We give a new and short proof of the Mallows-Sloane upper bound for self-dual codes. We formulate a version of Greene’s theorem for normalized weight enumerators. We relate normalized rank-generating polynomials to two-variable zeta functions. And we show that a selfdual code has the Clifford property, but that the same property does not hold in general for formally self-dual codes.

BACKGROUND AND PURPOSE For more widespread clinical use advanced imaging methods such as relative cerebral blood volume must be both accurate and repeatable. The aim of this study was to determine the repeatability of relative CBV measurements in newly diagnosed glioblastoma multiforme by using several of the most commonly published estimation techniques. MATERIALS AND METHODS The relative CB...

The accurate determination of distances from Hip-parcos allows to compare the position in the HR diagram of constant, known variable and chemically peculiar stars in the lower part of the instability strip, including the available new information on variability. Distances are larger and luminosities are slightly higher than those derived from previous calibrations. Masses are then higher. Conse...

We have developed a Prolog visualization system that is intended to support Prolog programming education. The system uses Logichart diagrams to visualize Prolog programs. The Logichart diagram is designed to visualize the Prolog execution flow intelligibly and to enable users to easily correlate the Prolog clauses with its parts. The system has the following functions. (1) It visually traces Pr...

Symbolic data structures for multi-valued logics are useful in a number of applications, from model-checking to circuit design and switch-level circuit verification. Such data structures are referred to as decision diagrams, and are typically considered effective if they are small, i.e., common co-factors of a function are shared, and canonical, i.e., given a variable ordering, there is a uniqu...

In recent years, renewable energy has developed to address energy security and climate change drivers. And yet, as energy resources, they possess a variable and uncertain nature that significantly complicates grid balancing operations. As a result, an extensive academic and industrial literature has developed to determine how much such variable energy resources may be integrated and how to best...

In recent years, renewable energy has developed to address energy security and climate change drivers. And yet, as energy resources, they possess a variable and uncertain nature that significantly complicates grid balancing operations. As a result, an extensive academic and industrial literature has developed to determine how much such variable energy resources may be integrated and how to best...

We present a $VI$ CCD photometric study and membership analysis of the globular cluster M56 (NGC 6779). This produced decontaminated CMD from field stars, which enabled better confrontation with theoretical isochrones; Zero-Age Horizontal Branches (ZAHB) post-ZAHB evolutionary tracks. Post He-flash models He-core mass 0.5 M$_\odot$ envelopes 0.04 - 0.18 M$_\odot$, cover complete Branch. Models ...