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# Body Shape Calculator 3d

@prince_16 Many python snippets written 7 years ago were written in python 2. 86 x10 5 kilometers (3. Find Section Properties Now. \square! \square!. com you can easily calculate model size or model scale. Ruler or Banana Shape. We recommend that you undress in front of a mirror so you can really see the shape of your body in order to answer the questions better and it helps to be honest with. The criteria for Bottom Hourglass shape are bust-to-waist and hips-to-waist ratios that are significant with hips measurement being slightly larger than the bust. Now that you know a little bit about the purpose of a body measurement chart, let’s dive in a little deeper about some of the various parts of the body that you can measure. Geometry is all about shapes and their properties. Once you know your dimensions you can quickly use the body type calculator and find out whether you have an apple shaped body, a pear body, a banana or an hourglass type. For example, a 2004 study reported that descriptions of female bodies have historically been described in categories based on shapes, such as triangle, rectangle, diamond, oval, and hourglass. com's basic geometry & shapes calculators, formulas & examples to deal with length, area, surface, volume, points, lines, dimensions, angles & curves calculations of 2 or 3 dimensional (2D or 3D) geometric shapes. A 90 degree angle is typically denoted in diagrams as a square in the corner of the. Derivative calculator Integral calculator Definite integrator Limit calculator Series calculator Equation solver Expression simplifier Factoring calculator Expression calculator Inverse function Taylor series Matrix calculator Matrix arithmetic Graphing calculator: 2D shape calculators 3D shape calculators Prime numbers Number factorizer. This reshape photo editor allows you to make the body slimmer, improve hips, enlarge breasts, remove a double chin, slim down the waist and make face contours thinner. Turn off atom manipulation Off; Hydrogen H; Lithium Li; Beryllium Be; Carbon C. Along with this, remember to love your body and keep it fit. Interactive: Build your own shape. By ScaleCalculator. Set Model Color. The calculation is equally valid for children as. Your baby is still tiny, but already your body is changing. BMI Calculator for Women. Oct 05, 2020 · This quiz is designed to identify the body shape of the quiz taker. Estimates the volume of liquid plaster needed to make a one-part casting mold or a section of a two-part casting mold, based on the calculated volume of your model and container (ie. H o w i t w o r k s SHAPESCALE The first scale that scans you in 3D Digitizes your body shape in less than a minute Creates a full color high fidelity 3D model Tells you how your body changes over time Showing your losses And gains Scroll down to learn more or. Then I extract surface and calculate the volume based on this algorithm. Find: For the shaded shape provided, a) Estimate the area and the x and y centroids. com wishes everyone to BE WELL, STAY WELL, GET WELL. For some devices, you stand on a rotating platform for. G, for Complex Shapes Some problems with a fairly complex shape, such as a drum or multi-flanged pulley, will give the body's mass m and a radius of gyration, k G, that you use to calculate I G. The distance between the parallel sides is known as the altitude. Feb 2, 2019 - Body shape calculator determines your body type basing on your measurements. Introducing the F770™, to print bigger for less. Intuitive 3D Body Shape Modeling. Your body type can be either Hourglass, Pear, Apple, Inverted Triangle and Straight. Free online body shape calculator supporting the four basic body types - pear, rectangle, inverted triangle, and hourglass. The radius of a circle is the distance from its center point to any other point on the edge. To use the calculator and figure out your body shape, just choose whether you would like to enter your measurements in metric or imperial, type in your hips, waist and bust measurements and click "Calculate". Then arrange the remaining shapes in. 3D models were created using. Instant generation of custom measurements and 3D avatars from only 2 photos. See your shape and BMI: Body Mass Index (BMI) is a measure calculated using your height and weight to estimate how much body fat you have. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. Have wider shoulders and bust, and narrower hips. This reshape photo editor allows you to make the body slimmer, improve hips, enlarge breasts, remove a double chin, slim down the waist and make face contours thinner. Custom 3D shapes are drawn using beginShape(), endShape(), and vertex() by placing multiple polygons side by side. Geometric shapes and trigonometric functions. Rigid body dynamics -- the movement and interaction of solid, inflexible objects -- is by far the most popular kind of effect simulated in games. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. Andreas Lindner. You therefore work out the area of each face, and then add them together. Halls amazing body mass index calculator also takes into account your age and gender. The drag coefficient Cd is equal to the drag D divided by the quantity: density r times reference area A times one half of the velocity V squared. If the angle is 90 degrees, the two sides of the triangle enclosing the angle will form an "L" shape. Different Female Body Types. Body analytics and retail insights. centroids for a select group of shapes ! The point labeled C is the location of the centroid of that shape. We have also included information regarding Leptin. THE TORUS IN SCIENCE. We use revolutionary 3D body mapping technology that captures key measurements and helps you understand what they mean to your health, allowing you to set goals and visualise changes in your body over time. TIE Phantom (Cloaked) 1/270. Muscles are clearly defined and separated, and vascularity is. H o w i t w o r k s SHAPESCALE The first scale that scans you in 3D Digitizes your body shape in less than a minute Creates a full color high fidelity 3D model Tells you how your body changes over time Showing your losses And gains Scroll down to learn more or. Determine your wrist size by measuring your wrist just below your wrist bone with a tape measure. The Math / Science. Show how to measure and determine a plus size body shape to find the most flattering clothes that fit and accentuate the bodily curves 15 49. Find Out More. (b) Hint: obtain the expression for and set it equal to , and solve for and. Maine Coon Cats are the largest breed of domestic cat and are distinguished by their long silky coats. Not to be confused with your Waist/Hip Ratio (WHR), your WHtR calculates your body fat distribution and can be a significant early indicator of risk of diabetes, heart disease and stroke. Shown below are the structures of chlorophyll a and chlorophyll b ; the magnesium-free forms of these molecules are called pheophytin a and pheophytin b. The 3D Shape Calculators are completely free for anyone to use and we hope that they provide the user with all of their needs. Estimates your body type based on your bust, waist, and hip measurements. This airfoil shape can be different if the slice is taken at different locations on the wing. How does Fit3D calculate BMR? Fit3D uses the Mifflin St. Male – NEW!. Just as with 2D areas, shape symmetry can provide a shortcut in many centroid calculations. Use your outfit to balance your shoulders, bust, waist, and hips. Our designers tell you exactly what is right and wrong for your body type. Moreover, it includes tools for adding tattoos, six-pack abs and other muscles. Simulating physics in video games is very common, since most games are inspired by things we have in the real world. Export Body Shape Model. Females has different body shapes (figure). The Body Visualizer Is A Fun 3D Body Shape Before & After Weight Loss Tool! It Helps You Visualize Your Ideal Weight & Monitor Your Progress. Lucy on 4 Aug 2014. The Perfect Pair of Pants Is Just a 3D Body Scan Away A customer wears the garment—a sports bra with sensors and a Bluetooth chip sewn in—and the exact size and shape of her body is. Calculate the volume of shape descibed by 3d points. Edges are the lines where two faces meet. So, if the x-intercept is -3 then that second point is (-3, 0). The equation for the volume of a sphere is as follows: V = 4/3•π•r³. 3D physics engines provide collision detection algorithms, most of them based on bounding volumes as well. Raw 3D scan data consists of millions of XYZ data points, called "point clouds," which can be manipulated and delivered in a number of native file formats. Personalized size recommendation. The body itself is very thick compared to the neck, that is why the body wood type and form have very limited influence on the sound of electric guitar. How To: Calculate X, Y, and Z values in an attribute table using Field Calculator Summary. In your first few months of pregnancy, hormones flood your body. Turn off atom manipulation Off; Hydrogen H; Lithium Li; Beryllium Be; Carbon C. net is a resource for the exercise professional, coach, or fitness enthusiast. No more fretting in the fitting room. Because the centroid of a shape is the geometric center of an area or volume, the average distance to any one point in a body is at a minimum. Body fat deposits in. Recent studies* indicate that the WHR. Determine your wrist size by measuring your wrist just below your wrist bone with a tape measure. Body Visualizer. A rectangular cuboid has a shape of a rectangular box, which is also called as a right rectangular prism. Fad diets don't work. Designer advice 24/7. The drag coefficient Cd is equal to the drag D divided by the quantity: density r times reference area A times one half of the velocity V squared. Calculate the First moment of area (Statical Moment of Inertia. The BMI may be determined using a table or chart which displays BMI as a function of mass and height using contour lines or. This Body Shape Calculator will surely tell you - your actual body shape. Rotate the body to get a full 360 o degree view. As a matter of fact, the calculation of BMI - body mass index for both women and men is carried out according to the same BMI formula. (This BMI calculator is for use in the evaluation of adults, not for children. A major focus of IGIGI is to provide its customer with the custom design and right fit for her body shape. The radius of a circle is the distance from its center point to any other point on the edge. Autodesk Inventor Professional 2017. (the fact that yours is convex doesn't matter). Have you got a diet plan? Why not check out our free diet planning calculator too? Remember - your body shape may change as you lose weight, so check back regularly. The bmi calculation is based on the mathematical formula of your body weight in kilograms divided by your height in metres squared. where a - radius along x axis, b - radius along y axis, c - radius along z axis. The essential body fat for a woman is 8%, while for a man is only 2%. Find Section Properties Now. Slide the controls or type in values to adjust the parameters. Frame3DD is free open-source software for static and dynamic structural analysis of 2D and 3D frames and trusses with elastic and geometric stiffness. This tool goes beyond civil/structural applications to include mechanical, aerospace, manufacturing, and construction industries. See full list on tips. Creatung a solid through rotation of a graph round the x- or y-axis. 10 by moleculestore. Body Visualizer. External link. Bust: measure at the fullest point of your bust with a soft measuring tape. Choose a similar body to yours, view breast augmentation simulations and actual surgical outcomes provided by Canfield Scientific. Using just a measuring tape, we can guide you through the process of finding your accurate bra size. Read VECTRA testimonials. A 3D body avatar generation - scanning time of 3 seconds. Export Landmarks. These elements can be used as references to attach sketches and primitive objects. Find Out More. Once you have selected the value and units for force and length, two conversion scales will be produced to show a range of torque values calculated for different values of force and length while the other. Find the shape of your face to get suggestions on the hair style that suits you the most, the sunglasses that go with you face, make up tips and much much more. Head size (measure around at forehead height) Pelvis size (the widest part of your pelvis) Knee size. You can get these measurements from using a tape measure to measure each body part. This is where the ketosis stage begins to take place. Virtual try-on. A comparative outlook review of different BSA formulae. When 1 Point and Y-intercept Are Known We can calculate the second point from the y-intercept, because the x value for the y-intercept will always be 0. Name the three divisions as Area 1, Area 2, and Area 3. Open with QR Code. Subdivision in 3D. See how you you will look now. Then I extract surface and calculate the volume based on this algorithm. How to correctly measure your hips, waist and bust. Body Shape. * Inches only. You also need to include details about your body shape, For example, apple, pear, or hourglass. The calculator uses the physical characteristics you report to make the same assessment a doctor would make in determining how far you have developed. Your baby is still tiny, but already your body is changing. In general, the dependence on body shape, inclination, air viscosity, and compressibility is very complex. Open with QR Code. The RC airplane design calculator has been created in order to provide an approximation of specific airframe parameters. The Good Calculators 3D Shape Calculators are specially programmed so that they can be used on a variety of browsers as well as mobile and tablet devices. The waist measurement is less than 9 inches smaller than the bust or hips measurement. The neck space is 1/4 of one head length, under the chin of the top first head. In addition explore many other calculators addressing finance, math, health, and fitness. Need help figuring out human body proportions? Use this handy calculator!. com - how much does electric guitar's body physics affect the tone and playability. Personalized size recommendation. Free online body shape calculator supporting the four basic body types - pear, rectangle, inverted triangle, and hourglass. The bmi calculation is based on the mathematical formula of your body weight in kilograms divided by your height in metres squared. Tip: You can add individual shapes to a chart, or add shapes on top of a SmartArt. 126 Monday, October 26, 2009 11:04 AM. Wrist site. TraceParts offers digital marketing services to help part vendors, 3D printing suppliers, software and computer hardware vendors promote their products and services and generate high-quality B2B sales leads. Introduction Geometry 3-D Shapes is an interactive Web site where students can learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. the cottles used to surround the model being molded). An interactive 3D graphing calculator in your browser. Again, we must translate an object so that its center lies on the origin before scaling it. Interactive: Build your own shape. Solids to get the center of mass of the shape's component solids. body_shape_exited (int body_id, Node body, int body_shape, int local_shape ) Emitted when the collision between one of this RigidBody's Shape s and another PhysicsBody or GridMap 's Shape s ends. Area of the base or end shape × the height of the cone/pyramid × 1 / 3. The second head starts under this neck space. BMI Meaning Based on the body mass index, people are categorized as normal weight, overweight, or obese. IGIGI plus-size designs accentuate and celebrate the beauty of the curvy female figure. If we pick a different point or axis to take the moment of inertia about, then on average all the distances in our moment integral will be a little bit bigger. Laser scanners from Micro-Epsilon are among the highest performing profile sensors in the world with respect to accuracy and measuring rate. Then, write down the measurements of each section and use them to calculate the volume of each part using their respective formulas. TOROIDAL SPACE. First, I get volume from solid mesh. Subdivision in 3D. The neck space is 1/4 of one head length, under the chin of the top first head. This free body fat calculator estimates body fat percentage based on the U. This tool goes beyond civil/structural applications to include mechanical, aerospace, manufacturing, and construction industries. Divide the compound shape into basic shapes. Body mass index, or BMI, is an easy-to-calculate measure of obesity based on the ratio of your weight and your height. We shall see that in the general three-dimensional case, the angular velocity of the body can change in magnitude as well as in direction, and, as a consequence, the motion is considerably more complicated than that in two dimensions. Vertices (or corners) are where two or more edges meet. Visible Body Web Suite Now with Flashcards! Web Suite has all the visual and interactive content you need to learn about human anatomy, general physiology, and common conditions. Set Model Color. It's either a solid or hallow object with three vertices meeting at all the points. The available models are suitable for numerous industrial applications. All of our Scanatic™ 360 Body Scanner models offer. ASTM International is an open forum for the development of high-quality, market-relevant technical standards for materials, products, systems, and services used around the globe. The first step is to ask, What body shape am I? Rather than compare your body to pictures of celebrities or fruit today, we're using Oprah fashion expert Bradley Bayou's foolproof technique. Jan 31, 2020 · How to Use a Body Measurement Chart The Right Way. A-line Balance happens when a triangle-shaped dress meets an inverted triangle frame. This shape is the one that is considered in the collision detection. (the fact that yours is convex doesn't matter). Need help figuring out human body proportions? Use this handy calculator!. Author: Andreas Lindner. Set Model Color. Directions: Use the calculator above to calculate your square inches. 3D Body Shape Calculator. Details of each stage can be found below. Solid Geometry is about three dimensional objects like cubes, prisms. Muscles are clearly defined and separated, and vascularity is. The surface area of a general ellipsoid cannot be expressed exactly by an elementary function. Our BMI calculator makes it a piece of cake for you to find your number. Have you got a diet plan? Why not check out our free diet planning calculator too? Remember – your body shape may change as you lose weight, so check back regularly. In other words, choose the shape that you can clearly identify yourself with. Body shape is one of the aspect used to describe a person's outlook or skeletal structure. More info See in Glossary to match the shape of the GameObject's mesh exactly. These include age, muscle-fat ratio, height, sex, and body fat distribution, or body shape. See full list on tips. Automatic and remote updates when a new system software becomes available for zero maintenance. via Model My Diet. You therefore work out the area of each face, and then add them together. By using similar triangles, it is easy to see the result is Up. A major focus of IGIGI is to provide its customer with the custom design and right fit for her body shape. The volume (and thus the weight assuming a standard density) and the circumference of the bust, waist and hips of these 3D models can then be measured. Name the three divisions as Area 1, Area 2, and Area 3. All of our Scanatic™ 360 Body Scanner models offer. This free body fat calculator estimates body fat percentage based on the U. I would have no problems calculating the inertia of each individual polygon in the shape with the formulas provided on the moments of inertia Wikipedia article. Export Landmarks. 3D Body Shape Calculator. Note: The online body type calculator will calculate body shape by measurements from 5 basic categories i. If we pick a different point or axis to take the moment of inertia about, then on average all the distances in our moment integral will be a little bit bigger. The body shapes calculator for women and men shows: The shape of your body will be given; The waist to hip ratio is given. We’ll also tell you if you are an endomorph, ectomorph, or mesomorph. Body mass index, or BMI, is an easy-to-calculate measure of obesity based on the ratio of your weight and your height. BMI (Body Mass Index) Calculate your "New BMI" In its 5 January 2013 issue the Economist published this letter from me: SIR - The body-mass index that you (and the National Health Service) count on to assess obesity is a bizarre measure. BMI values apply to both men and women, regardless of age or frame size. 3D Shape Calculators. The height of a head is considered to be the unit of measurement for the human body. Body shape is one of the aspect used to describe a person's outlook or skeletal structure. However they can be easily adapted to python 3 with minor changes or with the help of the 2to3 tool. Shape diagrams and formulas for geometric solids including capsule, cone, conical frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere. Body Shape. We have also included information regarding Leptin. Diagonal of a Cuboid = √ (l 2 + w 2 + h 2 ) Where, l = Length w = Width h = Height. Question: evaluate the width of the 2D rankine half-body. 5 - 14 Sample Problem 5. For the first time organizations can quickly make their health, medical and life science education more immersive using BioDigital's software. The Body Type Calculator is designed for females to find their "body shape," which can be used for getting targeted outfit Ideas. Find the shape of your face to get suggestions on the hair style that suits you the most, the sunglasses that go with you face, make up tips and much much more. See full list on tips. Body Type Calculator. Calculate limits, integrals, derivatives and series step-by-step. Body type calculator. High-resolution MR images of the pelvis were acquired 6 weeks and 8 months postsurgery. [ Read: Female Body Shape Calculator] 12. Here's what happened when one website gave the same photo to editors across the globe and asked them to give the woman pictured the. Bell, Pear or Spoon Shape. A-line Balance happens when a triangle-shaped dress meets an inverted triangle frame. First select your gender. MPI IS Perceiving Systems. May 30, 2018 · Enter your height and weight below, and Scars1’s unique Advanced BMI calculator will let you know the estimated impact of your present body weight and shape upon your overall health. Chest/Bust. To use the calculator and figure out your body shape, just choose whether you would like to enter your measurements in metric or imperial, type in your hips, waist and bust measurements and click "Calculate". They detect, measure and evaluate profiles on different object surfaces without contact. ASTM International is an open forum for the development of high-quality, market-relevant technical standards for materials, products, systems, and services used around the globe. Lollipop Body Shape. Mathematics of subdivision. In this proof-of-principle study, one patient with severe anterior vaginal wall prolapse was implanted with an MR-visible mesh. It's that easy. A comparative outlook review of different BSA formulae. centroids for a select group of shapes ! The point labeled C is the location of the centroid of that shape. Bayou ' s system uses math—it is a little intensive, but we ' ll walk you through it — to double-check that you ' ve found your real shape. Take the Ellipse Tool (L) and create an ellipse in the shape of human head. We estimate a full 3D mesh and show that 2D joints alone carry a surprising amount of information. Even though there is some research linking certain body shapes with some health risks, the body shape result of this calculator is not intended to be a serious indication of health or an ideal that must be met. Molecule Shapes - PhET Interactive Simulations. Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Our designers tell you exactly what is right and wrong for your body type. Go ahead and measure yourself and fill in the body shape calculator correctly to get the real picture. Maine Coon Cats are the largest breed of domestic cat and are distinguished by their long silky coats. With advancement in technology, 3D depth camera is designed to capture the shape of a human body in seconds and further produce its true-to-scale 3D body model. located immediately below the skin) muscles of the body. The chest and the abdomen look larger while the thighs and legs are usually slimmer. Most Individuals Initially Are Excited To Lose Weight. Body analytics and retail insights. Use this online body shape calculator to find what body type you have. Rigid body dynamics -- the movement and interaction of solid, inflexible objects -- is by far the most popular kind of effect simulated in games. Your Virtual 3D Look Alike Model, Online Body Type Calculator, Style Advice according to Body Type and 3D Virtual Fitting Room: https://www. Determine your wrist size by measuring your wrist just below your wrist bone with a tape measure. The second head starts under this neck space. External link. Body shape is one of the aspect used to describe a person's outlook or skeletal structure. Anton 2008-11-19 18:42:11. In this case, the irregular shape has a semicircle, rectangle, and right triangle. It offers evidence based exercise prescription tools and resources including reference articles, comprehensive exercise libraries, and fitness calculators. K-12 students may refer the below formulas of cube to know what are all the input parameters are being used to find the volume, surface area or diagonal length of cube. Bayou ’ s system uses math—it is a little intensive, but we ’ ll walk you through it — to double-check that you ’ ve found your real shape. Diagrams of solid geometry shapes leading to specific solid geometry calculators. Ellipsoid is a sphere-like surface for which all cross-sections are ellipses. Its shape is uniquely determined by the parameter $$a = {\large\frac{{{T_0}}}{{\rho gA}}\normalsize}$$ as shown in Figure \(3. Your iOS App. 13 Find the centroid of the volume obtained by rotating the shaded area about the x -axis. How 3D Body Scanners Work. or the ones provided in an awesome collision detection & response article. And thanks to Who What Wear’s brilliant co-founder Hillary Kerr, we know that not every trend is for every body type, and that’s okay. We describe the first method to automatically estimate the 3D pose of the human body as well as its 3D shape from a single unconstrained image. Weight (lb) Body Mass Index (BMI) is a measure calculated using your height and weight to. View, isolate, and learn human anatomy structures with Zygote Body. Fast drawing for everyone. Wireframe View On/Off. However, for any given slice, we body axis points out the right hand wing, then the moment about the y axis, using the right hand We can calculate the slope from the data: , and Therefor the aerodynamic center is located at the 23. The direct coating, triangulation, and surface integration, body surface area techniques by Boyd in 1935 were initially considered to be more. Again, we must translate an object so that its center lies on the origin before scaling it. You enter your body measurements and it will show your shape in 3D form. Calculators for plane geometry, solid geometry and trigonometry. Zygote Body is a free online 3D anatomy atlas. Your seasonal styletips will be created. This calculator also calculates the parameters needed for the construction of a frustrum given R, r and h. Body Shape Calculator. That doesn't define anything. The drag coefficient is a number which aerodynamicists use to model all of the complex dependencies of drag on shape, inclination, and some flow conditions. Requires contact_monitor to be set to true and contacts_reported to be set high enough to detect all the collisions. Visible Body Web Suite Now with Flashcards! Web Suite has all the visual and interactive content you need to learn about human anatomy, general physiology, and common conditions. It computes the static deflections, reactions, internal element forces, natural frequencies, mode shapes and modal participation factors of two- and three- dimensional elastic structures using direct stiffness and mass assembly. Females has different body shapes (figure). Use this online body shape calculator to find what body type you have. For three-dimensional shapes, we talk about surface area, to avoid confusion. Frame3DD is free open-source software for static and dynamic structural analysis of 2D and 3D frames and trusses with elastic and geometric stiffness. 3D scaling matrix. The Body Weight Planner allows users to make personalized calorie and physical activity plans to reach a goal weight within a specific time period and to maintain it afterwards. We describe the first method to automatically estimate the 3D pose of the human body as well as its 3D shape from a single unconstrained image. Refer back to our page Calculating Area if you cannot remember how to calculate the area of a circle or triangle. You need to ensure that you don't unbalance the body frame by making it either top- or bottom-heavy. Now with 360° body imaging and circumferential measurements. Mode Shapes, i Although the displacement amplitudes {v} are indeterminate, the shape of {v} can be determined by assigning a value to one element of {v} and solving for the remaining amplitudes Arbitrarily let v1 = 1 ‐20000000 ‐10000000 0 10000000 20000000 30000000 determ 02468 10 12 [E] f, Hz. Ruler or Banana Shape. Simply select the cross section and use the default density for the material choices such as steel, titanium, nickel, plastics, or ceramics. Muscle Anatomy. Wrist site. You will not extract statistical data or 3D meshes from any of the files loaded by this website. WHO table: Meaning BMI; Normal weight: 19-24,9: Overweight: 25-29,9: Obesity level I: 30-34,9: Obesity level II:. 99, try on hundreds of garments created for your body shape. A-line Balance happens when a triangle-shaped dress meets an inverted triangle frame. You enter your body measurements and it will show your shape in 3D form. Launch the Body Weight Planner. A PartDesign Body is the base element to create solids shapes with the PartDesign Workbench. Body Visualizer. centroids for a select group of shapes ! The point labeled C is the location of the centroid of that shape. BMI Calculator - Online Calculator. Export Body Dimentions. Note: Accuracy can vary for people such as athletes, children, the elderly, endomorphic or ectomorphic frames. This tool goes beyond civil/structural applications to include mechanical, aerospace, manufacturing, and construction industries. How to correctly measure your hips, waist and bust. It is amazingly simple to use and understand and has a guide on how to accurately measure your hips, waist and bust. To understand how the body scanner works, let's look at a couple of specific examples. Go ahead and measure yourself and fill in the body shape calculator correctly to get the real picture. 3D laser scanning, the process of converting physical objects into precise digital models, enables you to quickly and accurately capture your object's shape and geometries. 5 - 11 •Calculate the first moments of each area with respect to the axes. The Origin® One, to print more parts with remarkable accuracy and breadth of materials. Then enter either your wrist size or elbow breadth. These 3D Shape Calculators are part of the suite of free online math calculators designed and maintained by iCalculator. Usually, only by healthy eating, your body gets in shape, but that is only the case when you are not THAT overweight. net is a resource for the exercise professional, coach, or fitness enthusiast. We shall see that in the general three-dimensional case, the angular velocity of the body can change in magnitude as well as in direction, and, as a consequence, the motion is considerably more complicated than that in two dimensions. These 3D shapes cannot be positioned via arguments, rather you should use the translate() and rotate() methods described previously. Visible Body Web Suite Now with Flashcards! Web Suite has all the visual and interactive content you need to learn about human anatomy, general physiology, and common conditions. Collect the areas and centroid coordinates, and. For the three-body problem, scientists can calculate, statistically, where each body might end up by precisely computing the volume inside its phase space that represents chaotic motion. The drag coefficient is always associated with a. Use this information, along with other health indices, to assess your need to adjust your weight. Divide the body into small masses of the particle and (X 1,y 1), (X 2,y 2), (X 3, y 3)…. Body analytics and retail insights. Now, look at the graphic with the formulas and you will see that the 'm' in the formula stands for the mass of both orbital bodies. Click Calculate to receive the final dimensions or percentage. PROPORTIONS OF THE BODY A perfect body is 8 heads high, total. Complete 3D Imaging Solution for Body, Breast, and Face. But you can’t change your body frame size. Over 250 sets of body measurement data* specific to pattern making. Land area calculation. Take this quiz to know more about your body shape and what exercises to do to bring it in perfect shape, or maybe you already have a toned body! Go ahead!. Requires contact_monitor to be set to true and contacts_reported to be set high enough to detect all the collisions. Divide the compound shape into basic shapes. You can get these measurements from using a tape measure to measure each body part. This can be accessed under any of our Paid Accounts, which also includes a full structural analysis software. com - how much does electric guitar's body physics affect the tone and playability. 38624 arrow 0 both 1 4000 0 horizontal https://www. Body Visualizer. More info See in Glossary to match the shape of the GameObject's mesh exactly. The point is there is no need to stress out over this waist to height ratio calculator. When the circles are tangent to the cylinder portion, we call say this is a tangent ogive. We live in a three-dimensional world, yet the BMI is defined as weight divided by height squared. Get your body scanned with an iOS or Android (coming soon) mobile phone or tablet using side or front-facing device cameras and use Nettelo cloud services to obtain 3D body digital models with your personal body shape and accurate body measurements right on the mobile device. More info See in Glossary to match the shape of the GameObject's mesh exactly. Note: uploaded pictures may be used to improve the algorithm, more info and opt out. 3D shape features from these models were then used to predict body composition, serum biomarkers, and strength measurements. This 3D Body Shape Simulator uses your weight and height to show you at your goal weight. Radius of Gyration (in Mechanics) The Radius of Gyration is the distance from the rotation axis where a concentrated point mass equals the Moment of Inertia of the actual body. One quarter of one head down on this second head is the shoulder line and clavicle. be the coordinates of the centre of the gravity from a fixed point O. Volume of each cone is 1 3 × (height) × (area of face). When solving for the moment of inertia of a composite area, divide the composite area into basic geometric elements (rectangle, circle, triangle, etc) for which the moments of inertia are known. The models feature predicting standard anthropometric values and anatomical landmark. The typical Maine Coon Cat has an overall height of 10"-16" (25-40 cm) and body length of 19"-32" (48-81 cm). BMI Meaning Based on the body mass index, people are categorized as normal weight, overweight, or obese. In only 35 seconds, we extract millions of measurements with 2mm accuracy and reconstruct your body in 3D. Using the front-end camera of any mobile device, Sizer's proprietary, computer vision technology, precisely calculates a person's body measurements with the. Interactive: Subdivision in 3D. Females has different body shapes (figure). BMI values apply to both men and women, regardless of age or frame size. 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# Integrating length for input-space feature PC projections in kernel PCA

I read a paper detailing the algebraic process of kernel PCA. I have question though: the paper details the projection of new points onto the new eigenvectors in the feature space, but what if I want eigenvectors themselves? I am performing an analysis that compares eigenvector magnitudes in a Gaussian inner product space.

The closest I found in the paper was the definition of the eigenvectors as a hypothetical linear combination of data vectors in the kernel space:

$$\mathbf{V} = \sum_{i = 1}^l \alpha_i \Phi\left(\mathbf{x}_i\right).$$

From the paper, it seems that you derive all such $\alpha$ with the relation

$$\ell\lambda\mathbf{\alpha}=K\mathbf{\alpha}$$ (where $\mathbf{\alpha}$ is supposed to look bold as a vector).

But even after you obtain $\alpha_i$, you can't compute the eigenvectors in the feature space from the previous formula because, in the case of a Gaussian kernel that operates on $\|\mathbf{x} - \mathbf{y}\|$, there are infinitely many dimensions in the the "hidden" range of $\Phi$.

How can I compute $\mathbf{V}$, the eigenvectors in the $\mathbf{\Phi}$?

## Edit 0

I understand that we can't formalize eigenvectors in a infinite-dimensional space implied by a Gaussian-norm inner product kernel. What I actually want is the length of the eigenvector. In the linear case, that would be the semimajor axes of the imaginary ellipse. I want to be able to have, for a "classification" PCA case as this one, a graph like the one on the left showing a curved (for lack of a better word) eigenvector projected down to the input space. I'd prefer a parametric form over which I may compute an arclength integral.

## Edit 1

Oops. I meant principal component, not eigenvector.

• Depending on the kernel, feature space can be very large; for example, for the Gaussian kernel the feature space is infinite-dimensional. How would you want to "compute" $V$ in such a case? What that would even mean? Each eigenvector has infinitely many coordinates! – amoeba Jan 2 '15 at 22:36
• @amoeba, thanks for the comment. Please consider my revision. – Simon Kuang Jan 2 '15 at 23:46
• Hmm, remember that all eigenvectors have (by construction) the length $1$. So what you want is definitely not "the length of the eigenvector". I am not sure I understand your actual goal; maybe it is going to be helpful if you spend more time explaining the question that you actually want to get an answer to. Then we can try to formalize it mathematically. – amoeba Jan 3 '15 at 0:04
• @amoeba Sorry about the confusion. I meant the principal components, these vectors. – Simon Kuang Jan 3 '15 at 0:05
• But these are just [square roots of] the respective eigenvalues, no? You directly compute them in kernel PCA. They seem to have nothing to do with "integrating length for the input-space feature PC projections" (as much as I can understand what this should mean). – amoeba Jan 3 '15 at 0:07

[I apologize that I have not posted this answer earlier, as promised.]

This question seems to have been built upon series of confusions (partly clarified in the comments above and reflected in the edits).

Q1: How can one obtain eigenvectors [of the covariance matrix] in the target space?

This is generally not possible. For some kernels, like e.g. Gaussian kernel, the target space is infinite-dimensional. There is no way one can obtain an eigenvector there: it would need to have infinitely many coordinates! The beauty of the "kernel trick" is that it allows to compute projections of the data onto this eigenvector without ever computing the eigenvector itself.

Q2: Okay, but can one at least compute the length of an eigenvector?

Yes. The length is equal to $1$, because that's how we choose to normalize eigenvectors.

Q3: But what about the length of an eigenvector, like it's depicted on 2D examples of PCA?

This length is simply the square root of the respective eigenvalue. They are directly computed in kPCA.

Having said all that, here is my best guess about what you actually wanted to get.

I want to be able to have, for a "classification" PCA case as this one, a graph like the one on the left showing a curved (for lack of a better word) eigenvector projected down to the input space. I'd prefer a parametric form over which I may compute an arclength integral.

It seems you want to get the length of the decision boundary between two classes in the original feature space. The main problem here is that kPCA is not a classification technique. There is no way kPCA will give you a decision boundary: it's simply projects all your data to some subspace of the target space. If you are lucky, the classes will be linearly separated. But if you need a decision boundary, you will need to use some other, additional, approach to obtain it, and it should be a supervised algorithm (kPCA is unsupervised).

After you come up with or choose an algorithm, then you can ask yourself how to compute the length of the decision boundary. E.g. perhaps you can use some linear classifier (such as LDA, logistic regression, or linear SVM) to get a linear boundary in the kPCA space, and then ask what is the length of the corresponding boundary in the original space. It is not going to be very easy, as far as I can see.

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# Give an example in which $a_0=a_1<a_2=a_3<a_4=a_5<a_6=\cdots$ for the bisection method. [closed]

Give an example in which $a_0=a_1<a_2=a_3<a_4=a_5<a_6=\cdots$ for the bisection method.

I don't see how to make an example of this form. I'm sure there is something simple/elegant that does the trick, but I don't see it. Any hints or solutions are greatly appreciated.

## closed as unclear what you're asking by Chappers, Claude Leibovici, Mario Carneiro, Empty, wythagorasOct 3 '15 at 8:25

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Draw an example. By $a_k$ I presume you mean the bisection interval $[a_k,b_k]$. – copper.hat Oct 3 '15 at 2:33

We solve the equation $3x=1$ using the Bisection Method, with initial values $a_0=0$ and $b_0=1$. The root is given by $x=1/3$.
The root is in $[0,1/2]$, so $a_1=0=a_0$ and $b_1=1/2$.
The root is in $[1/4,1/2]$, so $a_2=1/4\gt a_1$ and $b_2=1/2$.
Now look at the points $1/4,1/3,1/2$. The distance from $1/4$ to the root is $1/12$ and the distance from the root to $1/2$ is $1/6$, the same $1$ to $2$ ratio we started with. So the pattern will repeat.
Remark: The above example is in a (weak) sense the only one. Suppose we start with an interval $[a_0,b_0]$ and a continuous $f(x)$ that has different sign at $a_0$ than at $b_0$. Apply the Bisection Method. Suppose we get the pattern in the OP. Then the root of $f(x)=0$ that we converge to is one-third of the way from $a_0$ to $b_0$. However, there is a fair bit of latitude in the choice of $f(x)$.


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# A Dual-Engine for Early Analysis of Critical Systems

Author: Place: Aboubakr Achraf El Ghazi, Ulrich Geilmann, Mattias Ulbrich, Mana Taghdiri links: [pdf][talk] Dependable Software for Critical Infrastructures (DSCI), 2011

Abstract

This paper presents a framework for modeling, simulating, and checking properties of critical systems based on the Alloy language -- a declarative, first-order, relational logic with a built-in transitive closure operator. The paper introduces a new dual-analysis engine that is capable of providing both \emph{counterexamples} and \emph{proofs}. Counterexamples are found fully automatically using an SMT solver, which provides a better support for numerical expressions than the existing Alloy Analyzer. Proofs, however, cannot always be found automatically since the Alloy language is undecidable. Our engine offers an economical approach by first trying to prove properties using a fully-automatic, SMT-based analysis, and switches to an interactive theorem prover only if the first attempt fails. This paper also reports on applying our framework to Microsoft's COM standard and the mark-and-sweep garbage collection algorithm.

# BibTex

@InProceedings{a.a.elghazi-dsci2011,
    author    = {Aboubakr Achraf {El Ghazi} and Ulrich Geilmann and Mattias Ulbrich and Mana Taghdiri},
    title     = {A Dual-Engine for Early Analysis of Critical Systems},
    booktitle = {Workshop on Dependable Software for Critical Infrastructures (DSCI)},
    address   = {Berlin, Germany},
    year      = {2011},
    urn       = {urn:nbn:de:swb:90-422258}
}


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# How do you factor x^2 + 13x + 36 ?

May 24, 2015

$\left(x + 4\right) \left(x + 9\right) = 0$

Explanation::

$\left(x + 4\right) \left(x + 9\right)$
$x \text{ times } x = {x}^{2}$
$x \left(9\right) + x \left(4\right) = 13 x$
$4 \text{ times } 9 = 36$
= ${x}^{2} + 13 x + 36$

May 24, 2015

${x}^{2} + 13 x + 36 =$ (x - p)(x - q).
Find p, and q, knowing sum = b = 13 and product c = 36. Compose factor pairs of 36-> (2, 18)(2, 12)(4, 9). this last sum is 9 = b. Then p = 4 and q = 9

y = (x + 4)(x + 9)


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ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# инвариантная связность

## Three-dimensional Homogeneous Spaces, Not Admitting Invariant Connections

The purpose of the work is the classification of three-dimensional isotropy-faithful homogeneous spaces, not admitting invariant connections. The local classification of homogeneous spaces is equivalent to the description of effective pairs of Lie algebras. If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariant connections.

## Connections of Nonzero Curvature on Three-dimensional Non-reductive Spaces

When a homogeneous space admits an invariant affine connection? If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariantconnections. If a homogeneousspace is reductive, then the space admits an invariant connection.Thepurposeoftheworkisadescriptionofthree-dimensionalnon-reductivehomogeneousspaces, admitting invariant affine connections of nonzero curvature only, and the affine connections, curvature and torsion tensors.


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# pitchRx, meet openWAR

Both pitchRx and openWAR scrape Gameday data, but are quite different in their implementation. This post will help expose those differences and show how to combine them to make 1 + 1 > 2.

## Similarities/differences between openWAR and pitchRx

Both openWAR and pitchRx can obtain so-called “play-by-play” Gameday data, but provide it in a different format. One reason for this difference is due to pitchRx’s agnostic approach to the type of analysis you’d like to perform. It simply returns data in a collection of tables that closely resembles the raw form. On the other hand, openWAR returns the play-by-play data in a format which is convenient for computing openWAR estimates. Fortunately, I think this format is quite useful for a wide variety of problems and enhances a PITCHf/x database created using pitchRx.

On a side note, the data format returned by openWAR::getData could be produced from tables returned by scrape, but it’s not easy (the ‘atbat’, ‘runner’, ‘action’, ‘hip’, and ‘player’ tables collectively contain the same info). So, in effect, it does not add new data to a pitchRx database, but it can dramatically simplify certain queries (e.g. searching for PITCHf/x by catcher, shortstop, center fielder, etc). Before “Adding openWAR data to your PITCHf/x database” (the last section below), I’ll explain in detail how to acquire play-by-play data for a particular set of games since both pitchRx and openWAR have this capability. Along the way, we’ll also learn how to merge openWAR’s play-by-play data with pitchRx pitch-by-pitch data.

## Game specific data acquistion

Just like pitchRx::scrape, openWAR::getData can acquire data from any set of games using MLBAM’s gameday identifiers. pitchRx comes prepackaged will all the available game identifiers which we can use to query a specific set of games over an extended period of time. To understand how this works, let’s take a look at the format of these identifiers.

### Understanding gameday identifiers

library(pitchRx)
data(gids, package = "pitchRx")
head(gids)
## [1] "gid_2008_02_26_fanbbc_phimlb_1" "gid_2008_02_26_flsbbc_detmlb_1"
## [3] "gid_2008_02_26_umibbc_flomlb_1" "gid_2008_02_26_umwbbc_nynmlb_1"
## [5] "gid_2008_02_27_cinmlb_phimlb_1" "gid_2008_02_27_colmlb_chamlb_1"

All the ids have the general form ‘gid_YYYY_MM_DD_xxxaaa_yyybbb_1’. The ‘gid_’ part of this identifier is the only part that does not change from game to game. Most identifiers will end with ’_1’, but only if it is not the second game of a doubleheader. The ‘YYYY’, ‘MM’ and ‘DD’ parts are numeric representations of the year, month and day (respectively). The ‘xxx’ part is an abbreviation for the away team name and the ‘aaa’ part is an abbreviation of the away team’s league. The same goes for the ‘yyybbb’ part except this abbreviation is for the home team. As you can see from the output above, some of these identifiers correspond to preseason games (the regular season doesn’t usually begin until the start of April).

### Using regular expressions

Regular expressions are useful for extracting a particular set of gameday identifiers since they allows us to search for patterns in a set of strings. For instance, this regular expression would match every Twins home game in 2013:

reg.ex <- "2013_[0-9]{2}_[0-9]{2}_[a-z]{6}_minmlb"

For those not familiar with regular expressions, the [0-9]{2} bit says “any two numbers may go here” and the [a-z]{6} bit says “any six letters (from the Roman alphabet) may go here”. Remember that gids contains preseason, regular season and postseason games. So, if by “every home game” we really meant “every regular season home game”, we can easily restrict to games in April through September (if we change [0-9]+ to 0[4-9] in the month slot).

home <- "2013_0[4-9]_[0-9]{2}_[a-z]{6}_minmlb"

Now, to use this expression to obtain the relevant gids, we can use the base R function grepl (or grep). grepl returns a logical vector the same length the object it is searching. A particular element of that vector will be TRUE if and only if the regular expression found a match. Thus, we can extract the relevant elements of gids by passing this logical vector to R’s [ operator like so:

reg.home <- gids[grepl(home, gids)]

Let’s do the same thing for away games so that we have every Twins’s regular season game from 2013.

reg.away <- gids[grepl("2013_0[4-9]_[0-9]{2}_minmlb_[a-z]{6}", gids)]
reg.season <- c(reg.home, reg.away)
length(reg.season)

### Not all identifiers are created equal

According to reg.season, the Twin’s played 167 regular season games. This is clearly more than the usual 162 games that we would expect. Just for investigative purposes, I’ll search my PITCHf/x database to find out which of these games were not considered “Final”.

library(dplyr)
db <- src_sqlite("~/pitchfx/pitchRx.sqlite3")
games <- tbl(db, "game") %>% select(gameday_link, status) %>%
filter(status != "Final") %>% collect()
subset(games, gameday_link %in% sub("gid_", "", reg.season))
## Source: local data frame [5 x 2]
##
## 324 2013_04_14_nynmlb_minmlb_1 Postponed
## 328 2013_04_17_anamlb_minmlb_1 Postponed
## 333 2013_04_19_minmlb_chamlb_1 Postponed
## 334 2013_04_22_miamlb_minmlb_1 Postponed
## 350 2013_06_07_minmlb_wasmlb_1 Postponedminor

These “Postponed” games would explain the discrepancy between the length of reg.season and the true length of the regular season. Fortunately, both pitchRx::scrape and openWAR::getData are smart enough to “ignore” this issue when collecting play-by-play and/or PITCHf/x data. In fact, if we navigate to the gameday page specific to gid_2013_04_14_nynmlb_minmlb_1, we’ll see that the ‘inning’ directory where play-by-play and PITCHf/x would appear is missing.

### Combining forces

At this point, once we have the gameday identifiers of interest, it is very simple to use openWAR::getData and/or pitchRx::scrape to obtain data for these specific games. Just for the sake of not abusing MLBAM’s website, I’ll acquire data from just the first two regular season games.

plays <- openWAR::getData(gameIds = reg.season[1:2])
dat <- pitchRx::scrape(game.ids = reg.season[1:2])

The data returned by openWAR::getData could be seen as a replacement of sorts to the ‘atbat’ table returned by pitchRx::scrape. Both of them have one atbat per record (meaning the atbat order and gameday identifier columns together form a unique key). Before we merge openWAR’s play-by-play data with pitchRx’s pitch-by-pitch data, we’ll have to clean up a few of the column names.

# Get column names to match (needed in order to join play-by-play & pitch-by-pitch)
names(plays) <- sub("ab_num", "num", names(plays))
names(plays) <- sub("gameId", "gameday_link", names(plays))
# There are two set of 'x' and 'y' columns that mean two different things
# Let's rename the pitch location 'x' and 'y' to 'old_x' and 'old_y' since
# these are pitch locations under the 'old' Gameday coordinate system
names(dat$pitch) <- sub("^x$", "old_x", names(dat$pitch)) names(dat$pitch) <- sub("^y$", "old_y", names(dat$pitch))
pitchfx <- dplyr::inner_join(dat$pitch, plays, by = c("num", "gameday_link")) Now we can easily do stuff like search pitches by player positions. For instance, maybe you want to called strikes where Joe Mauer was playing catcher. The pitchfx data.frame currently has player IDs for each player position, but we can easily map those to player names using the players data.frame which comes with pitchRx. data(players, package = "pitchRx") names(players) <- c("playerId.C", "catcherName") pitchfx %>% dplyr::left_join(players, by = "playerId.C") %>% filter(catcherName == "Joe Mauer") %>% filter(des == "Called Strike") %>% strikeFX() + facet_wrap( ~ stand) + theme_bw() + coord_equal() ## Adding openWAR data to your PITCHf/x database If you have a PITCHf/x database that was obtained using pitchRx, it’s pretty simple to add openWAR’s play-by-play data to your database. db <- src_sqlite("~/pitchfx/pitchRx.sqlite3") # Acquire 2008 play-by-play data dat08 <- openWAR::getData(start = "2008-01-01", end = "2009-01-01") # Creates new table named 'openWAR' in database with 08 data pitchRx::export(db$con, value = dat08, name = "openWAR")
# Acquire 2009 play-by-play
dat09 <- openWAR::getData(start = "2009-01-01", end = "2010-01-01")
# Appends 09 data to the 'openWAR' table
pitchRx::export(db\$con, value = dat09, name = "openWAR")
# Keep repeating this process...

To query your database with your newly added openWAR table, you can follow the principles outlined here (replacing the ‘atbat’ table with the ‘openWAR’ table)


text:
# Double Integration change of variables

1. Feb 29, 2008

### Economist08

Hi
I just cannot understand the following transformation, where $$\phi(t)$$ is the displacement of an optimal path using standard calculus of variations. All functions are defined between 0 and T. $$\phi$$ equals zero at 0 and T. r is some discount rate, e it the Euler number, t is time.

$$\int^{T}_{0}\theta(y(t))e^{-rt}\int^{t}_{0}\phi(\tau)d\tau]dt$$

This should be equal to

$$\int^{T}_{0}\int^{T}_{t}\theta(y(\tau))e^{-r\tau}d\tau]\phi(t)]dt$$

If anybody knows the answer, I would be very happy to get some help here.

2. Feb 29, 2008

### tiny-tim

I think you're being blinded by the detail.

Look carefully and you'll see that the only difference in the two integrands is that t and $$\tau$$ have been swapped over.

Now, you can always change the names of the variables. For example, ∫f(x)dx = ∫f(y)dy, or ∫∫f(x,y)dxdy = ∫∫f(z,w)dzdw.

In your example, x = w and y = z: ∫∫f(x,y)dxdy = ∫∫f(y,x)dydx.

The only place you have to be careful is in choosing the range of integration.

It is the triangular area 0 < $$\tau$$ < t; 0 < t < T.

In other words, all pairs of t and $$\tau$$ with $$\tau$$ < t < T.

Swapping t and $$\tau$$ gives: all pairs of t and $$\tau$$ with t < $$\tau$$ < T, or:
t < $$\tau$$ < T; 0 < t < T.

3. Feb 29, 2008


text:
# What are the enthalpy and entropy contributions to carboxylic acids dissociating in water?

Carboxylic acids such as acetic acid do not dissociate much in the gas phase. In aqueous solution, however, they act as acids (proton donors).

$$\ce{CH3COOH(aq) <=> H+(aq) + CH3COO-(aq)}$$

Are reaction entropy and reaction enthalpy positive or negative, and what are there magnitudes?

In the gas phase, we have clear expectations:

$$\ce{CH3COOH(g) <=> H+(g) + CH3COO-(g)}$$

The reaction enthalpy will be positive (we need to break a bond) while the reaction entropy will be positive (more gas particles). As the reaction does not go forward in the gas phase, the enthalpic contribution must be of larger magnitude.

So another way of stating the question is to ask what the effect of solvation is on the enthalpy and entropy of reaction.

• @Withnail The article you cited in a different thread, pubs.acs.org/doi/pdf/10.1021/ed048p338 Journal of Chemical Education, Vol. 48,pg.338, 1971, encouraged me to ask this question even though it is related to this one: Solvent effects on acidity of ethanoic acid May 9 '19 at 12:57
• This site lists the heat of solution for acetic acid as -1.5 kJ/mol: webserver.dmt.upm.es/~isidoro/dat1/… May 10 '19 at 7:28

Electrostatic screening associated with solvation is obviously the key factor enabling dissociation in aqueous solution when compared to the gas phase. Without such dielectric screening, dissociation would be too costly ($$\approx \pu{1 MJ/mol}$$ or $$\approx\pu{14 eV}$$, roughly the energy required to ionize a hydrogen atom) to occur to a significant extent at RT. The dielectric constant of water reduces the energy of the gas phase electrostatic interaction by a factor of $$\approx 80$$. This is an enthalpic effect. This energy is further reduced by water oxygen bonding to $$\ce{H^+}$$ to form $$\ce{H3O+}$$ (proton to hydronium).
Differences between dissociation constants of different carboxylic acid groups originate from enthalpy or entropy changes due to anion formation (since the formation of protium is something shared in common by all acids, its solvation cannot explain differences in behaviour of different acids). The effects on the solvent are often described in terms of "structure making or breaking". As a rule there is an entropic penalty ($$\Delta S^\circ<0$$) with dissociation that can be attributed to solvent rearrangement around the ensuing charged species. The penalty is seen in thermodynamic data for many weak acids. Trends are otherwise not quite as clearcut. Beyond the entropic penalty, other factors (enthalpic or entropic) may play a role in encouraging or discouraging dissociation, for instance charge delocalization (inductive, mesomeric effects) or intramolecular rearrangements.


text:
### Still have math questions?

Algebra
Question

Use the fact that $$13$$ inches is approximately the same length as $$33$$ centimeters to find a mathematical model that relates centimeters $$y$$ to inches $$x$$ . Then use the model to find the numbers of centimeters in $$10$$ inches and $$20$$ inches.

$$y= \frac{33}{13}x$$
x=10 inches$$, y= \frac{330}{13}$$=25.38 cm
x=20 inches,$$y= \frac{660}{13}$$=50.77 cm


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## Saturday, January 5, 2008

### Find all package from a repository that install a file somewhere

As I'm trying to provide a much cleaner way to wrap java programs into scripts for Debian, I need to know how many of the package maintained by the Debian Java Team install scripts in /usr/bin/. I first thought that the way to go was to use apt-file for doing so, running apt-file show on each package found in the repository. Bad idea: it takes, say, 10 seconds to run apt-file show on my machine. Mutliply that by around 600 binary packages, it takes some time.

So, I wrote a script based on the same idea (using Contents files, see apt-file(1)) that does the both the lookup of all binary packages produced by source trees present in the current directory and looking up a pattern in the Contents file. You can download it here. Typical uses:

• find all binary packages generated from source tree in the current directory:
find-packages

• find all of them that install a file in /usr/bin:
find-packages usr/bin ~/.apt-file/ftp.fr.debian.org_debian_dists_unstable_Contents-amd64.gz

The file ~/.apt-file/ftp.fr.debian.org_..._Contents-amd64.gz or a similar one can be found in apt-file's cache.

Meanwhile, out of nearly 600 packages, there are only 61 binaries out of 35 packages. Java packages are mostly libraries, then.


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## 3.1 Operating system

R works on all three major operating systems (OSs): Linux, Mac and Windows. R is predominantly platform-independent, meaning that it should behave in the same way on each of these platforms. This is partly facilitated by CRAN tests which ensure that R packages work in all major operating systems. There are some operating system specific quirks that may influence the choice of OS and how it is set-up for R programming in the long-term.

### 3.1.1 Operating system and resource monitoring

Minor differences aside,1 R’s computational efficiency is the same across different operating systems. This is important as it means the techniques will, in general, work equally well on different OSs. Beyond the $$32$$ vs $$64$$ bit issue (covered in the next chapter) and process forking (covered in Chapter 6) the main issue for many will be user friendliness and compatibility other programs used alongside R for work. Changing operating system can be a time consuming process so our advice is usually to stick to whatever OS you are most comfortable with.

Some packages (e.g. those that must be compiled and that depend on external libraries) are best installed at the operating system level (i.e. not using install.packages) on Linux systems. On Debian-based operating systems such as Ubuntu, these are named with the prefix r-cran- (see Section 2.4).

Regardless of your operating system, it is good practice to track how system resources (primarily CPU and RAM use) respond when running time-consuming tasks. Alongside R profiling functions such as profvis (see Section XXX), system monitoring can help identify performance bottlenecks and opportunities for making tasks run faster.

A common use case for system monitoring of R processes is to identify how much RAM is being used and whether more is needed (covered in Chapter 3). System monitors also report the percentage of CPU resource allocated over time. On modern multi-threaded CPUs, many tasks will use only a fraction of the available CPU resource because R is by default a single-threaded program (see Chapter 6 on parallel programming). Monitoring CPU load in this context can be useful for identifying whether R is running in parallel (see Figure @ref{2-1}).

System monitoring is a complex topic that spills over into system administration and server management. Fortunately there are many tools designed to ease monitoring all major operating systems.

• On Linux, the shell command top displays key resource use figures for most distributions. htop and Gnome’s System Monitor (gnome-system-monitor, see Figure 2-1) are more refined alternatives which use command-line and graphical user interfaces respectively. A number of options such as nethogs monitor internet usage.
• On Windows the Task Manager provides key information on RAM and CPU use by process. This can be started in modern Windows versions by typing Ctl-Alt-Del or by clicking the task bar and ‘Start Task Manager’.
• On Mac the Activity Monitor provides similar functionality. This can be initiated form the Utilities folder in Launchpad.

### 3.1.2 Exercises

1. What is the exact version of your computer’s operating system?
2. Start an activity monitor then type and execute the following code. How do the results on your system compare to those presented in Figure 2-1?

# 1: Create large dataset
X = data.frame(matrix(rnorm(1e8), nrow = 1e7))

# 2: Find the median of each column using a single core
r1 = lapply(X, median)

# 3: Find the median of each column using many cores
# XXX: Change to function from package
r2 = parallel::mclapply(X, median) # runs in serial on Windows
3. What do you notice regarding CPU usage, RAM and system time, during and after each of the three operations?
4. Bonus question: how would the results change depending on operating system?


text:
SEARCH HOME
 Math Central Quandaries & Queries
 Question from deeqa, a parent: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster, the trip could have been made in 1hr less time. Find the speed 2. The average weekly allowance A of children varies directly as their grade level, G. If the average allowance of an 8th-grade student is $8.56 per week, what is the average weekly allowance of a 5th-grade The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4 working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12 volunteers to complete the job? Hi Deeqa, For your first question look at Stephen's response to an earlier question. The statement that the average weekly allowance A varies directly as the grade G means that there is a constant number k, a number that doesn't change with grade level, so that A = k × G. Since grade 8 students (G = 8) have an average weekly allowance of$8.56 (A = $8.56) you know that$8.56 = k × 8

and hence

k = $8.56/8 =$1.07

Thus A = \$1.07 × G. If G = 5 what is A?

The time T required to do a job varies inversely as the number of people P working means that there is a constant number k so that T = k × 1/P. As I did in the previous problem use the known values to determine k and then apply this value to answer the question.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.


text:
# static constexpr unsigned long is C++’s “lovely little old French whittling knife”

There’s a meme going around (extracted from Mark Forsyth’s 2013 book The Elements of Eloquence) that postulates an unwritten rule of English:

Adjectives in English absolutely have to be in this order: opinion-size-age-shape-colour-origin-material-purpose Noun. So you can have a lovely little old rectangular green French silver whittling knife. But if you mess with that word order in the slightest you’ll sound like a maniac.

The existence of compound modifiers complicates matters: personally I would interpret “French silver knife” as meaning a knife composed of French silver, not a silver knife that was French. I’ve also never heard of a rectangular knife; but I think part of Forsyth’s point is that the word order is largely invariant regardless of whether the overall image makes sense. Consider Noam Chomsky’s nonsensical, but grammatical, “colorless green ideas” — would “green colorless ideas” feel just a bit less grammatical?

Over on Language Log Jason A. Quest observes that this rule ranks adjectives

in terms of how intrinsic and fundamental they are to the object, from least to most. “Whittling knife” is essentially a compound noun […] What it’s made of and where it comes from are unchangeable characteristics of it, so those have to be close. Working back from there the adjectives become more superficially descriptive and possibly changeable, and then finally subjective. You could even extend the rule to say that ownership (“Jimmy’s”) goes before all else, which is a fully extrinsic adjective.

(Commenter Martha points out that an “adjective” like “Jimmy’s” is in fact a possessive determiner, and indeed it is a written rule that possessive determiners should precede the entire noun phrase no matter what.)

(Commenter Hector adds that we see the most-fundamental-binds-tightest rule also in insults to masculinity: if you want to insult a guy, you call him an “ugly little whatever,” because “little” is the most salient insult; but if he’s tall then you reverse the order to “you big ugly whatever,” because “big” isn’t particularly insulting at all.)

## I thought this blog was about C++

C++, like English, gives us plenty of freedom to rearrange our adjectives without breaking the written grammar of the language. But in C++, as in English, the rule of “most important descriptor binds tightest” still applies. Consider these two declarations (Godbolt):

static inline constexpr unsigned long long int x = 42;
long int long inline unsigned constexpr static y = 42;

C++ considers these declarations equally grammatical. But which one would you rather see in a code review? I hope it’s the first one!

C++’s rule for things-that-come-before-the-identifier is pretty amorphous. [dcl.spec.general] simply lists all the possible decl-specifier keywords — friend, virtual, explicit, inline, constexpr, typedef… — and lets you put them together in any order you choose, just as English allows you to put together adjectives in any order you choose. This lax formal grammar was inherited from C89: C allowed long unsigned const x, so it remained valid in C++.

But when you actually write C++ code, I’d appreciate it if you’d channel Mark Forsyth and think of decl-specifiers as absolutely having to be in this order: attributes-friendness-storage-constness-virtualness-explicitness-signedness-length-type Identifier.

Signedness-length-type: Write unsigned long, not long unsigned. Observe that unsigned long int is intimately related to long int in a way that unsigned int and unsigned long int are not: there are places where signedness is ignored by the language, and there’s a make_signed type trait but no “make_long” trait. So longness is in a real sense more “fundamental,” more “important,” than signedness.

As for the “type” part: I write unsigned, not unsigned int; and unsigned long, not unsigned long int. But if I ever had to use C++’s long double type, you can bet I’d write long double and not double long!

Explicitness: All of your constructors and conversion operators should always be explicit, except for the ones you intend to call implicitly (i.e., your copy and move constructors, plus rare special cases like string(const char *)). So my mental model of explicit is as a keyword that says nothing more than “Look out, reader, here comes a constructor or conversion operator!” It’s essentially part of the name of the member function, and belongs right next to the identifier.

constexpr explicit operator bool() const;
//~~~~~~~~~~~~~~~~~~~~
// This whole thing is the "name"

explicit constexpr operator bool() const;
//~~~~~~           ~~~~~~~~~~~~~
// Splitting up the "name" obfuscates the code

Virtualness: Observe that virtual affects the semantics of a function a lot more than constexpr does. It also conveys more information in the strictly information-theoretic sense: the average class (that uses virtual at all) tends to have some virtuals and some non-virtuals, whereas the average class tends to have pretty much all of its methods be constexpr or else none of them be constexpr. It’s pretty common to take an existing class like

struct S {
S(int);
virtual int do_foo();
bool bar() const;
};

and slap a big streak of constexpr paint down the left margin:

struct S {
constexpr S(int);
constexpr virtual int do_foo();  // since C++20
constexpr bool bar() const;
};

Nobody does that with virtual (and if they do, they need to stop).

Constness: C++20 introduces a lot more constness-related keywords besides constexpr, but at least so far they are all mutually exclusive: any given declaration can be constexpr OR consteval OR constinit but never more than one at a time.

C++11 replaced the “static const” idiom with the “static constexpr” idiom:

static const bool a = ...;
static constexpr bool b = ...;

and I hope nobody’s out there using the “constexpr static” ordering!

Notice that west const style falls naturally out of this “important things bind tighter” rule. The style shown above de-emphasizes the constness of bool b, it’s true; but that’s better than a style that de-emphasizes the boolness of const b!

Now, constinit is a little weird. It fills the same grammatical niche as const and constexpr (and now consteval), so you’d think we should also write

static constinit bool c = ...;

But actually, I could totally see putting constinit before the storage class:

constinit static bool d = ...;

The more salient thing about d is that it’s not a const variable; you can modify it at runtime. Subordinate to that, incidentally, it happens to be initialized with a compile-time constant value. Just as with constexpr, I could see someone slapping a big streak of constinit-colored paint down the left margin of their global variable definitions, regardless of storage class. So maybe constinit is better off further left, at least in some cases. (Ralph Waldo Emerson once said that constinitcy was the hobgoblin of little minds. I agree — at least in some cases.)

Storage class: The C++ storage-class specifiers are extern, static, thread_local, and mutable; to which we can add inline for historical reasons. As with static const, there’s a long C tradition of writing static inline (not inline static). And, re our general rule of “more important adjectives bind tighter,” we observe that the inline-ness of a function in practice matters even less (to the caller) than its constexpr-ness. So:

static inline constexpr int f() { ... }

Indeed, between constexpr inline and inline constexpr, the C++ Standard itself prefers inline constexpr.

I rarely see static inline together anymore in C++. Static free functions don’t benefit from inline. For static member functions, I recommend putting inline on the definition, never on the declaration (this reduces clutter in the class body, and also reduces churn when you move a member function from the .h file into the .cpp file or vice versa); whereas the static keyword goes on the declaration inside the class body, and is grammatically forbidden to go on the definition.

But in C++17 we got static inline member variables, which can be initialized directly in the class body even if they’re non-const or non-scalar. This may cause the wild population of static inline to rebound slightly.

Friendness: To befriend an entity in C++, you copy-and-paste its declaration directly into the body of your class, and then you slap a friend keyword on the front.

constexpr unsigned int f();

class Secretive {
friend constexpr unsigned int f();
};

Slapping the friend keyword into the middle of the declaration would just be weird.

Unfortunately, to befriend a template you must put the template-head (if any) in front of the friend keyword:

template<class T> int f(T);

class Secretive {
friend template<class T> int f(T);  // invalid, sadly
template<class T> friend int f(T);  // OK
template<class T> int friend f(T);  // technically valid, but please don't

friend int f(auto);  // valid since C++20 (but probably don't?)
};

Finally, attributes: C++11 attributes are not decl-specifiers, and therefore the formal grammar requires that they come either first-of-all or last-of-all:

[[nodiscard]] constexpr int f() { return 1; }  // OK
constexpr int f [[nodiscard]]() { return 1; }  // valid, but please don't

If you accidentally place an attribute in the middle of your decl-specifier-seq, the compiler will give you a diagnostic if you’re lucky, and then proceed to ignore it. (Clang and ICC error; GCC warns; MSVC doesn’t even warn. Ironically, if you put the attribute in the right place, ICC will ignore it anyway. Godbolt.)

constexpr [[nodiscard]] int f() { return 1; }  // invalid

int main() { f(); }  // no diagnostic here because f is not a nodiscard function

By the way, constinit was originally proposed as an attribute, and probably should have remained one; it was changed to a keyword only after discussion within WG21.

## What about the stuff at the end of a declaration?

C++’s very lax decl-specifier-seq was inherited from C. But the idea of putting stuff after the function parameter list was a C++ invention, so C++ has been able to enforce stricter formal rules about the ordering of those clauses. The relevant grammar is given in the standard under parameters-and-qualifiers and member-declarator, and it goes pretty rigidly like this:

• Function name and parameter list
• Cv-qualifier
• Ref-qualifier
• Exception specification (noexcept)
• Trailing return type
• override, final, or requires
• Body, =0, =default, or =delete

For example:

auto f() const & noexcept -> int override = 0;

int g() && noexcept(false) requires true = delete;

Notice that as a general rule, we work toward completing the function’s type first, because the function type is the most important thing. (Noexceptness became part of the function type in C++17.) Only once we’ve completed the function type do we move on to lesser properties such as its constraints and whether it is a virtual overrider. This general rule explains the awkward not-so-trailing placement of the trailing return type:

// OK, looks great
auto f() noexcept
-> std::conditional_t<B, X, Y>;

// Awkward
auto g()
-> std::conditional_t<B, X, Y>
override;

// Awkward
auto h()
-> std::conditional_t<B, X, Y>
requires (N < 7);

Virtual functions can’t be constrained, so you’ll never see the override or final keyword coexist with a requires-clause. Although it’s possible to write either final override or override final, you shouldn’t; just write final alone. (Vaguely related: “A hole in Clang’s -Wsuggest-override (2021-02-19).)

C++’s syntax expands, gaslike, to fill the available space: int h() requires true && override is also a valid declaration, if a constexpr bool override is visible in the current scope. Fortunately, int h() requires true && noexcept(false) is invalid: the constraints in a requires-clause must all be primary-expressions, and noexcept(false) is a unary-expression. See “Why do we require requires requires?” (2019-01-15).

Guidelines mentioned or alluded to in this post:

• Attributes-friendness-storage-constness-virtualness-explicitness-signedness-length-type Identifier.

• Make every constructor explicit (except for copy, move, and very special cases).

• Make every conversion operator explicit: especially explicit operator bool() const.

• For a virtual function, use exactly one of virtual, override, or final.

• Indent trailing requires-clauses the same way you’d indent trailing return types.

• West const.

Posted 2021-04-03


text:
# What is the vertex form of y=13x^2 + 14x + 24?

Jul 17, 2018

Vertex form of equation is $y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$

#### Explanation:

$y = 13 {x}^{2} + 14 x + 24$ or

$y = 13 \left({x}^{2} + \frac{14}{13} x\right) + 24$ or

$y = 13 \left\{{x}^{2} + \frac{14}{13} x + {\left(\frac{7}{13}\right)}^{2}\right\} - \frac{49}{13} + 24$ or

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - \frac{263}{13}$ or

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$. Comparing with standard vertex

form of equation  f(x)=a(x-h)^2+k ; (h,k) being vertex

we find here $h = - \frac{7}{13} , k = - 20 \frac{3}{13} \therefore$ Vertex is at

$\left(- \frac{7}{13} , - 20 \frac{3}{13}\right)$ . Vertex form of equation is

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$ [Ans]


text:
# Tagged: rank

## Problem 154

Define the map $T:\R^2 \to \R^3$ by $T \left ( \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\right )=\begin{bmatrix} x_1-x_2 \\ x_1+x_2 \\ x_2 \end{bmatrix}$.

(a) Show that $T$ is a linear transformation.

(b) Find a matrix $A$ such that $T(\mathbf{x})=A\mathbf{x}$ for each $\mathbf{x} \in \R^2$.

(c) Describe the null space (kernel) and the range of $T$ and give the rank and the nullity of $T$.

## Problem 140

Let $A$ be an $m\times n$ matrix. The nullspace of $A$ is denoted by $\calN(A)$.
The dimension of the nullspace of $A$ is called the nullity of $A$.
Prove the followings.

(a) $\calN(A)=\calN(A^{\trans}A)$.

(b) $\rk(A)=\rk(A^{\trans}A)$.

## Problem 136

Let $A$ be an $m\times n$ matrix. Prove that the rank of $A$ is the same as the rank of the transpose matrix $A^{\trans}$.

## Problem 135

Let $A$ be an $m \times n$ matrix and $B$ be an $n \times l$ matrix. Then prove the followings.

(a) $\rk(AB) \leq \rk(A)$.

(b) If the matrix $B$ is nonsingular, then $\rk(AB)=\rk(A)$.

## Problem 103

Find the rank of the following real matrix.
$\begin{bmatrix} a & 1 & 2 \\ 1 &1 &1 \\ -1 & 1 & 1-a \end{bmatrix},$ where $a$ is a real number.

(Kyoto University, Linear Algebra Exam)

## Problem 101

For which choice(s) of the constant $k$ is the following matrix invertible?
$A=\begin{bmatrix} 1 & 1 & 1 \\ 1 &2 &k \\ 1 & 4 & k^2 \end{bmatrix}.$
(Johns Hopkins University, Linear Algebra Exam)

## Problem 60

Let $T: \R^3 \to \R^3$ be the linear transformation given by orthogonal projection to the line spanned by $\begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix}$.

(a) Find a formula for $T(\mathbf{x})$ for $\mathbf{x}\in \R^3$.

(b) Find a basis for the image subspace of $T$.

(c) Find a basis for the kernel subspace of $T$.

(d) Find the $3 \times 3$ matrix for $T$ with respect to the standard basis for $\R^3$.

(e) Find a basis for the orthogonal complement of the kernel of $T$. (The orthogonal complement is the subspace of all vectors perpendicular to a given subspace, in this case, the kernel.)

(f) Find a basis for the orthogonal complement of the image of $T$.

(g) What is the rank of $T$?

(Johns Hopkins University Exam)