922,177 research outputs found
Division by zero in common meadows
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has been replaced by the stronger axiom (12), this appears to be necessary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
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
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
On The Exact Quotient Of Division By Zero
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
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
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