An Interactive Multiple Criteria Approach to Ranking Alternatives

In this paper we are concerned with ranking various orderings of a set of alternatives to a composite order as a multiple criteria problem. The orderings (called preference orderings) can be real preference orderings or any natural orderings. The objective is to find the most preferred order of the decision maker using the preference orderings as criteria.In principle, the problem can be formulated as a multiple objective linear programming problem using the model of Bowman and Colantoni and then solved with the interactive method proposed by Zionts and Wallenius. However, the fact that we are dealing with integer variables prohibits us from applying this approach as such. We discuss the problem formulation and propose a modified approach to that of Zionts and Wallenius for solving the problem.     

Consistency in explicitly broken N = 1 supergravity with matter couplings

Using N = 1 supergravity coupled to general, gauged, N = 1 matter, we show that the addition of a wide class of explicit supersymmetry breaking terms in the N = 1 matter fields can still lead to the spin $\text{3}\text{2}$ field satisfying an equation of motion in which propagation is causal. We argue that a similar result holds in the case of N = 2 supergravity coupled to matter, plus explicit terms.     

Carleson measures for weighted holomorphic Besov spaces

We obtain characterizations of positive Borel measures μ on B ⁿ so that some weighted holomorphic Besov spaces B _s ^p (ω,B ⁿ ) are embedded in L ^p (d μ).     

Harmonic maps between annuli on Riemann surfaces

Let ρ _Σ = h(|z|²) be a metric in a Riemann surface Σ, where h is a positive real function. Let H _{r 1} = {w = f(z)} be the family of a univalent ρ _Σ harmonic mapping of the Euclidean annulus A(r ₁, 1):= {z: r ₁ < |z| < 1} onto a proper annulus A _Σ of the Riemann surface Σ, which is subject to some geometric restrictions. It is shown that if A _Σ is fixed, then sup{r ₁: ℋ _{r 1} ≠ ∅} < 1. This generalizes similar results from the Euclidean case. The cases of Riemann and of hyperbolic harmonic mappings are treated in detail. Using the fact that the Gauss map of a surface with constant mean curvature (CMC) is a Riemann harmonic mapping, an application to the CMC surfaces is given (see Corollary 3.2). In addition, some new examples of hyperbolic and Riemann radial harmonic diffeomorphisms are given, which have inspired some new J. C. C. Nitsche-type conjectures for the class of these mappings.     

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N-fold integer minimization problems for which our approach provides polynomial time solution algorithms.     

Stability of Parametric Quasivariational Inequality of the Minty Type

In this paper, stability of a parametric quasivariational inequality of the Minty type is studied via various sufficient conditions characterizing upper and lower semicontinuity of the solution sets as well as the approximate solution sets. Sufficient conditions ensuring upper semicontinuity of the approximate solution sets of an optimization problem with quasivariational inequality constraints are also presented.     

Positive-Part Moments via the Fourier–Laplace Transform

Integral expressions for positive-part moments E X₊^pmathsf{E},X_{+}^{p} (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments.     

On complex matrices with simple spectrum that are unitarily similar to real matrices

Suppose that one should verify whether a given complex n × n matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before, the spectrum is required to be simple, but pairs of complex conjugate eigenvalues $ \lambda ,\bar \lambda $ \lambda ,\bar \lambda are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal.     

The coherent-constructible correspondence and Fourier-Mukai transforms

As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝ ⁿ . In this paper we investigate and reprove some of Kawamata’s results from this perspective.     

Geometric properties of the ridge function manifold

We study geometrical properties of the ridge function manifold \(\mathcal{R}_n\) consisting of all possible linear combinations of n functions of the form g(a· x), where a·x is the inner product in \({\mathbb R}^d\). We obtain an estimate for the ε-entropy numbers in terms of smaller ε-covering numbers of the compact class G _n,s formed by the intersection of the class \(\mathcal{R}_n\) with the unit ball \(B\mathcal{P}_s^d\) in the space of polynomials on \({\mathbb R}^d\) of degree s. In particular we show that for n?≤?s ^d???1 the ε-entropy number H _ε (G _n,s,L _q ) of the class G _n,s in the space L _q is of order nslog1/ε (modulo a logarithmic factor). Note that the ε-entropy number \(H_\varepsilon(B\mathcal{P}_s^d,L_q)\) of the unit ball is of order s ^d log1/ε. Moreover, we obtain an estimate for the pseudo-dimension of the ridge function class G _n,s.