Equiangular tight frames from complex Seidel matrices containing cube roots of unity

We derive easily verifiable conditions which characterize when complex Seidel matrices containing cube roots of unity have exactly two eigenvalues. The existence of such matrices is equivalent to the existence of equiangular tight frames for which the inner product between any two frame vectors is always a common multiple of the cube roots of unity. We also exhibit a relationship between these equiangular tight frames, complex Seidel matrices, and highly regular, directed graphs. We construct examples of such frames with arbitrarily many vectors.Comment: New version comments: A few minor typos corrected. Accepted for publication in Linear Algebra App

Use of reinforced inorganic cement materials for spark wire and drift chamber wire frames

The results of a survey, materials test, and analysis study directed toward the development of an inorganic glass-fiber reinforced cement material for use in the construction of space qualified spark wire frames and drift chamber frames are presented. The purpose for this research was to evaluate the feasibility of using glass fiber reinforced cement (GFRC) for large dimensioned structural frames for supporting a number of precisely located spark wires in multiple planes. A survey of the current state of the art in fiber reinforced cement materials was made; material sample mixes were made and tested to determine their laboratory performances. Tests conducted on sample materials showed that compressive and flexural strengths of this material could approach values which would enable fabrication of structural spark wire frames

Directed Mutations Recode Mitochondrial Genes: From Regular to Stopless Genetic Codes

Mitochondrial genetic codes evolve as side effects of stop codon ambiguity: suppressor tRNAs with anticodons translating stops transform genetic codes to stopless genetic codes. This produces peptides from frames other than regular ORFs, potentially increasing protein numbers coded by single sequences. Previous descriptions of marine turtle Olive Ridley mitogenomes imply directed stop-depletion of noncoding +1 gene frames, stop-creation recodes regular ORFs to stopless genetic codes. In this analysis, directed stop codon depletion in usually noncoding gene frames of the spiraling whitefly Aleurodicus dispersusʼ mitogenome produces new ORFs, introduces stops in regular ORFs, and apparently increases coding redundancy between different gene frames. Directed stop codon mutations switch between peptides coded by regular and stopless genetic codes. This process seems opposite to directed stop creation in HIV ORFs within genomes of immunized elite HIV controllers. Unknown DNA replication/edition mechanisms probably direct stop creation/depletion beyond natural selection on stops. Switches between genetic codes regulate translation of different gene frames

Duality for κ\kappa-additive complete atomic modal algebras

In this paper, we give a duality theorem between the category of $\kappa$-additive complete atomic modal algebras and the category of $\kappa$-downward directed multi-relational Kripke frames, for any cardinal number $\kappa$. Multi-relational Kripke frames are not Kripke frames for multi-modal logic, but frames for monomodal logics in which the modal operator $\Diamond$ does not distribute over (possibly infinite) disjunction, in general. We first define homomorphisms of multi-relational Kripke frames, and then show the equivalence between the category of $\kappa$-downward directed multi-relational Kripke frames and the category $\kappa$-complete neighborhood frames, from which the duality theorem follows. We also present another direct proof of this duality based on the technique given by Minari

Entailment systems for stably locally compact locales

The category SCFrU of stably continuous frames and preframe ho-momorphisms (preserving ¯nite meets and directed joins) is dual to the Karoubi envelope of a category Ent whose objects are sets and whose morphisms X ! Y are upper closed relations between the ¯nite powersets FX and FY . Composition of these morphisms is the \cut composition" of Jung et al. that interfaces disjunction in the codomains with conjunctions in the domains, and thereby relates to their multi-lingual sequent calculus. Thus stably locally compact locales are represented by \entailment systems" (X; `) in which `, a generalization of entailment relations,is idempotent for cut composition. Some constructions on stably locally compact locales are represented in terms of entailment systems: products, duality and powerlocales. Relational converse provides Ent with an involution, and this gives a simple treatment of the duality of stably locally compact locales. If A and B are stably continuous frames, then the internal preframe hom A t B is isomorphic to e A ­ B where e A is the Hofmann-Lawson dual. For a stably locally compact locale X, the lower powerlocale of X is shown to be the dual of the upper powerlocale of the dual of X

Video content delivery for the ESL classroom with vodcasting technology

In this paper I will explain the means by which video content can be delivered to the ESL classroom via a technology known as vodcasting. The ability to deliver video to the ESL classroom CAN profoundly change the learning process, and I will explore the implications of this new technology in this paper. It must be emphasized, however, that the ABILITY to deliver video does not NECESSARILY enhance the learning experience. Content material needs to be appropriate and delivered in a manner that leads toward mastery of required language skills. To meet that goal, I will explain how material can be organized into “knowledge units”, as defined by B.F. Skinner in his work on programmed learning techniques. Using these knowledge units we will progress beyond the linguistic competence emphasized in traditional classrooms and work toward achieving true communicative competence. The American psychologist B.F. Skinner believed people are best able to learn when the cognitive domain, or target material, is divided into knowledge units he called “learning frames”. He defined a learning frame as a limited set of new facts coupled with an incomplete statement or question the learner was required to complete based on information provided from within the frame itself, or from previous frames. Skinner’s “programmed learning” approach required that frames be ordered so that knowledge units required for subsequent frames were mastered before they were needed. Learning was made possible through a series of very small and rigidly ordered steps directed toward mastery of a series of learning frames and the inferences that could be associated with the facts contained within those learning frames. The step-by-step approach advocated by Skinner provided reinforcement for correct responses, and kept the student focused on the material being studied. Skinner was especially critical of traditional education’s inability to provide sufficient reinforcement for the material being studied. “Perhaps,” said Skinner, “the most serious criticism of the current classroom is the relative infrequency of reinforcement.” (Skinner, 1962, page 25) Skinner believed reinforcement was crucial to the learning process because it was only through repetition and reinforcement that a behavior, or acquired skill, could be maintained in strength. Skills not used frequently were easily lost, as language teachers and students can attest to. The concept of programmed learning based on learning frames and the sequential mastery of material became extremely influential in textbook development in the 1960s, even 3 though the practice of computerized programmed learning itself was limited by access to the rather expensive computers of the time. Ironically, interest in programmed learning techniques seemed to have waned just as the development of personal computers made it truly possible to implement the practices Skinner had advocated