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International Journal of Advanced Mathematical Sciences    [4 followers]  Follow    
  This is an Open Access Journal Open Access journal
     ISSN (Print) 2307-454X - ISSN (Online) 2307-454X
     Published by Science Publishing Corporation Homepage  [9 journals]
  • On closed-form solutions to a class of ordinary differential equations
    • Authors: Dhrushil Badani
      Abstract: In this paper,closed-form solutions in terms of integral(s) to any second and third order linear non-homogeneous constant-coefficient ordinary differential equations as well as the second order non-homogeneous Cauchy-Euler equation, are derived. The method is generalized for nth order linear non-homogeneous constant-coefficient ordinary differential equations. A similar method is used to derive closed-form solutions to second order linear non-homogeneous non- constant coefficient ordinary differential equations. We then demonstrate an application of the method to recurrence relations of the second order.   Keywords: Closed-form, Ordinary Differential Equations, Recurrence Relations
      PubDate: 2014-01-24
      Issue No: Vol. 2 (2014)
       
  • Perturbation of n dimensional AQ - mixed type functional equation via
           Banach spaces and Banach algebra : Hyers direct and alternative fixed
           point methods
    • Authors: M. Arunkumar
      Abstract: In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of n dimensional additive quadratic functional equation in Banach spaces using direct and fixed point methods. We also investigate the stability of the above  equation in Banach algebra using direct and fixed point approach.
      PubDate: 2014-01-10
      Issue No: Vol. 2 (2014)
       
  • Solution and intuitionistic fuzzy stability of n- dimensional quadratic
           functional equation: direct and fixed point methods
    • Authors: M. Arunkumar, S. Karthikeyan
      Abstract: In this paper, the authors established the solution in vector space and Intuitionistic Fuzzy stability of n-dimensional quadratic functional equation using direct and fixed point methods.
      PubDate: 2014-01-10
      Issue No: Vol. 2 (2014)
       
  • g*bp-Continuous Multifunction
    • Authors: Alias B. Khalaf, Suzan N. Dawod
      Abstract: In this paper we introduce a new class of multifunction called Upper(lower) g*bp-continuous multifunction, Up-per(lower) almost g*bp-continuous multifunction, Upper(lower) weakly g*bp-continuous multifunction and Up-per(lower) contrag*bp-continuous multifunction in topological spaces,and study some of their basic properties andrelations among them.

      PubDate: 2013-12-07
      Issue No: Vol. 2 (2013)
       
  • Then We Characterize Primes and Composite Numbers Via Divisibility
    • Authors: Ikorong Gilbert, Rizzo Karl-Joseph
      Abstract: In this paper, we show a Theorem which helps us to characterize prime numbers and composite numbers via divisibility; and we use the characterizations of primes and composite numbers to characterize twin primes, Mersenne primes, even perfect numbers, Sophie Germain primes, Fermat primes, Fermat composite numbers and Mersenne composite numbers (we recall that a logic (non recursive) proof of problems posed by twin primes, Mersenne primes, perfect numbers, Sophie Germain primes, Fermat primes, Fermat composite numbers and Mersenne composite numbers, is given in [12]. [[ Prime numbers are well kwown ( see [15] or [19]) and we recall that a composite number is a non prime number. We recall (see [1] or [2] or [3] or [6] or [9] or [10] or [12] or [13] or [14] or [17]) that a {\it{Fermat prime }} is a prime of the form F_{n}=2^{2^{n}}+1, where n is an integer \geq 0; and a {\it{Fermat composite}}  is a non prime number of the form F_{n}=2^{2^{n}}+1, where n is an integer \geq 1; it is known that for every j\in \lbrace 0, 1,2,3,4\rbrace, F_{j} is a Fermat prime,  and it is also known that F_{5} and F_{6} are Fermat composite. We recall (see [11]) that a prime h is called a {\it{Sophie Germain prime}}, if both h and 2h+1 are prime; the first few Sophie Germain primes are 2, 3,5,11,23,29,41, ...; it is easy to check that 233 is a Sophie  Germain prime. A {\it{Mersenne prime }} (see [6] or [10] or [11] or [16] or [19] or [20] or [21]) is a prime of the form M_{m}=2^{m}-1, where m is prime; for example M_{13} and M_{19} are Mersenne prime. A Mersenne composite ( see [7] or [9])  is a non prime number of the form M_{m}=2^{m}-1, where m is prime; it is known that M_{11} and M_{67} are Mersenne composite. We also recall (see [4] or [5] or [7] or [8] or [10] or [11] or [18] or [19] or [20] or [22]) that an integer t is a twin prime, if t is a prime \geq 3 and if t-2 or t+2 is also a prime \geq 3; for example, it is easy to check that (881,883) is a couple of twin primes. Finally, we recall that Pythagoras saw {\it{perfection}} in any integer that equaled the sum of all the other integers that divided evenly into it (see [7] or [9]). The first perfect number is 6. It's evenly divisible by 1, 2, and 3, and it's also the sum of 1, 2, and 3, [note 28, 496 and  33550336 are also  perfect numbers (see [7] or [9])]; and perfect numbers are known for some integers  >33550336 ]].
      PubDate: 2013-12-06
      Issue No: Vol. 2 (2013)
       
 
 
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