Notes on the Solution of certain Equations

1891 ◽  
Vol 17 ◽  
pp. 139-142
Author(s):  
R. E. Allardice

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.

1992 ◽  
Vol 267 ◽  
Author(s):  
W. Stanley Taft ◽  
James W. Mayer

ABSTRACTAt Cornell University we are in the third year of teaching an interdisciplinary, undergraduate course on the physical properties and structures of works of Art, and the modern analytical methods used to investigate them: Art, Isotopes, and Analysis. The challenge is to explain concepts familiar to museum scientists and conservators to a group of 150 undergraduate students with a background that ranges from Art History to Computer Science. Painting techniques (Fresco, Tempera, Oil, etc.) are demonstrated to the class. The analytical techniques involve the interactions of electrons, photons, ions and neutrons with pigments and other materials. This instructional approach serves as an introduction to published analyses of works of art.


Author(s):  
Xian-Wen Kong

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.


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).


1992 ◽  
Vol 70 (10) ◽  
pp. 2569-2573 ◽  
Author(s):  
Meguru Nagamori

The concept of classical regular solutions has been expanded by considering both first and second nearest-neighbor interactions between randomly distributed molecules. While the present model requires an ideal entropy of mixing, as does the classic regularity model, its heat of mixing is expressed by a more flexible equation which attributes the second-order terms of the Margules formalism to first nearest-neighbor interactions, and the third-order terms to second nearest-neighbor interactions. The activity–composition relations have been expressed by a single equation of the grand partition function, which converges to that of the classical regularity with decreasing contributions from second nearest-neighbor molecules.


1999 ◽  
Vol 14 (2) ◽  
pp. 48-53
Author(s):  
M. Pocek ◽  
M. R. Guazzaroni ◽  
G. Sodani ◽  
M. N. Guazzaroni ◽  
R. Cancellieri ◽  
...  

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.


2006 ◽  
Vol 4 (1) ◽  
pp. 0-0
Author(s):  
Narimantas Evaldas Samalavičius ◽  
Tomas Poškus

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


2019 ◽  
Vol 19 (1) ◽  
pp. 1
Author(s):  
Abeer Obeid Al-Shbiel ◽  
Qusaiyen Aly

There are various reasons for our choice of this period of the scientific Arab history: the first is the richness in thought, culture, philosophy and experimentation, following the internationalization of the peoples of the Abbasid Caliphate. The second is the maturity of the individual creative tools of scientists in most fields of knowledge, especially in the linguistic ones which formed the basis from which all Arab sciences sprang. Based on the above, we follow the analytical methods of miracle scholars. The first of these scholars was Ramani, who was interested in individual performances and in rhetorical art in its individuality. The second was Abu Suleiman al-Khattabi, who preoccupied himself with researching in the depths of the problem. The third was Baqalani Abu Bakr Muhammad, the author of the theory of equanimity and inequality. The fourth was judge Abduljabbar who tried to link between the mind and language. The fifth was Abdulqahir Al-Jerjani, the founder of the theory of systems. Indeed each of these scholars has studied the issue of Quranic miracle in a way which suited their methods, and then discussed the ways his views were received in private and in public. We claim that we have paid special attention to the specificity of grammar as a basis, for all of them, for the study of miracles, and none of them has been freed from the study of poetry. However, Al-Jarjani attributed poetry as the necessary basis for the knowledge of miracles, and we did come out with some conclusions which we have noted at the end of our research.


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