scholarly journals PAIR CORRELATOR IN THE ITZYKSON-ZUBER INTEGRAL

1992 ◽  
Vol 07 (37) ◽  
pp. 3503-3507 ◽  
Author(s):  
A. MOROZOV
Keyword(s):  
Explicit Expression ◽  
Unitary Group ◽  
Pair Correlator

An explicit expression is suggested for the average [Formula: see text] over the unitary group SU (N) with the Itzykson-Zuber measure [dU] exp tr ΦUΨU†.

scholarly journals Inventory decision in a periodic review inventory model with two complementary products

2021 ◽  
Author(s):  
Saeed Poormoaied
Keyword(s):  
Approximation Algorithm ◽  
Explicit Expression ◽  
Interaction Effect ◽  
Expected Profit ◽  
Base Stock ◽  
Optimal Solutions ◽  
Periodic Review ◽  
Profit Rate ◽  
Complementary Products ◽  
Demand Processes

AbstractInteraction effect across complementary products plays an important role in characterizing the optimal inventory policy. The inventory levels of complementary products are interrelated due to interaction between demand streams. In this paper, we consider a periodic review base-stock policy in the presence of two complementary products with interrelated demands and joint replenishment. Demands are modeled by a Poisson process and any unmet demand is lost. Demands can be in sets of one unit of each or jointly. If an arrival demand requests two products jointly and one of the products is not in stock, then the whole demand is lost. We aim to investigate how this interrelated demand phenomenon influences the optimal base-stock levels and the period length of a periodic review policy. We utilize the renewal reward theorem to derive the explicit expression of the expected profit rate in the system. The goal is to determine the optimal period length and the base-stock levels such that the expected profit rate is maximized. Enumeration and approximation algorithms are employed to find the optimal and near-optimal solutions, respectively. The approximation algorithm is based on a scenario with independent demand processes which results in an explicit expression for the long-run profit per time unit and leads to analytical solutions for optimal policies. Our numerical results reveal that the solutions obtained by the approximation algorithm are close to optimal solutions. Numerical experiences show that the maximum profit in the system is achieved if the proportion of customers with jointly demand increases. Moreover, the interaction effect between demand processes has a significant impact on the control policy performance when the units lost sales and unit holding costs are high, and the demand rare is low.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

Modification of HAM/3 excitation energies for ΠΠ* transitions of linear molecules

1980 ◽  
Vol 58 (16) ◽  
pp. 1687-1690 ◽  
Author(s):  
Delano P. Chong
Keyword(s):  
Excitation Energy ◽  
Explicit Expression ◽  
Excited States ◽  
Configuration Interaction ◽  
Excitation Energies ◽  
Carbon Suboxide ◽  
Numerical Examples ◽  
Energy Correction ◽  
Linear Molecules ◽  
Configuration Interaction Calculations

The excitation energies calculated by the HAM/3 procedure for ΠΠ* transitions in linear molecules can be internally inconsistent by as much as ± 0.6 eV. In the recent study by Åsbrink etal., the problem was avoided by adopting Recknagel's expressions and requiring the proper average ΠΠ* excitation energy. In this paper, we trace the small inconsistency back to its origin in HAM/3 theory and derive the analytical expression for the energy correction as well as Recknagel's formulas. Numerical examples studied include all seven linear molecules investigated by Åsbrink etal. The explicit expression for the correction enables us to perform meaningful configuration-interaction calculations on the excited states, as illustrated by the carbon suboxide molecule.

A bivariate optimal replacement policy for a repairable system

1994 ◽  
Vol 31 (4) ◽  
pp. 1123-1127 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Explicit Expression ◽  
Average Cost ◽  
Replacement Policy ◽  
Repairable System ◽  
Optimal Replacement ◽  
Long Run ◽  
Optimal Replacement Policy ◽  
Working Age ◽  
Better Than

In this paper, a repairable system consisting of one unit and a single repairman is studied. Assume that the system after repair is not as good as new. Under this assumption, a bivariate replacement policy (T, N), where T is the working age and N is the number of failures of the system is studied. The problem is to determine the optimal replacement policy (T, N)∗such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, under some conditions, we show that the policy (T, N)∗ is better than policies N∗ or T∗.

The Franklin's Tale: Chaucer or the Critics

PMLA ◽  
1974 ◽  
Vol 89 (3) ◽  
pp. 454-462 ◽  
Author(s):  
Gertrude M. White
Keyword(s):  
Explicit Expression ◽  
Canterbury Tales ◽  
Moral Ideal ◽  
The Canterbury Tales ◽  
The Relationship

The Franklin's Tale, which has caused much disagreement among critics of Chaucer, may best be understood in the light of Chaucer's own writings, particularly The Merchant's Tale and three short lyrics, “Truth,” “Gentilesse,” and “Lak of Stedfastnesse.” The relationship between the characters and events of the two Tales dramatizes a moral ideal that operates throughout The Canterbury Tales and is given explicit expression in the lyrics. It may be summed up as “gentilesse,” which consists, in the Knight's words, of “Trouthe and honour, fredom and curteisie.” In a variety of contexts, this standard operates throughout Chaucer's writings. An understanding of it puts The Franklin's Tale into clear perspective, identifies its true theme, answers its critics, accounts for its apparent absurdities, inconsistencies, and contradictions, and reveals its suitability to its teller.

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