We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite @math -systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems.
12 @cite_18 . Okado constructed bijections between the rigged configurations and the crystals (resp. virtual crystals) corresponding to @math , with @math for @math , for @math and @math (resp. @math ). As a corollary, the type II formula of those @math was proved for @math and @math .
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A device having utility in interfering with a person's desire to hold an object such as a cigarette, cigar or pipe, between his lips, i.e., an anti-smoking device. In the form of a cigarette holder, it includes a generally tubular shell having first and second ends, with the first end being adapted to receive a cigarette; the second end thereof includes structure adapted to be held between a person's lips. A DC voltage source (such as a dry cell battery) of at least six volts and preferably nine volts is mounted within the shell. First and second electrically conductive members are connected to the output of the DC source, with the distal ends of said conductive members extending alongside the lip-contacting structure so that they may be readily touched by a person's lips. The distal ends of said conductive members are separated so as to form a normally open electrical path, such that placing the lip-contacting structure between a person's lips will instantaneously close the electrical path and result in the discharge of DC current from said source through the lips. A potentiometer is optionally provided to adjust the flow of current from a minimum of about one milliamp (in order to be discernable) to a maximum of about five milliamps (so as to avoid intolerable sensations). Additionally, means are disclosed for re-charging a battery which is permanently mounted within the shell of a cigarette holder or the like.