Of the Rule of Bombelli for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree

1972 ◽  
pp. 278-282
Author(s):  
Leonard Euler
Keyword(s):  
Fourth Degree ◽  
The Third

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

Cromwell Mortimer, F. R. S. ( c . 1698-1752) and the invention of the metalline thermometer for measuring high temperatures

1969 ◽  
Vol 24 (1) ◽  
pp. 113-135 ◽  
Keyword(s):  
Eighteenth Century ◽  
Seventeenth Century ◽  
High Temperatures ◽  
Boiling Point ◽  
Early Years ◽  
Fourth Degree ◽  
The Third ◽  
Upper Limit

Although the liquid-in-glass thermometer came into use either in the last decade of the sixteenth or during the early years of the seventeenth century (1), it was not until the eighteenth century that reproducible scales of temperature were established, arising from the work of Fahrenheit (2), Reaumur (3) and Celsius (4). So far as eighteenth-century chemists were concerned, the upper limit of temperature to which the liquid-in-glass thermometer could be used was set by the boiling point of mercury, at that time assumed to be 600 °F (5). In the latter half of the seventeenth century any temperatures attained in chemical operations could be indicated only by reference to a scale comprising some seven ‘degrees of heat’. In the middle to upper ranges, for example, to quote from Glaser’s The Compleat Chymist , the third ‘degree’ was that of hot ashes; the fourth ‘degree’ was that of hot sand, and the fifth that of hot iron filings; the sixth ‘degree’ was attained in the closed reverberatory charcoal fire, and the seventh and highest ‘degree’ was the ‘Flaming-Fire or Fire of Fusion’, made with wood or charcoal (6).

Four Years' Follow-up Results of Three Different Percutaneous Treatments for Male Varicocele

1999 ◽  
Vol 14 (2) ◽  
pp. 48-53
Author(s):  
M. Pocek ◽  
M. R. Guazzaroni ◽  
G. Sodani ◽  
M. N. Guazzaroni ◽  
R. Cancellieri ◽  
...  
Keyword(s):  
Combined Therapy ◽  
Combined Treatment ◽  
Duplex Ultrasound ◽  
Fourth Degree ◽  
The Third ◽  
University Of Rome ◽  
Radiological Procedures ◽  
Gianturco Coils

Objective: To evaluate the efficacy of three different interventional radiological procedures for the treatment of venous reflux in symptomatic male varicocele. Design: Prospective study with a 48-month colour duplex ultrasound (CD) follow-up. Setting: Department of Radiology, Tor Vergata University of Rome. Patients: From January 1991 to December 1993, 45 symptomatic patients with third- to fourth-degree varicocele, according to Sarteschi's CD classification, were randomly divided into three equal groups (15 patients each). Interventions: The first group received sclerotherapy (Athoxysclerol), the second underwent embolisation (Gianturco coils), while the third group received combined sclero–embolisation therapy (Athoxysclerol and Gianturco coils). Main outcomes measures: The frequency of recurrence for each procedure. Results: Two recurrences (13%) after 1 and 2 years occurred in patients who underwent sclerotherapy. In the embolisation group, two patients showed residual varices (13%). Neither recurrence nor residue was seen in the third group, who received combined therapy. Conclusions: Sclerotherapy provides good immediate results but drug dilution may cause a relapse shortly after treatment. Embolisation has a lower immediate success but better long-term success. Combined treatment provides the highest long-term success rate.

scholarly journals Mechaninės siūlės hemoroidektomija: 29 operacijų patirtis

2006 ◽  
Vol 4 (1) ◽  
pp. 0-0
Author(s):  
Narimantas Evaldas Samalavičius ◽  
Tomas Poškus
Keyword(s):  
Late Results ◽  
University Hospital ◽  
Recurrent Bleeding ◽  
Stapled Hemorrhoidectomy ◽  
Fourth Degree ◽  
The Third ◽  
Prolonged Pain ◽  
Vilnius University ◽  
One Year ◽  
Age Range

Narimantas Evaldas Samalavičius1, Tomas Poškus21 Vilniaus universiteto Onkologijos instituto Chirurgijos klinika,Santariškių g. 1, LT-08660 Vilnius2 Vilniaus universiteto ligoninės Santariškių klinikųCentro filialo III abdominalinės chirurgijos skyriausKoloproktologijos poskyris,Žygimantų g. 3, LT-01102 VilniusEl paštas: [email protected] Tikslas Įvertinti ankstyvuosius ir vėlyvuosius mechaninės siūlės hemoroidektomijų, atliktų Vilniaus universiteto ligoninės Santariškių klinikų Centro filialo III pilvo chirurgijos skyriaus koloproktologijos poskyryje, rezultatus. Ligoniai ir metodai Per ketverius metus, nuo 2001 metų gruodžio iki 2005 metų sausio, mechaninės siūlės hemoroidektomija atlikta 29 ligoniams, sirgusiems III laipsnio (26 ligoniai) ir IV laipsnio (3 ligoniai) hemorojumi. Iš jų buvo 15 moterų ir 14 vyrų, jų amžius – 32–80 metų, vidurkis – 54 metai. Operacijai buvo naudojamas PPH. Operacija truko nuo 10 iki 40 minučių, vidutiniškai 30 minučių. Rezultatai Vidutinė hospitalizacijos trukmė buvo 5 dienos (nuo 2 iki 8). Chirurginių komplikacijų po operacijos nebuvo. Sisteminių analgetikų po operacijos prireikė 21 pacientui vidutiniškai 2 paras (1–3 paros). Dviem pacientams konstatuotas užsitęsęs pooperacinis skausmas, kurį reikėjo malšinti vaistais atitinkamai 7 ir 10 dienų po operacijos. Pacientai į darbą ar prie įprastinės gyvenimo veiklos grįžo vidutiniškai aštuntą parą po operacijos (nuo 5 iki 14 paros). Po vienerių metų iš apklaustų 24 pacientų operaciją gerai ir labai gerai vertino 19 (79,2%), patenkinamai – 3 (12,5%) ir blogai – 2 (8,3%) pacientai: iš pastarųjų vienam liko iškritimas, o vienam pasikartojo kraujavimas, uždegimas ir skausmas. Viena pacientė buvo mirusi. Keturių pacientų apklausti nepavyko. Išvados Mūsų patirtis parodė, jog mechaninės siūlės hemoroidektomija yra saugi ir patikima. Vėlyvieji operacijos rezultatai yra geri. Reikšminiai žodžiai: išangė, hemorojus, mechaninė siūlė, chirurginis gydymas, rezultatai Stapled hemorrhoidectomy: experience after 29 operations Narimantas Evaldas Samalavičius1, Tomas Poškus21 Vilnius University, Institute of Oncology, Clinic of Surgery,Santariškių str. 1, LT-08660 Vilnius, Lithuania2 Vilnius University Hospital "Santariškių klinikos",Central Branch, 3rd Department of Abdominal Surgery,Division of Coloproctology,Žygimantų str. 3, LT-01102 Vilnius, LithuaniaE-mail: [email protected] Objective To evaluate early and late results after stapled hemorrhoidectomy in the colorectal subunit of the third departament of surgery in Vilnius University Hospital "Santariškių klinikos" Central Branch. Patients and methods 29 patients underwent stapled hemorrhoidectomy over a period of four years (from December 2001 to January 2005). 26 patients had third and 3 patients had fourth degree hemorrhoids. There were 15 females and 14 males, age range from 32 to 80 years (mean 54 years). The PPH kit (Procedure for prolapsed hemorrhoids), Ethicon, Johnson and Johnson was used. Operations lasted from 10 to 40 minutes, on average 30 minutes. Results The mean in-hospital stay was 5 days (2–8). No surgical complications occurred. Analgesic medications were needed for 21 patients, on average for 2 days (1–3). Prolonged pain was observed in two patients who required analgesic medications for 7 and 10 days. Patients resumed their routine activities on the 8th postoperative day (5–14 days). After one year, 19 of 24 (79.2%) patients regarded their operation as good or very good, 3 (12.5%) as satisfactory and two (8.3%) as bad: in those patients one had recurrent prolapse, another one had recurrent bleeding, the third one had bleeding and thrombotic episodes. One patient had died of the causes unrelated to the operation, and the other four were out of reach. Conclusions Our experience shows that stapled hemorrhoidectomy is safe and effective. Late follow-up results are good. Key words: anus, haemorrhoids, surgical treatment, stapling, results

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Direct Methods ◽  
Historical Background ◽  
Random Errors ◽  
Practical Application ◽  
Fourth Degree ◽  
Numerical Errors ◽  
The Third ◽  
Numeral Systems ◽  
The Given

Textbook, established at several universities. Second edition. *** Written primarily for students at technical studies. Valuable handbook for engineers, PhD students and scientists. *** Published in several variants. *** Seven chapters. In the first chapter, a historical background and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are described. This helps the reader to choose precision and range limits of stored numbers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The fourth and fifth chapters explain random variables and related random errors, uncertainty, confidence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of the third and fourth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. *** Why the presented topics are so important? Simply, they are common to all numerical methods. *** Practical application is supported by 84 examples and 17 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be implemented in any computer program. Finally, the given text with 98 figures and 52 tables represents a valuable background for understanding, applying and developing various numerical analyses.

Introduction of a New Variable Asa Universal Technique of the Solution of Rational Equations Above the Second Degree

2018 ◽  
Vol 6 (2) ◽  
pp. 31-37
Author(s):  
И. Ульянова ◽  
I. Ulyanova
Keyword(s):  
Mathematics Teachers ◽  
Educational Institutions ◽  
Higher Educational Institutions ◽  
Fourth Degree ◽  
The Third ◽  
Higher Educational ◽  
And Mathematics ◽  
Second Degree

The article reveals the role of equations at the basic and profi le levels of teaching students mathematics at school. Various ways of solving rational equations of the third and fourth degree, based on the technique of the introduction of a new variable, are demonstrated. This technique is universal in mathematics. It fi nds its application both in algebra, in the solution of inequalities, in equations and their systems, and in geometry, where the additionally constructed geometric fi gure — a segment, an angle, a circle, a triangle — appears as a new variable. The methods of solving rational equations, shown by the author in this article, will be especially useful and interesting for students of profi le classes, as well as for applicants and students of higher educational institutions and mathematics teachers.

Notes on the Solution of certain Equations

1891 ◽  
Vol 17 ◽  
pp. 139-142
Author(s):  
R. E. Allardice
Keyword(s):  
Analytical Methods ◽  
Single Equation ◽  
Algebraic Solution ◽  
Small Class ◽  
Single Variable ◽  
Fourth Degree ◽  
The Third ◽  
Solution Of Equations

The equations considered are equations of the third and fourth degree in a single variable, and systems consisting of two equations in two variables. This is a comparatively small class; but if there be added systems consisting of a single equation of the third or fourth degree and a number of others all of the first degree, it will include all equations which admit, in general, of an algebraic solution.The object of these notes is to point out the advantage of making greater use, than is generally the custom, of the discriminant in the solution of equations, and to emphasise the importance of looking for geometrical illustrations of analytical methods whenever this is possible. The usefulness of such illustrations is well known in considering, for example, limiting cases in the solution of equations, such as the cases of infinite roots and of equal roots, of the meaning of which it is almost impossible to form an adequate conception, without the use of such illustrations.

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