iosr-Jm   Volume-20 ~ Issue-1 ~ Jan. – Feb. 2024

Abstract : In this article, some aspects of subjectivity are studied using the set theory, specifically those related to interpersonal contacts and the difficulties that arise in them. The material that is analysed comes from verbal expressions of the patients who come into consultation at the Psychopathology and Psychoanalysis Association of Seville (APPS), to which the corresponding set operations were applied. As a result, it has been discovered that formalisation enables finding "binary relationships" and "graphs" in the comparisons that occur between different individuals. This allows us to see hidden connections, hardly inferable from the observed data......

Keywords: Intersubjectivity. Set Theory. Binary Relations. Graphs. Feeling of inferiority

[1]. American Psychiatric Association (2013). Manual Diagnóstico Y Estadístico De Los Trastornos Mentales (Dsm-5). Madrid: Panamericana.
[2]. Freud S. (1983). La Interpretación De Los Sueños. En Obras Completas (Vol. 1). Madrid: Biblioteca Nueva.
[3]. Lewin K. (1967). Teoría Del Campo En Ciencia Social. Buenos Aires: Paidós.
[4]. Rojo Sierra M. (1978). Fundamentos Doctrinales Para Una Psicología Médica. Barcelona: Toray.
[5]. García Arroyo Jm. (2003). George Cantor: Genio Y Locura (Parte I). Anales De Psiquiatría; 19(9): 361-366.

Abstract : The charged black hole in string theory is firstly found by Gibbons and Maeda and independently found by Garfinkle,Horowitz, and Strminger. Reissner-Nordstro¨m Anti-de Sitter (RNAdS) black holes are unstable against the charged scalar field perturbations due to the well-known superradiance phenomenon.

[1] F. Rahaman,The General Theory Of Relativity-A Mathematical Approach,(University Printing House,Cambridge Cb2 8bs,United Kingdom).
[2] Ran Li,Stability Of The Charged Black Holes In String Theory Under Charged Massive Scalar Perturbations.
[3] Sayan Saha,Discussion On Some Characteristics Of The Noncommutative Inspired Black Holes In Regular 4d Einstein- Gauss-Bonnet Space-Time.
[4] M.Kalam,F.Rahaman And S.Mondal,Particle Motion Around Monopole.
[5] F.Rahaman,M.Kalam,S.Chakraborty,K.Maity And B.Raychaudhuri,Discussion On A Special Static Spherically Symmetric Perfect Fluid Solution Of Einstein's Equa- Tions.

Abstract : Let 𝑀𝑛 be an n-dimensional differentiable manifold.....

Keywords:- Finsler space, (𝛼,𝛽) metric, Cartan connection, 𝛽-change , conformal change

[1]. Abed, S.H. Conformal Β-Change In Finsler Space Proc. Math, Phys. Soc. Egypt 86 (2008), 79-89 Ar Xiv No : Math D G′/0602404.
[2]. Abed, S.H. :Cartan Connection Associated With A Β-Conformal Change In Finsler Geometry. Tensor, N.S. 70 (2008)
[3]. Hashiguchi, M., Hojo, S. And Matsumoto, M. : On Landsberg Spaces Of Two Dimensions With (Α,Β) - Metric. J Korean Math. Soc. 10(1973), 17-26.
[4]. Hashiguchi, M. : On Conformal Transformation Of Finsler Metric. J. Math. Kyoto University 16 (1976) Pp 25-50.
[5]. Ingarden, R.S. : On The Geometrically Absolute Representation In The Electron Microscope. Trav. Soc. Sci. Lett. Wroclaw, B 45 (1957), 60 Pp.

Abstract : Develop of circle and rhombus of same center and area in squares......

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Abstract : In this paper for a Banach space....

[1]. S. Lang, Introduction To Differentiable Manifolds, Wiley, New York, (1962).
[2]. V. E., Fomin, Differential Geometry Of Banach Manifolds, Kazan Univ., Kazan, U. S. S. R., 1983.
[3]. V. E., Fomin, Methods And Indications To Special Course In Differential Geometry Of Banach Manifolds, Kazan Univ., Kazan, U. S. S. R., 1986.
[4]. J. Diodone, Essentials Of Modern Analysis, M. Mir, 1964.
[5]. H. Borbaki, Differentiable And Analytic Manifolds, M.Mir, 1964.

Abstract :In this paper we try to find the approximation solution of Forced Sine Gordon equation with Positive Integer
forcing term by the Modified Homotopy Perturbation Method, Firstly we formulae the model of our equation by
using the Modified Homotopy Perturbation method so as to construct our Homotopy equations which can be
solved by a normal integration. The summation solutions of these integration equations give us the final
solution of our eqution. Then by use Mathematica programmed we found our graphs solutions with positive and
negative soliton solutions.

Keywords: Forced Sine Gordon equation, modified homotopy Perturbation, Positive force

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Abstract :The introduction of special functions like hypergeometric function, Bessel function, Legendre function, etc. and accepting the new functions beyond the scope of elementary functions like the error function, Fried Conte function, Fresnel function, exponential integral, sine and cosine integrals, logarithmic integral, etc. have ended the study of searching special types of nonelementary integrals. Due to the less research on it has terminated the development of new....

Key-Words: Conjecture, Nonelementary Integral, Strong Liouville Theorem

[1]. Anton, H., Bivens, I, & Davis, S. (2014). Calculus (7th Edition), Wiley Student Edition, 318-360. [2]. Cherry, G. W. (1985). Integration In Finite Terms With Special Functions: The Error Function. Journal Of Symbolic Computation, 1(3), 283-302[3]. Cherry, G. W. (1986). Integration In Finite Terms With Special Functions: The Logarithmic Integral. SIAM Journal On Computing, 15(1), 1-21. [4]. Corliss, G., & Krenz, G. (1989). Indefinite Integration With Validation. ACM Transactions On Mathematical Software (TOMS), 15(4), 375-393. [5]. Hardy, G. H. (2018). The Integration Of Functions Of A Single Variable, Hawk Press, 1-12

Abstract : The introduction of nonelementary integrals as standard functions like error function, exponential integral, sine and cosine integrals, logarithmic integral, etc. has stopped the interest in the study of searching new elementary and nonelementary integrals, which has stopped the development of new properties in integration in context of antiderivatives. Due to this the present generation students are not taught the basic properties of antiderivative like Laplace Theorem, Abel Theorem, Liouville Theorem, Liouville Hardy theorem, etc., which make the integration more beautiful, attractive and informative. So it is the need to introduce these concepts to mathematics learners and teachers to make them aware about these properties of integration........

Key-Words: Conjecture, Elementary Integral, Laplace's Theorem, Mathematica Software.

[1] Anton, H., Bivens, I, & Davis, S. (2014). Calculus (7th Edition), Wiley Student Edition, 318-360. [2] Cherry, G. W. (1985). Integration In Finite Terms With Special Functions: The Error Function. Journal Of Symbolic Computation, 1(3), 283-302. [3] Cherry, G. W. (1986). Integration In Finite Terms With Special Functions: The Logarithmic Integral. SIAM Journal On Computing, 15(1), 1-21. [4] Corliss, G., & Krenz, G. (1989). Indefinite Integration With Validation. ACM Transactions On Mathematical Software (TOMS), 15(4), 375-393. [5] Hardy, G. H. (2018). The Integration Of Functions Of A Single Variable, Hawk Press, 1-12.

Abstract : This work focused on a new semi-analytical method called modified Laplace transform with Homotopy Perturbation Method for solving nonlinear differential equations convolution type. The modified Laplace transform and homotopy perturbation method are used to solve the suggested problems. Some fundamental theorems have been established about the transforms of function convolution type and nth order derivatives. Theorems that had already been established were employed in conjunction with homotopy perturbation method capable of simplifying nonlinear functions of convolution type. The correctness of the suggested method was evaluated by considering some nonlinear differential equations convolution type. The findings were then compared to the referenced solutions, showing a favourable comparison. MLHPM can be implemented to solve nonlinear problems convolution type because it has a straightforward implementation.

Keywords: Modified Laplace Transform, Convolution, Homotopy Perturbation Method.

[1]. Aland p v and Singh p (2022), Solution of Non-Linear Partial Differential Equations Using Laplace Transform Modified Adomian Decomposition Method, Journal of Physics: Conference Series 2267012156.\\
[2]. Alzaidi J. F and Alderremy A. A. (2018), Improvement of the Homotopy Perturbation Method to Nonlinear Problems, International Journal of Physical Science,Vol. 13(4), pp. (43-53).
[3]. Amina K.H.,Fadhel S.F., and Zainor R .Y (2016), Variational Iteration Method (VIM) for solving Partial Integro-differential Equations, Journal of Theoretical and Applied Information Technology vol. 88. No 2, pp (1-8).
[4]. Amit Prakash, Manish Goyal, and Shivangi Gupta (2018), Fractional variational iteration method for solving time-fractional Newell-Whitehead-Segel equation, Journal of Nonlinear Engineering, vol. 8, pp. (164?171).
[5]. Elzaki M. and Mohmod M. (2013), combine Laplace Transform and Variational Iteration Method to Solve Convolution Differential Equationss, the $6^{th}$ International Conference on Information Technology, pp (1-5).

Abstract : The relation 𝑥2 + 𝑦2 = 25 is an implicit solution of the nonlinear differential equation

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Abstract : Along the same line undertaken in a previous work, subjective processes are now studied with the "set theory", in this case, through "order relations". Cantor already pointed out the possible application of the latter to different disciplines. As before, the material corresponds to the speech issued by individuals who reach out for help to the Psychopathology and Psychoanalysis Association of Seville (APPS) which has been faithfully registered during the interviews. The result of the application of the setist notions to the verbal material was revealing how the subject that makes the comparison, distances himself from the rest of the people, feeling "special", which can be seen in how an "outstanding element of a set" is formed ("upper bound" or "lower bound", as the case may be).......

Keywords: Intersubjectivity. Set. Order relation Venn diagrams. Feeling of inferiority. Notable elements of an ordered set.

[1]. American Psychiatric Association (2014). Manual Diagnóstico Y Estadístico De Los Trastornos Mentales. Dsm-5. Barcelona: Panamericana.
[2]. Wetzler S. (1989). Medición De Las Enfermedades Mentales: Evaluación Psicométrica Para Casos Clínicos. Barcelona: Ancora.
[3]. García Arroyo Jm. (2001a). Lo Cuantitativo Y Lo Cualitativo En Psicopatología: Una Aproximación Desde La Subjetividad (Primera Parte). Anales De Psiquiatría; 17(7): 319-324.
[4]. García Arroyo Jm. (2001b). Lo Cuantitativo Y Lo Cualitativo En Psicopatología: Una Aproximación Desde La Subjetividad (Segunda Parte). Anales De Psiquiatría; 17(7): 325-332.