dnd 5e – Does the optional Overrun rule override the creature size requirements on moving through a hostile creature’s space?

The standard rule on moving through other creatures’ spaces state that in order to move through a hostile creature’s space, a creature must be two sizes larger or smaller than the one whose space they want to pass through.

The optional overrun rules in the DMG (p. 272, in chapter 9) now require a roll, but does it remove the size differential as well and completely replace the rules around moving through other creatures’ spaces?

dnd 5e – Does the optional Overrun rule override the creature size requirements?

The standard moving through creatures spaces rules state that in order to do this, a creature must be two sizes larger than the one they want to pass through.

The optional overrun rules in the DMG (chapter 9) now require a roll, but does it remove the size differential as well and completely replace the rules around moving through other creatures?

What is the "Sunny 16" rule of thumb?

I’ve heard of the “Sunny 16” rule. What is it? How, and in what situations, can I use it?

mathematical physics – Functional Derivative with Difficult Chain Rule

I am trying to evaluate the functional derivatives $dfrac{delta F(phi(textbf{r}))}{delta n_{1}}$ and $dfrac{delta F(phi(textbf{r}))}{delta n_{2}}$ where

begin{gather}
F(phi_1(textbf{r}), phi_2(textbf{r})) = int d textbf{r} bigl ( f (phi_{1}(textbf{r}), phi_{2}(textbf{r}), nablaphi_{1}(textbf{r}), nablaphi_{2}(textbf{r}) ) bigr ) \
n_{1}(phi_1(textbf{r})) = int dtextbf{r} , g_{1} (phi_{1}) \
n_{2}(phi_2(textbf{r})) = int dtextbf{r} , g_{2} (phi_{2})
end{gather}

I have explicit expressions for $f$, $g_1$ and $g_2$. I believe the appropriate chain rule for functional derivatives is given by

begin{equation}
frac{delta F(phi_1, phi_2)}{delta n_{1}} = int dtextbf{r} left ( frac{delta F}{delta phi_1} frac{delta phi_{1}}{delta n_1} + frac{delta F}{delta phi_2} frac{delta phi_{2}}{delta n_1}right) textrm{.}
end{equation}

But the chain rule is only useful if I know $phi_1(n_1)$, when in fact I have the inverse. How can I evaluate these derivatives?

Related: Derivative of a functional with respect to another functional

calculus and analysis – Leibniz Integral Rule Bug

I was trying to answer this question: $frac{mathrm d}{mathrm dt}int_{t-mathrm d1}^t int_h^t f(s) ,mathrm ds,mathrm dh$. I got the accepted answer by hand (using the Leibniz integral rule) but why does Mathematica (and Maple) give the seemingly wrong $mathrm d_{{1}}f left( t right) color{orange}{-}int_{t-mathrm d_{{1}}}^{t}!f left( s right) ,{rm d}s=mathrm d_{{1}}f left( t right) color{orange}{-}F left( t right) color{orange}{+} F left( t-mathrm d _{{1}} right)$ instead of $mathrm d_{{1}}f left( t right) color{lime}{+}int_{t-mathrm d_{{1}}}^{t}!f left( s right) ,{rm d}s=mathrm d_{{1}}f left( t right) color{lime}{+}F left( t right) color{lime}{-} F left( t-mathrm d _{{1}} right)$

The Mathematica code I used is D(Integrate(Integrate(f(s), {s, h, t}), {h, t - d1, t}), t).

plotting – Replacement Rule Line Thickness

I have a plot with imported data that I have used a replacement rule to make the data a line rather than individual points. However, I want to increase the thickness of that line. How do I do this? I have tried looking at Changing style of label boxes in TimelinePlot for an example of changing the line thickness but it is different than what I want to do. Here is what I have:

Show(ListPointPlot3D(Sidata1((1 ;; 59, 3 ;; 5)), PlotStyle -> {Red}, PlotRange -> All),
  ListPointPlot3D(Sidata1((60 ;; 89, 3 ;; 5)), PlotStyle -> {Gray}, PlotRange -> All),
  ListPointPlot3D(Sidata1((90 ;; 110, 3 ;; 5)), PlotStyle -> {Red}, PlotRange -> All),
  ListPointPlot3D(Sidata1((111 ;; 141, 3 ;; 5)), PlotStyle -> {Gray}, PlotRange -> All),
  ListPointPlot3D(Sidata1((142 ;; 201, 3 ;; 5)), PlotStyle -> {Red}, PlotRange -> All), 
  AxesLabel -> {"q", "s2", "alpha"}, LabelStyle -> {16}, PlotLabel -> None, ViewPoint -> {.5, -2, 1}, 
  AxesStyle -> Directive(Black, 16), BoxStyle -> Directive(Black), TicksStyle -> Directive(Black, 16), 
  AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}}, ImageSize -> Large) /. Point -> Line

I’ve tried increasing the line thickness at the end of the input with this code that does not work:

/. Point -> Line(PlotStyle -> Thickness(0.1))

Here is my data:

{{0, 0.00586554, 1.85613, 4.76551*10^-28, 5.26926}, {1, 0.00586038, 
  1.85857, 0.00496208, 5.26553}, {2, 0.00583292, 1.86694, 0.00737286, 
  5.28264}, {3, 0.00578611, 1.88105, 0.00995626, 5.31438}, {4, 
  0.00572788, 1.90041, 0.0195179, 5.34518}, {5, 0.0056491, 1.92576, 
  0.026371, 5.3971}, {6, 0.00555664, 1.95654, 0.0357567, 5.4579}, {7, 
  0.005454, 1.99256, 0.0488175, 5.52469}, {8, 0.00533414, 2.03443, 
  0.0587529, 5.61315}, {9, 0.00520924, 2.08121, 0.0728039, 
  5.70511}, {10, 0.00507624, 2.13333, 0.0868532, 5.80991}, {11, 
  0.00493048, 2.19114, 0.0969574, 5.937}, {12, 0.00479085, 2.25265, 
  0.111276, 6.06199}, {13, 0.00464483, 2.31891, 0.12169, 
  6.20612}, {14, 0.00449348, 2.3895, 0.12767, 6.36945}, {15, 
  0.00435635, 2.46022, 0.134399, 6.52873}, {16, 0.00421573, 2.53408, 
  0.13467, 6.70861}, {17, 0.00408066, 2.60798, 0.130038, 
  6.89764}, {18, 0.003962, 2.67731, 0.122165, 7.08088}, {19, 
  0.0038446, 2.74659, 0.107359, 7.27855}, {20, 0.0037445, 2.80767, 
  0.0891022, 7.46372}, {21, 0.00366125, 2.85969, 0.0685708, 
  7.63264}, {22, 0.00358362, 2.90781, 0.0439095, 7.80201}, {23, 
  0.00353606, 2.93743, 0.0254055, 7.91445}, {24, 0.00350441, 2.9569, 
  0.0112019, 7.99332}, {25, 0.00348267, 2.96992, 4.2709*10^-28, 
  8.05004}, {26, 0.00350619, 2.95655, 0.0140871, 7.98594}, {27, 
  0.00354397, 2.9359, 0.0380519, 7.88204}, {28, 0.0036054, 2.90368, 
  0.077481, 7.71557}, {29, 0.00371579, 2.84915, 0.145356, 
  7.43302}, {30, 0.00384706, 2.78696, 0.22453, 7.10949}, {31, 
  0.00402225, 2.70695, 0.319264, 6.71886}, {32, 0.00425262, 2.60492, 
  0.42526, 6.26836}, {33, 0.00451347, 2.4927, 0.533519, 5.80028}, {34,
   0.00484984, 2.35888, 0.635259, 5.31261}, {35, 0.0052487, 2.21331, 
  0.726175, 4.82797}, {36, 0.00569123, 2.06324, 0.807586, 
  4.35526}, {37, 0.00625698, 1.90488, 0.858761, 3.92207}, {38, 
  0.00689091, 1.74683, 0.894649, 3.51698}, {39, 0.00759815, 1.59081, 
  0.915479, 3.14207}, {40, 0.00847396, 1.44051, 0.907596, 
  2.82513}, {41, 0.00943069, 1.29475, 0.890287, 2.53427}, {42, 
  0.0105185, 1.15519, 0.860229, 2.27889}, {43, 0.0117991, 1.02388, 
  0.81632, 2.06547}, {44, 0.0131859, 0.897942, 0.767916, 
  1.87227}, {45, 0.0147797, 0.780792, 0.713042, 1.70999}, {46, 
  0.0165753, 0.670983, 0.65441, 1.57258}, {47, 0.0184995, 0.565447, 
  0.594737, 1.44957}, {48, 0.0207039, 0.467657, 0.533712, 
  1.35086}, {49, 0.0230828, 0.374668, 0.47279, 1.26641}, {50, 
  0.025591, 0.285255, 0.412327, 1.1928}, {51, 0.0283735, 0.201725, 
  0.353629, 1.13931}, {52, 0.0312372, 0.119185, 0.295722, 
  1.09523}, {53, 0.0341712, 0.0377658, 0.238978, 1.06272}, {54, 
  0.0370919, -0.0411159, 0.184837, 1.04753}, {55, 0.03991, -0.118284, 
  0.132156, 1.04359}, {56, 0.0424219, -0.189196, 0.0842067, 
  1.05721}, {57, 0.0443678, -0.245829, 0.0451427, 1.09405}, {58, 
  0.0458307, -0.287877, 0.0134487, 1.15053}, {59, 
  0.0461722, -0.273939, 0.00724523, 1.25192}, {60, 0.04547, -0.189799,
   0.029489, 1.40789}, {61, 0.0439536, -0.040825, 0.0760268, 
  1.61787}, {62, 0.0410509, 0.287135, 0.188407, 1.98092}, {63, 
  0.0374884, 0.737128, 0.339519, 2.48104}, {64, 0.0334165, 1.32035, 
  0.529929, 3.15253}, {65, 0.0292259, 2.16715, 0.792678, 
  4.24807}, {66, 0.0249774, 3.20952, 1.09423, 5.70677}, {67, 
  0.0209618, 4.54328, 1.4547, 7.76466}, {68, 0.0175535, 6.37734, 
  1.90226, 10.9599}, {69, 0.0142979, 8.71509, 2.3962, 15.3082}, {70, 
  0.0116484, 11.9196, 2.96614, 21.8363}, {71, 0.00952234, 16.4455, 
  3.46263, 31.8198}, {72, 0.00756156, 22.4422, 3.69173, 45.7099}, {73,
   0.00637376, 29.2974, 3.10612, 62.8753}, {74, 0.00557852, 35.9338, 
  1.7877, 80.5131}, {75, 0.0050232, 41.7985, 8.59236*10^-27, 
  96.93}, {76, 0.00564134, 35.4285, 2.17511, 78.8748}, {77, 
  0.00664996, 27.396, 4.4568, 56.9122}, {78, 0.00830127, 18.7827, 
  5.93387, 34.9235}, {79, 0.0112518, 12.1619, 5.34133, 20.6996}, {80, 
  0.0147477, 7.27342, 4.38667, 11.0649}, {81, 0.0192714, 4.31069, 
  3.28923, 6.07815}, {82, 0.0249166, 2.64861, 2.36017, 3.78892}, {83, 
  0.0310646, 1.44104, 1.61259, 2.25868}, {84, 0.038089, 0.763281, 
  1.11354, 1.51843}, {85, 0.0455155, 0.323334, 0.756884, 
  1.08172}, {86, 0.0530392, -0.00833097, 0.480004, 0.764547}, {87, 
  0.0602388, -0.191606, 0.314908, 0.599}, {88, 0.0669456, -0.322307, 
  0.19112, 0.476188}, {89, 0.0729913, -0.407595, 0.101166, 
  0.385506}, {90, 0.0773187, -0.422702, 0.0563086, 0.338125}, {91, 
  0.0808823, -0.415833, 0.0252911, 0.301559}, {92, 
  0.0833385, -0.387366, 0.00888385, 0.276938}, {93, 
  0.0845245, -0.347873, 0.00355736, 0.262038}, {94, 
  0.085323, -0.310296, 0.000716217, 0.249179}, {95, 
  0.0854916, -0.278922, 0.00021299, 0.239806}, {96, 
  0.0853257, -0.253975, 0.000358958, 0.232963}, {97, 
  0.0851545, -0.232974, 0.000267074, 0.227071}, {98, 
  0.0848481, -0.218693, 0.000354803, 0.223956}, {99, 
  0.084646, -0.209427, 0.000303089, 0.222006}, {100, 
  0.0846189, -0.204535, 3.2539*10^-31, 0.220639}, {101, 
  0.084646, -0.209427, 0.000303089, 0.222006}, {102, 
  0.0848481, -0.218693, 0.000354803, 0.223956}, {103, 
  0.0851545, -0.232974, 0.000267074, 0.227071}, {104, 
  0.0853257, -0.253975, 0.000358958, 0.232963}, {105, 
  0.0854916, -0.278922, 0.00021299, 0.239806}, {106, 
  0.085323, -0.310296, 0.000716217, 0.249179}, {107, 
  0.0845245, -0.347873, 0.00355736, 0.262038}, {108, 
  0.0833385, -0.387366, 0.00888385, 0.276938}, {109, 
  0.0808823, -0.415833, 0.0252911, 0.301559}, {110, 
  0.0773187, -0.422702, 0.0563086, 0.338125}, {111, 
  0.0729913, -0.407595, 0.101166, 0.385506}, {112, 
  0.0669456, -0.322307, 0.19112, 0.476188}, {113, 
  0.0602388, -0.191606, 0.314908, 0.599}, {114, 
  0.0530392, -0.00833097, 0.480004, 0.764547}, {115, 0.0455155, 
  0.323334, 0.756884, 1.08172}, {116, 0.038089, 0.763281, 1.11354, 
  1.51843}, {117, 0.0310646, 1.44104, 1.61259, 2.25868}, {118, 
  0.0249166, 2.64861, 2.36017, 3.78892}, {119, 0.0192714, 4.31069, 
  3.28923, 6.07815}, {120, 0.0147477, 7.27342, 4.38667, 
  11.0649}, {121, 0.0112518, 12.1619, 5.34133, 20.6996}, {122, 
  0.00830127, 18.7827, 5.93387, 34.9235}, {123, 0.00664996, 27.396, 
  4.4568, 56.9122}, {124, 0.00564134, 35.4285, 2.17511, 
  78.8748}, {125, 0.0050232, 41.7985, 5.2584*10^-27, 96.93}, {126, 
  0.00557852, 35.9338, 1.7877, 80.5131}, {127, 0.00637376, 29.2974, 
  3.10612, 62.8753}, {128, 0.00756156, 22.4422, 3.69173, 
  45.7099}, {129, 0.00952234, 16.4455, 3.46263, 31.8198}, {130, 
  0.0116484, 11.9196, 2.96614, 21.8363}, {131, 0.0142979, 8.71509, 
  2.3962, 15.3082}, {132, 0.0175535, 6.37734, 1.90226, 10.9599}, {133,
   0.0209618, 4.54328, 1.4547, 7.76466}, {134, 0.0249774, 3.20952, 
  1.09423, 5.70677}, {135, 0.0292259, 2.16715, 0.792678, 
  4.24807}, {136, 0.0334165, 1.32035, 0.529929, 3.15253}, {137, 
  0.0374884, 0.737128, 0.339519, 2.48104}, {138, 0.0410509, 0.287135, 
  0.188407, 1.98092}, {139, 0.0439536, -0.040825, 0.0760268, 
  1.61787}, {140, 0.04547, -0.189799, 0.029489, 1.40789}, {141, 
  0.0461722, -0.273939, 0.00724523, 1.25192}, {142, 
  0.0458307, -0.287877, 0.0134487, 1.15053}, {143, 
  0.0443678, -0.245829, 0.0451427, 1.09405}, {144, 
  0.0424219, -0.189196, 0.0842067, 1.05721}, {145, 0.03991, -0.118284,
   0.132156, 1.04359}, {146, 0.0370919, -0.0411159, 0.184837, 
  1.04753}, {147, 0.0341712, 0.0377658, 0.238978, 1.06272}, {148, 
  0.0312372, 0.119185, 0.295722, 1.09523}, {149, 0.0283735, 0.201725, 
  0.353629, 1.13931}, {150, 0.025591, 0.285255, 0.412327, 
  1.1928}, {151, 0.0230828, 0.374668, 0.47279, 1.26641}, {152, 
  0.0207039, 0.467657, 0.533712, 1.35086}, {153, 0.0184995, 0.565447, 
  0.594737, 1.44957}, {154, 0.0165753, 0.670983, 0.65441, 
  1.57258}, {155, 0.0147797, 0.780792, 0.713042, 1.70999}, {156, 
  0.0131859, 0.897942, 0.767916, 1.87227}, {157, 0.0117991, 1.02388, 
  0.81632, 2.06547}, {158, 0.0105185, 1.15519, 0.860229, 
  2.27889}, {159, 0.00943069, 1.29475, 0.890287, 2.53427}, {160, 
  0.00847396, 1.44051, 0.907596, 2.82513}, {161, 0.00759815, 1.59081, 
  0.915479, 3.14207}, {162, 0.00689091, 1.74683, 0.894649, 
  3.51698}, {163, 0.00625698, 1.90488, 0.858761, 3.92207}, {164, 
  0.00569123, 2.06324, 0.807586, 4.35526}, {165, 0.0052487, 2.21331, 
  0.726175, 4.82797}, {166, 0.00484984, 2.35888, 0.635259, 
  5.31261}, {167, 0.00451347, 2.4927, 0.533519, 5.80028}, {168, 
  0.00425262, 2.60492, 0.42526, 6.26836}, {169, 0.00402225, 2.70695, 
  0.319264, 6.71886}, {170, 0.00384706, 2.78696, 0.22453, 
  7.10949}, {171, 0.00371579, 2.84915, 0.145356, 7.43302}, {172, 
  0.0036054, 2.90368, 0.077481, 7.71557}, {173, 0.00354397, 2.9359, 
  0.0380519, 7.88204}, {174, 0.00350619, 2.95655, 0.0140871, 
  7.98594}, {175, 0.00348267, 2.96992, 4.34023*10^-27, 8.05004}, {176,
   0.00350441, 2.9569, 0.0112019, 7.99332}, {177, 0.00353606, 2.93743,
   0.0254055, 7.91445}, {178, 0.00358362, 2.90781, 0.0439095, 
  7.80201}, {179, 0.00366125, 2.85969, 0.0685708, 7.63264}, {180, 
  0.0037445, 2.80767, 0.0891022, 7.46372}, {181, 0.0038446, 2.74659, 
  0.107359, 7.27855}, {182, 0.003962, 2.67731, 0.122165, 
  7.08088}, {183, 0.00408066, 2.60798, 0.130038, 6.89764}, {184, 
  0.00421573, 2.53408, 0.13467, 6.70861}, {185, 0.00435635, 2.46022, 
  0.134399, 6.52873}, {186, 0.00449348, 2.3895, 0.12767, 
  6.36945}, {187, 0.00464483, 2.31891, 0.12169, 6.20612}, {188, 
  0.00479085, 2.25265, 0.111276, 6.06199}, {189, 0.00493048, 2.19114, 
  0.0969574, 5.937}, {190, 0.00507624, 2.13333, 0.0868532, 
  5.80991}, {191, 0.00520924, 2.08121, 0.0728039, 5.70511}, {192, 
  0.00533414, 2.03443, 0.0587529, 5.61315}, {193, 0.005454, 1.99256, 
  0.0488175, 5.52469}, {194, 0.00555664, 1.95654, 0.0357567, 
  5.4579}, {195, 0.0056491, 1.92576, 0.026371, 5.3971}, {196, 
  0.00572788, 1.90041, 0.0195179, 5.34518}, {197, 0.00578611, 1.88105,
   0.00995626, 5.31438}, {198, 0.00583292, 1.86694, 0.00737286, 
  5.28264}, {199, 0.00586038, 1.85857, 0.00496208, 5.26553}, {200, 
  0.00586554, 1.85613, 4.76551*10^-28, 5.26926}}

query variable – Rewrite Rule for Post Meta

I would like to create an endpoint for a custom field. For example, I already have a custom ‘competition’ post type for which rewriting is working great and resolving at website.com/competitions/my-competition. Within that competition I have award categories created using Advanced Custom Fields, all of which have a unique ID.

I would like to be able to visit website.com/competitions/competition_slug/award-category/category_slug.

I’ve got as far as passing the unique ID of the category to the query vars and loading a custom template but am stuck on website.com/award-category/category_slug and can’t figure out how to have my rewrite rule include the parent competition. Here’s my code:

function aca_award_cat_rewrite_rule() {

    add_rewrite_rule( '^award-category/((^/)*)/?', 'index.php?award_category=$matches(1)', 'top' );
}

function aca_set_award_cat_query_var( $vars ) {

    array_push( $vars, 'award_category' );
    return $vars;
}

function aca_include_award_cat_template( $template ) {
    if( get_query_var('award_category') ) {
        $award_category_template = plugin_dir_path( dirname( __FILE__ ) ) . 'public/award-category-template.php';
        if( file_exists( $award_category_template ) )
            $template = $award_category_template;
    }
    return $template;
}

I realise that right now my rewrite_rule is sending the user via index.php but I can’t figure out how to accommodate the awards/award_slug bit without interfering with the existing rewrite rules for the post type.

Higher order derivatives and chain rule [closed]

I tried to apply the chain rule, but I just don't get the right answer. Can anyone help me? :]

Chain rule problem

How to configure two or more discount promotions in a price basket rule in Magento 2?

I want to set up several promotions each with the same promo code
I wonder if this is possible on magento 2?

Or is there a script to apply this type of functionality?

magento2 – The basket rule on the package element does not work in magento 2.2.8

I have created a basket rule for the sub-selection of grouped products, but this does not work correctly, because the basket rule is applied against & # 39; base_row_total & # 39; child items, but in the quote items table, these fields are always 0 compared to child items but have only one value against the parent product.
enter description of image here

is this a bug reported in Magento 2.2.8? Any solution?