Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency

A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of weight systems generating weighted prenucleoli that satisfy SAM is open, which implies that for weight systems close enough to any regular system, the weighted prenucleolus satisfies SAM. We also provide a necessary condition for SAM for symmetrically weighted nucleoli. Moreover, we show that the per capita nucleolus on balanced games is characterized by single-valuedness (SIVA), translation covariance (TCOV) and scale covariance (SCOV), and equal adjusted surplus division (EASD), a property that is comparable to but stronger than ESD. These properties together with ESD characterize the per capita prenucleolus on larger sets of TU games. EASD and ESD can be transformed to independence of (adjusted) proportional shifting, and these properties may be generalized for arbitrary weight systems p to I(A)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IASp and on larger sets by additionally requiring ISp.

ON A NEW FAMILY OF KALMAN FILTER ALGORITHMS FOR INTEGRATED NAVIGATION

Here we present a review on a new family of Kalman filter algorithms which recently developed for integrated navigation. In particular it is useful for vision based navigation due to the type of data. Here we mainly focus on three algorithms namely weighted Total Kalman filter (WTKF), integrated Kalman filter (IKF) and constrained integrated Kalman filter (CIKF). The common characteristic of these algorithms is that they can consider the neglected random observed quantities which may appear in the dynamic model. Moreover, our approach makes use of condition equations and straightforward variance propagation rules. The WTKF algorithm can deal with problems with arbitrary weight matrixes. Both of the observation equations and system equations can be dynamic-errors-in-variables (DEIV) models in the IKF algorithms. In some problems a quadratic constraint may exist. They can be solved by CIKF algorithm. Finally, we compare four algorithms WTKF, IKF, CIKF and EKF in numerical examples.

Linear invariants and the quantum dynamics of a nonstationary mesoscopic RLC circuit with a source

In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussian wave packet solutions for this electromagnetic oscillation circuit and employ them to calculate the quantum fluctuations of the charge and the magnetic flux as well as the associated uncertainty product. We also show that the width of the Gaussian packet and the fluctuations do not depend on the external power.

CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES

In this paper, we construct free commutative integro-differential algebras by applying the method of Gröbner–Shirshov bases. We establish the Composition-Diamond Lemma for free commutative differential Rota–Baxter (DRB) algebras of order n. We also obtain a weakly monomial order on these algebras, allowing us to obtain Gröbner–Shirshov bases for free commutative integro-differential algebras on a set. We finally generalize the concept of functional monomials to free differential algebras with arbitrary weight and generating sets from which to construct a canonical linear basis for free commutative integro-differential algebras.

ON IHARA'S LEMMA FOR DEGREE ONE AND TWO COHOMOLOGY OVER IMAGINARY QUADRATIC FIELDS

We prove a version of Ihara's Lemma for degree q = 1, 2 cuspidal cohomology of the symmetric space attached to automorphic forms of arbitrary weight (k ≥ 2) over an imaginary quadratic field with torsion (prime power) coefficients. This extends an earlier result of the author [Ihara's lemma for imaginary quadratic fields, J. Number Theory128(8) (2008) 2251–2262] which concerned the case k = 2, q = 1. Our method is different from [Ihara's lemma for imaginary quadratic fields, J. Number Theory128(8) (2008) 2251–2262] and uses results of Diamond [Congruence primes for cusp forms of weight k ≥ 2, Astérisque196–197 (1991) 205–213] and Blasius–Franke–Grunewald [Cohomology of S-arithmetic subgroups in the number field case, Invent. Math.116(1–3) (1994) 75–93]. We discuss the relationship of our main theorem to the problem of the existence of level-raising congruences.

Framework for Decision-Making

This chapter presents a framework for assessing competition rules. An economic approach to limiting coordinated oligopolistic price elevation seeks to determine liability and apply sanctions based primarily on the deterrence benefits that result as well as any chilling of desirable behavior that may ensue, while also considering the expense of operating the regime. In assessing the cost of false positives, attention focuses on incidental negative behavioral effects, not on mistakes that are defined by reference to proxy legal standards and then given arbitrary weight. An example that will prove important involves imposing sanctions on firms that actually charged elevated oligopoly prices, the prospect of which deters such behavior. This outcome is favorable in terms of social welfare but under some legal standards would be deemed to be an undesirable error in cases in which the firms did not employ forbidden modes of communication.

DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS OF HIGHER ORDER AND ARBITRARY WEIGHT

We consider the Dirichlet problem for a degenerate differential-operator equation of higher order with arbitrary weight-function ρ(t). We establish some embedding and compactness theorems in weighted Sobolev spaces, show existence and uniqueness of the generalized solutions. We also give a description of the spectrum for the corresponding operator.

Computing coefficients of modular forms

This chapter applies the main result on the computation of Galois representations attached to modular forms of level one to the computation of coefficients of modular forms. It treats the case of the discriminant modular form, that is, the computation of Ramanujan's tau-function at primes, and then deals with the more general case of forms of level one and arbitrary weight k, reformulated as the computation of Hecke operators Tⁿ as ℤ-linear combinations of the Tᵢ with i < k = 12. The chapter gives an application to theta functions of even, unimodular positive definite quadratic forms over ℤ.