922,177 research outputs found

    Division by zero in common meadows

    Get PDF
    Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.Comment: 17 pages, 4 tables; differences with v3: axiom (14) of Mda (Table 2) has been replaced by the stronger axiom (12), this appears to be necessary for the proof of Theorem 3.2.

    Division by zero in non-involutive meadows

    Get PDF
    Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study `non-involutive meadows', i.e.\ variants of meadows in which the multiplicative inverse of zero is not zero, and pay special attention to non-involutive meadows in which the multiplicative inverse of zero is one.Comment: 14 page

    Adaptive poleplacement: the division by zero problem

    Get PDF
    We re-examine the division by zero problem which occurs in certainty equivalence based indirect adaptive control algorithms applied to linear systems. By exploiting a parametrization for linear systems induced by the continued fraction description of its transfer function, the division by zero problem obtains a very simple geometric representation that can be used to virtually eliminate the problem in the adaptive algorith

    Division by zero in common meadows

    Get PDF

    On The Exact Quotient Of Division By Zero

    Full text link
    This paper aims to present the solution to the most significant problem in all of analysis, namely, the problem of assigning a precise quotient for the division by zero, . It is universally acknowledged that if nbspand nbspare two integers where , the fraction , when evaluated, gives rise to only one rational quotient. But, here in analysis, at least three quotients have been assigned to the fraction nbspby various departments of analysis. Moreover, so much hot debate has emerged from the discussion which has arisen from this subject. It is, therefore, the purpose of this paper to furnish the exact quotient for the special and most significant case of division by zero, the fraction .nbs

    Loosely synchronized spreading code aided network performance of quasi-synchronous UTRA-like TDD/CDMA systems

    No full text
    In this paper we investigate the achievable capacity of a UTRA-like Time Division Duplex (TDD) Code Division Multiple Access (CDMA) system employing Loosely Synchronized (LS) spreading codes. The family of operational CDMA systems is interference limited, suffering from Inter-Symbol-Interference (ISI), since the orthogonality of the spreading sequences is destroyed by the frequency selective channel. They also suffer from Multiple-Access-Interference (MAI) owing to the non-zero cross-correlations of the spreading codes. By contrast, the family of LS codes exhibits a so-called Interference Free Window (IFW), where both the auto-correlation and cross-correlation of the codes become zero. Therefore LS codes have the promise of mitigating the effects of both ISI and MAI in time dispersive channels. Hence, LS codes have the potential of increasing the capacity of CDMA networks. This contribution studies the achievable network performance in comparison to that of a UTRA-like TDD/CDMA system using Orthogonal Vari- MSO able Rate Spreading Factor (OVSF) codes
    • …
    corecore