iosr-Jm   Volume-15 ~ Issue-6 ~ Nov – Dec 2019

Abstract: We investigate the relation between some spin l/2 ferromagnetic models with long range interaction of Statistical Mechanics (in the presence of the Lee-Yang and others theorems on the zeros of the partition functions)
and polynomial truncations of the Riemann ξ function, especially in a high temperature region. We obtain a new possible periodic lower "bound" on the Li-Keiper coefficients valid for all N.

Key Words: Ferromagnetic spin ½ models,Lee-Yang theorem, non trivial zeros, ξ function,Li-Keiper coefficients, Koebe function, periodic function,background Riemann wave, Riemann Hypothesis(RH).

[1]. D.Merlini, L. Rusconi and N.Sala: "I numeri naturali come autovaloridi un modello di oscillatori classici a bassa temperatura",Bollettino della Società Ticinese di Scienze Naturali,87:29-32 (1999) ("Natural numbersaseigenvaluesof a model of classicaloscillatorsatlowtemperature". In this work Mehta Dyson Polynomials were introduced).
[2]. D. Merlini and L.Rusconi : "The Quantum Riemann Wave", Chaos and Complexity Letters,Vol.11,Number 2(2017), 219-238.
[3]. D. Merlini and L. Rusconi: "Small ferromagnetic spin systems and Polynomial truncations of the Riemann ξ function",Chaos and Complexity Letters,Vol.12,Number 2(2018), 102-122.
[4]. D.Merlini,M.Sala and N.Sala : "Quasi Fibonacci approximation to the low tiny fluctuations of the Li-Keiper coefficients: a numericalcomputation",arXiv:1904.07005(math GM) (2019).
[5]. D.Merlini,M.Sala and N.Sala: "Analysis of a Complex approximation to the Li-Keiper coefficients around the K function", arXiv: 1907.01903(math GM)(2019) (See also D. Merlini, M. Sala and N. Sala: "Fluctuation around the Gamma function and a Conjecture", IOSR Journal of Mathematics (IOSR-JM) 15.1(2019), 57-70)..

Abstract: In this paper, the number of cofinite topologies and non-cofinite topologies are determined for ....

Key Words: Topological Space, Cofinite, non-cofinite, Cardinility, Hasse Diagram

[1]. Benoumhani M. The number of topologies on finite set. Journal of interger sequences, vol (2006); (9), article 06.2.6.
[2]. Francis M.O. and Adeniji A.O. On Number of k-Element in Open and Clopen Topological Space with Corresponding Graph for n≤4. Academic Journal of Applied Mathematical Sciences. (2019); 5(9): 130-135.
[3]. Ern´e, M. &Stege, K. Counting finite posets and topologies. Order, (1991); 8(3): 247-265.
[4]. Kolli M. On the cardinality of the T0-topologies on a finite sets. Internatonal journal of combinatories. Article ID (2014). 798074, 7.
[5]. Stanley R. P On the number of open sets of finite topologies, J. Combinatorial Theory (1971); (10): 75-79.

Abstract: This paper looked into the factorization of minimal normal subgroups of innately transitive groups. Some deductions from these theorems are presented. Some results about normalizers of subgroups of characteristically simple groups were proved and some implications of these results examined. It further extended these results to that of the centralizers of subgroups of characteristically simple groups. Some applications of the results obtained are also presented

Key Words: Minimal normal subgroups, finite simple groups, centralizers, normalizers

[1]. Baddeley R. W., Praeger C. E. & Schneider C. (2006). Innately transitive subgroups of wreath products in product action. Trans. Amer. Math. Soc., 358, 1619-1641.
[2]. Baddeley R. W., Praeger C. E. & Schneider C. (2008). Intransitive Cartesian Decomposition preserved by innately transitive permutation groups. Trans. Amer. Math. Soc., 360(2), 743-764.
[3]. Bamberg J. (2008). Permutation Group theory, Retrieved from homepages.vub.ac. be/~pcara/Teaching/PermGrps/PermGroups.pdf. December 2008.
[4]. Praeger C. E. & Schneider C. (2002). Factorizations of characteristically simple groups. J. Algebra, 255(1), 198–220.

Abstract: I. As of august 1, 2002, 100 billion zeros have been shown to satisfy RH. Besides the actual number of zeros, also of interest is their height up the critical line, and the accuracy (number of decimal places) in their value.
II. There is a formula for the number N(T) of zeroes up to a given height T: namely, it is approximately (T/2pi) log (T/2pi)- T/2pi.
III. The harmonic series adds up to infinity, mean given any number "s‟, no matter how large, the sum of the harmonic series eventually exceeds s. No "infinity". The whole of the analysis was rewritten in this kind of language in the middle third of the nineteenth century. Any statement that cannot be so rewritten is not allowed in modern mathematics. You can consider the relation as mapping by their domain and range. Is each relation a function? The answer is not function......

Keywords: RH, Riemann Hypothesis, NYAYSANGAT FOUNDATION

[1]. CNO"7", CN5O7 –A patented formulas based on Riemann Hypothesis. Author – Ekta Singh, Director, NYAYSANGAT FOUNDATION. Published by Amazon.
[2]. Research Paper – Proof of the Yang Mills Theory Exists on R4 and has a mass gap delta > 0, author – Ekta Singh, Director, NYAYSANGAT FOUNDATION, published in International Journal of Professional Studies, IJPS, 2019, Volume No. 7, Jan – Jun. eISSN – 2455-6270; p-ISSN: 2455-7455.
[3]. Research Paper – A New Proposed Elementary Proof that 7 is Pi Exact Value, author Ekta Singh, Director – NYAYSANGAT FOUNDATION. MIJ 2019, VOL. No. 5, Jan – Dec. eISSN 2954 – 924X; p-ISSN: 2454-8103
[4]. GOD is logically exist in words – 2019, published by International Research Publications, New Delhi.
[5]. I am thankful to EXL organization for the fruitful trainings. Trainings are very helpful to solve the equations.

Abstract: Recurrence sequence of bases can be used to construct number systems representations where algorithm of addition can be easily derived from definition of sequence

[1]. Rènyi A. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungary. vol 8, 1957, 477–493
[2]. A. Avizienis. Signed-Digit Numbe Representations for Fast Parallel Arithmetic. IRE Trans. Electronic 1961, 381–400
[3]. Knuth D., An Imaginary Number System, Communications of the ACM, 1960, vol. 3, pp. 245-247
[4]. Ch. Frougny, M. Pavelka, E. Pelantová, and M. Svobodová. On-line algorithms for multiplication and division in real and complex numeration systems, Discrete Mathematics and Theoretical Computer Science, vol. 21 no. 3 (2019)
[5]. Frougny Ch.,Pelantova E., Svobodova M. Minimal Digit Sets for Parallel Addition in Non-Standard Numeration Systems. Journal of Integer Sequences. 2013. Vol. 16, № 13.2.17

Abstract: Continuous implicit linear multistep methods are developed for the solution of initial value problems of first-order ordinary differential equations. The linear multistep methods are derived via interpolation and collocation approach using Laguerre polynomials as basis functions. The discrete form of the continuous methods are evaluated and applied to solve first-order ordinary differential equations.The proposed optimal order methods producedbetter approximations than the Adams-Moulton methods.

Keywords:Linear Multistep Methods, Laguerre Polynomial, Collocation, Interpolation, Optimal Order Scheme.

[1]. Lambert, J. D. (1973). Computational Methods in Ordinary Differential Equations. John Wiley and Sons. New York.
[2]. Awoyemi, D. O., Kayode, J. S. and Adoghe, L. O. (2014). A Four-Point Fully Implicit Method for the Numerical Integration of Third-Order Ordinary Differential Equations. International Journal of Physical Sciences, 9(1): 7-12.
[3]. Alabi, M. O. (2008). A Continuous Formulation of Initial Value Solvers with Chebyshev Basis Function in a Multistep Collocation Technique. Ph.D. Thesis. Department of Mathematics, University of Ilorin. 136pp.
[4]. Ehigie, J. O., Okunuga, S. A., Sofoluwe, A. B. &Akanbi, M. A. (2010). On Generalized Two-Step Continuous Linear Multistep Method of Hybrid Type for the Integration of Second Order ODEs. Archieves of Applied Science and Research, 2(6): 362-372.
[5]. Anake, T. A. (2011). Continuous Implicit Hybrid One-Step Methods for the Solution of Initial Value Problems of General Second-Order Ordinary Differential Equations. Ph.D. Thesis. School of Postgraduate Studies, Covenant University, Ota, Nigeria. 170pp.

Abstract: This article includes an automatic mesh generation scheme foran arbitrary convex domain constituted by straight lines or curves employing lower or higher-order quadrilateral finite elements.First, we develop the general algorithm for h- and p- version meshes, which require the information of sides of the domain and the choice of the order as well as the type of elements.The method also allows one to form the desired fine mesh by providing the number of refinements. Secondly, we develop the MATLAB program based on the algorithm that provides all the valuable and needful outputs of the nodal coordinates, relation between local and global nodes of the elements, and displays the desired meshes. Finally, we substantiate the suitability and efficiency of the scheme through the demonstration of several test cases of mesh generation. We firmly believe that the automatic h- and p- version........

Keywords: Finite element method, Mesh generation, Quadrilateral elements,Convex domain, h- version mesh refinement, p-version mesh refinement

[1]. Karim, M.S.(2000) Integration of some Bivariate Polynomials with Rational Denominators- An Application to Finite Element Method. A PhD Thesis, Dept. of Math., Bangalore University, Bangalore-560001, India.
[2]. https://en.wikipedia.org/wiki/Finite_element_method
[3]. Szabó, B. A. and Mehta, A. K., "p-Convergent Finite Element Approximations in Fracture Mechanics." International Journal for Numerical Methods in Engineering 12, pp. 551-560, 1978
[4]. Dhainaut, M. (1997), A Comparison Between Serendipity and Lagrange Plate Elements in The Finite Element Method. Commun. Numer. Meth. Engng., 13: 343-353. DOI:10.1002/(SICI)1099-0887(199705)13:5<343::AID-CNM60>3.0.CO;2-2
[5]. Bar–Yoseph, P. (1981), A comparison of various finite elements schemes for the solution of the Navier-Stokes equations in rotating flow. International Conference on Finite Elements in Flow Problems, 3rd, Banff, Alberta, Canada, June 10-13, 1980, Proceedings. Volume 1. (A82-17651 06-34) Calgary, Alberta, Canada, University of Calgary, 1981, p. 132-142.