Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
At the heart of this book is the generalized theoretical approach that is applied to investigate the geoelectrical structure of the Earth’s mantle. It also analyzes the results of regional and global induction sounding of the Earth’s mantle and compares them with the results obtained by other geophysical methods. The generalized theoretical approach employs the Induction Law as a basis for identifying extended relations between magnetic field components, including their plane divergence, impedances and spatial derivatives. The estimations of impedance values and spatial derivatives are performed using the theory of stochastic processes. The book also considers the external sources of magnetic fields used for sounding the Earths mantle from the modern theory perspective, as well as the problem of coincidence of magneto-variation and magnetotelluric methods. Further, it discusses secular variations in the Earth’s resistance caused by non-induction sources, factors that are correlated with the number of earthquakes in the region and shifted in time with global indexes. It is a valuable resource for scientists applying deep induction soundings or interested in the structures of and processes in the Earth’s interior.
TRANSLATOR'S PREFACE The following account of the battle of Tsu-shima, fought on 27th May 1905, is a translation of the narrative of Captain Vladimir Semenoff, a Russian naval officer who was on board the flag-ship (Knyaz Suvoroff) during the engagement. It is of more than usual interest, as the writer had previously served in the Cesarevitch at Port Arthur, and had taken part in the disastrous sally from that port on 10th August 1904. At the great battle of which he now relates his experiences, he was present in an unofficial capacity, which gave him unlimited opportunity for observation. Moreover, the fact of his being able to make a series of notes at the time (till too seriously wounded) puts an additional stamp of reality on to his already most graphic account. It should be remembered that the Russian Baltic fleet-Russia's final and supreme appeal to the God of Battles-left Cronstadt for the Far East on 11th September 1904, and during all the long months till the following May was slowly making its way, viâ the Cape of Good Hope, to Japanese waters. The difficulties encountered during that prolonged voyage were enormous. The nerves of officers and men, who constantly apprehended attempts to destroy the fleet, were in a continual state of tension: news of the outside world and especially of events in the Far East was practically unobtainable: and yet officers and men, despite the additional disadvantage of having to take their ships into action after these many months at sea, fearlessly entered into an engagement which they knew meant death, and fought their ships with a self-devotion and courage which has earned for them the admiration of the world. Admiral Togo-flying his flag on the Mikasa-awaited the enemy in Japanese waters. His fleet, which, since the fall of Port Arthur on 2nd January 1905, had been relieved of its blockading duties, had spent the intervening months in repairing damage and bringing itself up to the highest state of preparation in expectation of the coming of the Baltic fleet. To a nation like ourselves, whose first line of defence is the Navy, I venture to think that these pages will give food for thought, as, besides enabling the reader to see the paralysing and awful effect of high explosives thrown on board a modern battleship in action, they supply us with a picture of what a losing engagement means to those who lose. When first I took up the original volume I read it merely with a view to extracting information re fire effect, gun power, weather conditions, formations, and other factors complementary to the result of the battle. But the narrative appeared so realistic that the thought occurred to me to place the following translation before the public. The speed maintained by the opposing fleets during the battle is shown in the diagram attached. Dates have been expressed according to the English calendar (which is thirteen days in advance of the Russian)-otherwise the writer's own words and colloquial style have, as far as possible, been faithfully adhered to, to the detriment of literary style in translating. It may be mentioned that this narrative comes as a supplement to the very interesting account by Politovsky of the voyage of the Baltic fleet to the Far East-recently translated by Major Godfrey and published by John Murray under the title "From Libau to Tsu-shima." Politovsky went down in the Suvoroff, and his story ends with the arrival of the fleet at Shanghai on 23rd May, the date on which he posted his last letter to Russia. The following narrative commences on 25th May, as the fleet swung out of Shanghai to meet its destiny. A. B. L. 7th November 1906.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
By covering theory, design, and fabrication of nanostructured superconducting materials, this monograph is an invaluable resource for research and development. Examples are energy saving solutions, healthcare, and communication technologies. Key ingredients are nanopatterned materials which help to improve the superconducting critical parameters and performance of superconducting devices, and lead to novel functionalities. Contents Tutorial on nanostructured superconductors Imaging vortices in superconductors: from the atomic scale to macroscopic distances Probing vortex dynamics on a single vortex level by scanning ac-susceptibility microscopy STM studies of vortex cores in strongly confined nanoscale superconductors Type-1.5 superconductivity Direct visualization of vortex patterns in superconductors with competing vortex-vortex interactions Vortex dynamics in nanofabricated chemical solution deposition high-temperature superconducting films Artificial pinning sites and their applications Vortices at microwave frequencies Physics and operation of superconducting single-photon devices Josephson and charging effect in mesoscopic superconducting devices NanoSQUIDs: Basics & recent advances Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks as emitters of terahertz radiation| Interference phenomena in superconductor-ferromagnet hybrids Spin-orbit interactions, spin currents, and magnetization dynamics in superconductor/ferromagnet hybrids Superconductor/ferromagnet hybrids
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).
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