Tridiagonal pairs and the q-tetrahedron algebra

In this paper we further develop the connection between tridiagonal pairs and the q-tetrahedron algebra $\boxtimes_q$. Let V denote a finite dimensional vector space over an algebraically closed field and let A, A^* denote a tridiagonal pair on V. For $0 \leq i \leq d$ let $\theta_i$ (resp. $\theta^*_i$) denote a standard ordering of the eigenvalues of A (resp. A^*). Fix a nonzero scalar q which is not a root of unity. T. Ito and P. Terwilliger have shown that when $\theta_i = q^{2i-d}$ and $\theta^*_i = q^{d-2i}$ there exists an irreducible $\boxtimes_q$-module structure on V such that the $\boxtimes_q$ generators x_{01}, x_{23} act as A, A^* respectively. In this paper we examine the case in which there exists a nonzero scalar c in K such that $\theta_i = q^{2i-d}$ and $\theta^*_i = q^{2i-d} + c q^{d-2i}$. In this case we associate to A,A^* a polynomial P and prove the following equivalence. The following are equivalent: (i) There exists a $\boxtimes_q$-module structure on V such that x_{01} acts as A and x_{30} + cx_{23} acts as A^*, where x_{01}, x_{30}, x_{23} are standard generators for $\boxtimes_q$. (ii) P(q^{2d-2} (q-q^{-1})^{-2}) \neq 0. Suppose (i),(ii) hold. Then the $\boxtimes_q$-module structure on V is unique and irreducible.Comment: 30 pages, bibliography added (references were missing in first version), published in Linear Algebra and its Application

The consequences of endogenous timing for diversification strategies of multimarket firms

When firms diversify into new markets in spite of the existence of diseconomies of scope, not only firms' profits are affected, but also potential welfare is reduced. Nevertheless, multimarket competition is the outcome of a game when players move simultaneously. A Cournot model is developped where players can choose the timing of their action before deciding over quantities. This helps firms to avoid the inefficiencies that ocur with multimarket competition. Whenever the timing game has an impact on the outcome of the basic game, the consequences for welfare are positive. -- Die Diversifikation von Unternehmen in neue Märkte führt zu Effizienzverlusten und Gewinneinbußen, wenn dadurch Spezialisierungsvorteile nicht mehr genutzt werden können. Dennoch ist Diversifikation das Ergebnis eines simultanen Cournotspiels, in welchem sich zwei Unternehmen auf zwei Märkten als potentielle Wettbewerber gegenüberstehen. Die Einführung einer Vorstufe zum Cournotspiel, in welcher Unternehmen den Zeitpunkt ihrer Angebotsentscheidung in beiden Märkten wählen können, kann einen Teil dieser Ineffizienzen beseitigen. Unternehmen konzentrieren sich auf je einen Markt. Wegen der Existenz potentieller Konkurrenz sind die Wohlfahrtswirkungen trotz der resultierenden monopolistischen Marktstruktur im Vergleich zum Ausgangsspiel positiv.

Interdivisional information sharing: the strategic advantage of knowing nothing

Divisional managers of multiproduct firms often only have precise information about market conditions of their own market. They may have expectations about the demand function of markets served by other divisions. When divisional profits are linked due to interrelated costs or demand parameters, it may be advantageous for a firm to provide each division with information about the other division's demand parameters. I study the incentives of owners to implement such an information structure and the value of intrafirm information sharing in a two firm - two market setting where there are interdivisional cost linkages. It is shown, that the value of bilateral information consists of a (positive) efficiency and a (negative) revenue effect, the weight of which depends on the incentive scheme used to evaluate managers. Regardless of managers' incentive scheme, owners of both firms always choose interdivisional information sharing, even if profits are lower than in a situation of noninformation. -- Manager divisionaler Mehrproduktunternehmen sind oftmals in der Lage, Nachfragebedingungen innerhalb der von ihnen betreuten Märkte einzuschätzen. Marktparameter von Märkten außerhalb ihres Verantwortungsbereich sind ihnen i.d.R. nicht bekannt. Der Wert von und die Anreize zu interdivisionalem Informationsaustausch, wenn divisionale Profite über eine gemeinsame Kostenfunktion miteinander verbunden sind, wird im Rahmen eines zweistufigen Modells untersucht, in welchem zwei Zweiproduktunternehmen miteinander im Wettbewerb stehen. In einer ersten Stufe entscheiden sich die Eigner über die Einführung eines Managementinformationssystems, in der zweiten Stufe treten treffen divisionale Manager ihre Mengenentscheidungen. Der Wert der Information und das Ergebnis des Spiels hängen u.a. von dem Anreizsystem ab, nach welchem Manager beurteilt werden: Information ist nur dann vorteilhaft, wenn Manager divisionale Gewinne maximieren; sie hat negative Wirkungen bei Anreizsystemen, welche Manager zur Internalisiering divisionsexterner Effekte induzieren.

The effects of inorganic nitrogen and phosphorus enrichment on herbaceous species growth of the Kimages Creek wetland (VA)

Dissolved inorganic nitrogen (DIN) and dissolved inorganic phosphorus (DIP) infiltrate waterways through fertilizer application, urban stormwater runoff, and sewer infrastructure leaks. As surrounding waterbodies experience increased DIN and DIP inputs, wetlands can experience corresponding nutrient enrichment. Vegetation uses DIN and DIP for structural growth, color, and seed production. Changes in DIN and DIP availability can influence species distribution due to differences in photosynthetic rates, root morphology and structure, and tissue type. DIP and DIN inputs are projected to increase 15-30% and 30-60% in the next fifty years¹. It is of interest to examine plant growth characteristics within this nutrient enrichment projection as well as nutrient enrichment from a potential 100-year projection to analyze future species composition responses within a freshwater tidal marsh

Optimization of multimagnetometer systems on a spacecraft

Magnetometers on a radial boom may be employed to determine the first N-1 multipole contributions to the spacecraft field and improve the total accuracy of a magnetic field experiment. The total error for systems of one to four magnetometers is investigated. The optimal magnetometer locations, for which the total error is a minimum, are found for given boom-length, instrument errors and magnetic field models characteristic for spacecraft with only a restricted or ineffective magnetic cleanliness program

Theoretical limits on Jovian radio belts

An attempt is made to establish safety limits for space missions near Jovian radio belts. A proton belt model was constructed and analyzed in an effort to set these limits based on the possible stability of radiation belts. Calculation results are graphed