We study classical and quantum phases in the adiabatic BornOppenheimer context. These include a classical astronomical case, the general dual description of the phases, a new “Paradox” connected to scattering Berry phase and its resolution and various elaboration of topological/geometrical/non-abelian phases.

The talk surveys both recent and ‘classical’ studies of k-server queueing systems. There will not be time to do justice to more than a selection of the following topics. 1. EXISTENCE. Kiefer and Wolfowitz’ (1955) proof of the existence of a stationary regime for the GI/GI/k FCFS system relies on ‘An Essential Lemma’. In reality it hinges on a strong law of large numbers, of which variants are u...

Classical stability results and tests on the stability of a given polynomial are proved and derived here using a simple continuity property. The resulting new proofs given of the Hermite-Bielei theorem and the Routh and Jury tests are elementary and insightful. Most important, the proofs given here would allow the instructor to present these fundamental topics of control theory, for the first t...

This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known as Hibi ideals, determinantal ideals of generic matrices of indeterminates, and ideals generated by Pfaffians of generic skew symmetric matrices. We give a s...

We construct an analogue of the Stickelberger ideal for real abelian fields by means of cyclotomic units and a Kummer-type pairing with values in a completed p-adic group-ring. We give several different descriptions of this ideal, prove the analogue of Stickelberger's Theorem using Thaine's methods and establish links with certain Fitting ideals in a particular case. Our construction fits into ...

This note is a report on a computer investigation of some small classical Ramsey numbers. We establish new lower bounds for the classical Ramsey numbers R(3, 11) and R(4, 8). In the first case, the bound is improved from 46 (a record that had stood for 46 years) to 47; and in the second case the bound is improved from 57 to 58. The classical Ramsey number R(s, t) is the smallest integer n such ...

This paper introduces economists to some fixed point theorems for discontinuous mappings with non-convex images on a non-convex domain. These theorems have recently been developed based on a new approach by mathematical economists and mathematicians. The new method of proof is first transformed into a sort of metatheorem, which is then used to obtain a set of necessary and sufficient conditions...

‎we consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎we present a class of problems that are easily solved by reduction to the classi...

The quest of this work is to present discussions some fundamental questions economics in the era quantum technology, which require a treatment different from studied thus far literature. A study economic behavior will become center attention economists coming decades. We analyze economy players produce and consume goods. They meet randomly barter with neighbors bilaterally for goods they produc...

in line with the unprecedented development of public sector in the 20th century, many economists have studied the efficiency of the public sector in economic growth and development. evidently, one of the important aspects of these studies is to determine the optimum size of government whose theoretical principles and approaches as well as practical methods have been argued about in public secto...