Math : Topology T1, T2, T3 Space.

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

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Math : Diffusion Equation or Heat Equation

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

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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.
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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. 

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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.

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Spritual: Some times I become Thoughtless

Sometimes I become thoughtless and speechless, ask myself what do you want? My mind says don't know. Everything is within me so I don't need anything. Then I ask why are you searching here and there? In reply it says that to increase the awareness that Everything is within me. So why are you frustrated and fear about your job or work? Your job and work can't give anything to you except you. So don't fear do what you want.
Don't greed about anything as you can't get anything. You get what you are. So do what you love and what you think. Never mind what people say or think about you. You came in this world to search your love. For searching love don't afraid about physical pain of your body. In the physical pain of your body you will have your freedom and freedom  is the ultimate goal of your life. Anything isn't matter to you expect freedom. In love there may be physical pain but don't give up your love. In the World you come here to search your love. See everything but choose what you love. Think about the people whom love you most. Do the work what you love.
Don't fear to lose. You are doing what you  love. Don't think about result of the work as you are doing what you love.

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Tech : BHIM App lunched by Narendra Modi, Best UPI App Review

1 #BHiM  app is one the best upi app. It also very fast and transaction time is less than one sec. 9/10

2 Lotza by Federal bank
Lotza is also very fast app also another feature of this app you can use many upi address and many account at a time. 9/10

3 Sbi pay this app is very very slow. If you wrongly enter your mobile number you can't change it by again uninstaling it.
3/10

4 Axis pay this is axis bank upi app. this app is also not so bad. Some people are facing problem that scan option is not working on their phone. This is not as so fast as first two app. 6/10

5 PhonePe this upi app is also good but one main concern is that you can't transfer your money from phonepe to another upi app. Transaction failure rate is very much. 8/10.

6 other upi app are #pockets and hdfc  upi  etc . they also good

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