Pure and Applied Mathematics Journal

Volume 4, Issue 4, August 2015

  • A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics

    David F. Haight

    Issue: Volume 4, Issue 4, August 2015
    Pages: 139-146
    Received: 04 May 2015
    Accepted: 18 May 2015
    Published: 16 June 2015
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    Abstract: When the Fibonacci number sequence is based on the number seven and its multiples, the Fibonacci sequence self-reflexively reappears when differences are calculated between it and this new number-seven-based Fibonacci sequence. The same thing happens with Lucas numbers. Can this same procedure be applied to any two numbers at the beginning of a Fib... Show More
  • Mathematical Methodologies in Physics and Their Applications in Derivation of Velocity and Acceleration Theories

    Edward T. H. Wu

    Issue: Volume 4, Issue 4, August 2015
    Pages: 147-154
    Received: 12 May 2015
    Accepted: 23 May 2015
    Published: 19 June 2015
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    Abstract: The principles to use variables and mathematical methodologies in physics are addressed. A set of refined definitions with designated variables are used to derive the Velocity and Acceleration Theories in Distance Field and Vector Space. Mathematical methodologies such as Linear Algebra and Vector Calculus are used systematically in a step by step ... Show More
  • Fixed Point Theorems for Occasionally Weakly Compatible Maps in Intuitionistic Fuzzy Semi- Metric Space

    Harpreet Kaur, Saurabh Manro

    Issue: Volume 4, Issue 4, August 2015
    Pages: 155-158
    Received: 08 June 2015
    Accepted: 18 June 2015
    Published: 28 July 2015
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    Abstract: In this paper, using the concept of occasionally weakly compatible maps, we prove common fixed point theorems for two maps and pairs of maps in intuitionistic fuzzy semi-metric space. Example is also given to prove the validity of proved results. Our results extends and generalizes various known fixed point theorems in the setting of metric, fuzzy,... Show More
  • Fixed-point Theorems in G-complete Fuzzy Metric Spaces

    Naser Abbasi, Hamid Mottaghi Golshan, Mahmood Shakori

    Issue: Volume 4, Issue 4, August 2015
    Pages: 159-163
    Received: 25 June 2015
    Accepted: 13 July 2015
    Published: 30 July 2015
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    Abstract: In the present paper we introduce generalized contraction mapping in fuzzy metric space and some fixed-point theorems for G-complete fuzzy metric space are proved. Our results generalize and extend many known results in metric spaces to a (non-Archimedean) fuzzy metric space in the in the sense of George and Veeramani [George A, Veeramani P, On som... Show More
  • The Ito Formula for the Ito Processes Driven by the Wiener Processes in a Banach Space

    Badri Mamporia

    Issue: Volume 4, Issue 4, August 2015
    Pages: 164-171
    Received: 30 May 2015
    Accepted: 12 June 2015
    Published: 10 August 2015
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    Abstract: Using traditional methods it is possible to prove the Ito formula in a Hilbert space and some Banach spaces with special geometrical properties. The class of such Banach spaces is very narrow-they are subclass of reflexive Banach spaces. Using the definition of a generalized stochastic integral, early we proved the Ito formula in an arbitrary Banac... Show More
  • Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic

    Maydim A. Malkov

    Issue: Volume 4, Issue 4, August 2015
    Pages: 172-177
    Received: 22 July 2015
    Accepted: 03 August 2015
    Published: 12 August 2015
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    Abstract: Post stated that multi-valued logic has no principle difference with respect to two-valued logic. But Janov and Mucnik stated that multi-valued logic has essentially difference with respect to two-valued logic. We show that Post’s thesis is well but Janov-Mucnik’s statement is wrong
  • Fourier Coefficients of a Class of Eta Quotients of Weight 18 with Level 12

    Baris Kendirli

    Issue: Volume 4, Issue 4, August 2015
    Pages: 178-188
    Received: 20 June 2015
    Accepted: 04 August 2015
    Published: 12 August 2015
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    Abstract: Williams [16] and later Yao, Xia and Jin[15] discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n),σ(n/2),σ(n/3) and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficie... Show More