-
A Novel Way to Construct the Fibonacci Sequence and the Uni-Phi-cation of Mathematics and Physics
Issue:
Volume 4, Issue 4, August 2015
Pages:
139-146
Received:
4 May 2015
Accepted:
18 May 2015
Published:
16 June 2015
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 Fibonacci/Lucas-like sequence? The answer is in the negative. This special quality of the golden proportion casts light on the fine structure constant of hydrogen, which is the unique, lightest, and most pervasive element in nature, plus other constants in nature, all of which have a dimensionless number close to the golden proportion (Phi) of the Fibonacci sequence, and provides the basis for the binary computer code as well as a uni-Phi-ed theory of mathematics and physics.
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
Issue:
Volume 4, Issue 4, August 2015
Pages:
147-154
Received:
12 May 2015
Accepted:
23 May 2015
Published:
19 June 2015
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 derivation process. The proof of the theories can be easily achieved by substitution of the designated variables with a set of parameters that matches the same assumptions and conditions in every step of the derivation process.
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:
8 June 2015
Accepted:
18 June 2015
Published:
28 July 2015
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, intuitionistic fuzzy and modified fuzzy metric spaces.
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
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 some results in fuzzy metric spaces, Fuzzy Sets and Systems 1994;64:395-9].
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
Issue:
Volume 4, Issue 4, August 2015
Pages:
164-171
Received:
30 May 2015
Accepted:
12 June 2015
Published:
10 August 2015
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 Banach space for the case, when as initial Ito process was the Wiener process. For an arbitrary Banach space and an arbitrary Ito process it is impossible to find the sequence of corresponding step functions with the desired convergence. We consider the space of generalized random processes, introduce general Ito process there and prove in it the Ito formula. Afterward, from the main Ito process in a Banach space we receive the generalized Ito process in the space of generalized random processes and we get the Ito formula in this space. Then we check decompasibilility of the members of the received equality and as they turn out Banach space valued, we get the Ito formula in an arbitrary Banach space. We implemented this approach when the stochastic integral in the Ito process was taken from a Banach space valued non-anticipating random process by the one dimensional Wiener process. In this paper we consider the case, when the stochastic integral is taken from an operator- valued non-anticipating random process by the Wiener process with values in a Banach space.
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
Issue:
Volume 4, Issue 4, August 2015
Pages:
172-177
Received:
22 July 2015
Accepted:
3 August 2015
Published:
12 August 2015
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
Issue:
Volume 4, Issue 4, August 2015
Pages:
178-188
Received:
20 June 2015
Accepted:
4 August 2015
Published:
12 August 2015
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 coefficients of 104 eta quotients in terms of σ_3 (n),σ_3 (n/2),σ_3 (n/3) and σ_3 (n/6). Here, we will express the even Fourier coefficients of 324 eta quotients in terms of σ_17 (n),σ_17 (n/2),σ_17 (n/3),σ_17 (n/4),σ_17 (n/6) and σ_17 (n/12).
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
