Quirino Sugon Jr, PhD

Volume of a Cylinder  The volume \(V\) of a cylinder with radius \(r\), height \(h\) is given by \[V = \pi r^2 h.\] Notice that we have three parameters. If we hold one of them to be constant, then we can obtain the relationship between the other two parameters, especially if one of these two parameters is uniformly or linearly increasing, i.e., a linear function of a set of integers \(k =\{0, 1, 2, \ldots, n\}\), where \(n\) is an arbitrary integer ideally greater than or equal to 3.  Let us consider three cases: constant volume, constant radius, and constant height. Each of these cases will have two sub-cases, with each sub-case dictating the design of a row of Montessori knobbed cylinders. Thus, in principle, you can design a total of 6 rows of knobbed cylinders, with each row containing \(n\) cylinders. 1. Constant volume \(V\) If the volume \(V=V_0\) is constant, then the radius \(r\) of the cylinder is inversely proportional to the square root of the height \(h\): \[r =\...

Fig. 1. Overleaf's user interface for the Optica journal template. The menu button is at the upper left corner.  Newsletter: Volume 1, Issue 1 (Feb 2023)  Topic: Research Contents: Optica's directions for downloading LaTeX files Overleaf's menu button for downloading source files My rendered LaTeX code using pdflatex in TeXworks I was using the free Overleaf account and one of its deal-breaking restrictions is the one-minute compile time. I can increase the compile time to 4 min if I get the Personal (USD 129), Standard (USD 199), and or Professional (  USD 399) Overleaf plan .  If your project has too many figures and style files, Overleaf would need more time to compile it, which can exceed the 1 minute mark.  One way to go around these restrictions is to compile your LaTeX code in your computer using the journal style files from Overleaf. Optica, for example, states that this manual compilation is possible: Choose the journal-specific "Access on Overleaf" li...

  Newsletter: Volume 1, Issue 1/ Topic: Research Contents Title Abstract Introduction Methodology Expected Results References  Budget Gantt chart  1. Title Write your thesis title in about 13 words. Just remember Friday the 13th if you have triskaidekaphobia . Or perhaps October 13 if you are a devotee of Our Lady of Fatima . As a rule of thumb, do not go beyond two lines for your thesis title in a given thesis template.  Remember that your thesis title is the first thing that the reader sees if they pick up your thesis on the shelf or search for it in your library catalog and online search engines like Google. A good title should accurately reflect the contents of your thesis. This is truth in advertising , since your thesis title is already an ad for your buyers—your potential readers, which includes your thesis adviser and panel members. Will they buy  your idea and read the rest of your proposal or your full thesis? Many marketing campaigns can succeed or fa...

Vincent S. Cronin wrote A Primer on Focal Mechanism Solutions for Geologists (2010) . My interest in his work is in his descriptions of fault vectors and angles. I need to use these standard names if I wish to write a paper on Focal Mechanism of Earthquakes. Based on Cronin's diagram in p. 6, the reference strike, which we shall denote by $\mathbf e_{strike}$ appears to be the direction of the fault line as seen from a drone camera flying overhead high above the fault. The dip vector, which we shall denote by $\mathbf e_{dip}$, is a vector perpendicular to the reference strike $\mathbf e_{strike}$ and lies along the fault plane. The direction of $\mathbf e_{dip}$ is downward along the fault in Cronin. In this way, if we define the rake $\mathbf e_{rake}$ as the direction of the movement of the one side of the fault, then $\mathbf e_{rake}$ can be expressed as a rotation of $\mathbf e_{strike}$ about $\mathbf e_{dip}\times\mathbf e_{strike}$ by an angle $\theta_{rake}$, which is...