<Emphasis Type="Italic">P</Emphasis>-adic sets of range uniqueness

We study sets of range uniqueness (SRU’s) in a complete, ultrametric, algebraically closed fieldK for analytic elements. We find monotonic distances sequences which appear to be SRU’s completely different from those known in ©. On the other hand, most of open closed sets cannot be SRU’s.     

The F<Subscript>4</Subscript>-algorithm for Euclidean rings

In this short note, we extend Faugére’s F₄-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F₄-algorithm is based on the simultaneous reduction of several polynomials.     

A Convex-Analytical Approach to Extension Results for <Emphasis Type="Italic">n</Emphasis>-Cyclically Monotone Operators

Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem. In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.     

Strong openness of multiplier ideal sheaves and optimal <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> extension

In this paper, we reveal that our solution of Demailly’s strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Kollár and Jonsson-Mustat? implies the truth of twisted versions of the strong openness conjecture; our optimal L ² extension implies Berndtsson’s positivity of vector bundles associated to holomorphic fibrations over a unit disc.     

Smoothed nonparametric tests and approximations of <Emphasis Type="Italic">p</Emphasis>-values

We propose new smoothed sign and Wilcoxon’s signed rank tests that are based on kernel estimators of the underlying distribution function of the data. We discuss the approximations of the p-values and asymptotic properties of these tests. The new smoothed tests are equivalent to the ordinary sign and Wilcoxon’s tests in the sense of Pitman’s asymptotic relative efficiency, and the differences between the ordinary and new tests converge to zero in probability. Under the null hypothesis, the main terms of the asymptotic expectations and variances of the tests do not depend on the underlying distribution. Although the smoothed tests are not distribution-free, making use of the specific kernel enables us to obtain the Edgeworth expansions, being free of the underlying distribution.     

Stochastic calculus with respect to <Emphasis Type="Italic">G</Emphasis>-Brownian motion viewed through rough paths

We study rough path properties of stochastic integrals of Itô’s type and Stratonovich’s type with respect to G-Brownian motion. The roughness of G-Brownian motion is estimated and then the pathwise Norris lemma in G-framework is obtained.     

When <Emphasis Type="Italic">q</Emphasis> theory meets large losses risks and agency conflicts

We incorporate large losses risks into the DeMarzo et al.(2012) model of dynamic agency and the q theory of investment. The large losses risks induce losses costs and losses arising from agency conflicts during the large losses prevention process. Both of them reduce firm’s value, distort investment policy and generate a deeper wedge between the marginal and average q. In addition, we study the implementation of the contract to enhance the practical utility of our model. The agent optimally manages the firm’s cash flow and treats the cash reservation and credit line as the firm’s financial slack, and hedges the productivity shocks and large losses shocks via futures and insurance contracts, respectively.     

On chief factors of parabolic maximal subgroups of the group <Superscript>2</Superscript><Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript>(<Emphasis Type="Italic">q</Emphasis><Superscript>2</Superscript>)

We consider the pseudovariety generated by all finite monoids on which Green’s relations R and H coincide. We find a new algorithm that determines if a given finite monoid belongs to this pseudovariety.     

Multipliers on Vector-valued <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-spaces for Hypergroups

In this article, we extend the well known Wendel’s theorem to the context of vector-valued L¹-spaces on hypergroups. In this regard, various cases have been studied.     

A new functor from <Emphasis Type="Italic">D</Emphasis><Subscript>5</Subscript>-Mod to <Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript>-Mod

We find a new representation of the simple Lie algebra of type E ₆ on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen’s idea of mixed product, we construct a new functor from D ₅-Mod to E ₆-Mod. A condition for the functor to map a finite-dimensional irreducible D ₅-module to an infinite-dimensional irreducible E ₆-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant’s characteristic identities plays a key role.     

<Emphasis Type="Italic">K</Emphasis><Subscript>4</Subscript>-free subgraphs of random graphs revisited

In Combinatorica 17(2), 1997, Kohayakawa, ?uczak and Rödl state a conjecture which has several implications for random graphs. If the conjecture is true, then, for example, an application of a version of Szemerédi’s regularity lemma for sparse graphs yields an estimation of the maximal number of edges in an H-free subgraph of a random graph G _{n, p} . In fact, the conjecture may be seen as a probabilistic embedding lemma for partitions guaranteed by a version of Szemerédi’s regularity lemma for sparse graphs. In this paper we verify the conjecture for H = K ₄, thereby providing a conceptually simple proof for the main result in the paper cited above.     

An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-inequality

An estimate of an optimal argument in the sharp Jackson-Stechkin inequality in the space L ₂(? ⁿ ) is proved in the case of a generalized modulus of continuity; its special case is the classical modulus of continuity. Similar statements hold for the torus \(\mathbb{T}^n \). The obtained results agree with Chernykh’s classical one-dimensional theorems and refine some results by S.N. Vasil’ev, A.I. Kozko, and A.V. Rozhdestvenskii.     

Arrow's theorem is not a surprising result

Arrow's theorem asserts that it is impossible to find a procedure which aggregates n given complete preorders into one complete preorder and which has ‘rational’ properties.Some authors have proposed to solve this problem in building what could be called ‘preaggregation methods’. The purpose of this paper is to study the Arrow's problematic in this context.The obtained results lead to an interpretation of Arrow's theorem which shows that it is rather natural, although many authors present it as a surprising result or even as a paradox.The last section compares the structures of the sets of decisive sets associated to aggregation and preaggregation procedures.     

Transcendental values of class group <Emphasis Type="Italic">L</Emphasis>-functions

Let K be an algebraic number field and f a complex-valued function on the ideal class group of K. Then, f extends in a natural way to the set of all non-zero ideals of the ring of integers of K and we can consider the Dirichlet series \({L(s,f) =\sum_{{\mathfrak a}} f({\mathfrak a}){\bf N}({\mathfrak a})^{-s}}\) which converges for \({{\mathfrak R}(s) >1 }\). After extending this function to \({{\mathfrak R}(s)=1}\), and in the case that f does not contain the trivial character, we study the special value L(1, f) when f is algebraic valued and K is an imaginary quadratic field. Applying Kronecker’s limit formula and Baker’s theory of linear forms in logarithms, we derive a variety of results related to the transcendence of this special value.     

Constructive extensions of three summation formulas for <Emphasis Type="Italic">q</Emphasis>-series and their applications to Bailey pairs

This paper is devoted to three constructive extensions associated with the Pfaff–Saalschütz \({}_3\phi _2\), Watson’s \({}_6\phi _5\), and Jackson’s \({}_8\phi _7\) summation formulas in basic hypergeometric series. All these lead to new general recurrence approaches to well-known Bailey pairs and well-poised Bailey pairs, as well as the emergence of new Pfaff–Saalschütz pairs. Some new applications to q-series are also investigated.     

On Tutt's Characterization of graphic matroids—a graphic proof

In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of ‘signed graph’ and it is ‘graphic’ in the sense that it can be presented almost entirely by drawing (signed) graphs. © 1995 John Wiley & Sons, Inc.     

A Note on Complex <Emphasis Type="Italic">p</Emphasis>-Adic Exponential Fields

In this paper we apply Ax-Schanuel’s Theorem to the ultraproduct of p-adic fields in order to get some results towards algebraic independence of p-adic exponentials for almost all primes p.     

A note on levene's tests for equality of variances

Consider testing for equality variances in a one-way analysis of variance. Levene's test is the usual F-test for equality of means computed on psuedo-observations, which one defines as the absolute deviations of the data points from an estimate of the group ‘center’. We show that, asymptotically, Levene's test has the correct level whenever the estimate of group ‘center’ is an estimate of group median. This explains why published Monte-Carlo studies have found that Levene's original proposal of centering at the sample mean has the correct level only for symmetric distributions, while centering at the sample median has correct level even for asymmetric distributions. Generalizations are discussed.     

Basic aspects of geopotential field approximation from satellite‐to‐satellite tracking data

The satellite‐to‐satellite tracking (SST) problems are characterized from mathematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth's gravitational potential by ‘scalar basis systems’ and (vectorial) approximation of the gravitational field by ‘vectorial basis systems’. Finally, the mathematical justification is given for approximating the external geopotential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi‐poles) consistent to a given set of SST data. Copyright © 2001 John Wiley & Sons, Ltd.