SCIENCE CAPSULES

  We grow as an adult; complete our studies; find a good carrier; then select a suitable spouse; get married.  Offsprings get portions of our genes.  They grow as adults…. The story continues generation after generation.  The point here is; the fittest get married and produce off-springs. This principle can be used to solve a maths problem.   f(x) = 3.x-x^2/6.62 The above function yields different results for different values of X.  I want to find a particular value of X for which the function yields maximum.  That is, I want to maximize the function.  Let us assume that X can only take values from 0 to 31.  In a binary system, the range is 00000 to 11111(for the explanation of binary number see note 1) Let us randomly select six x values in the range 0 to 31 and evaluate the function. X- decimal X- binary f(x) = 3.x-x^2/6.62 selected? 2 00010 5.395 yes 8 01000 14.33 yes 12 01100 14.24 ...

    One cannot think of  a mathematical step without 'is equal to ' .  It balances right hand side and left hand side.  It aids simplification and manipulation of a mathematical expression. example: 2(A+B)  = C 2A+2B  = C         2A = C-2B           A = C-2B/ 2   In an electronic calculator,  the pressing of ' = " sign executes an asthmatic expression  or simply calculates.       In computer languages, it plays very important role.                                                                 A = B   When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A .  After execution both A and B will have the same value an...

  What is the solution of X^2 + 1 = 0 ?   X^2 = -1     X = ROOT OF -1 = i    Root of -1 is meaningless and does not have any physical or real attribute.  So we call it imaginary number i.  Now a new number system is born 1i, 2i, 3i,...      Normally, positive numbers are represented in positive X - axis and negative numbers are represented in negative X - axis.  That is, 180 degree opposite to the positive numbers .Since i = (-1)^1/2 , the imaginary number should be represented half way between positive and negative numbers.  That is in Y - axis perpendicular to the X-axis.  So finally i means 90 degree rotation.      Now we take one real example.  Let there be a square table on the floor.  Let us assume that you and your friend push the table at the two sides.  that is, both of you push the table perpendicular to each other.  Commonsense says that table will move i...

  Throw a stone on the sheet of water in a pond.  Circular waves are created and spread throughout the water surface.  The waves travels as crests and troughs.  We are going to model this waves mathematically.       In a right angled triangle, opposite side divided by hypotenuse gives the sine of the angle x   as illustrated in the figure.     Trigonometry says:  As the angle goes from zero degree to 90 degree, the sine value goes from 0 to 1.  When the angle increases to 180 degree, the sine goes down to 0.  As the angle further increases to 270 and to 360 degree,  the sine goes to -1 and then back to 0.  So when the angle makes one rotation, the sine makes one wavy motion as given in the figure.      So sine function is very suitable to represent a wave.   Y = sin x        As the x goes from 0 to 360 degree or in radian 0 to 2 pi, Y oscillat...

        We know, the flow of electrons is electric current.  Electrons are said to be negative charge carriers.        In a molecular structure, if there is a vacancy for an electron,  it is called hole .  When an electron from somewhere in the structure fills-up  this hole, a new  hole will be created where the electron has just left.  Hence a hole can move opposite to the electron .  So the holes are said to be positive charge carriers.     In a germanium crystal, arsenic is infused.  We get electron rich material called N type (negative) material.  When boron is added to germanium, we get holes surplus P type (positive) substance.        A thin P type material is sandwiched between two N type material.  Now a transistor is made.  These three pieces NPN are respectively called emitter, base, and collector.      By co...

     Why the city like ship floats on the water?  For the simple question, the simple answer is ship is less denser than water.  Yes, really.  The ship is designed and shaped so that it average density (mass/unit volume) is less than that of water.  That is why the ship can only have ship-shape .  But the usual explanation is based on Archimedes principle.       In this article, we are going to speak about density, even though it appears to be elementary concept, it has deeper meanings.       Density indicates how much matter is really packed in the unit volume.  Common sense says, cotton package is lighter than a bar of iron.  Physics says, mercury is 13.6 times heavier than water.  That is, 1 cc of water weighs 1 gm.  But 1 cc of mercury weighs 13.6 gm.  Hence mercury is used in pressure-meters, thermometers etc,.      Osnium is the heaviest metal avail...

       We use remote control that triggers TV, AC, etc,. How it works?  How the eye's vision is communicated to the brain? How a bar code reader in a mall works? How the smartphone camera shoots a picture?      "When light waves, infra red rays, ultraviolet falls on certain chemicals like zinc, electrons are ejected out and electric current starts flowing".  This process is known as photoelectric effect .  It is instantaneous .  How can the waves push electron?  Can sound waves push an object?  No.  Can  stream of fire disturb a concrete wall? No. So there must be 'something' in the photoelectric effect.      Einstein investigated and proved that light waves sometimes behave like pockets of energy or particles called photons .  When one photon strike an atom in a material, one electron is ejected out instantly.  It is like throwing a heavy stone on the wall and forcing out ...