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In this paper we propose a classification scheme to isolate truly benign tumors from those that initially start off as benign but subsequently show metastases. A non-parametric artificial neural network methodology has been chosen because of the analytical difficulties associated with extraction of closed-form stochastic-likelihood parameters given the extremely complicated and possibly non-linear behavior of the state variables., Comment: 14 pages, 2 tables

In this paper we have devised an alternative methodological approach for quantifying utility in terms of expected information content of the decision-maker's choice set. We have proposed an extension to the concept of utility by incorporating extrinsic utility; which we have defined as the utility derived from the element of choice afforded to the decision-maker by the availability of an object within his or her object set. We have subsequently applied this extended utility concept to the case of investor utility derived from a structured, financial product - an custom-made investment portfolio incorporating an endogenous capital-guarantee through inclusion of cash as a risk-free asset, based on the Black-Scholes derivative-pricing formulation., Comment: 18 pages, 3 tables

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study. It does a survey on Chinese philosophy. The paper aims to solve the chaos of logic and exhibit the potential power of neutrosophy: a new branch of scientific philosophy., Comment: 10 pages, 6 figure. "Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics", Florentin Smarandache editor, Xiquan, Phoenix, ISBN: 1-931233-55-1, 147 p., 2002

In this paper we take a look at a simple portfolio insurance strategy using a protective put and computationally derive the investor's governing utility structures underlying such a strategy under alternative market scenarios. Investor utility is deemed to increase with an increase in the excess equity generated by the portfolio insurance strategy over a simple investment strategy without any insurance. Three alternative market scenarios (probability spaces) have been explored -- 'Down', 'Neutral' and 'Up', categorized according to whether the price of the underlying security is most likely to go down, stay unchanged or go up. The methodology used is computational, primarily based on simulation and numerical extrapolation. The Arrow-Pratt measure of risk aversion has been used to determine how the investors react towards risk under the different scenarios., Comment: 24 pages, 28 tables, 3 graphs

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors., Comment: 16 pages, 3 tables

Each individual investor is different, with different financial goals, different levels of risk tolerance and different personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It's really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook - essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about two-dozen questions that each has to be answered with values from 1 to 5. The questions range from personal background (age, marital state, number of children, job type, education type, etc.) to what the customer expects from an investment (capital protection, tax shelter, liquid assets, etc.). A fuzzy logic system has been designed for the evaluation of the answers to the above questions. We have investigated the notion of fuzziness with respect to funds allocation., Comment: 21 pages

In this paper we have suggested two classes of estimators for population median M_Y of the study character Y using information on two auxiliary characters X and Z in double sampling. It has been shown that the suggested classes of estimators are more efficient than the one suggested by Singh et al (2001). Estimators based on estimated optimum values have been also considered with their properties. The optimum values of the first phase and second phase sample sizes are also obtained for the fixed cost of survey., Comment: 21 pages, 3 tables

This paper is speculated to propose a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties., Comment: 20 pages, 2 tables, 1 figure

The paper presents a fresh new start on the neutrality of neutrosophy in that "both A and Non-A" as an alternative to describe Neuter-A in that we conceptualize things in both intentional and unintentional background. This unity of opposites constitutes both objective world and subjective world. The whole induction of such argument is based on the intensive study on Buddhism and Daoism including I-ching. In addition, a framework of contradiction oriented learning philosophy inspired from the Later Trigrams of King Wen in I-ching is meanwhile presented. It is shown that although A and Non-A are logically inconsistent, but they are philosophically consistent in the sense that Non-A can be the unintentionally instead of negation that leads to confusion. It is also shown that Buddhism and Daoism play an important role in neutrosophy, and should be extended in the way of neutrosophy to all sciences according to the original intention of neutrosophy., Comment: 7 pages, 2 figures. Presented to the First International Conference on Neutrosophy, Neutrosophic Logic, Set, and Probability, University of New Mexico, Gallup, December 1-3, 2001. To appear in the Proceedings of the Conference, 2002

In this book one makes an introduction to non-standard analysis in the first part, needed to the next four chapters in order to study the neutrosophics: 1. Neutrosophy - a new branch of philosophy. 2. Neutrosophic Logic - a unifying field in logics. 3. Neutrosophic Set - a unifying field in sets. 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics., Comment: 157 pages, many figures. First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics, December 1-3, 2001, University of New Mexico. Conference's web site is hosted by The York University, Toronto, at http://at.yorku.ca/cgi-bin/amca/cagu-01

A Generalized Numeration Base is defined in this paper, and then particular cases are presented, such as Prime Base, Square Base, m-Power Base, Factorial Base, and operations in these bases. These bases are important for partitions of integers into primes, squares, cubes, generally into m-powers, also into factorials, and into any strictly increasing sequence., Comment: 6 pages

In this paper a small survey is presented on eighteen new functions and four new sequences, such as: Inferior/Superior f-Part, Fractional f-Part, Complementary function with respect with another function, S-Multiplicative, Primitive Function, Double Factorial Function, S-Prime and S-Coprime Functions, Smallest Power Function., Comment: 20 pages

In this paper a small survey is presented on fourteen sequences, such as: G Add-on Sequences, Sieve Sequences, Digital Sequences, Non-Arithmetic Progressions, recreational sequences (Lucky Method/Operation/Algorithm/Differentiation/Integration etc.), General Periodical Sequences, and numerical functions., Comment: 14 pages. Many sequences were analyzed by C. Dumitrescu, V. Seleacu, H. Ibstedt, F. Luca, Y. Chebrakov, V. Shmagin, I. Balacenoiu, C. Rocsoreanu, L. Tutescu, etc. to the First International Conference on Smarandache type Notions in Number Theory, University of Craiova, 21-24 August 1997

One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems., Comment: 16 pages. Tables of numbers. Presented to the Pedagogical High School Student Conference in Craiova, 1969

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and geometric progressions are exposed., Comment: 38 pages, Published in "Only Problems, Not Solutions!", by Florentin Smarandache, Xiquan Publ. Hse., Phoeix, 1991

In this paper 101 new integer sequences, sub-sequences, and sequences of sequences, together with related unsolved problems and conjectures, are presented. Also, definitions, examples, solved or open questions, and references for each sequence are given., Comment: 42 pages, many tables of numbers. Partially published in "Only Problems, Not Solutions!", by Florentin Smarandache, Xiquan Publ. Hse., Phoenix, 1991

The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to Diophantine linear equations with $n$ unknowns and then to Diophantine linear systems. The proprieties of the general integer solution are determined (both for a Diophantine linear equation and for a Diophantine linear system). Seven original integer algorithms (two for Diophantine linear equations, and five for Diophantine linear systems) are exposed. The algorithms are strictly proved and an example for each of them is given. These algorithms can be easily implemented on the computer., Comment: 57 pages. Partially included in author's M. Sc. Thesis, University of Craiova, Department of Mathematics and Computer Science, 1979. Partially published in Bullet. Univ. Brasov, Series C, Vol. XXIV, 37-39, 1982, under the title: "General Integer Solution Properties for Linear Equations"

Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have more an educational interest, because make the students think different! For each "solution" a funny logic is invented in order to give the problem a sense., Comment: 6 pages. Part of a project with UNM-G students. Partially publisehd in "Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry", edited by M. L. Perez, 86 p., Xiquan Publishing House, Phoenix, 2000

Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes and tautologies one grammatically adjusts the sentences., Comment: 12 pages

74 new integer sequences are introduced in number theory, and for each of them is given a characterization, followed by open problems. each one a general question: how many primes each sequence has., Comment: 84 pages, may tables of numbers. Presented to the Pedagogical High School Student Conference in Craiova, 1972. "Collected Papers", Vol. II, book by Florentin Smarandache, University of Kishinev Press, Kishinev, 200 p., 1997

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into as-heterogeneous-as-possible other fields., Comment: 23 pages, 1 figure. Presented to the Department of Mathematics and Computer Sciences, Bloomsburg University, Pennsylvania, on 13 November 1995.

New notions are introduced in algebra in order to better study the congruences in number theory. For example, the makes an important such contribution., Comment: 4 pages, 1 table

In this article one investigates Rugina's Orientation Table and one gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's Orientation Table in systems which are s% stable and 100-s% unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. The Classical Logic and Modern Logic are united in Rugina's Integrated Logic, and then generalized in the Neutrosophic Logic., Comment: 30 pages, 1 figure

In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schr"dinger's Cat Theory, and the state of bosons which do not obey Pauli's Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from "neutrosophy"., Comment: 11 pages, no figures. Presented the "Amiral Vasile Urseanu" National Observatory in Bucharest, 20 May 2000. In "Collected Papers", Vol. III, book by Florentin Smarandache, Abaddaba, Oradea, 2000