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Math : Diffusion Equation or Heat Equation

Diffusion equation at finite rod, Semi-infinite rod and infinite rod have been discussed. Thank you. Feel free to comment.

5/14/2017

Some Quotes of Ronaldo


1. Your love makes me strong. Your hate makes me unstoppable.
2. I’m living a dream I never want to wake up from.
3. We don’t want to tell our dreams. We want to show them.
4. I’ve never tried to hide the fact that it is my intention to become the best.
5. If we can’t help our family, who are going to help?
6. We should make the most of life, enjoy it because that’s the way it is.
7. But I don’t want to be compared to anyone – I’d like to impose my own style of play and do the best for myself and for the club here.
8. Today there are opportunities that no one knows if they will come round again in the future.
9. Scoring goals is a great feeling, but the most important thing to me is that the team is successful – it doesn’t matter who scores the goals as long as we’re winning.
10. I would be very proud if, one day, I’m held in the same esteem as George Best or Beckham. It’s what I’m working hard towards.
11. I want to consistently play well and win titles. I’m only at the beginning.
12. There is no harm in dreaming of becoming the world’s best player. It is all about trying to be the best. I will keep working hard to achieve it but it is within my capabilities.
13. When you lose a person you love so much, surviving the loss is difficult.
14. After I joined, the manager asked me what number I’d like. I said 28. But Ferguson said ‘No, you’re going to have No. 7’ and the famous shirt was an extra source of motivation. I was forced to live up to such an honor.
15. It gives me the happiest feeling in the world. I just love scoring. It doesn’t matter if it’s a simple goal from close range, a long shot or a dribble around several players, I just love to score all goals.
16. I don’t have to show anything to anyone. There is nothing to prove.
Your only competition is the person you were yesterday. Challenge yourself, not others.
17. I see football as an art and all players are artists.If you are a top artist, the last thing you would do is paint a picture somebody else has already painted.
18. I am not a perfectionist, but I like to feel that things are done well. More important than that, I feel an endless need to learn, to improve, to evolve.
19. When I win awards, I think of my father.
20. Talent without working hard is nothing.
21. There are people out there who hate me and who say I'm arrogant, vain, and whatever. That's all part of my success. I am made to be the best.
22. In football, I don't have a lot of friends. The people who I really trust, there are not many... Most of the time, I'm alone.
23.I don't have to show anything to anyone. There is nothing to prove.

Feel free to comment. thanks.

5/08/2017

Spritual : Some Quotes of Swami Vivekananda

1. This is the first lesson to learn: be determined not to curse anything outside, not to lay the blame upon anyone outside, but stand up, lay the blame on yourself. You will find that is always true. Get hold of yourself.
2. I, for one, thoroughly believe that no power in the universe can withhold from anyone anything they really deserve.
3. Fear is death, fear is sin, fear is hell, fear is unrighteousness, and fear is wrong life. All the negative thoughts and ideas that are in the world have proceeded from this evil spirit of fear.
4. If there is one word that you find coming out like a bomb from the Upanishads, bursting like a bombshell upon masses of ignorance, it is the word “fearlessness.”
5. Great work requires great and persistent effort for a long time. … Character has to be established through a thousand stumbles.
6. That man has reached immortality who is disturbed by nothing material.
7. Fill the brain with high thoughts, highest ideals, place them day and night before you, and out of that will come great work.
8. Every action that helps us manifest our divine nature more and more is good; every action that retards it is evil.
9. Knowledge can only be got in one way, the way of experience; there is no other way to know.
10. Condemn none: if you can stretch out a helping hand, do so. If not, fold your hands, bless your brothers, and let them go their own way.
11. The less passion there is, the better we work. The calmer we are the better for us and the more the amount of work we can do. When we let loose our feelings, we waste so much energy, shatter our nerves, disturb our minds, and accomplish very little work.
12. Superstition is our great enemy, but bigotry is worse.
13. Be a hero. Always say, ‘I have no fear.’ Tell this to everyone – ‘Have no fear.’
14. The world is the great gymnasium where we come to make ourselves strong.
15. This, I have seen in life – those who are overcautious about themselves fall into dangers at every step. Those who are afraid of losing honor and respect, get only disgrace; and those who are always afraid of loss, always lose.
16. Where can we go to find God if we cannot see Him in our own hearts and in every living being.
17. We are responsible for what we are, and whatever we wish ourselves to be, we have the power to make ourselves.
18. It is the patient building of character, the intense struggle to realize the truth, which alone will tell in the future of humanity.
19. Whatever you think, that you will be. If you think yourself weak, weak you will be; if you think yourself strong, strong you will be.
20. Work and worship are necessary to take away the veil, to lift off the bondage and illusion.
21. Truth does not pay homage to any society, ancient or modern. Society has to pay homage to Truth or die.
22. Are great things ever done smoothly? Time, patience, and indomitable will must show.
23. Impurity is a mere superimposition under which your real nature has become hidden. But the real you is already perfect, already strong.
24. As body, mind, or soul, you are a dream; you really are Being, Consciousness, Bliss (satchidananda). You are the God of this universe.
25. It is our own mental attitude which makes the world what it is for us. Our thought make things beautiful, our thoughts make things ugly. The whole world is in our own minds. Learn to see things in the proper light.
26. Truth can be stated in a thousand different ways, yet each one can be true.
27. It is the duty of every person to contribute in the development and progress of India.
28. ‘Comfort’ is no test of truth; on the contrary, truth is often far from being ‘comfortable’.
29. Nature, body, mind go to death, not we. We neither go nor come. The man Vivekananda is in nature, is born and dies. But the Self we see as Vivekananda is never born and never dies. It is the eternal and unchangeable Reality.
30. You cannot believe in God until you believe in yourself.
31. Don’t look back – forward, infinite energy, infinite enthusiasm, infinite daring, and infinite patience. Then alone can great deeds be accomplished.
32. The less passion there is, the better we work. The calmer we are the better for us and the more the amount of work we can do.
33. This life is a hard fact; work your way through it boldly, though it may be adamantine; no matter, the soul is stronger.
34. However we may receive blows, and however knocked about we may be, the Soul is there and is never injured. We are that Infinite.
35. You have to grow from the inside out. None can teach you, none can make you spiritual. There is no other teacher but your own soul.
36. A few heart-whole, sincere, and energetic men and women can do more in a year than a mob in a century.
37. As soon as I think that I am a little body, I want to preserve it, to protect it, to keep it nice at the expense of other bodies; then you and I become separate. First get rid of the delusion ‘I am the body’, then only will we want real knowledge.
38. Astrology and all these mystical things are generally signs of a weak mind. Therefore as soon as they are becoming prominent in our minds, we should see a physician, take good food, and rest.
39. All the powers in the universe are already ours. It is we who have put our hands before our eyes and cry that it is dark.
40. The mind is but the subtle part of the body. You must retain great strength in your mind and words.
41. There is one thing to be remembered: that the assertion ‘I am God’ cannot be made with regard to the sense-world.
42. If superstition enters, the brain is gone.
43. Stand as a rock; you are indestructible. You are the Self (atman), the God of the universe.
44. “Face the brutes.” That is a lesson for all life—face the terrible, face it boldly. Like the monkeys, the hardships of life fall back when we cease to flee before them.
45. The Land where humanity has attained its highest towards gentleness, towards generosity, towards purity, towards calmness – it is India.
46. There is no limit to the power of the human mind. The more concentrated it is, the more power is brought to bear on one point.
47. The will is not free – it is a phenomenon bound by cause and effect – but there is something behind the will which is free.
48. Look upon every man, woman, and everyone as God. You cannot help anyone, you can only serve: serve the children of the Lord, serve the Lord Himself, if you have the privilege.
49.  Our first duty is not to hate ourselves, because to advance we must have faith in ourselves first and then in God. Those who have no faith in themselves can never have faith in God.
50. The moment I have realized God sitting in the temple of every human body, the moment I stand in reverence before every human being and see God in him – that moment I am free from bondage, everything that binds vanishes, and I am free.
51. “The brain and muscles must develop simultaneously. Iron nerves with an intelligent brain — and the whole world is at your feet.
52. We came to enjoy; we are being enjoyed. We came to rule; we are being ruled. We came to work; we are being worked. All the time, we find that. And this comes into every detail of our life.
53. Each work has to pass through these stages—ridicule, opposition, and then acceptance. Those who think ahead of their time are sure to be misunderstood.
54. Neither seeks nor avoids, take what comes.
55. Comfort is no test of truth. Truth is often far from being comfortable.
56. Arise, awake, stop not until your goal is achieved.

2/06/2017

Math : Topology T1, T2, T3 Space.

In this topic we discuss the definition on Topology, T1, T2, T3  space.
Thank you.

1/29/2017

Math : Diffusion Equation or Heat Equation

Diffusion equation at finite rod, Semi-infinite rod and infinite rod have been discussed.


Thank you. Feel free to comment.

1/27/2017

Tech : Some Information about Payment Banks in India. What is Payment Banks and it's function?

Payments Banks:

                            This is a new model of bank in India incited by former RBI (Reserve bank of India ) governor Raghuram Rajan (2013-2016) in 2014.

These banks can accept a deposit upto  ₹100,000 ($ 1500 around) per customer.

They can't issue loans and credit cards but can operate savings and current  accounts.  Also they can give services like ATM Cards, Debit Cards,  Online Banking,  Mobile Banking,  UPI Banking  ( Unified Payment Interface,  This service launched by RBI), Aadhaar Banking  (banking system use biometric authentication for payment no need any password or pin)


Requirement for Payments Banks :

                                                           The minimum capital requirement is  ₹100 crore ($ 15m).         Foreign share holding will be allowed in these banks as per rules of FDI ( foreign direct investment ) in the private banks in India.

These banks must use "Payments bank " term in their name. 70% of its deposited amount should be invest in the government bond ( India ) and 25% of its branches must be in the unbanked rural area.

Launched  Payments banks :

                                            Currently "Airtel Payments bank " has been launched on 15th January 2017, India Post has been launched on 30th january 2017 and "Paytm Payments bank" will be launched on the 1st week of February 2017.


RBI already given to these companies to launch Payments bank


1.India Post

  2.Airtel M commerce

3. Airtel M commerce Services

4. Cholamandalam Distribution Services

5. Fino Pay Tech

6. National securities Depository

7. Reliance  Industries

8. Sun pharmaceuticals

9. Paytm

10. Tech Mahindra

11. Vodafone  M pesa   etc.
Thank you.  Come again. Feel free to comment.

Mathematics Syllabus for competitive exams and gate

Section  1:  Linear Algebra

  Finite dimensional  vector  spaces;  Linear  transformations  and  their  matrix representations, rank;  systems  of  linear  equations,  eigenvalues  and  eigenvectors,  minimal  polynomial, Cayley-Hamilton  Theorem,  diagonalization,  Jordan-canonical  form,  Hermitian,  SkewHermitian  and  unitary  matrices;  Finite dimensional  inner  product  spaces,  Gram-Schmidt orthonormalization  process,  self-adjoint  operators,  definite forms.

Section 2: Complex Analysis 

Analytic  functions,  conformal  mappings,  bilinear  transformations;  complex  integration: Cauchy’s  integral  theorem  and  formula;  Liouville’s  theorem,  maximum  modulus  principle; Zeros  and  singularities;  Taylor  and  Laurent’s  series;  residue theorem  and  applications  for evaluating  real  integrals.

Section 3: Real Analysis 
   Sequences  and  series  of  functions,  uniform  convergence,  power  series,  Fourier  series, functions  of  several  variables,  maxima,  minima;  Riemann integration,  multiple integrals, line,  surface and  volume  integrals,  theorems  of  Green,  Stokes  and  Gauss;  metric  spaces, compactness,  completeness,  Weierstrass  approximation  theorem;  Lebesgue measure, measurable functions;  Lebesgue integral,  Fatou’s  lemma,  dominated  convergence theorem.
Section  4: Ordinary  Differential  Equations 

First  order  ordinary  differential  equations,  existence and  uniqueness  theorems  for  initial value  problems,  systems  of  linear  first  order  ordinary  differential  equations,  linear  ordinary differential  equations  of  higher  order  with constant  coefficients;  linear  second  order ordinary  differential  equations  with variable coefficients;  method  of  Laplace transforms  for solving  ordinary  differential  equations,  series  solutions  (power  series,  Frobenius  method); Legendre and  Bessel functions  and  their  orthogonal  properties.

Section  5:  Algebra

Groups,  subgroups,  normal  subgroups,  quotient  groups  and  homomorphism  theorems, automorphisms;   cyclic  groups  and  permutation  groups,  Sylow’s  theorems  and  their applications;   Rings,  ideals,  prime and  maximal  ideals,  quotient  rings,  unique factorization domains,  Principle ideal  domains,  Euclidean domains,  polynomial  rings  and  irreducibility criteria;  Fields,  finite fields,  field  extensions.

Section  6: Functional  Analysis

  Normed  linear  spaces,  Banach  spaces,  Hahn-Banach  extension theorem,  open mapping and  closed  graph  theorems,  principle  of  uniform  boundedness;  Inner-product  spaces, Hilbert  spaces,  orthonormal  bases,  Riesz  representation  theorem,  bounded  linear operators.

Section  7:  Numerical Analysis  Numerical  solution  of  algebraic  and  transcendental  equations:  bisection,  secant  method, Newton-Raphson method,  fixed  point  iteration;  interpolation:  error  of  polynomial interpolation,  Lagrange,  Newton interpolations;  numerical  differentiation;  numerical integration:  Trapezoidal  and  Simpson  rules;  numerical  solution  of  systems  of  linear equations:  direct  methods  (Gauss  elimination,  LU  decomposition);  iterative  methods :Jacobi  and  Gauss-Seidel);  numerical  solution of  ordinary  differential  equations:  initial value problems:  Euler’s  method,  Runge-Kutta  methods  of  order  2.

Section  8:  Partial  Differential  Equations

Linear  and  quasilinear  first  order  partial  differential  equations,  method  of  characteristics; second  order  linear  equations  in  two  variables  and  their  classification;  Cauchy,  Dirichlet and  Neumann problems;  solutions  of  Laplace,  wave in  two  dimensional  Cartesian coordinates,  Interior  and  exterior  Dirichlet  problems  in polar  coordinates;  Separation of variables  method  for  solving  wave and  diffusion equations  in one space  variable;  Fourier series  and  Fourier  transform  and  Laplace  transform  methods  of  solutions  for  the  above equations.

Section  9: Topology

Basic  concepts of  topology,  bases,  subbases,  subspace  topology,  order  topology, product  topology,  connectedness,  compactness,  countability  and  separation axioms, Urysohn’s Lemma.

Section  10: Probability  and  Statistics Probability  space,  conditional  probability,  Bayes  theorem,  independence,  Random variables,  joint  and  conditional  distributions,  standard  probability  distributions  and  their properties  (Discrete  uniform,  Binomial,  Poisson,  Geometric,  Negative binomial,  Normal, Exponential,  Gamma,  Continuous  uniform,  Bivariate normal,  Multinomial),  expectation, conditional  expectation,  moments;  Weak  and  strong  law  of  large numbers,  central  limit theorem;  Sampling  distributions,  UMVU  estimators,  maximum  likelihood  estimators;  Interval estimation;  Testing  of  hypotheses,  standard  parametric  tests  based  on  normal, , ,    distributions;  Simple  linear  regression.

 Section  11:  Linear  programming

Linear  programming  problem  and  its  formulation,  convex  sets  and  their  properties, graphical  method,  basic  feasible solution,  simplex  method,  big-M  and  two  phase methods;  infeasible  and  unbounded  LPP’s,  alternate optima;  Dual  problem  and  duality theorems,  dual  simplex method  and  its  application in post  optimality  analysis;  Balanced and  unbalanced  transportation problems,  Vogel’s  approximation method  for  solving transportation problems;  Hungarian method  for  solving  assignment  problems. 

Thank you.                                               https://amathscholar.blogspot.in/

SPIRITUAL : SILENCE IS THE MOST POWERFUL WORD IN WORLD

What is the powerful things in the world ?
money? people? No.
#Silence as It has no boundary. So don't think about people or money just about your love and passion. People and money can't give you peace but you can give it to you. It is not matter what people say about you. It is matter what you say about yourself and think about yourself.
You see people are selling each other because other are doing so.
Do you want to be like that people then you can do what they are doing. But if you don't want that do what you think and like.
some people may have bound to do this thing but why should you come in this bound? why would you see world by the other people mirror but your own mirror. ...  It isn't that physical work is so much effective but #Silence . 
Do you have seen Silence sea? Do you know how dangerous is a silence sea? You can't judge anything by seen a silence sea.   If your mind go to the silence position think what mind can do.Is anything impossible for this mind? Silence can can create infinite possibility in the mind. Silence is the more effective than anything in the leaving creature.  
What is the difference between men and other animals? Nothing but Silence. For this men are unstoppable.


Thank you. Come again. Please feel free to comment.