text:
# Is the Solar Wind comprised of actual matter along with energy? If so, is there a point at which the gravitational attraction of the Sun overcomes the Solar Wind?

Jun 12, 2016

#### Answer:

The solar wind does have matter as well as energy. But instead of being reined in by the Sun's gravity, it eventually merges into the interstellar medium.

#### Explanation:

The region where tge solar wind dominates the fliw of matter in space is callef the heliosphere. The outer limit of the heliosphere where the merger with the stellar wind happens is called the heliopause. See here:

http://home.strw.leidenuniv.nl/~keller/Teaching/Planets_2011/Planets2011_L01_SolarSystem.pdf


text:
ISSN 1947-6221(online) ISSN 0065-9266(print)

 Papers accepted for publication in Memoirs of the American Mathematical Society which have not yet been published Papers are displayed alphabetically by first author listed. Jim Agler; Zinaida Lykova; Nicholas Young Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc A. Agrachev; L. Rizzi; D. Barilari Curvature: A variational approach Oskari Heikki Ajanki; László Erdős; Torben Krüger Quadratic vector equations on complex upper half-plane Ethan Akin; Eli Glasner WAP systems and labeled subshifts Antonio Alarcón; Franc Forstnerič; Francisco J. López New complex analytic methods in the study of non-orientable minimal surfaces in $\mathbb {R}^n$ T. Alazard; N. Burq; C. Zuily Strichartz estimates and the Cauchy problem for the gravity water waves equations Luigi Ambrosio; Andrea Mondino; Giuseppe Savare Nonlinear diffusion equations and curvature conditions in metric measure spaces Cristian Anghel; Iustin Coandă; Nicolae Manolache Globally generated vector bundles with small $c_1$ on projective spaces Michael Aschbacher On fusion systems of component type Atanas Atanasov; Eric Larson; David Yang Interpolation for normal bundles of general curves Arthur Bartels; Christopher L. Douglas; André Henriques Fusion of defects Jacob Bedrossian; Pierre Germain; Nader Masmoudi Dynamics near the subcritical transition of the 3D Couette flow: Below threshold case Victor Beresnevich; Alan Haynes; Sanju Velani Sums of reciprocals of fractional parts and multiplicative Diophantine approximation Laurent Berger; Peter Schneider; Bingyong Xie Rigid character groups, Lubin-Tate theory, and $(\varphi ,\Gamma )$-modules Lisa Berger; Chris Hall; René Pannekoek; Jennifer Park; Rachel Pries; Shahed Sharif; Alice Silverberg; Douglas Ulmer Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields Massimiliano Berti; Riccardo Montalto Quasi-periodic standing wave solutions of gravity-capillary water waves Pavel M. Bleher; Guilherme L. F. Silva The mother body phase transition in the normal matrix model Alexander Blokh; Lex Oversteegen; Ross Ptacek; Vladlen Timorin Laminational models for some spaces of polynomials of any degree Andrew J. Blumberg; Michael A. Mandell Localization for $THH(ku)$ and the topological Hochschild and cyclic homology of Waldhausen categories Sergey Bobkov; Michel Ledoux One-dimensional empirical measures, order statistics, and Kantorovich transport distances Lien Boelaert; Tom De Medts; A. Stavrova Moufang sets and structurable division algebras Joan Bosa; Nathanial P. Brown; Yasuhiko Sato; Aaron Tikuisis; Stuart White; Wilhelm Winter Covering dimension of C*-algebras and 2-coloured classification Nawaf Bou-Rabee; Eric Vanden-Eijnden Continuous-time random walks for the numerical solution of stochastic diffirential equations Carles Broto; Jesper M. Møller; Robert Alan Oliver Automorphisms of fusion systems of finite simple groups of Lie type/Tameness of fusion systems of sporadic simple groups Roelof Bruggeman; Youngju Choie; Nikolaos Diamantis Holomorphic automorphic forms and cohomology David M. J. Calderbank; Michael G. Eastwood; Vladimir S. Matveev; Katharina Neusser C-projective geometry David Joseph Carchedi Higher orbifolds and Deligne-Mumford stacks as structured infinity-topoi Sebastiano Carpi; Yasuyuki Kawahigashi; Roberto Longo; Mihály Weiner From vertex operator algebras to conformal nets and back Ángel Castro; Diego Cordoba; Javier Gómez-Serrano Global smooth solutions for the inviscid SQG equation Jérémie Chalopin; Victor Chepoi; Hiroshi Hirai; Damian Osajda Weakly modular graphs and nonpositive curvature David Chataur; Martintxo Saralegi-Aranguren; Daniel Tanré Intersection cohomology. Simplicial blow-up and rational homotopy Chuanqiang Chen; Xi-Nan Ma; Paolo Salani On space-time quasiconcave solutions of the heat equation Vasilis Chousionis; Jeremy Tyson; Mariusz Urbanski Conformal graph directed Markov systems on Carnot groups Charles Collot; Pierre Raphaël; Jeremie Szeftel On the stability of type I blow up for the energy super critical heat equation Christophe Cornut Filtrations and buildings Jean-Francois Coulombel; Mark Williams Geometric optics for surface waves in nonlinear elasticity Sean N. Curry; A. Rod Gover CR embedded submanifolds of CR manifolds Raul E. Curto; In Sung Hwang; Woo Young Lee Matrix functions of bounded type: An interplay between function theorem and operator theory Anne-Laure Dalibard; Laure Saint-raymond Mathematical study of degenerate boundary layers: A large scale ocean circulation problem Christopher L. Douglas; Robert Lipshitz; Ciprian Manolescu Cornered Heegaard Floer homology Christopher L. Douglas; Christopher Schommer-Pries; Noah Snyder Dualizable tensor categories Rod Downey; Keng Meng Ng; Reed Solomon Minimal weak truth table degrees and computably enumerable Turing degrees Maurice Duits; Kurt Johansson On mesoscopic equilibrium for linear statistics in Dyson’s Brownian motion Zhaobing Fan; Chun-Ju Lai; Yiqiang Li; Li Luo; Weiqiang Wang Affine flag varieties and quantum symmetric pairs Paul M. N. Feehan; Thomas G. Leness An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants Paul M. N. Feehan; Manousos Maridakis Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functionals Felix Finster; Niky Kamran Spinors on singular spaces and the topology of causal fermion systems Matthias Fischmann; Andreas Juhl; Petr Somberg Conformal symmetry breaking differential operators on differential forms Lior Fishman; David Samuel Simmons; Mariusz Urbański Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces Gonzalo Fiz Pontiveros; Simon Griffiths; Robert Morris The triangle-free process and the Ramsey number $R(3,k)$ Sergey Fomin; Dylan P Thurston Cluster algebras and triangulated surfaces. Part II: Lambda lengths Sy David Friedman; David Schrittesser Projective measure without projective Baire Olivier Frécon Algebraic $\overline {\mathbb {Q}}$-groups as abstract groups Kenji Fukaya; Yong-Guen Oh; Hiroshi Ohta; Kaoru Ono Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory Jeffrey Galkowski Distribution of resonances in scattering by thin barriers Jonathan Gantner Operator theory on one-sided quaternionic linear spaces: Intrinsic $S$-functional calculus and spectral operators Cristian Gavrus; Sung-Jin Oh Global well-posedness of high dimensional Maxwell-Dirac for small critical data William Goldman; Greg Mcshane; George Stantchev; Ser Poew Tan Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane J. I. Hall Moufang loops and groups with triality are essentially the same thing Michael Handel; Lee Mosher Subgroup decomposition on $\textrm {Out}(F_n)$ Matthew Harrison-Trainor Degree spectra of relations on a cone Kazuyuki Hatada Hecke operators and systems of eigenvalues on Siegel cusp forms J. William Helton; Igor Klep; Scott McCullough; Markus Schweighofer Dilations, linear matrix inequalities, the matrix cube problem and beta distributions Viktoria Heu; Frank Loray Flat rank 2 vector bundles on genus two curves Mike Hochman On self-similar sets with overlaps and inverse theorems for entropy in $\mathbb {R}^d$ Werner Hoffmann; Satoshi Wakatsuki On the geometric side of the Arthur trace formula for the symplectic group of rank 2 Shouhei Honda Elliptic PDEs on compact Ricci limit spaces and applications Chin-Yu Hsiao Szegö kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds Alexandru D. Ionescu; Fabio Pusateri Global regularity for 2D water waves with surface tension Bogdan Ion; Siddhartha Sahi Double affine Hecke algebras and congruence groups Hiroshi Iritani; Todor Milanov; Yongbin Ruan; Yefeng Shen Gromov-Witten theory of quotient of Fermat Calabi-Yau varieties Daniel C. Isaksen Stable stems Paata Ivanisvili; Dmitriy M. Stolyarov; Vasily I. Vasyunin; Pavel B. Zatitskiy Bellman function for extremal problems in BMO II: Evolution S. V. Ivanov The bounded and precise word problems for presentations of groups Benjamin Jaye; Fedor Nazarov; Maria Carmen Reguera; Xavier Tolsa The Riesz transform of codimension smaller than one and the Wolff energy Dominic Joyce Algebraic geometry over $C^\infty$-rings Yulia Karpeshina; Roman Shterenberg Extended states for the Schrödinger operator with quasi-periodic potential in dimension two Ines Kath; Martin Olbrich Compact quotients of Cahen-Wallach spaces Elias G. Katsoulis; Christopher Ramsey Crossed products of operator algebras Jun Kigami Time changes of the Brownian motioin: Poincaré inequality, heat kernel estimate and protodistance Joachim Krieger On stability of type II blow up for the critical nonlinear wave equation on $\mathbb {R}^{3+1}$ Laurent Lazzarini; Jean-Pierre Marco; David Sauzin Measure and capacity of wandering domains in Gevrey near-integrable exact symplectic systems Francesco Lin A Morse-Bott approach to monopole Floer homology and the triangulation conjecture Robert Lipshitz; Peter S. Ozsvath; Dylan P. Thurston Bordered Floer homology Alastair J. Litterick On non-generic finite subgroups of exceptional algebraic groups Henri Lombardi; Daniel Perrucci; Marie-Françoise Roy An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem Oliver Lorscheid; Thorsten Weist Quiver Grassmanninas of type $\widetilde {D}_n$, part 1: Schubert systems and decompositions into affine spaces Camille Male Traffic distributions and independence: Permutation invariant random matrices and the three notions independence Elizabeth Milićević; Petra Schwer; Anne Thomas Dimensions of affine Deligne-Lusztig varieties: A new approach via labeled folded alcove walks and root operators Mircea Mustaţă; Mihnea Popa Hodge ideals Alexander Joseph Nagel; Fulvio Ricci; Elias M. Stein; Stephen Wainger Algebras of singular integral operators with kernels controlled by multiple norms Jaroslav Nešetřil; Patrice Ossona de Mendez A unified approach to structural limits and limits of graphs with bounded tree-depth Paul-Emile Paradan; Michele Vergne Witten non abelian localization for equivariant $K$-theory, and the $[Q,R]=0$ theorem Stefan Patrikis Variations on a theorem of Tate Gabriella Pinzari Perihelia reduction and global Kolmogorov tori in the planetary problem Peter Poláčik Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on $\mathbb {R}$ Feliks Przytycki; Juan Rivera-Letelier Geometric pressure for multimodal maps of the interval Zhi Qi Theory of fundamental Bessel functions of high rank Harold Rosenberg; Graham Smith Degree theory of immersed hypersurfaces Andreas Seeger; Charles K. Smart; Brian Street Multilinear singular integral forms of Christ-Journé type Yorck Sommerhauser; Yongchang Zhu Corrigenda to “Hopf algebras and congruence subgroups” Tvrtko Tadić Time-like graphical models Adam R. Thomas The irreducible subgroups of exceptional algebraic groups Chen Wan A local relative trace formula for the Ginzburg-Rallis model: The geometric side Yuesheng Xu; Qi Ye Generalized Mercer kernels and reproducing kernel banach spaces Gang Zhou; Dan Knopf; Israel Michael Sigal Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

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# $50 \:\:W/m^{2}$  energy density of sunlight is normally incident on the surface of a solar panel . Some part of incident energy  $(25 \:^{o}/_{o})$   is reflected from the surface snd the rest is absorbed . The force exerted on $1\:m^{2}$ surface area will be close to   $(c=3\times10^{8}\:m/s)$ : Option 1) $15\times10^{-8}\:\:N$ Option 2) $20\times10^{-8}\:\:N$ Option 3) $10\times10^{-8}\:\:N$ Option 4) $35\times10^{-8}\:\:N$

Energy density =  $50 \:\:W/m^{2}$

Total energy / time for $1\:m^{2}$ area =  $50\times1=50\:\:W$

$T.E.=50\:\:W\\\\F=0.25\left ( 2\times\frac{T.E.}{C} \right )+0.75\left ( \frac{T.E.}{C} \right )$

$\Rightarrow 1.25\left ( \frac{T.E.}{C} \right )\\\\F\Rightarrow 1.25\times\frac{50}{3\times10^{8}}=20\times10^{-8}\:\:N$

Option 1)

$15\times10^{-8}\:\:N$

Option 2)

$20\times10^{-8}\:\:N$

Option 3)

$10\times10^{-8}\:\:N$

Option 4)

$35\times10^{-8}\:\:N$

Exams
Articles
Questions


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I will be away from my home institution for an extended period. I plan to leave programs running on machines there. These programs periodically (every several hours) output updated results (improved estimates).

I would like to remotely keep track of these updated estimates.

Would it facilitate matters to run the programs in the Wolfram Cloud?

In any case, should I have the results saved both locally and in iCloud, and if how? (I am using Apple devices.)

I don't think I need to remotely control these programs--but, I presume, one could via some remote kernel setup.

P. S. Somewhat in line with my third comment immediately below and my first comment to user6014's detailed answer, my attempt to use the command >>> "~/iCloud/Results/myData.txt" yielded a Mathematica PutAppend error. I, then (in line with the resident consultant's advice), checked/activated the "Desktop and Documents Folder" on my iCloud Drive's option. Then, I employed the output command >>"~/Desktop/results". Now, the Desktop did in fact appear on iCloud.com, but not the particular new file "results".

• What do you mean by "results". If it is just numbers and plots there are many things you could do including: using SendMail to email you the results, save the results to Dropbox, and so on – Mike Honeychurch Oct 26 '18 at 22:37
• Running the evaluations in the Wolfram Cloud is not an option here. It has laughably small timeouts on any evaluation. If you're just interested in just the results, then the easiest thing to do in my opinion would be just append the results to a file stored on some cloud file service, like iCloud/Dropbox. I imagine that would be pretty painless. – ktm Oct 26 '18 at 22:47
• Helpful comments, thanks! (The results are, in fact, just numbers.) But what specific command(s) might I employ--say "results>>?" I'd appreciate it if the comments could be "fleshed out" just a little--or some suitable reference/example given. Like how do I set up the iCloud/Dropbox file to which to append? – Paul B. Slater Oct 26 '18 at 23:26
• I assume ssh'ing into the machines is not an option. I recently discussed this w/ Wolfram myself and they said parallelworks.com/solutions might be able to help (I'm not affiliated w/ them and am vaguely irked they haven't gotten back to me) – user1722 Oct 27 '18 at 15:15

Let's assume you use Dropbox/iCloud, and one of these services is integrated both with the file system on your local computer, as well as the remote computer doing the computations. I'll assume Dropbox in my example, iCloud would likely follow in exactly the same manner.

By default, Dropbox's integrated directory is in your home directory, ~/Dropbox. We'll assume a subdirectory, ~/Dropbox/Results.

The simplest implementation would probably use PutAppend to over time add the results and a timestamp to your text file.

As an example which at its core hopefully mimics your scenario, consider the following While loop which runs indefinitely, and triggers every 5 seconds:

While[True,
val = RandomReal[];
{DateString[], val} >>> "~/Dropbox/Results/myData.txt";
Pause[5]
]

Over time this appends whatever {DateString[], val} evaluates to to the end of myData.txt in my Dropbox directory, and the results look like this:

{"Fri 26 Oct 2018 21:02:30", 0.7724352272599528}
{"Fri 26 Oct 2018 21:02:35", 0.8972132205624115}
{"Fri 26 Oct 2018 21:02:40", 0.20307012057476914}
{"Fri 26 Oct 2018 21:02:45", 0.38503563713747524}
{"Fri 26 Oct 2018 21:02:50", 0.0959652843934331}

At 5 second intervals the file would grow quite rapidly, but in your case where you're only adding every few hours I don't think this is a concern.

And now, since it's in a synced Dropbox folder, I can immediately view the data in the Dropbox web interface from any browser:

Not that difficult to set up, and quite handy! Hope this achieves what you're after. If you've got further questions/specifications let me know.

• OK-the key words to me now are: "Let's assume you use Dropbox/iCloud, and one of these services is integrated both with the file system on your local computer, as well as the remote computer doing the computations." So, how do I accomplish this "integration"? – Paul B. Slater Oct 31 '18 at 22:22

To supplement the answer of user6014, I enabled (checked) the Desktop & Documents Folder on iCloud Drive and used an output command of the form

results >> "~/Desktop/results"

where the file "results" is simply a list of three numbers.

Then, upon logging into iCloud.com and accessing iCloud Drive and the Desktop icon that appears, and clicking on "results" there, a file "results.dms" was downloaded, which could (we found) be opened with TextEdit, thus completing the task put forward in the title question.


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# A question on trig series

Assume $$\{a_k\}_{k\ge1}$$ is a real sequence such that $$u(x) = \sum_{k\ge 1}a_k\sin(kx)$$ is a smooth function, and for every $$x \in [-\pi, \pi]$$ $$\left(\sum_{k\ge 1}\frac{a_k}{k}\sin(kx)\right)\left(\sum_{k\ge1}a_k\cdot k\cos(kx)\right) = \left(\sum_{k\ge1}a_k\sin(kx)\right)\left(\sum_{k\ge1}a_k\cos(kx)\right).$$ What can we say about $$\{a_k\}$$? Can we show that there exists at most one term of $$a_k$$ that is nonzero?

• Your sums should be surrounded by parentheses, right? (I initially read them as nested sums, which doesn't make much sense.) – LSpice Feb 13 at 3:41
• Yes, this says that $fg'=gf'$ (defining $f,g$ as the two series with the sines), so $(f/g)'=0$ and thus also $a_k/k=ca_k$, so $a_k=0$ for $k>1$. (There are probably other ways of doing it too.) – Christian Remling Feb 13 at 4:32
• Thanks for your comment, Christian. This is the first intuition to this question, but the problem is that $g$ may have strange zero sets even the function is smooth. The fraction $f/g$ is not always defined. So we cannot use this to prove the argument rigorously. – Cohen Lu Feb 13 at 4:56
• I think we need to be careful about whether $f/g$ is defined. For example, let $f = x\exp(-\frac{1}{x^2})$. Define the function $g$ as $g = f$when $x\ge 0$, $g = -f$ when $x < 0$. One can check that both $f$ and $g$ are smooth and $f'g = fg'$. But $f/g$ is not a constant in this situation. The problem is that $x = 0$ is a zero point of infinite order. Thus if $g$ has weird zero set, $f/g$ may have strange behaviour. – Cohen Lu Feb 13 at 6:30
• Yes, you are right, if both $f$ and $g$ are analytic, then everything should be ok. The question is what happens if we only assume smoothness of $f$ and $g$. I think I should modify the question to make it more clear. – Cohen Lu Feb 14 at 3:18


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# Using subcaption package but subfigures end up stacked rather than side by side

I'm trying to put two jpegs side by side using the subcaption package, but the images are consistently stacking on top of each other rather than side by side. All the solutions I've found simply state that the pictures have to be small enough to actually be side by side but I've tried making them smaller, too small even and they stay stacked. My code looks like this:

\begin{figure}[H]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{inclusion.jpg}
\caption{inclusions}
\label{fig:inclu}
\end{subfigure}

\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{deform}
\caption{grain deformation}
\label{fig:deform}
\end{subfigure}
\caption{filler text}
\end{figure}

Help would be greatly appreciated.

• Welcome to TeX.SX! Please make your code compilable (if possible), or at least complete it with \documentclass{...}, the required \usepackage's, \begin{document}, and \end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – Adam Liter Feb 26 '14 at 3:48

Don't leave blank lines in between (a blank line tantamounts to \par, so the next subfigure starts a new paragraph), and remove spurious blank spaces (see the % after the first \end{subfigure}):

\begin{figure}[H]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{inclusion.jpg}
\caption{inclusions}
\label{fig:inclu}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{deform}
\caption{grain deformation}
\label{fig:deform}
\end{subfigure}
\caption{filler text}
\end{figure}

A complete example:

\documentclass{article}
\usepackage{subcaption}
\usepackage[demo]{graphicx}

\begin{document}

\begin{figure}[H]
\centering
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{inclusion.jpg}
\caption{inclusions}
\label{fig:inclu}
\end{subfigure}%
\begin{subfigure}{0.5\textwidth}
\centering
\includegraphics[width=0.3\linewidth]{deform}
\caption{grain deformation}
\label{fig:deform}
\end{subfigure}
\caption{filler text}

The demo option for graphicx simply replaces actual figures with black rectangles; do not use that option in your actual document.


text:
+0

# If , how many of the natural-number factors of are multiples of 150?

0
57
2

If $$n = 2^{10} \cdot 3^{14} \cdot 5^{8}$$, how many of the natural-number factors of $$n$$ are multiples of 150?

I got 702, but that was wrong...

Apr 6, 2020

#1
+20967
0

I'm not the best at this, but this is my attempt:

150  =  2 x 3 x 5 x 5  --  so every multiply must have at least 1 two, 1 three, and 2 fives.

So, from the 210 (which consists of 10 twos),

you can select either 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 twos  -- 10 different selections.

From 314 (which consists of 14 threes),

you can select either 1, 2, 3, ... 14 threes  --  14 different selections.

From 58, you must select at least 2 fives, but it could also be 3, 4, 5, 6, 7, or 8 fives

--  7 different selections.

Multiplying 10 x 14 x 7, I get 980 different ways.

Apr 6, 2020
#2
0

That is correct! Thank you so much, geno!

Guest Apr 6, 2020


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# CNF form of variable assignment problem

There are n variables $x_1$, $x_2$,..., $x_n$ and each one of them takes values from 1 to k (k>= n) and all are distinct. How can I represent this in the CNF form? (I tried the trivial way of trying all assignments and then checking if they are distinct, but I think it could be done better)

• By "better" do you mean something shorter than (for $n=3, k=4$) $(x_1\ge 1)\land(x_1\le 4) \land(x_2\ge 1)\land(x_2\le 4)\land(x_3\ge 1)\land(x_3\le 4)\land(x_1\ne x_2)\land(x_1\ne x_3)\land(x_2\ne x_3)$ Sep 15 '16 at 20:16
• @Rick : Yes, this's the basic implementation Sep 16 '16 at 9:31

If you only have to encode this (and don't have any other constraints on $x_i$), you can then use the following constraints: $x_1 < x_2 < \dots < x_{n-1} < x_n \leq k$ which is $n$ constraints.

Let $m=\lceil \log_2 k\rceil$ and $x_i = b_{im}, b_{i(m-1)}, \dots, b_{i1}$, where $m$ is the high bit and $1$ is the low bit. Define $d_{ij} = b_{ij}\textrm{ XOR }b_{(i+1)j}$. Then, the constraint $x_1 < x_2$ is representable as: $$\bigvee_{i=1}^{m} \left[\left(\bigwedge_{j=i+1}^m d_{1j}'\right)\left(b_{2i}b_{1i}'\right)\right] = 1$$ basically the i-th clause encodes that the top $m-i$ bits are identical and the $i$-th bit is $1$ in $x_2$ and $0$ in $x_1$.

Abusing notation slightly (taking the constants in the representation of $k$ for $x_{n+1}$), a similar technique can be used for $x_n \leq k$, where one would add an extra clause $\bigwedge_i d_{ni}'$ for handling the equality.

The above formula is a DNF. To get to CNF, one would simple encode $\textrm{NOT}(x_2 \leq x_1)$.

Finally, if it's needed to represent $x_1 \geq 1$ one can do this by adding a CNF clause $\bigvee_i b_{1i}$.

Note that the complexity here is really good. $O(nm)$ clauses, and $O(nm^2)$ literals. In particular if $n$ and $k$ are large this is much better than for other techniques (but it isn't applicable in other settings where other constraints could change the ordering).

This is sometimes known as an "alldiff" constraint. There are some encodings listed here: Requiring at least one alldiff constraint to be satisfied converted to SAT.

Alternatively, you might do better to use a CSP solver, rather than trying to express this in CNF and then use a SAT solver. Handling "alldiff" constraints is exactly the sort of thing that constraint satisfaction solvers are designed to do well. See When to use SAT vs Constraint Satisfaction?.


text:
• # Developing an Isometric Plugin for Unity3D

Engines and Middleware

• Posted By MATov

It's a story on how to write a plugin for Unity Asset Store, take a crack at solving the well-known isometric problems in games, and make a little coffee money from that, and also to understand how expandable Unity editor is. Pictures, code, graphs and thoughts inside.

# Prologue

So, it was one night when I found out I had pretty much nothing to do. The coming year wasn't really promising in my professional life (unlike personal one, though, but that's a whole nother story). Anyway, I got this idea to write something fun for old times sake, that would be quite personal, something on my own, but still having a little commercial advantage (I just like that warm feeling when your project is interesting for somebody else, except for your employer). And all this went hand in hand with the fact that I have long awaited to check out the possibilities of Unity editor extension and to see if there's any good in its platform for selling the engine's own extensions.

I devoted one day to studying the Asset Store: models, scripts, integrations with various services. And first, it seemed like everything has already been written and integrated, having even a number of options of different quality and detail levels, just as much as prices and support. So right away I've narrowed it down to:

• code only (after all, I'm a programmer)
• 2D only (since I just love 2D and they've just made a decent out-of-the-box support for that in Unity)

And then I remembered just how many cactuses I've ate and how many mice've died when we were making an isometric game before. You won't believe how much time we've killed on searching viable solutions and how many copies we've broken in attempts to sort out this isometry and draw it. So, struggling to keep my hands still, I searched by different key and not-so-much-key words and couldn't find anything except a huge pile of isometric art, until I finally decided to make an isometric plugin from scratch.

## Setting the goals

The first I need was to describe in short what problems this plugin was supposed to solve and what use the isometric games developer would make of it. So, the isometry problems are as follows:

• sorting objects by remoteness in order to draw them properly
• extension for creation, positioning and displacement of isometric objects in the editor

Thus, with the main objectives for the first version formulated, I set myself  2-3 days deadline for the first draft version. Thus couldn't being deferred, you see, since enthusiasm is a fragile thing and if you don't have something ready in the first days, there's a great chance you ruin it. And New Year holidays are not so long as the might seem, even in Russia, and I wanted to release the first version within, like, ten days.

## Sorting

To put it short, isometry is an attempt made by 2D sprites to look like 3D models. That, of course, results in dozens of problems. The main one is that the sprites have to be sorted in the order in which they were to be drawn to avoid troubles with mutual overlapping.

On the screenshot you can see how it's the green sprite that is drawn first (2,1), and then the blue one goes (1,1)

The screenshot shows the incorrect sorting when the blue sprite's drawn first

In this simple case sorting won't be such a problem, and there are going to be  options, for example:

- sorting by position of Y on the screen, which is (isoX + isoY) * 0.5 + isoZ
- drawing from the remotest isometric grid cell from left to right, from top to down [(3,3),(2,3),(3,2),(1,3),(2,2),(3,1),...]
- and a whole bunch of other interesting and not really interesting ways

They all are pretty good, fast and working, but only in case of such single-celled objects or columns extended in isoZ direction After all, I was interested in more common solution that would work for the objects extended in one coordinate's direction, or even the "fences" which have absolutely no width, but are extended in the same direction as the necessary height.

The screenshot shows the right way of sorting extended objects 3x1 and 1x3 with "fences" measuring 3x0 and 0x3

And that's where our troubles begin and put us in place where we have to decide on the way forward:

• split "multi-celled" objects into "single-celled" ones, i.e. to cut it vertically and then sort the stripes emerged
• think about the new sorting method, more complicated and interesting

I chose the second option, having no particular desire to get into tricky processing of every object, into cutting (even automatic), and special approach to logic. For the record, they used the first way in few famous games like Fallout 1 and Fallout 2. You can actually see those strips if you get into the games' data.

So, the second option doesn't imply any sorting criteria. It means that there is no pre-calculated value by which you could sort objects. If you don't believe me (and I guess many people who never worked with isometry don't), take a piece of paper and draw small objects measuring like 2x8 and, for example, 2x2. If you somehow manage to figure out a value for calculation its depth and sorting - just add a 8x2 object and try to sort them in different positions relative to one another.

So, there's no such value, but we still can use dependencies between them (roughly speaking, which one's overlapping which) for topological sorting. We can calculate the objects' dependencies by using projections of isometric coordinates on isometric axis.

Screenshot shows the blue cube having dependency on the red one

Screenshot shows the green cube having dependency on the blue one

A pseudocode for dependency determination for two axis (same works with Z-axis):

bool IsIsoObjectsDepends(IsoObject obj_a, IsoObject obj_b) {
var obj_a_max_size = obj_a.position + obj_a.size;
return
obj_b.position.x < obj_a_max_size.x &&
obj_b.position.y < obj_a_max_size.y;
}

With such an approach we build dependencies between all the objects, passing among them recursively and marking the display Z coordinate. The method is quite universal, and, most importantly, it works. You can read detailed description of this algorithm, for example, here or here. Also they use this kind of approach in popular flash isometric library (as3isolib).

And everything was just great except that time complexity of this approach is O(N^2) since we've got to compare every object to every other one in order to create the dependencies. I've left optimization for later versions, having added only lazy re-sorting so that nothing would be sorted until something moves. So we're going to talk about optimization little bit later.

## Editor extension

From now on, I had the following goals:

• sorting of objects had to work in the editor (not only in a game)
• there had to be another kind of Gizmos-Arrow (arrows for moving objects)
• optionally, there would be an alignment with tiles when object's moved
• sizes of tiles would be applied and set in the isometric world inspector automatically
• AABB objects are drawn according to their isometric sizes
• output of isometric coordinates in the object inspector, by changing which we would change the object's position in the game world

And all of these goals have been achieved. Unity really does allow to expand its editor considerably. You can add new tabs, windows, buttons, new fields in object inspector. If you want, you can even create a customized inspector for a component of the exact type you need.  You can also output additional information in the editor's window (in my case, on AABB objects), and replace standard move gizmos of objects, too. The problem of sorting inside the editor was solved via this magic ExecuteInEditMode tag, which allows to run components of the object in editor mode, that is to do it the same way as in a game.

All of these were done, of course, not without difficulties and tricks of all kinds, but there was no single problem that I'd spent more than a couple of hours on (Google, forums and communities sure helped me to resolve all the issues arisen which were not mentioned in documentation).

Screenshot shows my gizmos for movement objects within isometric world

## Release

So, I got the first version ready, took the screenshot. I even drew an icon and wrote a description. It's time. So, I set a nominal price of \$5, upload the plugin in the store and wait for it to be approved by Unity. I didn't think over the price much, since I didn't really want to earn big money yet. My purpose was to find out if there is a general demand and if it was, I would like to estimate it. Also I wanted to help developers of isometric games who somehow ended up absolutely deprived of opportunities and additions.

In 5 rather painful days (I spent about the same time writing the first version, but I knew what I was doing, without further wondering and overthinking, that gave me the higher speed in comparison with people who'd just started working with isometry) I got a response from Unity saying that the plugin was approved and I could already see it in the store, just as well as its zero (so far) sales. It checked in on the local forum, built Google Analytics into the plugin's page in the store and prepared myself to wait the grass to grow.

It didn't take very long before first sales, just as feedbacks on the forum and the store came up. For the remaining days of January 12 copies of my plugin have been sold, which I considered as a sign of the public's interest and decided to continue.

## Optimization

So, I was unhappy with two things:

• Time complexity of sorting - O(N^2)
• Troubles with garbage collection and general performance

### Algorithm

Having 100 objects and O(N^2) I had 10,000 iterations to make just to find dependencies, and also I'd have to pass all of them and mark the display Z for sorting. There should've been some solution for that. So, I tried a huge number of options, could not sleep thinking about this problem. Anyway, I'm not going to tell you about all the methods I've tried, but I'll describe the one that I've found the best so far.

First thing first, of course, we sort only visible objects. What it means is that we constantly need to be know what's in our shot. If there is any new object, we got to add it in the sorting process, and if one of the old one's gone - ignore it. Now, Unity doesn't allow to determine the object's Bounding Box together with its  children in the scene tree. Pass over the children (every time, by the way, since they can be added and removed) wouldn't work - too slow. We also can't use OnBecameVisible and other events because these work only for parent objects. But we can get all Renderer components from the necessary object and its children. Of course, it doesn't sound like our best option, but I couldn't find another way, same universal and acceptable by performance.

List<Renderer> _tmpRenderers = new List<Renderer>();

bool IsIsoObjectVisible(IsoObject iso_object) {
iso_object.GetComponentsInChildren<Renderer>(_tmpRenderers);
for ( var i = 0; i < _tmpRenderers.Count; ++i ) {
if ( _tmpRenderers[i].isVisible ) {
return true;
}
}
return false;
}

There is a little trick of using GetComponentsInChildren function that allows to get components without allocations in the necessary buffer, unlike another one that returns new array of components

Secondly, I still had to do something about O(N^2). I've tried a number of space splitting techniques before I stopped at a simple two-dimensional grid in the display space where I project my isometric objects. Every such sector contains a list of isometric objects that are crossing it. So, the idea is simple: if projections of the objects are not crossed, then there's no point in building dependencies between the objects at all. Then we pass over all visible objects and build dependencies only in the sectors where it's necessary, thereby lowering time complexity of the algorithm and increasing performance. We calculate the size of each sector as an average between the sizes of all objects. I found the result more than satisfying.

### General performance

Of course, I could write a separate article on this... Okay, let's try to make this short. First, we're cashing the components (we use GetComponent to find them, which is not fast). I recommend everyone to be watch yourselves when working with anything that has to do with Update. You always have to bear in mind that it happens for every frame, so you've got to be really careful Also, remember about all interesting features like custom == operator. There are a lot to things to keep in mind, but in the end you get to know about every one of them in the built-in profiler. It makes it much easier to memorize and use them

Also you get to really understand the pain of garbage collector. Need higher performance? Then forget about anything that can allocate memory, which in C# (especially in old Mono compiler) can be done by anything, ranging from foreach(!) to emerging lambdas, let alone LINQ which is now prohibited for you even in the simplest cases. In the end instead of C# with its syntactic sugar you get a semblance of C with ridiculous capacities.

Here I'm gonna give some links on the topic you might find helpful: Part1, Part2, Part3.

### Results

I've never known anybody using this optimization technique before, so I was particularly glad to see the results. And if in the first versions it took literally 50 moving objects for the game to turn it into a slideshow, now it works pretty well even when there're 800 objects in a frame: everything's spinning at top speed and re-sorting for just for 3-6 ms which is very good for this number of objects in isometry. Moreover, after initialization it almost haven't allocate memory for a frame

## Further opportunities

After I read feedbacks and suggestions, there were a few features which I added in the past versions.

### 2D/3D Mixture

Mixing 2D and 3D in isometric games is an interesting opportunity allowing to minimize drawing of different movement and rotations options (for instance, 3D models of animated characters). It's not really hard thing to do, but requires integration within the sorting system. All you need is to get a Bounding Box of the model with all its children, and then to move the model along the display Z by the box's width.

Bounds IsoObject3DBounds(IsoObject iso_object) {
var bounds = new Bounds();
iso_object.GetComponentsInChildren<Renderer>(_tmpRenderers);
if ( _tmpRenderers.Count > 0 ) {
bounds = _tmpRenderers[0].bounds;
for ( var i = 1; i < _tmpRenderers.Count; ++i ) {
bounds.Encapsulate(_tmpRenderers[i].bounds);
}
}
return bounds;
}

that's an example of how you can get **Bounding Box** of the model with all its children

and that's what it looks like when it's done

### Custom isometric settings

That is relatively simple. I was asked to make it possible to set the isometric angle, aspect ratio, tile height. After suffering some pain involved in maths, you get something like this:

### Physics

And here it gets more interesting. Since isometry simulates 3D world, physics is supposed to be three-dimensional, too, with height and everything. I came up with this fascinating trick. I replicate all the components of physics, such as Rigidbody, Collider and so on, for isometric world. According to these descriptions and setups I make the copy of invisible physical three-dimensional world using the engine itself and built-in PhysX. After that I take the simulation data calculated and get those bacl in duplicating components for isometric world. Then I do the same to simulate bumping and trigger events.

The toolset physical demo GIF

## Epilogue and conclusions

After I implemented all the suggestions from the forum, I decided to raise the price up to 40 dollars, so it wouldn't look like just another cheap plugin with five lines of code I will be very much delighted to answer questions and listen to your advices. I welcome all kinds of criticism, thank you!

Unity Asset Store page link: Isometric 2.5D Toolset

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• So this is the problem that I have :- https://youtu.be/kU8Dm5bDJXg
This is the code i am using:-
using System.Collections; using System.Collections.Generic; using UnityEngine; namespace SA { public class AnimatorHook : MonoBehaviour { Animator anim; StateManager states; public void Init(StateManager st) { states = st; anim = st.anim; } void OnAnimatorMove() { if (!states.canMove) anim.ApplyBuiltinRootMotion(); states.rigid.drag = 0; float multiplier = 1; Vector3 delta = anim.deltaPosition; delta.y = 0; Vector3 v = (delta * multiplier) / states.delta; states.rigid.velocity = v; } } } For additional reference see the following code
using System.Collections; using System.Collections.Generic; using UnityEngine; namespace SA { public class StateManager : MonoBehaviour { [Header("Init")] public GameObject activeModel; [Header("Inputs")] public float vertical; public float horizontal; public float moveAmount; public Vector3 moveDir; public bool rt, rb, lt, lb; [Header("Stats")] public float moveSpeed = 5f; public float runSpeed = 8f; public float rotateSpeed = 20; public float toGround = 0.5f; [Header("States")] public bool onGround; public bool run; public bool lockOn; public bool inAction; public bool canMove; [Header("Other")] public EnemyTarget lockOnTarget; [HideInInspector] public Animator anim; [HideInInspector] public Rigidbody rigid; [HideInInspector] public AnimatorHook a_hook; [HideInInspector] public float delta; [HideInInspector] public LayerMask ignoreLayers; float _actionDelay; public void Init() { SetupAnimator(); rigid = GetComponent<Rigidbody>(); rigid.angularDrag = 999; rigid.drag = 4; rigid.constraints = RigidbodyConstraints.FreezeRotationX | RigidbodyConstraints.FreezeRotationZ; a_hook = activeModel.AddComponent<AnimatorHook>(); a_hook.Init(this); gameObject.layer = 8; ignoreLayers = ~(1 << 9); anim.SetBool("onGround",true); } void SetupAnimator() { if(activeModel == null) { anim = GetComponentInChildren<Animator>(); if(anim == null) { Debug.Log("no model found"); } else { activeModel = anim.gameObject; } } if(anim == null) { anim = activeModel.GetComponent<Animator>(); } //anim.applyRootMotion = false; } public void FixedTick(float d) { delta = d; rigid.drag = (moveAmount > 0 || !onGround) ? 0 : 4; DetectAction(); if (inAction) { // anim.applyRootMotion = true; _actionDelay += delta; if(_actionDelay > 0.3f) { inAction = false; _actionDelay = 0; } else { return; } } canMove = anim.GetBool("canMove"); if (!canMove) { return; } //anim.applyRootMotion = false; float targetSpeed = moveSpeed; if (run) targetSpeed = runSpeed; if(onGround) rigid.velocity = moveDir * (targetSpeed * moveAmount); /* if (run) lockOn = false; */ Vector3 targetDir = (lockOn == false) ? moveDir : lockOnTarget.transform.position - transform.position; targetDir.y = 0; if (targetDir == Vector3.zero) targetDir = transform.forward; Quaternion tr = Quaternion.LookRotation(targetDir); Quaternion targetRotation = Quaternion.Slerp(transform.rotation, tr, delta * moveAmount * rotateSpeed); transform.rotation = targetRotation; anim.SetBool("lockon", lockOn); if (lockOn == false) HandleMovementAnimations(); else HandleLockOnAnimations(moveDir); } public void DetectAction() { if (canMove == false) return; if (rb == false && rt == false && lt == false && lb == false) return; string targetAnim = null; if (rb) targetAnim = "Sword And Shield Attack"; if (rt) targetAnim = "Stable Sword Outward Slash"; if (lb) targetAnim = "Standing Melee Attack Horizontal"; if (lt) targetAnim = "Sword And Shield Slash (1)"; if (string.IsNullOrEmpty(targetAnim)) return; canMove = false; inAction = true; anim.CrossFade(targetAnim,0.2f); //rigid.velocity = Vector3.zero; } public void Tick(float d) { delta = d; onGround = OnGround(); anim.SetBool("onGround", onGround); } void HandleMovementAnimations() { anim.SetBool("run", run); anim.SetFloat("Vertical", moveAmount ,0.4f,delta); } void HandleLockOnAnimations(Vector3 moveDir) { Vector3 relativeDir = transform.InverseTransformDirection(moveDir); float h = relativeDir.x; float v = relativeDir.z; anim.SetFloat("Vertical", v, 0.2f, delta); anim.SetFloat("Horizontal", h, 0.2f, delta); } public bool OnGround() { bool r = false; Vector3 origin = transform.position + (Vector3.up * toGround); Vector3 dir = -Vector3.up; float dis = toGround + 0.3f; RaycastHit hit; if(Physics.Raycast(origin,dir,out hit,dis)) { r = true; Vector3 targetPosition = hit.point; transform.position = targetPosition; } return r; } } } I've been stuck on this for too long, any help will be highly appreciated
• By jb-dev
This is a short .gif showing off visuals effects for the parrying mechanic

Can programmers art? How far can creativity and programming take you?
I have summarized what I learned in several months into 7 key techniques to improve the visual quality of your game.

"Programmer art" is something of a running joke. For those unfamiliar with the term, it refers to the "placeholder" or "throw-together" art that programmers tend to use while developing games.
Some of us don't have the necessary artistic skills, however, sometimes we just can't be bothered to put in the effort. We're concerned about the technical side of things working - art can come later.
Here's what this usually means -

I worked on a game jam with some new people a few months ago. I just wanted to make sure that my gameplay and AI code was doing what it was supposed to do. This would have to interface with code from other teammates as well, so it was important to test and check for bugs. This was the result.
That's not what I'm going to talk about today though.

I'm going to take a different angle on "programmer art" - not the joke art that programmers often use, but the fact that there's a LOT that a programmer can do to improve the visual appeal of a game. I believe some of this falls under "technical art" as well.

My current job kind of forced me to think in this capacity.
I was tasked with visualizing some scientific data. Though this data was the result of years of hard work on the part of scientists, the result was unimpressive to the untrained eye - a heap of excel files with some words and numbers.
There are very few people in the world who can get excited by seeing a few excel files.
My job? To make this data exciting to everyone else.
My task was to visualize connectome data for a famous worm known as C. Elegans, made available by the wonderful people working on the OpenWorm project.
Part of the data parsing to read and display the data as a worm's body with neurons on it was done by my teammate. My main task was to improve the visuals and the overall graphical quality.

The first thing that comes to mind is using HD textures, PBR materials and high-poly models. Add in a 3D terrain using a height map, some post-processing and HDR lighting, and BOOM! Gorgeous 3D scene. I'm sure you've all seen loads of those by now.
Except, almost none of that would really help me.
The idea was very abstract - neurons and connections visible in a zoomed-in, x-ray-like view of a worm. I don't think rolling hills would have helped me much.
I had no 3D modelling skills or access to an artist - even if I did, I'm not sure what kind of 3D models would have helped.

As a result, what I've made isn't a gorgeous 3D environment with foliage and god-rays and lens flares. So it's not applicable in every case or the perfect example of how a programmer can make a gorgeous game.
But, it does provide a distinct viewpoint and result. The special sets of constraints in the problem I had to solve led to this.
So here's what I actually did:

The 7 things I did to improve the visuals of my Unity game
1. Conceptualizing the look
This could be considered a pre-production step for art or any visual project. Ideally, what should it look like? What's the goal? What are your references?
In this case, the viewer had a hologram-like feel to it (also there were plans to port it to a HoloLens eventually). I liked the idea of a futuristic hologram. And the metaphor of "AI bringing us towards a better future".
So what were my references? Sci-fi of course!
My first pick was one of my favourite franchises - Star Wars. I love how the holo-comms look in the movies.

Holograms became a key component of my design.
This is a HUD design from Prometheus that I found on Google -

In this case, the colours appealed to me more than the design itself. I ended up basing the UI design on this concept.

Key takeaway - Your imagination is the very first tool that helps you create impressive art. Use references! It's not cheating - it's inspiration. Your references will guide you as you create the look that you want.

I had some shader programming experience from University - D3D11 and HLSL. But that work had been about building a basic graphics engine with features like lighting, shadows, and some light post-processing. I had done some light Shader programming in Unity before as well.
What I really needed now was impressive visual effects, not basic lighting and shadows.
I was really lucky that this was about the time Unity made Shader Graph available, which made everything much easier. I can write Shader code, but being able to see in real time what each node (Which can be considered a line of code) does makes it so much easier to produce the effects you want.
I familiarized myself with all the samples Unity had included with this new tool. That wouldn't have been enough though. Thankfully due to my previous experience with Shaders, I was able to make some adjustments and improvements to make them suit my needs.
Some tweaking with speed, scaling, colours, and textures led to a nice hologram effect for the UI panels.

I wanted the viewer to feel good to interact with as well, and some work implementing a glow effect (alongside the dissolve effects) led to this -

Key takeaway - Shaders are an extremely powerful tool in a Game Programmer's repertoire. Tools like Unity's Shader Graph, the old Shader Forge asset, and Unreal's material editor make Shaders more accessible and easier to tune to get the exact look you want.
PS - Step 5 below is also really important for getting a nice glow effect.

3. Visual Effects and Animations using Shaders
I was able to extend the dissolve and hologram shaders to fake some animation-like visual effects.
And a combination of some timed Sine curves let me create an animation using the dissolve effect -

The work here was to move the animation smoothly across individual neuron objects. The animation makes it look like they're a single connected object, but they're actually individual Sphere meshes with the Shader applied to them. This is made possible by applying the dissolve texture in World Space instead of Object Space.
A single shader graph for the neurons had functionality for colour blending, glow, and dissolve animation.
All of this made the graphs really large and difficult to work with though. Unity was constantly updating the Shader Graph tools, and the new updates include sub-graphs which make it much easier to manage.
Key takeaway - There is more to shaders than meets the eye. As you gain familiarity with them, there are very few limits to the effects you can create. You can create animations and visual effects using Shaders too.

4. Particle systems - more than just trails and sparks
I have no idea why I put off working with the particle systems for so long!
The "neurons" in the viewer were just spheres, which was pretty boring.
Once I started to understand the basics of the particle system, I could see how powerful it was. I worked on some samples from great YouTube tutorials - I'm sharing a great one by Gabriel Aguiar in the comments below.
After that, I opened up Photoshop and experimented with different brushes to create Particle textures.
Once again, I referred to my sources of what neurons should look like. I wanted a similar look of "hair-like" connections coming out of the neurons, and the core being bright and dense.
This is what it looked like finished, and the particle system even let me create a nice pulsating effect.

Part of my work was also parsing a ton of "playback data" of neurons firing. I wanted this to look like bright beams of light, travelling from neuron to neuron. This involved some pathfinding and multi-threading work as well.

Lastly, I decided to add a sort of feedback effect of neurons firing. This way, you can see where a signal is originating and where it's ending.

Key takeaway - Particle systems can be used in many ways, not just for sparks and trails. Here, I used them to represent a rather abstract object, a neuron. They can be applied wherever a visual effect or a form of visual "feedback" seems relevant.

5. Post-processing to tie the graphics and art together
Post-processing makes a HUGE difference in the look of a game scene. It's not just about colours and tone, there's much more to it than that. You can easily adjust colours, brightness, contrast, and add effects such as bloom, motion blur, vignette, and screen-space reflections.
First of all, Linear colour space with HDR enabled makes a huge difference - make sure you try this out.
Next, Unity's new post-processing stack makes a lot of options available without impacting performance much.
The glow around the edges of the sphere only appears with an HDR colour selected for the shader, HDR enabled, and Linear colour space. Post-processing helps bump this up too - bloom is one of the most important settings for this.
Colour grading can be used to provide a warm or cool look to your entire scene. It's like applying a filter on top of the scene, as you would to an image in Photoshop. You can completely override the colours, desaturate to black and white, bump up the contrast, or apply a single colour to the whole scene.

There is a great tutorial from Unity for getting that HD look in your scenes - if you want a visible glow you normally associate with beautiful games, you need to check this out.

Key takeaway - Post processing ties everything together, and helps certain effects like glows stand out.

6. Timing and animation curves for better "feel"
This is a core concept of animation. I have some training in graphic design and animation, which is where I picked this up. I'm not sure about the proper term for it - timing, animation curves, tween, etc.
Basically, if you're animating something, it's rarely best to do it with linear timing. Instead, you want curves like this -

Or more crazy ones for more "bouncy" or cartoon-ish effects.
I applied this to the glow effects on the neurons, as I showed earlier.
And you can use this sparingly when working with particle systems as well - for speed, size, and similar effects. I used this for the effect of neurons firing, which is like a green "explosion" outwards. The particles move outwards fast and then slow down.
Unity has Animation Curve components you can attach to objects. You can set the curve using a GUI and then query it in your C# scripts. Definitely worth learning about.
Key takeaway - Curves or tweens are an animation concept that is easy to pick up and apply. It can be a key differentiator for whether your animations and overall game look polished or not.

7. Colour Palettes and Colour Theory - Often overlooked
Colour is something that I tend to experiment with and work with based on my instincts. I like being creative, however, I really underestimated the benefits of applying colour theory and using palettes.
Here's the before -

Here are some of the afters -

I implemented multiple themes because they all looked so good.
I basically messed around with different types of "Colour harmony" - Monochrome, triad, complementary, and more. I also borrowed some colours from my references and built around that.
Key takeaway - Don't underestimate the importance of colour and colour theory. Keep your initial concept and references in mind when choosing colours. This adds to that final, polished look you want.

Bonus - consider procedural art
Procedural Generation is just an amazing technique. I didn't apply it on this project, but I learned the basics of it such as generating Value and Perlin noise, generating and using Height maps for terrains, and generating mazes.

Procedural art is definitely something I want to explore more.
A couple of interesting things (Links in the "extra resources" section below) -
Google deepdream has been used to generate art. There's an open-source AI project that can colour lineart. Kate Compton has a lot of interesting projects and resources about PCG and generative art. I hope this leads to tools that can be directly applied to Game Development. To support the creation of art for games. I hope I get the opportunity to create something like that myself too.
Conclusion
These 7 techniques were at the core of what I did to improve the visual quality of my project.
This was mostly the result of the unique set of constraints that I had. But I'm pretty sure some famous person said: "true creativity is born of constraints". Or something along those lines. It basically means that constraints and problems help channel your creativity.
I'm sure there is more that I could have done, but I was happy with the stark difference between the "before" and "after" states of my project.
I've also realized that this project has made me more of an artist. If you work on visual quality even as a programmer, you practice and sharpen your artistic abilities, and end up becoming something of an artist yourself.

Did I miss something obvious? Let me know in the comments!

Extra Resources
OpenWorm project
Great tutorial by Gabriel Aguiar
Unity breaks down how to improve the look of a game using Post processing
Another resource on post-processing by Dilmer Valecillos
Brackey's tutorial on post-processing
Adobe Colour wheel, great for colour theory and palettes
An open-source AI project that can colour lineart
A demo of generative art by Kate Compton

• THE PROJECT

INT is a 3D Sci-fi RPG with a strong emphasis on story, role playing, and innovative RPG features such as randomized companions. The focus is on the journey through a war-torn world with fast-paced combat against hordes of enemies. The player must accomplish quests like a traditional RPG, complete objectives, and meet lively crew members who will aid in the player's survival. Throughout the game you can side and complete missions through criminal cartels, and the two major combatants, the UCE and ACP, of the Interstellar Civil War.
Please note that all of our current positions are remote work. You will not be required to travel.
INT Official website
IndieDB page
Also follow social media platforms for the latest news regarding our projects.

TALENTS NEEDED
3D Animator
3D Character Modeler
3D Environment Modeler
Unity Engine Programmer

REVENUE-SHARE
The project is marching increasingly closer to be ready for our crowd-funding campaign. Being an Indie team we do not have the creative restrictions often imposed by publishers or other third parties. We are extremely conscientious of our work and continuously uphold a high level of quality throughout our project.
We are unable to offer wages or per-item payments at this time. However revenue-sharing from crowd-funding is offered to team members who contribute 15-20 hours per week to company projects, as well as maintain constant communication and adhere to deadlines. Your understanding is dearly appreciated.

TO APPLY
Please send your Cover Letter, CV, Portfolio (if applicable), and other relevant documents/information to this email: JohnHR@int-game.net
Thank you for your time! Please feel free to contact me via the email provided should you have any questions or are interested to apply for this position. We look forward to hearing from you!
John Shen
Starboard Games LLC

• Hello, I'm currently searching for additional talented and passionate members for our team that's creating a small horror game.

About the game: The game would be a small sci-fi/post-apocalyptic survival horror 3D game with FPS (First person shooter) mechanics and an original setting and story based in a book (which I'm writing) scene, where a group of prisoners are left behind in an abandoned underground facility. It would play similar to Dead Space combined with Penumbra and SCP: Secret Laboratory, with the option of playing solo or multiplayer.

Engine that'd be used to create the game: Unity

About me: I'm a music composer with 4 years of experience and I'm fairly new in this game development world, and I'm currently leading the team that'd be creating this beautiful and horrifying game. I decided that making the book which I'm writing into a game would be really cool, and I got more motivated about doing so some time ago when I got a bunch of expensive Unity assets for a very low price. However, I researched about how to do things right in game development so I reduced the scope of it as much as I could so that's why this game is really based in a scene of the book and not the entire thing. Also I'm currently learning how to use Unity and learning how to program.

Our team right now consists of: Me (Game Designer, Creator, Music Composer, Writer), 3 3D Modelers, 3 Game Programmers, 1 Sound Effect Designer, 1 Concept Artist, 1 3D Animator and 1 Community Manager.

Who am I looking for: We are looking for a talented, passionate and experienced 3D Environment Modeler who is able to create high poly realistic tunnels, rooms, props, in other words, small closed environments and is able to also texture them with a sci-fi/horror vibe.
Right now the game is in mid-early development and you can see more information about it and follow our progress in our game jolt page here: https://gamejolt.com/games/devilspunishment/391190 . We expect to finish some sort of prototype in 2-3 months from now.

This is a contract rev-share position

If you are interested in joining, contributing or have questions about the project then let's talk. You can message me in Discord: world_creator#9524
×


text:
# Does any operating system offer full system encryption, including RAM and SWAP?

I‘ve been looking around and did my research but I could not find any information if any operating system exists which would be able to encrypt all data, including RAM and the SWAP partition, to protects things while the OS is up-and-running. I found infos about disk encryption, file encryption, and much more, but I seem to have a hard time to find infos related to a “complete system being protected by the operating system”.

Simpler said: I’ld like to know if it’s possible to protect a computer system with such an OS so that – when anyone steals the hard disk of a webserver while it’s running – the thieve can’t decrypt the data.

Is there something like a fully encrypted OS, or is that impossible for some reason(s)? If, which reason(s) would that be?

• ram encryption is not common, as the performance hit would be unacceptable in most cases. swap encryption is common, and can be done in windows and linux separate from full drive encryption – Richie Frame Sep 14 '16 at 12:39
• I saw a build of BEAR out of Dartmouth that was fully encrypted, but i don't know the finer details. – b degnan Sep 14 '16 at 12:46
• Full disk encryption (including swap) is easy and commonly available for most operating systems. I think on Linux you typically use LUKS for that. On Windows you'd use BitLocker or a TrueCrypt derivate. – CodesInChaos Sep 14 '16 at 13:47
• RAM is tricky. I think Intel's SGX uses encrypted RAM. AMD is working on something for the upcoming Zen CPUs as well. – CodesInChaos Sep 14 '16 at 13:47

Yes and no.

Let's go through the requirements you have step-by-step:

So if anyone steals the hard disk [...] he cannot decrypt the data.

That is widely supported in modern operating systems and called full-disk-encryption (FDE). On Windows you'd use something like Bitlocker for this task and on Linux something like dm-crypt should do the trick. Note however that this would require entering a passphrase every, single time you boot the server up.

I mean all it's encrypted, also [...] the swap

Any decent full-disk encryption system hooks itself into the driver stack and encrypts everything going through this stack shortly before the drive is actually invoked to write, thus, as the swap is a normally written onto the drive, it will be encrypted as well by most full-disk-encryption programs.

I mean all it's encrypted, also the RAM [...]

This is where things get tricky and the answer becomes "no".
You can encrypt data in RAM, as it's just data and the algorithms don't care where the data resides. However this would also mean leaving the key in RAM, which makes this kinda pointless. BUT, there's Intel SGX and AMD's upcoming memory encryption techniques (PDF whitepaper). They both consider the OS an adversary and thus offer protection against him, even in RAM. So with a combination of standard encryption and SGX based encryption, you could get large parts of the RAM only holding encrypted content, but SGX also needs external management and because of that you can't encrypt everything in RAM (for now), as long as you don't put an encryption chip in between your CPU and the RAM. Also note: As these technologies are very recent, there isn't many products that use them right now, especially since Intel requires a business contract with SGX production-users.

"Encrypt everything" sounds nice in theory, but isn't practicable. There are trade-offs to be made. Full-disk-encryption will protect you against attackers stealing your physical disks and reading their contents and RAM-protection can at most defend against attackers who get root access and / or physically steal and try to read-out the RAM (note that RAM doesn't hold data for a long time), but the technology isn't there (yet).


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Subtraction of Fractions ( Read ) | Arithmetic | CK-12 Foundation
You are viewing an older version of this Concept. Go to the latest version.

# Subtraction of Fractions

%
Best Score
Practice Subtraction of Fractions
Best Score
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Subtraction of Fractions
0  0  0

Julian and Suz ordered a pizza that was cut into 10 slices. Suz ate 3 slices and Julian ate 4 slices. What fraction of the pizza did each person eat? What fraction of the pizza is left?

### Guidance

$\frac{5}{7}-\frac{2}{7}=?$

The problem above can be represented with fraction strips:

$\boxed{\frac{5}{7}-\frac{2}{7}=\frac{5-2}{7}=\frac{3}{7}}$

To subtract fractions, the fractions must have the same bottom numbers (denominators). In this case, both fractions have a denominator of 7. The answer is the result of subtracting the top numbers (numerators).

In order to subtract fractions that have different denominators, the fractions must be expressed as equivalent fractions with a least common denominator (LCD). The difference of the numerators can be written over the common denominator.

#### Example A

$\frac{8}{11}-\frac{6}{11}=?$

Solution:

$\boxed{\frac{8}{11}-\frac{6}{11}=\frac{8-6}{11}=\frac{2}{11}}$

#### Example B

Bessie is measuring the amount of soda in the two coolers in the cafeteria. She estimates that the first cooler is $\frac{2}{3}$ full and the second cooler is $\frac{1}{4}$ full. What single fraction could Bessie use to represent how much more soda is in the first cooler than in the second cooler?

Solution: Use fraction strips to represent each fraction.

$\frac{2}{3}$ and $\frac{8}{12}$ are equivalent fractions. $\frac{2}{3} \left(\frac{4}{4}\right)=\frac{8}{12}$ .

$\frac{1}{4}$ and $\frac{3}{12}$ are equivalent fractions. $\frac{1}{4} \left(\frac{3}{3}\right)=\frac{3}{12}$ .

The two green pieces will be replaced with eight purple pieces and the one blue piece will be replaced with three purple pieces.

The denominator of 12 is the LCD (least common denominator) of $\frac{2}{3}$ and $\frac{1}{4}$ because it is the LCM (least common multiple) of the denominators 3 and 4.

Therefore, there is $\frac{5}{12}$ more soda in the first cooler than in the second.

#### Example C

$1 \frac{3}{4}-\frac{1}{2}$

Solution: The number line is labeled in intervals of 4. This indicates that each interval represents $\frac{1}{4}$ . From zero, move to the number 1 plus 3 more intervals to the right. Mark the location. This represents $1 \frac{3}{4}$ . From there, move to the left $\frac{1}{2}$ or $\frac{1}{2}$ of 4, which is 2 intervals. An equivalent fraction for $\frac{1}{2}$ is $\frac{2}{4}$ .

The difference of $1 \frac{3}{4}$ and $\frac{1}{2}$ is $1 \frac{1}{4}$ .

#### Concept Problem Revisited

Julian and Suz ordered a pizza that was cut into 10 slices. Suz ate 3 slices and Julian ate 4 slices. What fraction of the pizza did each person eat? What fraction of the pizza is left?

Suz ate $\frac{3}{10}$ of the pizza because she ate 3 out of the 10 slices. Julian ate $\frac{4}{10}$ of the pizza. Together they ate $\frac{7}{10}$ of the pizza. $\frac{10}{10}-\frac{7}{10}=\frac{3}{10}$ . Therefore, $\frac{3}{10}$ of the pizza is left.

### Vocabulary

Denominator
The denominator of a fraction is the number on the bottom that indicates the total number of equal parts in the whole or the group. $\frac{5}{8}$ has denominator 8.
Fraction
A fraction is any rational number that is not an integer.
LCD
The least common denominator is the lowest common multiple of the denominators of two or more fractions. The least common denominator of $\frac{3}{4}$ and $\frac{1}{5}$ is 20.
LCM
The least common multiple is the lowest common multiple that two or more numbers share. The least common multiple of 6 and 5 is 30.
Numerator
The numerator of a fraction is the number on top that is the number of equal parts being considered in the whole or the group. $\frac{5}{8}$ has 'numerator 5.

### Guided Practice

1. $\frac{7}{10}-\frac{2}{5}=?$

2. $\frac{7}{8}-\frac{1}{2}$ .

3. $\frac{5}{8}-\frac{1}{3}=?$

4. $\frac{4}{5}-\frac{1}{4}=?$

1. $\frac{7}{10}-\frac{4}{10}=\frac{7-4}{10}=\frac{3}{10}$

2. $\frac{7}{8}-\frac{4}{8}=\frac{7-4}{8}=\frac{3}{8}$ .

3. $\frac{5}{8}-\frac{1}{3}=\frac{7}{24}$

4. $\frac{4}{5}-\frac{1}{4}=\frac{11}{20}$

### Practice

Complete the following subtraction problems using any method.

1. $\frac{3}{4}-\frac{5}{8}$
2. $\frac{4}{5}-\frac{2}{3}$
3. $\frac{5}{9}-\frac{2}{3}$
4. $\frac{6}{7}-\frac{2}{3}$
5. $\frac{7}{10}-\frac{1}{5}$
6. $\frac{2}{3}-\frac{1}{2}$
7. $\frac{3}{5}-\frac{3}{10}$
8. $\frac{7}{9}-\frac{1}{3}$
9. $\frac{5}{8}-\frac{1}{4}$
10. $\frac{2}{5}-\frac{2}{10}$
11. $\frac{7}{11}-\frac{1}{2}$
12. $\frac{5}{8}-\frac{5}{12}$
13. $\frac{5}{6}-\frac{3}{4}$
14. $\frac{5}{6}-\frac{2}{5}$
15. $\frac{4}{5}-\frac{3}{4}$

For each of the following questions, write a subtraction statement and find the result.

1. Sally used $\frac{2}{3} \ cups$ of flour to make cookies. Terri used $\frac{1}{2} \ cups$ of flour to make a cake. Who used more flour? How much more flour did she use?
2. Lauren used $\frac{3}{4} \ cup$ of milk, $1 \frac{1}{3} \ cups$ of flour and $\frac{3}{8} \ cup$ of oil to make pancakes. Alyssa used $\frac{3}{8} \ cup$ of milk, $2 \frac{1}{4} \ cups$ of flour and $\frac{1}{3} \ cup$ of melted butter to make waffles. Who used more cups of ingredients? How many more cups of ingredients did she use?
3. Write two fractions with different denominators whose difference is $\frac{3}{8}$ .
4. Jake’s dog ate $12 \frac{2}{3} \ cans$ of food in one week and $9 \frac{1}{4} \ cans$ the next week. How many more cans of dog food did Jake’s dog eat in week one?
5. Sierra and Clark each solved the same problem.
Sierra’s Solution
$& \frac{3}{4}-\frac{1}{6}\\& \frac{9}{12}-\frac{2}{12}\\& =\frac{7}{12}$
Clark’s Solution
$& \frac{3}{4}-\frac{1}{6}\\& \frac{9}{12}-\frac{2}{12}\\& =\frac{7}{0}$
Who is correct? What would you tell the person who has the wrong answer?


text:
# Professional Development Seminar MAT/STA 587

Agenda:
1.
- TOPIC: Intro to LyX
LyX is free software. It should be avilbale in our computer labs and on the cefns full remote desktop . You can also install it on your own machine.
- HW: produce the following quiz . Replace my name with yours. Keep all the features, including typefaces and placements. Turn in a pdf file. Sample lyx file (right click) to give you a starting point. Detexify might be useful to find latex macros.
2.
- DUE: quiz
- TOPIC: Professional article writing
- HW: write an article about the quadratic formula. You need to have all the parts we discussed in class including sections, theorems, proofs, examples, figures, cross references, citations with bibtex, etc. Make sure you include everything listed here. Solving an equation usually takes two steps. First we show that the equation implies that a solution must be one of a few candidates. Then we check which of the solution candidates actually work. Please read the equations article about this. Please also read the writing style article and try to follow the recommendations.
3.
- DUE: nothing
- TOPIC: Continue article writing
- TOPIC: Figures with Tikz
- TOPIC: Overleaf
- HW: Recreate the tikz figure about the derivative of the inverse. Use tikz to add your name to the figure at the top right corner.
Continue working on the quadratic article.
4.
- DUE: tikz figure
- TOPIC: GeoGebra
- HW: Recreate the Geogebra figure with a different color scheme. Use Geogebra to add your name to the figure at the top right corner. Can you spot a theorem in the figure? (not the Pythagorean Theorem)
5.
- DUE: geogebra figure
- TOPIC: Basic Web page design, HTML reference
6.
- DUE: web page
- TOPIC: Guest speaker: Natalie Coston (Senior Data Scientist, Lumen Technologies)
Please check the Zoom coordinates on Bblearn.
7.
- TOPIC: Beamer
- HW: Create a presentation about the Law of Sines. State and prove the full version of the theorem that includes the radius of the circle as discussed in class. State the theorem required for the proof. Include an example. Use GeoGebra to create the figures. Use the beamer lyx template, or the lyx template (also in pdf format) .
8.
- DUE: presentation
- TOPIC: Guest speaker: Edgar Fisher (Austin Community College)
Please check the Zoom coordinates on Bblearn.
- HW: Create a Resume or Curriculum Vitae.
9.
- DUE: CV or resume
- TOPIC: Guest speaker: Robert Buscaglia (NAU) Machine learning

10.
- DUE: nothing
- TOPIC: Train a neural net with Keras on google Colab to predict movie reviews. I recommend the book "Deep Learning With Python" by Francois Chollet ifyou are interested in deep learning. You can find many online resources by searching for the words scikit-learn, Tensorflow, automatic differentiation, GPU, CUDA
11.
- DUE: nothing
- TOPIC: Sage is essentially Python with mathematical extensions.
Sage tutorial
Another Sage tutorial
- HW: Create an account on CoCalc and work through the examples in this Sage worksheet. Submit a pdf of your work.
12.
- DUE: Sage worksheet
- TOPIC: Guest speaker: Arthur DeGraw (Actuary, GPW and Associates)
Please check the Zoom coordinates on Bblearn.
- HW: Write a formal letter of application for the job description. Keep in mind the following: An application is automatically rejected if the minimum qualifications are not met. The screening committee assigns a numerical score for every preferred qualification using an evaluation grid . Addressing these points is crucially important.
13.
- DUE: Letter of application
- TOPIC: Problem solving
- HW: Use LyX/LaTeX to write a professional sample solution to the following problem: "Solve the inequality $$| x + 1 | + | 2x - 3 | > 6$$ on the set of real numbers." Use Tikz/Geogebra when appropriate. Use 1-inch margins and 12 point font. Everything should read as a sentence. Equations written row-after-row are not appropriate without an explanation of their logical connection. Include the statement of the problem. This is an elementary problem. Avoid relying on analysis terms like increasing, continuous, Intermediate Value Theorem. This means you cannot use test points to justify that a function has a certain sign on a whole interval. You need to do case analysis and the definition of absolute value as a piecewised defined function. Use interval notation whenever it is appropriate.
14.
- DUE: Professional sample solution
- TOPIC: Coding with Sage.
- HW: Look at the problems on the Project Euler web site. Write Sage code on your CoCalc account to solve Problems 1, 2, 5. Send me a pdf of your worksheet. Make sure your answers to the questions are clearly shown. You might want to create a Project Euler account to check if your solutions are correct.
15.
- DUE: Project Euler problem solutions.
- TOPIC: Graphviz , Sketchviz , Dreampuf
- TOPIC: Publishing a research article
AMS web site, Mathscinet, Zentralblatt, Preprint server, Current index to statistics (we do not have access to it)


text:
Volume 4, Issue 3-4
Stabilization of Navier-Stokes Equations by Boundary Feedback

Int. J. Numer. Anal. Mod., 4 (2007), pp. 608-624.

Published online: 2007-04

Cited by

Export citation
• Abstract

In this paper, we consider the stabilization of steady state solutions to Navier-Stokes equations by boundary feedback control. The feedback control is determined by solving a linear quadratic regulator problem associated with the linearized Navier-Stokes equations. The control is effected through suction and blowing at the boundary. We show that the linear feedback control provides global exponential stabilization of the steady state solutions to the Navier-Stokes equations for arbitrary Reynolds number. This feedback is shown to provide global stability in both $L^2$ and $H^1$-norms.

76W05, 76D55, 35B40, 35Q30

• BibTex
• RIS
• TXT
@Article{IJNAM-4-608, author = {Ravindran , S. S.}, title = {Stabilization of Navier-Stokes Equations by Boundary Feedback}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {608--624}, abstract = {

In this paper, we consider the stabilization of steady state solutions to Navier-Stokes equations by boundary feedback control. The feedback control is determined by solving a linear quadratic regulator problem associated with the linearized Navier-Stokes equations. The control is effected through suction and blowing at the boundary. We show that the linear feedback control provides global exponential stabilization of the steady state solutions to the Navier-Stokes equations for arbitrary Reynolds number. This feedback is shown to provide global stability in both $L^2$ and $H^1$-norms.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/880.html} }
TY - JOUR T1 - Stabilization of Navier-Stokes Equations by Boundary Feedback AU - Ravindran , S. S. JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 608 EP - 624 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/880.html KW - Navier-Stokes equation, Riccati equation, stabilization, feedback control, linear quadratic regulator. AB -

In this paper, we consider the stabilization of steady state solutions to Navier-Stokes equations by boundary feedback control. The feedback control is determined by solving a linear quadratic regulator problem associated with the linearized Navier-Stokes equations. The control is effected through suction and blowing at the boundary. We show that the linear feedback control provides global exponential stabilization of the steady state solutions to the Navier-Stokes equations for arbitrary Reynolds number. This feedback is shown to provide global stability in both $L^2$ and $H^1$-norms.

S. S. Ravindran. (1970). Stabilization of Navier-Stokes Equations by Boundary Feedback. International Journal of Numerical Analysis and Modeling. 4 (3-4). 608-624. doi:
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text:
• R K SHUKLA

Articles written in Bulletin of Materials Science

• Impedance variation with different relative humidities of PAni/Mn nanofibres

This paper presents the humidity sensing properties of surface-modified polyaniline (PAni). In this study, the impedance response and dielectric properties of pure- and doped-PAni have been investigated as a function of relativehumidity (RH%) and frequency. PAni and PAni/Mn composite samples are synthesized by one-step interfacial polymerization process. The structural properties and surface morphologies of the prepared materials have been characterized by X-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM), respectively. XRD confirms the formation of PAni and it shows semi-crystalline behaviour. FESEM shows granular, porous and well-distributed structure. It has been observed that the porosity and nanogranular structure increased with increasing doping percentage. Here, we observe thatporous and granular structure of Mn-doped PAni shows better response and recovery time ($\sim$28 s) and decreases in electrical impedance. Dielectric constants, dielectric loss and AC conductivity have also been discussed with variations in frequency and relative humidity.

• # Bulletin of Materials Science

Volume 44, 2021
All articles
Continuous Article Publishing mode

• # Dr Shanti Swarup Bhatnagar for Science and Technology

Posted on October 12, 2020

Prof. Subi Jacob George — Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru
Chemical Sciences 2020


text:
## Prealgebra (7th Edition)

$0.215=\frac{43}{200}$
By dividing the nominator with the denominator in the fraction we get: $\frac{43}{200}=0.215$ 0.215 equals to 0.215


text:
Kamal Abdali k.abdali at acm.org
Tue Apr 24 23:09:27 CEST 2018

To get the index listed in the table of contents, I include these two lines
in the preamble of a xelatex+polyglossia+bidi program:

\usepackage[imakeidx]
\makeindex[intoc]

My problem is that while the index does get produced it doesn’t get listed
in the TOC. The trouble can be reproduced in this small program:

%%%%%%%%%%%%%%%%%%%
\documentclass{book}

\usepackage{imakeidx}
\makeindex[intoc]

\usepackage{polyglossia}
\usepackage{bidi}       %%%%%
\setmainlanguage{english}

\title{Facts}
\author{Aleck}
\date{}

\begin{document}
\maketitle
\tableofcontents
\chapter{Stars}
Sirius, the brightest star in the night sky, is actually a double star.
\index{Sirius}
\printindex
\end{document}
%%%%%%%%%%%%%%%%%%%%

The above program produces the index without listing it in the TOC.
However, if you comment out the  \usepackage{bidi} line, the index IS
produced and listed in TOC as expected.

Note that the above program doesn’t really need bidi as all of its output
text is in the Latin script. But I do need the bidi feature  in the actual
document that I need to process.

Any help will be appreciated.

Kamal Abdali
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text:
# NAG CL Interfacee05jhc (bnd_mcs_option_check)

## 1Purpose

e05jhc is used to check if you have set an optional parameter of e05jbc. The initialization function e05jac must have been called before calling e05jhc.

## 2Specification

 #include
 Integer e05jhc (const char *optstr, Nag_E05State *state, NagError *fail)
The function may be called by the names: e05jhc or nag_glopt_bnd_mcs_option_check.

## 3Description

e05jhc returns 1 if you have previously set the optional parameter contained in optstr, otherwise it returns 0.
A complete list of optional parameters, their symbolic names and default values is given in Section 12 in e05jbc.

None.

## 5Arguments

1: $\mathbf{optstr}$const char * Input
On entry: a string identifying an optional parameter (as described in Section 12 in e05jbc).
2: $\mathbf{state}$Nag_E05State * Communication Structure
state contains information required by other functions in this suite. You must not modify it directly in any way.
3: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_NOT_INIT
Initialization function e05jac has not been called.
The supplied optional parameter is invalid. A keyword or keyword combination was not recognized.

Not applicable.

## 8Parallelism and Performance

e05jhc is not threaded in any implementation.


text:
## The Annals of Mathematical Statistics

### On the Completeness of Order Statistics

#### Abstract

Let $X_1, X_2, \cdots, X_n$ be a sample of a one-dimensional random variable $X$; let the order statistic $T(X_1, X_2, \cdots, X_n)$ be defined in such a manner that $T(x_1, x_2, \cdots, x_n) = (x^{(1)}, x^{(2)}, \cdots, x^{(n)})$ where $x^{(1)} \leqq x^{(2)} \leqq \cdots \leqq x^{(n)}$ denote the ordered $x's$; and let $\Omega$ be a class of one-dimensional cpf's, i.e., cumulative probability functions. The order statistic, $T$, is said to be a complete statistic with respect to the class, $\{P^{(n)} \mid P \epsilon \Omega\}$, of $n$-fold power probability distributions if $E_p^{(n)}\{h\lbrack T(X_1, \cdots, X_n)\rbrack\} = 0$ for all $P \epsilon \Omega$ implies $h\lbrack T(x_1, \cdots, x_n)\rbrack = 0, a.e., P^{(n)}$, for all $F \epsilon \Omega$. The class $\Omega$ is said to be symmetrically complete whenever the latter condition holds. Since the completeness of the order statistic plays an essential role in nonparametric estimation and hypothesis testing, e.g., Fraser [2] and Bell [1], it is of interest to determine those classes of cpf's for which the order statistic is complete. Many of the traditionally studied classes of cpf's on the real line are known to be symmetrically complete, e.g., all continuous cpf's ([4], pp. 131-134, 152-153); all cpf's absolutely continuous with respect to Lebesgue measure ([3], pp. 23-31); and all exponentials of a certain form ([4], pp. 131-134). The object of this note is to present a different ([4], pp. 131-134, 152-153) demonstration of the symmetric completeness of the class of all continuous cpf's; and to extend this and other known completeness results to probability spaces other than the real line, e.g., Fraser [2], and Lehmann and Scheffe [5], [6]. The paper is divided into four sections. Section 1 contains the introduction and summary. In Section 2 the notation and terminology are introduced. The main theorem is presented in Section 3, and some consequences of the proof of the main theorem and known results are indicated in Section 4.

#### Article information

Source
Ann. Math. Statist., Volume 31, Number 3 (1960), 794-797.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177705808

Digital Object Identifier
doi:10.1214/aoms/1177705808

Mathematical Reviews number (MathSciNet)
MR116427

Zentralblatt MATH identifier
0101.12201

JSTOR


text:
## Friday, October 05, 2012 ... /////

### Sheldon Glashow: Does science evolve through blind chance or Intelligent Design?

Five months ago or so, Honeywell organized a series of lectures by the Nobel laureate Sheldon Glashow at the Czech Technical University (ČVUT) in Prague.

The lecture you can watch now asked the question whether science evolves by chance or by design.

It's a sort of a fun, light, philosophically and historically loaded talk.

Maybe the number of the historical episodes will be boring for you: he could be a professional historian of science right away.

Typical Czech engineering students are listening to Glashow. ;-)

But if you like the first part, continue with Part 2 and Part 3. If you make it to the third part, there will be some examples of his point from modern physics. Around 18:00, he also talks about Gell-Mann and quarks' and string theorists' delight when they deduced that string theory predicted gravity. Glashow doesn't count it as a prediction because he had known about gravity before string theory was born. Of course, from the viewpoint of the history of science, it wasn't a (new) prediction: the chronology guarantees that. However, from the viewpoint of science and the strength and validity of its hypotheses, the fact that string theory implies general relativity is exactly as important and consequential as a prediction! The chronology is just a part of the history, social science, it was accidental, and a scientist simply can't pay attention to such things.

On the other hand, I agree that both accidental discoveries as well as "planned research" have been important and will be important.

Some other not-too-demanding physics news: Australia opened the world's fastest radio telescope.

Robert Christy, a physicist who worked on the Manhattan Project and the first one who became hostile against Edward Teller after he identified Oppenheimer as a communist, died.

An 11-year-old maľchik (=Russian boy) discovered the mammoth of the century (the best preserved one in 100 years).

#### snail feedback (4) :

Retrodiction is a better term in this case.
(http://en.wikipedia.org/wiki/Retrodiction)

My brother works as a development engineer for Honeywell and he didn't mention the lecture. But I am not going to watch it anyway, since I do not find these philosophical topics that interesting, especially if presented by physicists who are mostly not that good in philosophy (with exeptions like Feynman, Einstein).
I imagine that the advancement of scientific theories is similar to the process of evolution. At every moment, there are several candidate alternative theories. As new experimental developments happen, some theories are eliminated and some survive and are refined. Observations generate hypotheses by induction, predictions are made by deduction from the hypotheses and are tested. Successfully tested hypothesis become theories etc. For me personally, it is more interesting how the creation of theories happens in the brain.