The theological class book; containing a system of divinity, in the form of question and answer, accompanied with Scripture proofs, etc.

Mode of access: Internet.

"Many infallible proofs": the evidences of Christianity. Or. The written and living word of God.

On cover. Revised edition.

Raphael's Madonna Gonzaga; technical proofs of authenticity and history of the painting,

CONDITION: Good.

Regional adjustments in grain production : a linear programming analysis : mathematical models, proofs, methods of data collection and estimation, and supplementary tables /

Cover title.

Proofs of the real existence, and dangerous tendency, of illuminism. Containing an abstract of the most interesting parts of what Dr. Robison and the Abbe Barruel have published on this subject, with collateral proofs and general observations.

Mode of access: Internet.

The history of Oregon and California, and the other territories on the north-west coast of North America: accompanied by a geographical view and map of those countries, and a number of documents as proofs and illustrations of the history.

"Answer to the strictures of Mr. T. Falconer": and "Mr. Falconer's reply to Mr. Greenhow's answer, with Mr. Greenhow's rejoinder".

Human science, or, Phrenology : its principles, proofs, faculties, organs, temperaments, combinations, conditions, teachings, philosophies, etc., etc. : as applied to health, its values, laws, functions, organs, means, preservation, restoration, etc. : mental philosophy, human and self improvement, civilization, home, country, commerce, rights, duties, ethics, etc. : God, His existence, attributes, laws, worship, natural theology, etc. : immortality, its evidences, conditions, relations to time, rewards, punishments, sin, faith, prayer, etc. : intellect, memory, juvenile and self education, literature, mental discipline, the senses, sciences, arts, avocations, a perfect life, etc., etc., etc. /

Mode of access: Internet.

The unequalled collection of engraved portraits of Napoleon Bonaparte and his family and marshals, belonging to Hon. James T. Mitchell ... embracing the most important collection of portraits in mezzotinto, aquatint, line, and stipple; including many printed in colors, as well as choice proofs, also the extraordinary collection of caricatures on Napoleon by Cruikshank, Gillray, Rowlandson, and others. To be sold ... December 18 ... and ... December 19, 1908 ... Catalogue compiled and sale conducted by Stan V. Henkels. At the book auction rooms of Samuel T. Freeman & co. ...

Red cancel drawn through the portraits.

Chicago, Milwaukee & St. Paul Railway Company, complaintants, vs. Wm. H. Tompkins, W.T. LaFollette and Alexander Kirkpatrick, constituting the Board of Railroad Commissioners of the state of South Dakota, et al., defendants. Pleadings and proofs.

Mode of access: Internet.

Elements of Christian theology : containing proofs of the authenticity and inspiration of the Holy Scriptures; a summary of the history of the Jews; a brief statement of the contents of the several books of the Old and New Testaments; a short account of the English translations of the Bible and a scriptural exposition of the Thirty-Nine Articles of Religion designed principally for the use of young students in Divinity /

Vol. 1, 11th ed. Vol. 2, 8th ed.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

What can be learned from failed proofs of non-theorems?

This paper reports an investigation into the link between failed proofs and non-theorems. It seeks to answer the question of whether anything more can be learned from a failed proof attempt than can be discovered from a counter-example. We suggest that the branch of the proof in which failure occurs can be mapped back to the segments of code that are the culprit, helping to locate the error. This process of tracing provides finer grained isolation of the offending code fragments than is possible from the inspection of counter-examples. We also discuss ideas for how such a process could be automated.

Using a Generalisation Critic to find Bisimulations for Coinductive Proofs

Coinduction is a method of growing importance in reasoning about functional languages, due to the increasing prominence of lazy data structures. Through the use of bisimulations and proofs that bisimilarity is a congruence in various domains it can be used to prove the congruence of two processes. A coinductive proof requires a relation to be chosen which can be proved to be a bisimulation. We use proof planning to develop a heuristic method which automatically constucts a candidate relation. If this relation doesn't allow the proof to go through a proof critic analyses the reasons why it failed and modifies the relation accordingly. Several proof tools have been developed to aid coinductive proofs but all require user interaction. Crucially they require the user to supply an appropriate relation which the system can then prove to be a bisimulation.

Efficient one-round key exchange in the standard model

We consider one-round key exchange protocols secure in the standard model. The security analysis uses the powerful security model of Canetti and Krawczyk and a natural extension of it to the ID-based setting. It is shown how KEMs can be used in a generic way to obtain two different protocol designs with progressively stronger security guarantees. A detailed analysis of the performance of the protocols is included; surprisingly, when instantiated with specific KEM constructions, the resulting protocols are competitive with the best previous schemes that have proofs only in the random oracle model.

Efficient one-round key exchange in the efficient one-round key exchange in the standard model

We consider one-round key exchange protocols secure in the standard model. The security analysis uses the powerful security model of Canetti and Krawczyk and a natural extension of it to the ID-based setting. It is shown how KEMs can be used in a generic way to obtain two different protocol designs with progressively stronger security guarantees. A detailed analysis of the performance of the protocols is included; surprisingly, when instantiated with specific KEM constructions, the resulting protocols are competitive with the best previous schemes that have proofs only in the random oracle model.