Mathematics Commons^™

Dialectics And The Dao: On Both, A And Non-A In Neutrosophy And Chinese Philosophy, Feng Liu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces readers to a new approach to dialectical logic: neutrosophy. Specifically it proposes a multi-valued logic in which the statement “both A and Non-A,” historically rejected as logically incoherent, is treated as meaningful. This unity of opposites constitutes both the objective world and the subjective world –a view with deep roots in Buddhism and Daoism, including the I-Ching. This leads in turn to the presentation of a framework for the development of a contradiction oriented learning philosophy inspired by the Later Trigrams of King Wen in the I-Ching. We show that although A and Non-A are logically inconsistent, …

Dynamical Properties Of Forced Shear Layers In An Annular Geometry, Evangelos A. Coutsias, Keith Bergeron, J.P. Lynov, A.H. Nielsen

Branch Mathematics and Statistics Faculty and Staff Publications

Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr-Sommerfeld operator for plane, circular Couette …

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

Smarandache Type Functions Obtained By Duality, Florentin Smarandache, C Dumitrescu, N Varlan, St Zamfir, E Radescu, N Radescu

Branch Mathematics and Statistics Faculty and Staff Publications

we extend the Smarandache function from the set N* of positive integers to the set Q of rationals

Conjectures On Partitions Of Integers As Summations Of Primes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

Pseudospectral Solution Of The Two-Dimensional Navier{Stokes Equations In A Disk, Evangelos A. Coutsias, David J. Torres

Branch Mathematics and Statistics Faculty and Staff Publications

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier-Stokes equations on a disk with no-slip boundary conditions is described. The vorticity stream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier-Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implicit-explicit time marching scheme are solved as banded systems using a postconditioned spectral tau-method. The polar coordinate singularity is handled by expanding fields radially over the entire diameter using a parity modified Chebyshev series and building partial regularity into the vorticity. The no-slip boundary condition is enforced …

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Optimized Preparation Of Quantum States By Conditional Measurements, G. Harel, G. Kurizki, Evangelos A. Coutsias, J. K. Mciver

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce a general strategy for preparation of arbitrary quantum states via optimal control of repeated conditional measurements. The effectiveness of this strategy in generating finite Fock-state superpositions with a high level of confidence from experimentally accessible coherent states is demonstrated for the simple and well known Jaynes-Cummings model dynamics.

The Approximate Functional Formula For The Theta Function And Diophantine Gauss Sums, Evangelos A. Coutsias, N.D. Kazarinoff

Branch Mathematics and Statistics Faculty and Staff Publications

By introducing the discrete curvature of the polygonal line, and by exploiting the similarity of segments of the line, for small w, to Cornu spirals (C-spirals), we prove the precise renormalization formula. This formula, which sharpens Hardy and Littlewood's approximate functional formula for the theta function, generalizes to irrationals, as a Diophantine inequality, the well-known sum formula of Gauss. The geometrical meaning of the relation between the two limits is that the first sum is taken to a point of inflection of the corresponding C-spirals. The second sum replaces whole C-spirals of the first by unit vectors times scale and …

There Is No Speed Barrier In The Universe And One Can Construct Any Speed, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this short paper, as an extension and consequence of Einstein-Podolski-Rosen paradox and Bell’s inequality, one promotes the hypothesis that: There is no speed barrier in the universe and one can construct any speed, even the infinite speed (instantaneous transmission).

Future research: to study the composition of faster-than-light velocities and what happens with the laws of physics at faster-than-light velocities?

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

An Efficient Spectral Method For Ordinary Differential Equations With Rational Function Coefficients, Evangelos A. Coutsias, Thomas Hagstrom, David Torres

Branch Mathematics and Statistics Faculty and Staff Publications

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple 3-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e., matrix representations of multiplication by a function) are banded for …

Mathematical Rebuses, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Acoustic-Wave Nonlinearity In Stimulated Brillouin Scattering, Evangelos A. Coutsias, Bruce S. Masson

Branch Mathematics and Statistics Faculty and Staff Publications

Stimulated Brillouin scattering is investigated here under conditions characterized by high optical pump intensity. Calculations are carried out at 1.3 and 3.8 /jm with pump intensities equal to approximately three times the threshold. Such strong optical forcing leads to significant self-distortion of the density profile in the material wave serving as the optical grating. The method of multiple scales is used to find a uniform asymptotic expansion in the coupling. At the first perturbation level the resonant portion of the problem yields abridged equations for the incident and the scattered waves with frequencies CWaLn d ws = L - 0 …

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Caustics And Virtual Cathodes In Electron Beams, Evangelos A. Coutsias

Branch Mathematics and Statistics Faculty and Staff Publications

A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic non-relativistic one-dimensional electron beam is injected through a conducting grid into a semi-infinite drift space. Attraction from image charges (and, possibly, an adverse externally applied electric field) cause particle reflection and the formation of a caustic where the charge density has an integrable singularity. The steady-state solution of the Vlasov equation describing the flow is known from numerical simulation to be unstable, but analytical demonstration of this instability has proved intractable. Here we derive an integral-delay equation describing …

Non Relativistic Kapitza-Dirac Scattering, Evangelos A. Coutsias, J.K. Mciver

Branch Mathematics and Statistics Faculty and Staff Publications

We use techniques of singular perturbation theory to investigate the scattering of nonrelativistic charged particles by a standing light wave (Kapitza-Dirac scattering). Unlike previous treatments, we give explicit results for the effects of the time-dependent part of the field. For low field intensity or low particle energy, we show that the leading-order effects can be found from an averaged equation, and we compute corrections. For the strong fields that can be produced by modern lasers and/or high particle energies, we show that the time dependence of the potential leads to focusing. Our methods can be applied to other problems with …

Space Charge Limit Instabilities In Electron Beams, Evangelos A. Coutsias, D.J. Sullivan

Branch Mathematics and Statistics Faculty and Staff Publications

The method of characteristics and multiple-scaling perturbation techniques are used to study the space-charge instability of electron beams. It is found that the stable oscillating state (virtual cathode) created when the space-charge limit is exceeded is similar to a collisionless shock wave. The oscillatory solution originates at the bifurcation point of two unstable steady states. Complementary behavior (virtual anode) results when an ion beam exceeds its space-charge limit. The virtual cathode can also exist in the presence of a neutralizing heavy-ion background. The Pierce instability, where the electron and ion charge densities are equal, is a special case of this …

Effects Of Thermal Spread On The Space Charge Limit Of An Electron Beam, Evangelos A. Coutsias

Branch Mathematics and Statistics Faculty and Staff Publications

An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally to the beam temperature T near T = O.

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.

New Relativistic Paradoxes And Open Questions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Following the Special Theory of Relativity, Florentin Smarandache generalized the Lorentz Contraction Factor to an Oblique-Contraction Factor, which gives the contraction factor of the lengths moving at an oblique angle with respect to the motion direction. He also proved that relativistic moving bodies are distorted, and he computed the Angle-Distortion Equations.

He then showed several paradoxes, inconsistencies, contradictions, and anomalies in the Theory of Relativity.

According to the author, not all physical laws are the same in all inertial reference frames, and he gives several counter-examples. He also supports superluminal speeds, and he considers that the …

Problemes Avec Et, Sans Problemes!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Long-Time Behavior Of Ginzburg-Landau Systems Far From Equilibrium, Evangelos A. Coutsias, B. A. Huberman

Branch Mathematics and Statistics Faculty and Staff Publications

Using singular-perturbation techniques, we study the stability of modulated structures generated by driving Ginzburg-Landau systems far from equilibrium. We show that, far from equilibrium, the steady-state behavior is controlled by an effective Lagrangian which possesses the same functional form as the original free energy but with renormalized coefficients. We study both linear and nonlinear sources and determine their influence on the long-term stability of the bifurcating solutions.

A Function In The Number Theory, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The definition of this function is:

S(n) is the smallest integer such that S(n)! is divisible by n.

It had become known as Smarandache Function.