iosr-Jm   Volume-20 ~ Issue-4 ~ Jul. – Aug. 2024

Abstract : The paper proposes a method for proving the Goldbach's binary conjecture, based on the properties of representations of even numbers and the rules of formal logic. The paper proves that an even number, in the representation of which there are no pairs of prime conjugate numbers, is identical to a number that does not exist. The connection between the Goldbach's conjecture and the Legendre hypothesis is considered..

Key words: number theory, prime numbers, Goldbach's binary conjecture. Classification code: 11A41 – Primes; 11D85 – Representation problems

[1] Deshouillers J.–M., Riele H.J.J.Te., Sauoter Y. New Experimental Results Concerning The Goldbach Conjecture. Amsterdam: Stichting Math. Centrum, 1998.
[2] Granville A., Lune J. Van De., Riele H.J.J.Te. Checking The Goldbach Conjecture On A Vector Computer. Amsterdam: Stichting Math. Centrum, 1988.
[3] Jutila M. On The Least Golbach's Number In An Arithmetical Progression With A Prime Difference. Turku, 1968.

Abstract :Mathematical and statistical models are used to model pandemics, providing information about disease dissemination and aiding in policy planning. Logistic growth models are best for predicting pandemic trajectory and infection size, with a peak time arising from control efforts. This study utilized secondary sources to gather and analyze data. Mathematical models have been applied in various fields, including psychology, economics, education, and humanities, to control the spread of epidemics and predict their consequences. The COVID-19 pandemic has led to the use of logistic growth models for predicting outcomes......

Key words: Logistic Model, Mathematical Models, Pandemic, Epidemiology

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Abstract : Numerical change in energy will be explained through new algebra. Introduction: we will try to give a new explanation of numerical change in energy etc. Main body:Suppose static energy of body a is 90 calories. Now.....

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Abstract : Solution of inverse population breakage equation is the process of finding the breakage rate and daughter particle distribution from given population density function. This paper describes the similarity behavior of daughter particle distribution. For different values of cumulative volume fraction 𝐹 (𝑥,𝑡), 𝑙𝑛 𝑡 versus 𝑙𝑛 𝑥 curves collapse into a single curve by translation parallel to the 𝑙𝑛 𝑡 axis. This indicates for similarity behavior

Keywords: Integro-differential equation, Breakage equation, Population density function, Similarity transformation, Kernel, Self-similarity.

[1]. D. Ramkrishna, Drop-Breakage In Agitated Liquid—Liquid Dispersions, Chemical Engineering Science, 29 (1974), 987– 992.
[2]. D. L. Brown, C. E. Glatz, Aggregate Breakage In Protein Precipitation, Chemical Engineering Science, 42 (1987), 1831-1839.
[3]. N. Sathyagal, D. Ramkrishna, G. Narsimhan, Solution Of Inverse Problems In Population Balances-Ii. Particle Break-Up, Computers & Chemical Engineering, 19 (1995), 437–451.
[4]. A. F. Filippov, On The Distribution Of The Sizes Of Particles Which Undergo Splitting, Theory Of Probability & Its Applications, 6 (1961), 275-294.
[5]. K. J. Valentas, O. Bilous, N. R. Amundson, Analysis Of Breakage In Dispersed Phase Systems, Industrial & Engineering Chemistry Fundamentals, 5 (1966), 271-279

Abstract : This work considered a real life problem of agricultural Production. It applied the Fuzzy Goal Programming technique to solve a chance constrained crop production problem. The objectives are considered as bi-criteria crisp functions, while the coefficient of the constraint matrix are considered as triangular fuzzy numbers. The right-hand side parameter of the system constraint is a gumbel random variable and also a right sided fuzzy number. The chance constrained fuzzy programming problem is transformed.....

Keywords:Fuzzy goal programming, triangular fuzzy numbers, chance constrained programming, gumbel random variables, membership function, bi-criteria optimization

[1] Akinsuyi,.Y.(2021):Local Government Intervention! Impact In Small Scale Farming. This Day Live. Www.Thisdaylive.Com, Accessed On The 4th July,2012.
[2] Arbaiy, N. B. (2012). Satisficing -Based Formulation Of Fuzzy Random Multi-Criteria Programming Models In Production Applications. Phd Thesis, Easeda University.
[3] Biswas, A. And Modak, N. (2012). Using Fuzzy Goal Programming Technique To Solve Multi- Objective Chance Constrained Programming Problems In A Fuzzy Environment. International Journal Of Fuzzy System Applications, 2(1):71 – 80
[4] Charnes, A. And Cooper, W. W. (1959). Chance Constrained Programming. Management Science, 6:73 – 79.
[5] Malik, Z. A., Kumar, R., Pathak, G., Roy, H., And Malik, M. A. (2023). Application Of Fuzzy Goal Programming Approach In The Real Life Problem Of Agricultural Sector. Brazzillian Journal Of Operations And Production Management, 20(1):1516 Https://Doi.Org/10.14488/BJOPM.1516.2022

Abstract : In this paper, the author introduces supra gpr-closed graphs and strongly supra gpr-closed graphs. The basic properties of these graphs by utilizing gprμ-open sets, gprμ*- continuous functions, supra gpr-irresolute functions and weakly supra gpr irresolute functions have been discussed.......

Keywords: gprμ-closed sets, gprμ-open sets, gprμ*-continuous functions, supra gpr- irresolute functions, supra gpr- closed graphs, strongly supra gpr- closed graphs

[1] K.K.Dube, J.Y.Lee And O.S.Panwar, A Note On Semi-Closed Graphs, U.I.T. Report,14(2) (1983),379-383.
[2] Jamal M. Mustafa, Hamzeh A. Qoqazeh, Supra D-Sets And Associated Separation Axioms, International Journal Of Pure And Applied Mathematics, 80(5) (2012), 657- 663.
[3] D.S.Jankovic, Beograd, On Functions With Α-Closed Graphs, Glasnik Matematicki, 18(38) (1983), 141-148.
[4] S. Kasahara, Operation - Compact Spaces, Math. Japonica, 24(1) (1979), 97-105.
[5] M. Lellis Thivagar And Nirmala Rebecca Paul, On Topological Closed Graphs In The New Form, Jordan Journal Of Mathematics And Statistics, 5(4) (2012), 251-266.

Abstract : In this paper, the definition of complete twin prime vertex and even edge weighted graph has been forwarded. The proof of existence of infinite twin primes has been discussed with a theorem taking the definition. In addition to this the existence of consecutive even number has been discussed in a theorem with the help of the definition and another theoretical result has been put forwarded to find the sum of all twin prime pairs . Two propositions and some remarks have been mentioned.

Keywords: Complete graph, Partition, Recurrence relation, weighted edge, complete twin prime vertex graph

[1] Kalita, B; Graph And Goldbach Conjecture, 2013, International Journal Of Pure And Applied Mathematics, Vol.82, No.4, 531-546 Doi: Http://Dx.Doi.Org/10.12732/Ijpm.V82i4.3
[2] Kalita, B, Etal; Consecutive Even Number Finding Graph (Cenfg) Related To Goldbach Conjecture, 2013, International Journal Of Pure And Applied Mathematics, Vol.89, No.1 ,55-70,Doi: Http://Dx.Doi.Org/10.12732/Ijpm.V89i1.7
[3] Kalita, B; Proof Of Goldbach Conjecture And Related Conjecture Of Prime,2006, Bulletin Of Pure And Applied Sciences, Vol. 25e(N0.2) 451-459.
[4] Kalita, B; Certain Forms Of Even Numbers And Their Properties, 2009, Global Journal Of Pure And Applied Mathematics, Vol.5 No.1,2009, 53-58
[5] Kalita, B; Etal; Some Properties Of Graphical Partitions,2009, International Journal Of Applied Engineering Research, Vol.4, No.10, 1851-1856.

Abstract : In this paper, some counter-examples are given to show that the results of [1] are not correct. Moreover, the reasons for these mistakes are given and some possible improvements are suggested.

Keywords: Lyapunov-type inequality; nth order equations; mixed nonlineariries

[1]
R.P.Agarwal And A.O¨ Zbekler, Lyapunov Type Inequalities For Nth Order Forced Differential Equations With Mixed Nonlinearities, Communications On Pure And Applied Analysis, 15(6), (2016), 2281-2300.
[2]
R.P.Agarwal And A.O¨ Zbekler, Lyapunov Type Inequalities For Second-Order Differential Equations With Mixed Nonlinearities, Analysis, 36, (2016) 245–252.
[3]
P.Hartmann, Ordinary Differential Equations, Wiley, New York, 1964.
[4]
A.M.Liapunov, Probleme General De La Stabilite Du Mouvement. Ann.Fac.Sci.Univ.Toulouse, 2, (1907) 203–407.
[5]
A.Wintner, On The Nonexistence Of Conjugate Poits, Amer.J.Math., 73, (1951) 368–380.

Abstract : Let G be a simple, finite, connected, undirected, non-trivial graph withes

Keywords: Hilbert numbers, Graceful labeling, Hilbert graceful labeling, Hilbert graceful graph

[1] Bapat, R. B. (2010). Graphs And Matrices (Vol. 27). New York: Springer.
[2] Rosa, A. (1966, July). On Certain Valuations Of The Vertices Of A Graph. In Theory Of Graphs (Internat. Symposium, Rome (Pp. 349-355).
[3] Gallian, J. A. (2022). A Dynamic Survey Of Graph Labeling. Electronic Journal Of Combinatorics, 6(25), 4-623.
[4] Cattell, R. (2007). Graceful Labellings Of Paths. Discrete Mathematics, 307(24), 3161-3176.
[5] Graf, A. (2014). Graceful Labelings Of Pendant Graphs. Rose-Hulman Undergraduate Mathematics Journal, 15(1), 10..

Abstract : This article analyses an 𝑀/𝑀/2 inventory system where production processes, inventory management, and server availability are integrated to optimise performance measures and the total expected costs. In this model, one server takes multiple vacations and the other server remains in the system even when the system is empty. The study compares how a heterogeneous and homogeneous system within a production inventory system affects efficiency and total system cost.s

Keywords: Cost Analysis; Matrix-Analytic Method; Heterogeneous Servers; Homogeneous Server; Multiple Vacations.

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