Home

Florentin Smarandache

  1. The Geometry of Homological Triangles.

    Tue, 04/10/2012 - 15:01 — SomNambul
    Authors: Florentin Smarandache, Ion Patrascu
    Subjects: General Mathematics
    Abstract

    This book is addressed to students, professors and researchers of geometry,
    who will find herein many interesting and original results. The originality of
    the book The Geometry of Homological Triangles consists in using the homology
    of triangles as a "filter" through which remarkable notions and theorems from
    the geometry of the triangle are unitarily passed. Our research is structured
    in seven chapters, the first four are dedicated to the homology of the
    triangles, while the last ones to their applications.

  2. Two Applications of Desargues' Theorem.

    Thu, 01/13/2011 - 16:01 — SomNambul
    Authors: Florentin Smarandache, Ion Patrascu
    Subjects: General Mathematics
    Abstract

    In this article we use the Desargues' theorem and its reciprocal to solve two
    problems.

  3. Two Remarkable Ortho-Homological Triangles.

    Tue, 09/07/2010 - 15:01 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    In a previous paper we have introduced the ortho-homological triangles, which
    are triangles that are orthological and homological simultaneously.

    In this article we call attention to two remarkable ortho-homological
    triangles (the given triangle and its first Brocard's triangle), and using the
    Sondat's theorem relative to orthological triangles, we emphasize on four
    important collinear points in the geometry of the triangle.

  4. Super Special Codes using Super Matrices.

    Thu, 07/01/2010 - 15:01 — SomNambul
    Authors: Florentin Smarandache, W.B.Vasantha Kandasamy, K.Ilanthenral
    Subjects: General Mathematics
    Abstract

    The new classes of super special codes are constructed in this book using the
    specially constructed super special vector spaces. These codes mainly use the
    super matrices. These codes can be realized as a special type of concatenated
    codes. This book has four chapters. In chapter one basic properties of codes
    and super matrices are given. A new type of super special vector space is
    constructed in chapter two of this book. Three new classes of super special
    codes namely, super special row code, super special column code and super
    special codes are introduced in chapter three.

  5. A Theorem about Simultaneous Orthological and Homological Triangles.

    Mon, 04/05/2010 - 15:01 — SomNambul
    Authors: Florentin Smarandache, Ion Patrascu
    Subjects: General Mathematics
    Abstract

    In this paper we prove that if $P_1, P_2$ are isogonal points in the triangle
    $ABC$, and if $A_1B_1C_1$ and $A_2B_2C_2$ are their corresponding pedal
    triangles such that the triangles $ABC$ and $A_1B_1C_1$ are homological (the
    lines $AA_1, BB_1, CC_1$ are concurrent), then the triangles $ABC$ and
    $A_2B_2C_2$ are also homological.

  6. \alpha-Discounting Multi-Criteria Decision Making (\alpha-D MCDM).

    Tue, 02/02/2010 - 16:02 — SomNambul
    Authors: Florentin Smarandache
    Subjects: Artificial Intelligence
    Abstract

    In this paper we introduce a new method called \alpha-Discounting
    Multi-Criteria Decision Making (\alpha-D MCDM), which is an aletrnative and
    extension of Saaty's Analytical Hierarchy Process (AHP). It works for any set
    of preferences that can be transformed into a system of homogeneous linear
    equations. A degree of consistency (and implicitly a degree of inconsistency)
    of a decision-making problem are defined. \alpha-D MCDM is then generalized to
    a set of preferences that can be transformed into a system of linear and/or
    non-linear equations and/or inequalities.

  7. District Level Analysis of Urbanization from Rural-to-Urban Migration in the Rajasthan State.

    Thu, 12/03/2009 - 16:01 — SomNambul
    Authors: Florentin Smarandache, Jayant Singh, Hansraj Yadav
    Subjects: General Mathematics
    Abstract

    Migration has various dimensions; urbanization due to migration is one of
    them. In Rajasthan State, district level analysis of urbanization due to
    migrants shows trend invariably for all districts of the state, though the
    contribution in urbanization by migrants varies from district to district. In
    some districts the share of migrants moving to urban areas is very impressive,
    in others it is not that much high. The migrants' contribution is on the
    raising over the decades.

  8. Partition of a Set Which Contains an Infinite Arithmetic (Respectively Geometric) Progression.

    Tue, 11/24/2009 - 16:01 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    We prove that for any partition of a set which contains an infinite
    arithmetic (respectively geometric) progression into two disjoint subsets, at
    least one of these subsets contains an infinite number of triplets such that
    each triplet is an arithmetic (respectively geometric) progression.

  9. A Method of Solving Certain Nonlinear Diophantine Equations.

    Wed, 10/14/2009 - 11:03 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    In this paper we propose a method of solving a Nonlinear Diophantine Equation
    by converting it into a System of Diophantine Linear Equations.

  10. A Method of Solving Certain Nonlinear Diophantine Equations.

    Wed, 10/14/2009 - 11:03 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    In this paper we propose a method of solving a Nonlinear Diophantine Equation
    by converting it into a System of Diophantine Linear Equations.

  11. Tracking object's type changes with fuzzy based fusion rule.

    Fri, 10/09/2009 - 18:27 — SomNambul
    Authors: Florentin Smarandache, Albena Tchamova, Jean Dezert
    Subjects: Artificial Intelligence
    Abstract

    In this paper the behavior of three combinational rules for
    temporal/sequential attribute data fusion for target type estimation are
    analyzed. The comparative analysis is based on: Dempster's fusion rule proposed
    in Dempster-Shafer Theory; Proportional Conflict Redistribution rule no.

  12. Reservation for Other Backward Classes in Indian Central Government Institutions like IITs, IIMs and AIIMs- A Study of the Role of Media using Fuzzy Super FRM models.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Florentin Smarandache, W.B. Vasantha Kandasamy, K.Kandasamy
    Subjects: General Mathematics
    Abstract

    In this book the authors introduce three new types of fuzzy model called the
    super column Fuzzy Relational Model using super column matrices, super row
    fuzzy relational model using super row matrices and super mixed fuzzy
    relational model using supermatrices. These new models are used to study the
    role of media on 27 percent reservation for the other backward classes in the
    educational institutions run by the Indian central Government. This book has
    four chapters. Chapter one introduces the new notion of super fuzzy relational
    models using supermatrices.

  13. Some Stationary Sequences.

    Mon, 09/07/2009 - 10:33 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    We define a sequence ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is
    a polynomial with real coefficients. We then find out for which values $a$ and
    for which polynomials $P(x)$ this sequence will be constant after a certain
    rank.

  14. Some Stationary Sequences.

    Mon, 09/07/2009 - 10:33 — SomNambul
    Authors: Florentin Smarandache
    Subjects: General Mathematics
    Abstract

    We define a sequence ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is
    a polynomial with real coefficients. We then find out for which values $a$ and
    for which polynomials $P(x)$ this sequence will be constant after a certain
    rank.

Math-arch

Syndicate content