scholarly journals A Simple Linkage for Describing Equal Areas

1912 ◽  
Vol 31 ◽  
pp. 105-110
Author(s):  
E. M. Horsburgh
Keyword(s):  

If H (Fig. 1) be the middle point of a straight bar QP and if a straight bar OH of length one-half of QP be pin-jointed to QP at H, a simple linkage is formed, which may be called a T -linkage.

Author(s):  
Simon Hornblower

Campania receives very full treatment by Kassandra. Naples is especially prominent, and the relevant section ends at the poem’s exact middle point. This is a deliberate emphasizing device: Naples was of maritime importance in the Roman war against Hannibal and earlier. Hannibal’s visit to the oracle of the dead at Campanian Aornos is hinted at by Kassandra. The important narrative about Aineias and the twins Romulus and Remus is examined for topicality in the 190s. Dido’s surprising absence from the Alexandra is noted and explained.


1851 ◽  
Vol 2 ◽  
pp. 173-175
Author(s):  
Forbes

This instrument is almost a faithful reproduction of S'Gravesande's apparatus described in his “Physices Elementa Mathematica,” 1742 (but not in the previous editions). It is described or alluded to by few modern writers, except Biot in his “Traité de Physique.” It consists of a strong wooden table or frame, with a vice at each end, between which a wire or lamina may be stretched with a determinate tension by means of a weight attached by a cord, passing over a pulley in the manner of the musical apparatus, called a Monochord. After the tension is adjusted, both vices are screwed fast, the space included between them being exactly 50 inches. If now, any deviation of the middle point of the wire included by the vices be made (similar to the action of sounding a harp-string), the force required to pull it a certain distance aside will depend, 1st, on the length of the wire; 2d, on its tension; 3d, on its extensibility, or the modulus of elasticity.


1847 ◽  
Vol 137 ◽  
pp. 69-77 ◽  

During the period of the summer recess, the system of automatic meteorological registration by photography has been rendered complete by the adaptation of the barometer and thermometer to the apparatus previously described. It having been found a matter of much difficulty to obtain a photographic base-line from the lamp already described as being placed near the magnet, the idea naturally arose that the base-line might be simultaneously described by a second lamp placed on the opposite side of the cylinder, as represented in fig.1, Plate V. A pencil of light proceeding from this lamp through a horizontal slit in the chimney is received by a cylindrical lens placed, as before, horizontally, and the focal line of light thus formed is allowed to pass through a corresponding slit in the covering of the cylinder. A small section only of this focal line is transmitted through a vertical slit in a piece of thin sheet brass attached to the stand on which the cylinders rest, and placed very near the surface of the outer cylinder. A line thus described maybe seen in Plate VIII. fig. 4,and Plate IX. figs. 6, 7, 8, and the same light has been by the following means rendered available for the registration of the barometer. A siphon barometer has been con­structed with a column of mercury a little more than one inch in diameter, Plate VI. figs. 1 and 2. As the weight of an entire column of this size would be inconvenient, and as it would be difficult to obtain a tube more than three feet long of so large a bore, both ends of which were of the same internal area, two adjacent short pieces of a very nearly cylindrical tube have been united to the extremities of a tube of small bore, and form the ends of the instrument which contain the surfaces of the mercury.A wooden cap about two inches high is fitted to the open end of the tube, at each end of which are fixed three small friction rollers, placed radially, vertical, and equidistant from each other. The stem of a glass float, having a bulb about half an inch in diameter, resting on the surface of the mercury, passes up vertically between these fric­tion rollers, by which the free vertical movement of the float is much facilitated. At the upper end of the stem is a cap containing a small grooved roller. The barometer tube is attached to a board by two clamps, so as to be capable of being raised or lowered at pleasure, and the bend at the lowest part rests on a piece of wood, which is likewise capable of a vertical adjustment. Another piece of wood, about half an inch thick, two inches wide, and five or six long, is made to slide horizontally between two slips fixed to the surface of the board at such a height that the top of the float may be opposite the middle point between them. To this sliding piece a pulley about three inches in diameter, having a fixed axis about 3 inches long, is attached by a suitable support; to this pulley two slender wooden arms are attached, one thirty inches, the other five inches long, and fixed at right angles to each other. A piece of wire with an adjustible balancing weight is fixed in the pulley in such a position that the axis of the pulley may be the centre of gravity of its appendages. The long arm passes through a slit in the stand of the apparatus, and carries a black paper screen with a vertical slit in front of the horizontal aperture in the cover above described (see Plate V. fig. 2); and is so placed that the point at which the slits cross each other is exactly thirty inches from the axis of the pulley. The short arm rests on the roller at the end of the float, and is marked at the distances of 3, 3.75, and 5 inches from the axis of the pulley. The mark which rests on the float may be changed at pleasure by sliding horizontally the piece to which the pulley is attached; and accordingly as the marks are respectively placed in the above position, it is evi­dent that the movement of the point of light transmitted through the slit in the moveable screen will be five, four, or three times the variation in the height of the column of mercury; and thus by the same lamp the base-line and the barometric curve are traced out. Of this, fig. 4, Plate VIII. and fig. 7, Plate IX. are given as examples. In these it may be remarked that both the lines are so sharply defined, that by ap­plying a scale divided into Troths of an inch, the position of both may be read to half a division, which is equivalent to 0.001 inch of mercury, if the first scale be adopted, which has been the case in these instances. A small weight suspended by a string passing round a groove in the pulley keeps the short arm in contact with the float, by a constant pressure. There being an annulus of mercury rather more than one-fourth of an inch wide between the tube and the float, the effect of capillarity is so much reduced as to exert scarcely any influence on the variations of the column, the weight of which is sufficient to over­ come the small amount of friction that exists in the various parts, without sensibly influencing its variation, and consequently the barometric curve is frequently continuous, and not interrupted by jerks. In one of the registers, not introduced for want of space, the passage of an aerial wave is recorded, equivalent to less than 1/300th of an inch of mercury, the duration of which was about 4 1/2 minutes.


2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Haixin Zhao ◽  
Lingkan Yao ◽  
Yong You ◽  
Baoliang Wang ◽  
Cong Zhang

In this study, we present a new method to calculate debris flow slurry impact and its distribution, which are critical issues for designing countermeasures against debris flows. There is no unified formula at present, and we usually design preventive engineering according to the uniform distribution of the maximum impact force. For conducting a laboratory flume experiment, we arrange sensors at different positions on a dam and analyze the differences on debris flow slurry impact against various densities, channel slopes, and dam front angles. Results show that the force of debris flow on the dam distributes unevenly, and that the impact force is large in the middle and decreases gradually to the both sides. We systematically analyze the influence factors for the calculation of the maximum impact force in the middle point and give the quantitative law of decay from the middle to the sides. We propose a method to calculate the distribution of the debris flow impact force on the whole section and provide a case to illustrate this method.


2011 ◽  
Vol 30 (5) ◽  
pp. E5 ◽  
Author(s):  
Emel Avcı ◽  
Erinç Aktüre ◽  
Hakan Seçkin ◽  
Kutluay Uluç ◽  
Andrew M. Bauer ◽  
...  

Object Although craniofacial approaches to the midline skull base have been defined and surgical results have been published, clear descriptions of these complex approaches in a step-wise manner are lacking. The objective of this study is to demonstrate the surgical technique of craniofacial approaches based on Barrow classification (Levels I–III) and to study the microsurgical anatomy pertinent to these complex craniofacial approaches. Methods Ten adult cadaveric heads perfused with colored silicone and 24 dry human skulls were used to study the microsurgical anatomy and to demonstrate craniofacial approaches in a step-wise manner. In addition to cadaveric studies, case illustrations of anterior skull base meningiomas were presented to demonstrate the clinical application of the first 3 (Levels I–III) approaches. Results Cadaveric head dissection was performed in 10 heads using craniofacial approaches. Ethmoid and sphenoid sinuses, cribriform plate, orbit, planum sphenoidale, clivus, sellar, and parasellar regions were shown at Levels I, II, and III. In 24 human dry skulls (48 sides), a supraorbital notch (85.4%) was observed more frequently than the supraorbital foramen (14.6%). The mean distance between the supraorbital foramen notch to the midline was 21.9 mm on the right side and 21.8 mm on the left. By accepting the middle point of the nasofrontal suture as a landmark, the mean distances to the anterior ethmoidal foramen from the middle point of this suture were 32 mm on the right side and 34 mm on the left. The mean distance between the anterior and posterior ethmoidal foramina was 12.3 mm on both sides; the mean distance between the posterior ethmoidal foramen and distal opening of the optic canal was 7.1 mm on the right side and 7.3 mm on the left. Conclusions Barrow classification is a simple and stepwise system to better understand the surgical anatomy and refine the techniques in performing these complex craniofacial approaches. On the other hand, thorough anatomical knowledge of the midline skull base and variations of the neurovascular structures is crucial to perform successful craniofacial approaches.


2013 ◽  
Vol 24 (6) ◽  
pp. 630-634 ◽  
Author(s):  
Juliana Abdallah Atoui ◽  
Daniela Nair Borges Felipucci ◽  
Valeria Oliveira Pagnano ◽  
Iara Augusta Orsi ◽  
Mauro Antonio de Arruda Nobilo ◽  
...  

This study evaluated the tensile and flexural strength of tungsten inert gas (TIG) welds in specimens made of commercially pure titanium (CP Ti) compared with laser welds. Sixty cylindrical specimens (2 mm diameter x 55 mm thick) were randomly assigned to 3 groups for each test (n=10): no welding (control), TIG welding (10 V, 36 A, 8 s) and Nd:YAG laser welding (380 V, 8 ms). The specimens were radiographed and subjected to tensile and flexural strength tests at a crosshead speed of 1.0 mm/min using a load cell of 500 kgf applied on the welded interface or at the middle point of the non-welded specimens. Tensile strength data were analyzed by ANOVA and Tukey's test, and flexural strength data by the Kruskal-Wallis test (α=0.05). Non-welded specimens presented significantly higher tensile strength (control=605.84±19.83) (p=0.015) and flexural strength (control=1908.75) (p=0.000) than TIG- and laser-welded ones. There were no significant differences (p>0.05) between the welding types for neither the tensile strength test (TIG=514.90±37.76; laser=515.85±62.07) nor the flexural strength test (TIG=1559.66; laser=1621.64). As far as tensile and flexural strengths are concerned, TIG was similar to laser and could be suitable to replace laser welding in implant-supported rehabilitations.


2005 ◽  
Vol 19 (2) ◽  
pp. 84-92 ◽  
Author(s):  
Qiang Wang ◽  
Shigeru Sonoda ◽  
Miho Hanamura ◽  
Hideto Okazaki ◽  
Eiichi Saitoh

Objective. To investigate the relationship between the bisection test and the severity of behavioral hemineglect and to verify if this test can predict the behavioral hemineglect. Methods. Thirty stroke patients with left hemiparesis were divided into 4 groups according to the Catherine Bergego Scale, which assessed the behavioral hemineglect: severe unilateral neglect (UN), moderate UN, mild UN, and lack of UN. Eleven healthy subjects served as age-matched control subjects. In the bisection test, 18 lines were presented on the left, middle, and right of an A4 paper, respectively. The subjects were asked to place a short cross mark in the exact middle point of each line on the paper using their right hand. The middle 6 lines in the above bisection test were extracted on another sheet of A4 paper for the rebisection test. The subjects were asked to divide a line into 4 segments by successive bisections. The proportion of the right part to the length of line for bisecting was calculated. Results. In the bisection test, the main effect of space was significant in every group except the mild neglect group. The crossover effect of space location was found in the severe UN group, the group without UN, and the controls. In the severe UN group, the patients bisected the left and middle lines with rightward bias (<50%) but bisected the right lines with leftward bias (>50%). In the group without UN and the controls, the subjects bisected the left lines with leftward bias (>50%) but bisected the middle and right lines with rightward bias (<50%). Almost the same results were seen in the rebisection test. Conclusions. This study showed that if the spatial crossover effect occurred in the right space condition, it was strongly supported that this patient had moderate to severe behavioral hemineglect. The crossover effect of the space location was explained by a new model.


1956 ◽  
Vol 23 (4) ◽  
pp. 522-526
Author(s):  
M. M. Abbassi

Abstract By using parametric equations in which the parameter is the angle included between the tangent at any point on the bow girder and the tangent at the middle point, the analysis of bow girders of shapes other than the circular arc can be treated mathematically. Exact and approximate formulas are given for symmetrical bow girders of any shape carrying a distributed load or two equal concentrated loads placed symmetrically with respect to the middle point of the girder.


2021 ◽  
Vol 105 ◽  
pp. 341-347
Author(s):  
Ming Gu

The recursive algorithm has two core issues which are the design of recursive parameter lists and exit condition. We summarized the types and characteristics of recursive algorithms, and extracted four types of representative recursive algorithms with different levels of difficulty. Pseudocodes of these algorithms are given and the core issues complexity of these algorithms is compared. The relatively complex and representative recursive algorithm of the maze path finding is described in detail. The description includes that the maze is expressed mathematically, using numbers from 0 to 9 to represent the path cost, using * to represent walls or obstacles, and abstracting the maze problem as a square maze represented by numbers and *. The maze path finding recursive algorithm has five steps which are the storage structure of the maze numbers and *, the consideration of the two core problems of the recursive algorithm, the recursive call in the four directions of the middle point and the printing of the maze path. The screenshot of the running result in C language is showed. Students are required to implement the maze path finding recursive algorithm in C language. Because the maze path finding recursive algorithm is interesting and challenging, it can stimulate students' enthusiasm and initiative in learning. In the current situation of online course teaching during the epidemic, considering the demand for C language programming ability, combining with the characteristics of higher vocational students and the difficulty of the maze path finding recursive algorithm, we designed and practiced the C Language online course teaching mode led by the recursive algorithms. The every step of the teaching mode is described in detail. From the feedback of students’ evaluation of teaching and teacher’s evaluation of learning, this teaching mode is praised by teachers and students.


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