Rⁿ → R is a polynomial of degree 2 with lim lim_|ξ|→∞h₀(ξ)| + |Δh₀(ξ)| = ∞, W_S a short range potential and W_L a smooth long range potential.     

0-Minimal Quasi-ideals of Generalized Linear Transformation Semigroups

Abstract

For vector spaces V and W over a field F, L _F (V, W) denotes the set of all linear transformations α : V → W, and for a cardinal number k > 0, let L _F (V, W, k) be the set of all α ∈ L _F (V, W) of rank less than k. For θ ∈ L _F (W, V), let (L _F (V, W, k), θ) denote the semigroup L _F (V, W, k) under the operation ? defined by α ? β = αθβ for all α, β ∈ L _F (V, W, k). In this paper, all 0-minimal quasi-ideals of the semigroup (L _F (V, W, k), θ) are completely characterized. It is also shown from this characterization that every nonzero semigroup (L _F (V, W, k), θ) always has a 0-minimal quasi-ideal.     

RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L2-METRIC

For two subsets W and V of a Banach space X, let Kn(W, V, X) denote the relative Kolmogorov n-width of W relative to V defined by Kn (W, V, X) := inf sup Ln f∈W g∈V∩Ln inf ‖f-g‖x,where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(△r) denote the class of 2w-periodic functions f with d-variables satisfying ∫[-π,π]d |△rf(x)|2dx ≤ 1,while △r is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2(△r) relative to W2(△r) in Lq([-r, πr]d) (1 ≤ q ≤∞), and obtain its weak asymptotic result.     

Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups

Let W be a finite Coxeter group, P a parabolic subgroup of W, and N _W (P) the normalizer of P in W. We prove that every element in N _W (P) is strongly real in N _W (P), and that every irreducible complex character of N _W (P) has Frobenius-Schur indicator 1.     

Stochastic anticipative calculus for functionals of a gaussian generalized random field

We give a construction of Skorohod integrals with respect to a Gaussian D'-valued random field W The method is based on the multiple Wiener integral expansion for L ₂-functionals of W We also give a representation of the Malliavin derivative operator of L ²-functionals of W     

When linear and weak discrepancy are equal

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |h_L(x)−h_L(y)|≤k, whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |h_W(x)−h_W(y)|≤k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing when the weak and linear discrepancy of a poset are equal. Although it is shown that determining whether a poset has equal weak and linear discrepancy is -complete, this paper provides a complete characterization of the minimal posets with equal weak and linear discrepancy. Further, these minimal posets can be completely described as a family of interval orders.     

Sum of weighted Lebesgue spaces and nonlinear elliptic equations

We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (W,A,m){(\Omega ,\mathcal{A},\mu)} and investigating the main properties of both the Banach space

Identifiability at the boundary for first-order terms

Let Ω be a domain in R ⁿ whose boundary is C ¹ if n≥3 or C ^1,β if n=2. We consider a magnetic Schrödinger operator L _{W , q} in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for L _{W , q} . We also consider a steady state heat equation with convection term Δ+2W·? and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary.     

Construction of non-linear semi-groups using product formulas

Under certain circumstances, the Trotter-Lie formulaW _t=lim(U _t/nV_t/n) ⁿ is used to construct a non-linear semi-groupW _t on closed subsets ofL ^P, 1≦p<∞. In particular we consider the situation whereU _t=e ^tA is a positivity preservingC ₀ (linear) semi-group andV _t is generated by a (non-linear) functionF with certain monotonicity properties. In general,A andF are “singular” onL ^p and no requirement is made that one of them be “relatively bounded” with respect to the other. The generator of the resulting semi-groupW _t turns out to be an extension ofA +F restricted to a suitable domain. Research supported by a Danforth Graduate Fellowship and a Weizmann Postdoctoral Fellowship.     

Irreducible Components of Fixed Point Subvarieties of Flag Varieties

Suppose G is a connected reductive algebraic group, P is a parabolic subgroup of G, L is a Levi factor of P, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus, T, and a Borel subgroup, B, of G, so that T?B∩L, B ? P and e ∈ Lie B. Let β be the variety of Borel subgroups of G and let ??_e be the subset of ?? consisting of Borel subgroups whose Lie algebras contain e. Finally, let W be the Weyl group of G with respect to T. For ω ∈ W let ??_ω be the B-orbit in ?? containing ^ωB. We consider the intersections ??_ω ∩ ??_e. The main result is that if dim ??_ω ∩ ??_e = dim ??_e, then ??_ω ∩ ??_e is an affine space. Thus, the irreducible components of ??_e are indexed by Weyl group elements. It is also shown that if G is of type A, then this set of Weyl group elements is a right cell in W.     

Averaging of directional derivatives in vertices of nonobtuse regular triangulations

For a shape-regular triangulation ${\mathcal{T}_h}For a shape-regular triangulation _h{\mathcal{T}_h} without obtuse angles of a bounded polygonal domain W ì ?²{\Omega\subset\Re^2} , let L_h{\mathcal L_h} be the space of continuous functions linear on the triangles from T_h{\mathcal{T}_h} and Π _h the interpolation operator from C([`(W)]){C(\overline\Omega)} to L<sub>h</sub>{\mathcal L_h} . This paper is devoted to the following classical problem: Find a second-order approximation of the derivative ?u/?z(a){\partial u/\partial z(a)} in a direction z of a function u ? C<sup>3</sup>([`(W)]){u\in C^3(\overline\Omega)} in a vertex a in the form of a linear combination of the constant directional derivatives ?P_h(u)/?z{\partial \Pi_h(u)/\partial z} on the triangles surrounding a. An effective procedure for such an approximation is presented, its error is proved to be of the size O(h ²), an operator W_h: L_h?L_h×L_h{\mbox{W}_h: \mathcal L_h\longrightarrow\mathcal L_h\times\mathcal L_h} relating a second-order approximation W _h [Π _h (u)] of ?u{\nabla u} to every u ? C³([`(W)]){u\in C^3(\overline\Omega)} is constructed and shown to be a so-called recovery operator. The accuracy of the presented approximation is compared with the accuracies of the local approximations by other known techniques numerically.     

Restricted summability of Fourier transforms and local Hardy spaces

A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W（hp, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.     

Type II Matrices of Size Five

. A type II matrix is an n×n matrix W with non-zero entries W _i,j which satisfies , i, j=1, …, n. Two type II matrices W, W′ are said to be equivalent if W′=P ₁Δ₁ WΔ₂ P ₂ holds for some permutation matrices P ₁, P ₂ and for some non-singular diagonal matrices Δ₁, Δ₂. In the present paper, it is shown that there are up to equivalence exactly three type II matrices in M ₅(C). Received: August 15, 1996 Revised: May 16, 1997     

Average Width and Optimal Interpolation of the Sobolev-Wiener Class Wpq(R) in the Metric Lq(R)

In this paper, we determine the exact value of average n − K width _n(W^r_pq(R), L_q(R)) of Sobolev-Wiener class W^r_pq(R) in the metric L_q(R) for 1 > q ≥ p > ∞ and get the value of _n(W^r_p(R), L_qp(R)) for the dual case. We also solve the optimal interpolation problems of W^r_pq(R) in the metric L_q(R) and W^r_p(R) in the metric L_qp(R) for 1 < q ≤ p < ∞.     

ECOLOGICAL‐ECONOMIC MODELS OF SUSTAINABLE HARVEST FOR AN ENDANGERED BUT EXOTIC MEGAHERBIVORE IN NORTHERN AUSTRALIA

ABSTRACT. How can one manage wildlife under a suite of competing values? In isolation, the ecological economics of native wildlife harvest, threatened species conservation and control of exotic species are all well established sub‐disciplines of wildlife management. However, the wild banteng (Bos javanicus) population of northern Australia represents an interesting combination of these aspirations. A native bovid of Southeast Asia now ‘endangered’ in its native range, banteng were introduced into northern Australia in 1849. Today, a population of 8,000–10,000 resides on one small, isolated peninsula in western Arnhem Land, Northern Territory and is harvested by both recreational (trophy) and aboriginal subsistence hunters. Indigenous, industry and conservationist stakeholders differ in their requirements for population management. Here we analyze the ecological and economic costs/benefits of a series of potential harvest management options for Australia's banteng population, with the aim being either to: (1) maximize sustainable yield (MSY); (2) maximize harvest of trophy males; (3) maximize indigenous off‐take; (4) suppress density or completely eradicate the population; (5) minimize risk of extinction whilst limiting range expansion; (6) scenarios incorporating two or more of options 1–5. The modeling framework employed stochastic, density‐regulated matrix population models with life‐history parameters derived from (i) allometric relationships (for estimating r_max, generation length, fecundity and densities for a banteng‐sized mammal) and (ii) measured vital rates for wild and captive banteng and other Bos spp. For each management option, we present a simple economic analysis that incorporates estimated costs of management implementation and associated profits projected. Results demonstrate that revenue of >Ä$200,000 is possible from meat production and safari hunting without compromising long‐term population stability or the conservation status of this endangered bovid.     

Abelian real W*-algebras

In this paper, we point out that most results on abelian (complex)W ^*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic toL _τ ^∞ ([0, 1]) (all real functions inL ^∞([0, 1])), orL ^∞([0, 1]) (as a realW ^*-algebra), orL _τ ^∞ ([0, 1]) ⋇L ^∞ ([0, 1]) (as a realW ^*-algebra), and it is different from the complex case. Partially supported by the NNSF     

Integral Lie powers of a lattice for the cyclic group of order 2

Let L_n denote the n-th homogeneous component of the free Lie ring L(W) on a given \Bbb ZC₂{{\Bbb Z}}C_{2}-lattice W. This paper gives explicit formulae for the multiplicities of the three indecomposable \Bbb ZC₂{{\Bbb Z}}C_{2}-lattices in a Krull-Schmidt decomposition of L_n. In the case where W is a free \Bbb ZC₂{{\Bbb Z}}C_{2}-lattice, L_n is shown to have no non-zero direct summand on which C₂ acts trivially - this extends a result of R. M. Bryant for the special case where W is the regular \Bbb ZC₂{{\Bbb Z}}C_{2}-lattice. As an application, the structure of the higher dimensional modules associated to a non-cyclic free presentation of C₂ is determined.     

Geometrization of 3-dimensional Coxeter orbifolds and Singer’s conjecture

Associated to any Coxeter system (W, S), there is a labeled simplicial complex L and a contractible CW-complex Σ _L (the Davis complex) on which W acts properly and cocompactly. Σ _L admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of , then Σ _L is a contractible n-manifold. In this case, the orbit space, K _L := Σ _L /W, is a Coxeter orbifold. We prove a result analogous to the JSJ-decomposition for 3-dimensional manifolds: Every 3-dimensional Coxeter orbifold splits along Euclidean suborbifolds into the characteristic suborbifold and simple (hyperbolic) pieces. It follows that every 3-dimensional Coxeter orbifold has a decomposition into pieces which have hyperbolic, Euclidean, or the geometry of . (We leave out the case of spherical Coxeter orbifolds.) A version of Singer’s conjecture in dimension 3 follows: That the reduced ℓ ²-homology of Σ _L vanishes.