T HE TERM “Bermudatriangle” has entered our lexicon as an eponymous synonym for mystery or confusion. Nominally denoting a largely open stretch of the Atlantic Ocean with its apices on Florida, Bermuda, and Puerto Rico, its lore is a seemingly disproportionate share of un- explained disappearances of ships and airplanes. Careful scrutiny of the actual record has revealed that the triangle is no more dangerous than any other equivalent stretch of open ocean and that a rational explanation (most commonly weather or human error) can explain the misfortunes that have occurred there. 1
The seminal work of Coombs et al. (1973) established a typology of educational programmes: (1) formal education programmes, structured and chronologically graded activities that go from primary school to universities and professional training; (2) non-formal education programmes, organised activities outside the curriculum; and (3) informal education programmes, lifelong educational processes developed through daily life experiences of the individual (Knapper and Cropley, 2000; Ngaka et al., 2012; Sharma and Choudhary, 2015). This 'educational triad' is theoretically clear, which has helped teachers and educators to design modules with specific educational objectives. Nonetheless, in the context of entrepreneurial learning, it results in confusion so a well-planned 'educational triad' becomes a 'BermudaTriangle' where planned formal and non-formal educational objectives mysteriously disappear and unplanned informal educational outcomes seem to spontaneously appear.
A "BermudaTriangle" of insults leads to neurondeath in PD. Known risk factors for the onset of Parkinson's disease (PD) include environmental (green), genetic (purple), and endogenous (blue) influences. Contributions from these risk factors trigger oxidative modifications, mitochondrial dysfunction, and impaired protein degradation that together form a "Bermudatriangle" of interrelated molecular events that underlie neurodegeneration. The interactions between these pathways are sup- ported by the following (for details and citations, please refer to text): (1) Disturbances in mitochondrial respiration generate reactive oxygen species. (2) Overexpression of SOD is protective against mitochondrial toxins. (3) NOS deficiency or inhibi- tion attenuates MPTP, paraquat, and rotenone toxicity. (4) Inhibition of degradation systems leads to increased sensitivity to oxidative stressors. (5) Impaired degradation leads to an accumulation of substrates, increasing the probability for oxidative modifications. (6) Excessive production of reactive oxygen and nitrogen species modifies proteins, leading to inactivation, crosslinking, and aggregation. (7) α-Synuclein modified by oxidized dopamine impedes CMA. (8) Oxidative modifications mod- ify the lysosomal membrane and crosslink membrane proteins. (9) UPS and CMA are not able to unfold and remove oxidatively proteins. (10) Oxidative modification of proteasome subunits inhibits UPS function. (11) Macroautophagy is the principle mech- anism for the degradation of damaged mitochondria. (12) Proteasome inhibition increases mitochondrial reactive species gen- eration and decreases complex I and II activity.
Swail, Redd, and Perna (2003) explored the concept of force-field analysis, based on a psychological environment that can be described mathematically and includes an organized set of constructs that change over time in response to external stimuli (Swail, Redd, & Perna, 2003). “Instead of a linear input-process-outcomes framework, the force-field approach represents the interplay of forces having positive and negative effects on student outcomes” (Hirschy, Bremer, & Castellano, 2011, p. 305). The geometric model developed by Swail et al. (2003) consists of a triangle representing the interactions of cognitive, social, and institutional factors. The triangle symbolizes the overall student experience. One side of the triangle is the cognitive factors, including academic rigor, aptitude, study skills, and time management (Swail, et al., 2003). Although these factors play an important part in student success, this project will not directly address them. As a proxy for academic rigor (readiness), this study will utilize the student’s ACT or COMPASS score, which is used to determine course placement. The second side of the
The same goes with the Tribonacci convolution triangle. Since we are comparing this triangle to the Fibonacci convolution triangle[KOS14], we will have to learn about that triangle first. We need to understand what a generating function is in order to understand the convolution of generating functions, then find the generating function to the Tribonacci sequence of numbers. Lastly, use the convolutions of those generating functions. For now, we should see that the following table shows the first five columns of the left-justified and offset by one row of the Tribonacci convolution triangle[KOS14].
Trade Marks and Service Marks are registered in Bermuda pursuant to the Trade Marks Act 1974 (as amended) ("the Act"). The statutory provisions were largely derived from similar provisions in the old 1938 U.K. legislation. Bermuda is not a party to any international convention on the protection of trade marks.
Using these properties of a limit triangle, we can find the radii of various other triangle circles. I will use the following format: lim(Original Radius)=Limit Radius. Note that R is the circumradius, and r is the inradius. As will be shown later, r=0 at the limit.
(without Hausdorff separation property, in general) and a noncontradictible axiomatic theory which contains the metric spaces as particular cases. For the obtained notion we have proposed the name of extrametric space, providing an interesting geometric model that illustrates the existence of the hyperbolic non-Euclidean geometry on the place where the triangle inequality is reversed.
Notice that the shape formed in the figures above is similar to the hockey stick pattern in Pascal’s Arithmetic Triangle (See Problem 3.3). However, the hockey stick design in Figure 3.8, Figure 3.9, Figure 3.10 and Figure 3.11 has the head of the stick located at the top of the triangle either on a boundary entry or an internal entry of the triangle with the handle of the stick headed towards the bottom of the triangle infinitely. Thus using the information from Problem 3.5 and Problem 3.6, a generalized formula for the hockey stick type pattern in Leibniz’s Harmonic Triangle can be developed.
Diaz and Metcalf  proved a reverse of the triangle inequality in the particular case of spaces with inner product. Several other reverses of the triangle inequality were obtained by Dragomir in . Also, in  some inequalities for the continuous version of the triangle inequality using the Bochner integrable functions are given. In , Rajić gives a charac- terization of the norm triangle equality in pre-Hilbert C -modules. In [, ], Maligranda
The second component is the collection of the audit process itself. The audit process is the core component of the framework; there are no frameworks which omit the audit process component. The form of the audit processes is various since each framework was derived based on specific purposes. In this study, the author selected the typical process of auditing. The activities used in the information audit triangle are adopted from methods by Orna (1999), Buchanan & Gibb (1998) and Henczel (2001). In addition, the techniques that will be applied in the framework also acquired from the list of techniques in section 3.5. The detail of the process will be explained in the next subsection 4.1.4.
Know What? Revisited The line that the vertical height is perpendicular to is the diagonal of the square base. This length (blue) is the same as the hypotenuse of an isosceles right triangle because half of a square is an isosceles right triangle. So, the diagonal is 230 √ 2. Therefore, the base of the right triangle with 146.5 as the leg is half of 230 √ 2 or 115 √ 2. Use the Pythagorean Theorem to ﬁnd the edge.
Reviewing the literature showed that researchers classified the motive side of the fraud triangle differently. Some researchers classified them as personal, employment, or external pressure, while others classified them as financial and non-financial pressures. However, it can be noticed that both classifications are some-how related. For instance, personal pressure can come from both financial and non-financial pressure. A personal financial pressure in this case could be gambling addiction or a sudden financial need, while a personal non-financial pressure can be lack of personal discipline or greed. By the same token, employment pressure and external pressure can come from either financial or non-financial pressure. Thus, external auditors have to keep in mind that pressure/motive to commit fraud can be either a personal pressure, employment pressure, or external pressure, and each of these types of pressures can also happen because of a financial pressure or a non financial pressure. They also need to understand the opportunity for fraud to help them in identifying which fraud schemes an individual can commit and how fraud risks occur when there is an ineffective or missing internal control.
What test cases do people miss with the triangle problem? In my observation, the most overlooked test case is one with a long side and a couple of short flaps, such as an input combination of [ 1, 3 and 1 ]. These three lines do not close to form a triangle: to qualify, the sum of any two sides must be greater than the third. If the system concludes that [ 1, 3 and 1 ] is an isosceles triangle instead of rejecting this combination as invalid, the
In the literature, one can find various beautiful ways to solve the problem see, e.g., 1–4. In short, the answer is as follows. If every angle of ABC measures less than 120 ◦ , then the point P in the interior of the triangle such that ∠AP B ∠BP C ∠CP A 120 ◦ minimizes the sum of the three distances. If one of the angles of ABC measures 120 ◦ or more, then the vertex corresponding to this angle minimizes the sum of the three distances to the vertices.
In the real hyperbolic case the triangle, and hence the group, is completely determined up to isometry by its angles. We thus have a countable family of non-isometric triangles whose reflection groups are non-conjugate in P SL(2, R ). However, Takeuchi proved there is only a finite number of arithmetic lattices among these groups  and gave a complete list, the most famous example being the modular group P SL(2, Z ) which is contained with index 2 in the triangle group with (p 1 , p 2 , p 3 ) = (2, 3, ∞). Since there are infinitely many triangle groups