Higher geometry and trigonometry : being the third part of a series on elementary and higher geometry, trigonomentary and mensuration : containing many valuable discoveries and improvements in mathematical science, especially in relation to the quadrature of the circle, and some other curves, as well as the cubature of certain curvilinear solids : designed as a text-book for collegiate and academic instruction, and as a practical compendium of mensuration /

With: Higher geometry and mensuration / by Nathan Scholfield.

Problems in the calculus, with formulas and suggestions,

Mode of access: Internet.

Royalty payments : hearings before the Committee on Patents, House of Representatives, seventy-seventh Congress, first session, on H.J. Res. 32, H.J. Res. 73 and H.J. Res. 123, joint resolutions to define the principle of international reciprocity in the protection of American patents, trade-marks, secret formulas and processes, and copyrights by providing a method for assuring the payments of amounts due to persons in the United States from users thereof in countries restricting international payments from their territories /

"317522."

Design of complementary UWB printed monopole antennas using simple formulas

Simple design formulas for designing ultra wideband (UWB) antennas in the form of complementary planar monopoles are described and their validity is tested using full electromagnetic wave simulations and measurements. Assuming dielectric substrate with relative permittivity of 10.2, the designed antennas feature a small size of 13 mmtimes26 mm. They exhibit a 10 dB return loss bandwidth from 3 to more than 15 GHz accompanied by near omnidirectional characteristics and good radiation efficiency throughout this band

Computing with noise: phase transitions in Boolean formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.

On reliable computation by noisy random Boolean formulas

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.

Measure Refutations and Metrics on Statements of Experts (Logical Formulas) in the Models for Some Theory

* This work was financially supported by the Russian Foundation for Basic Research, project no. 04-01-00858a.

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60

Theoretical Hyperbolic Model of a Partial Agonism: Explicit Formulas for Affinity, Efficacy and Amplification

The quantitative analysis of receptor-mediated effect is based on experimental concentration-response data in which the independent variable, the concentration of a receptor ligand, is linked with a dependent variable, the biological response. The steps between the drug–receptor interaction and the subsequent biological effect are to some extent unknown. The shape of the fitting curve of the experimental data may give some in-sights into the nature of the concentration–receptor–response (C-R-R) mechanism. It can be evaluated by non-linear regression analysis of the experimental data points of the independent and dependent variables, which could be considered as a history of the interaction between the drug and receptors. However, this information is not enough to evaluate such important parameters of the mechanism as the dissociation constant (affinity) and efficacy. There are two ways to provide more detailed information about the C-R-R mechanism: (i) an experimental way for obtaining data with new or

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.

Comparison of two formulas used to calculate summarized retinal vessel calibers

PURPOSE: To compare the Parr-Hubbard and Knudtson formulas to calculate retinal vessel calibers and to examine the effect of omitting vessels on the overall result. METHODS: We calculated the central retinal arterial equivalent (CRAE) and central retinal venular equivalent (CRVE) according to the formulas described by Parr-Hubbard and Knudtson including the six largest retinal arterioles and venules crossing through a concentric ring segment (measurement zone) around the optic nerve head. Once calculated, we removed one arbitrarily selected artery and one arbitrarily selected vein and recalculated all outcome parameters again for (1) omitting one artery only, (2) omitting one vein only, and (3) omitting one artery and one vein. All parameters were compared against each other. RESULTS: Both methods showed good correlation (r for CRAE = 0.58; r for CRVE = 0.84), but absolute values for CRAE and CRVE were significantly different from each other when comparing both methods (p < 0.000001): CRAE had higher values for the Parr-Hubbard (165 [±16] μm) method compared with the Knudtson method (148 [±15] μm). In addition, CRAE and CRVE values dropped for both methods when omitting one arbitrarily selected vessel each (all p < 0.000001). Arteriovenous ratio (AVR) calculations showed a similar change for both methods when omitting one vessel each: AVR decreased when omitting one arteriole whereas it increased when omitting one venule. No change, however, was observed for AVR calculated with six or five vessel pairs each. CONCLUSIONS: Although the absolute value for CRAE and CRVE is changing significantly depending on the number of vessels included, AVR appears to be comparable as long as the same number of arterioles and venules is included.

The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions

MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40

Legal Translation from English to Spanish in the Classroom: Problems when Translating Standard Formulas of Expression

The purpose of this paper is to identify problems when translating standard formulas of expression in English to Spanish legal translation. To achieve the goal, a total of 250 Spanish translations were analyzed of 10 sentences from legal texts in English. The degree of difficulty posed by the translation of these formulas is confirmed by the results obtained, which is related not so much to the intrinsic meaning of the words that compose them, but to their contextual meaning. An eclectic approach that combines discourse analysis with contrastive linguistics is proposed, and some specific didactic guidelines are indicated to facilitate the translation teaching of these standard formulas of expression. Lexical interpretation and contextual recreation allow the apprentice translator to make progress with the translation of these phrases and to improve his/her attitude when facing them to achieve a successful semantic and contextual interpretation, that is to say, getting the closest natural equivalent while respecting the genius of the language.