Transreal calculus

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails.

Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Transreal proof of the existence of universal possible worlds

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers

Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Transmathematical basis of infinitely scalable pipeline machines

We describe infinitely scalable pipeline machines with perfect parallelism, in the sense that every instruction of an inline program is executed, on successive data, on every clock tick. Programs with shared data effectively execute in less than a clock tick. We show that pipeline machines are faster than single or multi-core, von Neumann machines for sufficiently many program runs of a sufficiently time consuming program. Our pipeline machines exploit the totality of transreal arithmetic and the known waiting time of statically compiled programs to deliver the interesting property that they need no hardware or software exception handling.

Neural reprogramming in retinal degeneration.

PURPOSE: Early visual defects in degenerative diseases such as retinitis pigmentosa (RP) may arise from phased remodeling of the neural retina. The authors sought to explore the functional expression of ionotropic (iGluR) and group 3, type 6 metabotropic (mGluR6) glutamate receptors in late-stage photoreceptor degeneration. METHODS: Excitation mapping with organic cations and computational molecular phenotyping were used to determine whether retinal neurons displayed functional glutamate receptor signaling in rodent models of retinal degeneration and a sample of human RP. RESULTS: After photoreceptor loss in rodent models of RP, bipolar cells lose mGluR6 and iGluR glutamate-activated currents, whereas amacrine and ganglion cells retain iGluR-mediated responsivity. Paradoxically, amacrine and ganglion cells show spontaneous iGluR signals in vivo even though bipolar cells lack glutamate-coupled depolarization mechanisms. Cone survival can rescue iGluR expression by OFF bipolar cells. In a case of human RP with cone sparing, iGluR signaling appeared intact, but the number of bipolar cells expressing functional iGluRs was double that of normal retina. CONCLUSIONS: RP triggers permanent loss of bipolar cell glutamate receptor expression, though spontaneous iGluR-mediated signaling by amacrine and ganglion cells implies that such truncated bipolar cells still release glutamate in response to some nonglutamatergic depolarization. Focal cone-sparing can preserve iGluR display by nearby bipolar cells, which may facilitate late RP photoreceptor transplantation attempts. An instance of human RP provides evidence that rod bipolar cell dendrite switching likely triggers new gene expression patterns and may impair cone pathway function.

The Gcd10p/Gcd14p complex is the essential two-subunit tRNA(1-methyladenosine) methyltransferase of Saccharomyces cerevisiae

The modified nucleoside 1-methyladenosine (m1A) is found at position 58 in the TΨC loop of many eukaryotic tRNAs. The absence of m1A from all tRNAs in Saccharomyces cerevisiae mutants lacking Gcd10p elicits severe defects in processing and stability of initiator methionine tRNA (tRNAiMet). Gcd10p is found in a complex with Gcd14p, which contains conserved motifs for binding S-adenosylmethionine (AdoMet). These facts, plus our demonstration that gcd14Δ cells lacked m1A, strongly suggested that Gcd10p/Gcd14p complex is the yeast tRNA(m1A)methyltransferase [(m1A)MTase]. Supporting this prediction, affinity-purified Gcd10p/Gcd14p complexes used AdoMet as a methyl donor to synthesize m1A in either total tRNA or purified tRNAiMet lacking only this modification. Kinetic analysis of the purified complex revealed KM values for AdoMet or tRNAiMet of 5.0 μM and 2.5 nM, respectively. Mutations in the predicted AdoMet-binding domain destroyed GCD14 function in vivo and (m1A)MTase activity in vitro. Purified Flag-tagged Gcd14p alone had no enzymatic activity and was severely impaired for tRNA-binding compared with the wild-type complex, suggesting that Gcd10p is required for tight binding of the tRNA substrate. Our results provide a demonstration of a two-component tRNA MTase and suggest that binding of AdoMet and tRNA substrates depends on different subunits of the complex.

Preferential oxidation of CO in excess of H2 on Pt/CeO2–Nb2O5 catalysts

A series of CeO2–Nb2O5 mixed oxides with different Nb content, as well as the pure oxides, have been synthesized by co-precipitation with excess urea. These materials have been used as supports for platinum catalysts, with [Pt(NH3)4](NO3)2 as precursor. Both supports and catalysts have been characterized by several techniques: N2 physisorption at 77 K, X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, UV–vis spectroscopy, scanning electron microscopy, transmission electron microscopy, temperature-programmed reduction and temperature-programmed desorption (CO and H2), and their catalytic behaviour has been determined in the PROX reaction, both with an ideal gas mixture (CO, O2 and H2) and in simulated reformate gas containing CO2 and H2O. Raman spectroscopy analysis has shown the likely substitution of some Ce4+ cations by Nb5+ to some extent in supports with low niobium contents. Moreover, the presence of Nb in the supports hinders their ability to adsorb CO and to oxidize it to CO2. However, an improvement of the catalytic activity for CO oxidation is obtained by adding Nb to the support, although the Pt/Nb2O5 catalyst shows very low activity. The best results are found with the Pt/0.7CeO2–0.3Nb2O5 catalyst, which shows a high CO conversion (85%) and a high yield (around 0.6) after a reduction treatment at 523 K. The effect of the presence of CO2 and H2O in the feed has also been determined.

NOx storage and reduction over copper-based catalysts. Part 2: Ce0.8M0.2Oδ supports (M = Zr, La, Ce, Pr or Nd)

5% copper catalysts with Ce0.8M0.2Oδ supports (M = Zr, La, Ce, Pr or Nd) have been studied by rapid-scan operando DRIFTS for NOx Storage and Reduction (NSR) with high frequency (30 s) CO, H2 and 50%CO + 50%H2 micropulses. In the absence of reductant pulses, below 200–250 °C NOx was stored on the catalysts as nitrite and nitro groups, and above this temperature nitrates were the main species identified. The thermal stability of the NOx species stored on the catalysts depended on the acid/basic character of the dopant (M more acidic = NOx stored less stable ⇒ Zr4+ < none < Nd3+ < Pr3+ < La3+ ⇐ M more basic = NOx stored more stable). Catalysts regeneration was more efficient with H2 than with CO, and the CO + H2 mixture presented an intermediate behavior, but with smaller differences among the series of catalyst than observed using CO alone. N2 is the main NOx reduction product upon H2 regeneration. The highest NOx removal in NSR experiments performed at 400 °C with CO + H2 pulses was achieved with the catalyst with the most basic dopant (CuO/Ce0.8La0.2Oδ) while the poorest performing catalyst was that with the most acidic dopant (CuO/Ce0.8Zr0.2Oδ). The poor performance of CuO/Ce0.8Zr0.2Oδ in NSR experiments with CO pulses was attributed to its lower oxidation capacity compared to the other catalysts.

Fosca: melodramma in quattro atti

di Antonio Ghislanzoni ; musica di A. Carlos Gomes ; canto e pianoforte, riduzione di N. Celega.

Tārīkh ḥayāt al-maghfūr la-hu ʻAlī Mubārak Bāshā

istakhrajahā Muḥammad Bik Durrī al-Ḥakīm min kitāb al-Khiṭaṭ al-Tawfīqīyah al-maṭbūʻ sanat 1306.

Improved motorcyclist licensing and testing project. Annual report.

National Highway Traffic Safety Administration, Washington, D.C.

The teacher in literature as portrayed in the writings of Ascham, Moliere, Rousseau, Shenstone, Fuller, Pestalozzi, Cowper, Goethe, Irving, Mitford, Bronte, Thompson, Thackeray, Hughes, Dickens, Eliot and others. Including a biographical sketch and characterization of each author.

Mode of access: Internet.

Communication from Leland Stanford to the Committee on Corporations of the Senate.

Caption title.