Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

New Improved Version of J 1 ...J 4 Interferometry Method and its Application to Nanometric Vibration Measurements

Piezoelectric ceramics, such as PZT, can generate subnanometric displacements, bu t in order to generate multi- micrometric displacements, they should be either driven by high electric voltages (hundreds of volts ), or operate at a mechanical resonant frequency (in narrow band), or have large dimensions (tens of centimeters). A piezoelectric flextensional actuator (PFA) is a device with small dimensions that can be driven by reduced voltages and can operate in the nano- and micro scales. Interferometric techniques are very adequate for the characterization of these devices, because there is no mechanical contact in the measurement process, and it has high sensitivity, bandwidth and dynamic range. A low cost open-loop homodyne Michelson interferometer is utilized in this work to experimentally detect the nanovi brations of PFAs, based on the spectral analysis of the interfero metric signal. By employing the well known J 1 ...J 4 phase demodulation method, a new and improved version is proposed, which presents the following characteristics: is direct, self-consistent, is immune to fading, and does not present phase ambiguity problems. The proposed method has resolution that is similar to the modified J 1 ...J 4 method (0.18 rad); however, differently from the former, its dynamic range is 20% larger, does not demand Bessel functions algebraic sign correction algorithms and there are no singularities when the static phase shift between the interferometer arms is equal to an integer multiple of  /2 rad. Electronic noise and random phase drifts due to ambient perturbations are taken into account in the analysis of the method. The PFA nanopositioner characterization was based on the analysis of linearity betw een the applied voltage and the resulting displacement, on the displacement frequency response and determination of main resonance frequencies.

The New Testament of our Lord and Saviour Jesus Christ : the text carefully printed from the most correct copies of the present authorized version including the marginal readings and parallel texts, with a commentary and critical notes, designed as a help to a better understanding of the sacred writings /

Spine title: Clarke's commentary, New Testament.

A new and critical version of Rhymes on moral instruction attributed to Rabbi Hai ben Sherira gaon based on three mss. in the British museum,

English and Hebrew on opposite pages.

The family expositor: or, A paraphrase and version of the New Testament; with critical notes, and a practical improvement of each section ...

Edited by Job Orton.

The new Hamlet, intermixed and interwoven with a revised version of Romeo and Juliet; the combination being modernized, rewritten and wrought out on new-discovered lines, as indicated under the light of the higher criticism by Wm. Hawley Smith and the Smith family, farmers. Printed from the original manuscript, with text in full, and as first produced when done in action by the Smiths, their own company, under the haw tree, on their farm, at the ticket, June 17, 1902.

"Done into a book, and bound in boards (no. 2 fencing) by and, at the barn, on the farm, by farmers."

A new and easy method of learning Hebrew without points. : To which is annex'd, by way of praxis, The book of Proverbs, divided according to the metre: with the masoretical reading in Roman letters, the interlinear version of Santes Pagninus, &c. A grammatical analysis, and short notes critical and explanatory ... /

Errata: p. [2]-[3] at end.

The New Testament of our Lord and Saviour Jesus Christ : with text carefully printed from the most correct copies of the present Authorized version ... with a commentary and critical notes designed as a help to a better understanding of the sacred writings /

Mode of access: Internet.

The family expositor; or, A paraphrase and version of the New Testament; with critical notes, and a practical improvement of each section ...

Shaw-Shoemaker 12446.

The family expositor; or, A paraphrase and version of the New Testament; with critical notes, and a practical improvement to each section,

The portrait engraved by W.C. Edwards.

The Turkish New Testament incapable of defence, and the true principles of Biblical translation vindicated : in answer to Professor Lees "Remarks on Dr. Henderson's appeal to the Bible Society on the subject of the Turkish version of the New Testament, printed at Paris in 1819" /

Includes bibliographic references.

Remarks on the version of the New Testament edited by the Unitarians, with the title of "An improved version upon the basis of Archbishop Newcome's new translation ... London 1808" : being a dispassionate appeal to Christians of various denominations on some of the first ... doctrines of the Bible /

Includes indexes.

The book of the new covenant of our Lord and Saviour Jesus Christ: being a critical revision of the text and translation of the English version of the New Testament, with the aid of most ancient manuscripts unknown to the age in which that version was last put forth by authority.

Mode of access: Internet.

Discourses and dissertations on the scriptural doctrines of atonement and sacrifice : and on the principal arguments advanced, and the mode of reasoning employed, by the opponents of those doctrines, as held by the established church : with an appendix, containing some strictures on Mr. Belsham's account of the Unitarian scheme, in his review of Mr. Wilberforce's treatise, together with remarks on the version of the New Testament lately published by the Unitarians /

Mode of access: Internet.