The Boundary Theory between Laminar and Turbulent Flows
The basis of this paper is the assumption, that graviton
is a measurable entity of molecular gravitational acceleration and this
is not a hypothetical entity. The adoption of this assumption as an
axiom is tantamount to fully opening the previously locked door to
the boundary theory between laminar and turbulent flows. It leads to
the theorem, that the division of flows of Newtonian (viscous) fluids
into laminar and turbulent is true only, if the fluid is influenced by a
powerful, external force field. The mathematical interpretation of this
theorem, presented in this paper shows, that the boundary between
laminar and turbulent flow can be determined theoretically. This is a
novelty, because thus far the said boundary was determined
empirically only and the reasons for its existence were unknown.
n− Strongly Gorenstein Projective, Injective and Flat Modules
Let R be a ring and n a fixed positive integer, we
investigate the properties of n-strongly Gorenstein projective, injective
and flat modules. Using the homological theory , we prove that
the tensor product of an n-strongly Gorenstein projective (flat) right
R -module and projective (flat) left R-module is also n-strongly
Gorenstein projective (flat). Let R be a coherent ring ,we prove that
the character module of an n -strongly Gorenstein flat left R -module
is an n-strongly Gorenstein injective right R -module . At last, let
R be a commutative ring and S a multiplicatively closed set of R ,
we establish the relation between n -strongly Gorenstein projective
(injective , flat ) R -modules and n-strongly Gorenstein projective
(injective , flat ) S−1R-modules. All conclusions in this paper is
helpful for the research of Gorenstein dimensions in future.
Effect of Oxygen Annealing on the Surface Defects and Photoconductivity of Vertically Aligned ZnO Nanowire Array
Post growth annealing of solution grown ZnO
nanowire array is performed under controlled oxygen ambience. The
role of annealing over surface defects and their consequence on
dark/photo-conductivity and photosensitivity of nanowire array is
investigated. Surface defect properties are explored using various
measurement tools such as contact angle, photoluminescence, Raman
spectroscopy and XPS measurements. The contact angle of the NW
films reduces due to oxygen annealing and nanowire film surface
changes from hydrophobic (96°) to hydrophilic (16°). Raman and
XPS spectroscopy reveal that oxygen annealing improves the crystal
quality of the nanowire films. The defect band emission intensity
(relative to band edge emission, ID/IUV) reduces from 1.3 to 0.2 after
annealing at 600 °C at 10 SCCM flow of oxygen. An order
enhancement in dark conductivity is observed in O2 annealed
samples, while photoconductivity is found to be slightly reduced due
to lower concentration of surface related oxygen defects.
Preconditioned Jacobi Method for Fuzzy Linear Systems
A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.
Strongly ω-Gorenstein Modules
We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained.
Size Dependence of 1D Superconductivity in NbN Nanowires on Suspended Carbon Nanotubes
We report the size dependence of 1D superconductivity in ultrathin (10-130 nm) nanowires produced by coating suspended carbon nanotubes with a superconducting NbN thin film. The resistance-temperature characteristic curves for samples with ≧25 nm wire width show the superconducting transition. On the other hand, for the samples with 10-nm width, the superconducting transition is not exhibited owing to the quantum size effect. The differential resistance vs. current density characteristic curves show some peak, indicating that Josephson junctions are formed in nanowires. The presence of the Josephson junctions is well explained by the measurement of the magnetic field dependence of the critical current. These understanding allow for the further expansion of the potential application of NbN, which is utilized for single photon detectors and so on.
Conjugate Heat Transfer in an Enclosure Containing a Polygon Object
Conjugate natural convection in a differentially heated
square enclosure containing a polygon shaped object is studied numerically in this article. The effect of various polygon types on the
fluid flow and thermal performance of the enclosure is addressed for
different thermal conductivities. The governing equations are modeled
and solved numerically using the built-in finite element method of COMSOL software. It is found that the heat transfer rate remains
stable by varying the polygon types.
Problems and Possible Solutions with the Development of a Computer Model of Quantum Theory
A computer model of Quantum Theory (QT) has been
developed by the author. Major goal of the computer model was
support and demonstration of an as large as possible scope of QT.
This includes simulations for the major QT (Gedanken-) experiments
such as, for example, the famous double-slit experiment.
Besides the anticipated difficulties with (1) transforming exacting
mathematics into a computer program, two further types of problems
showed up, namely (2) areas where QT provides a complete mathematical
formalism, but when it comes to concrete applications the
equations are not solvable at all, or only with extremely high effort;
(3) QT rules which are formulated in natural language and which do
not seem to be translatable to precise mathematical expressions, nor
to a computer program.
The paper lists problems in all three categories and describes also
the possible solutions or circumventions developed for the computer
Piezomechanical Systems for Algae Cell Ultrasonication
Nowadays for algae cell ultrasonication the
longitudinal ultrasonic piezosystems are used. In this paper a
possibility of creating unique ultrasonic piezoelectric system, which
would allow reducing energy losses and concentrating this energy to
a small closed volume are proposed. The current vibrating systems
whose ultrasonic energy is concentrated inside of hollow cylinder in
which water-algae mixture is flowing. Two, three or multiply
ultrasonic composite systems to concentrate total energy into a
hollow cylinder to creating strong algae cell ultrasonication are used.
The experiments and numerical FEM analysis results using diskshaped
transducer and the first biological test results on algae cell
disruption by ultrasonication are presented as well.
Bifurcations and Chaotic Solutions of Two-dimensional Zonal Jet Flow on a Rotating Sphere
We study bifurcation structure of the zonal jet flow the
streamfunction of which is expressed by a single spherical harmonics
on a rotating sphere. In the non-rotating case, we find that a steady
traveling wave solution arises from the zonal jet flow through Hopf
bifurcation. As the Reynolds number increases, several traveling
solutions arise only through the pitchfork bifurcations and at high
Reynolds number the bifurcating solutions become Hopf unstable. In
the rotating case, on the other hand, under the stabilizing effect of
rotation, as the absolute value of rotation rate increases, the number
of the bifurcating solutions arising from the zonal jet flow decreases
monotonically. We also carry out time integration to study unsteady
solutions at high Reynolds number and find that in the non-rotating
case the unsteady solutions are chaotic, while not in the rotating cases
calculated. This result reflects the general tendency that the rotation
stabilizes nonlinear solutions of Navier-Stokes equations.
Soft Connected Spaces and Soft Paracompact Spaces
Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space
is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft closed mapping, soft open mappings, soft connected spaces and soft paracompact spaces. We also redefine the concept of soft points such that it is reasonable in soft topological spaces. Moreover, some basic properties of these concepts are explored.
A New Robust Stability Criterion for Dynamical Neural Networks with Mixed Time Delays
In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.
Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind
A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.
Equatorial Symmetry of Chaotic Solutions in Boussinesq Convection in a Rotating Spherical Shell
We investigate properties of convective solutions of the
Boussinesq thermal convection in a moderately rotating spherical
shell allowing the inner and outer sphere rotation due to the viscous
torque of the fluid. The ratio of the inner and outer radii of the
spheres, the Prandtl number and the Taylor number are fixed to 0.4,
1 and 5002, respectively. The inertial moments of the inner and outer
spheres are fixed to about 0.22 and 100, respectively. The Rayleigh
number is varied from 2.6 × 104 to 3.4 × 104. In this parameter
range, convective solutions transit from equatorially symmetric quasiperiodic
ones to equatorially asymmetric chaotic ones as the Rayleigh
number is increased. The transition route in the system allowing
rotation of both the spheres is different from that in the co-rotating
system, which means the inner and outer spheres rotate with the
same constant angular velocity: the convective solutions transit as
equatorially symmetric quasi-periodic solution → equatorially symmetric
chaotic solution → equatorially asymmetric chaotic solution
in the system allowing both the spheres rotation, while equatorially
symmetric quasi-periodic solution → equatorially asymmetric quasiperiodic
solution → equatorially asymmetric chaotic solution in the
On Fuzzy Weakly-Closed Sets
A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
On Convergence Property of MINRES Method for Solving a Complex Shifted Hermitian Linear System
We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.
A Functional Interpretation of Quantum Theory
In this paper a functional interpretation of quantum
theory (QT) with emphasis on quantum field theory (QFT) is proposed.
Besides the usual statements on relations between a functions
initial state and final state, a functional interpretation also contains
a description of the dynamic evolution of the function. That is, it
describes how things function. The proposed functional interpretation
of QT/QFT has been developed in the context of the author-s work
towards a computer model of QT with the goal of supporting
the largest possible scope of QT concepts. In the course of this
work, the author encountered a number of problems inherent in the
translation of quantum physics into a computer program. He came
to the conclusion that the goal of supporting the major QT concepts
can only be satisfied, if the present model of QT is supplemented
by a "functional interpretation" of QT/QFT. The paper describes a
proposal for that
Bi-linear Complementarity Problem
In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.
Robust Coherent Noise Suppression by Point Estimation of the Cauchy Location Parameter
This paper introduces a new point estimation algorithm, with particular focus on coherent noise suppression, given several measurements of the device under test where it is assumed that 1) the noise is first-order stationery and 2) the device under test is linear and time-invariant. The algorithm exploits the robustness of the Pitman estimator of the Cauchy location parameter through the initial scaling of the test signal by a centred Gaussian variable of predetermined variance. It is illustrated through mathematical derivations and simulation results that the proposed algorithm is more accurate and consistently robust to outliers for different tailed density functions than the conventional methods of sample mean (coherent averaging technique) and sample median search.
Explicit Solutions and Stability of Linear Differential Equations with multiple Delays
We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.
A Special Algorithm to Approximate the Square Root of Positive Integer
The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.
Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces
Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.
Performance Evaluation of Faculties of Islamic Azad University of Zahedan Branch Based-On Two-Component DEA
The aim of this paper is to evaluate the performance of the faculties of Islamic Azad University of Zahedan Branch based on two-component (teaching and research) decision making units (DMUs) in data envelopment analysis (DEA). Nowadays it is obvious that most of the systems as DMUs do not act as a simple inputoutput structure. Instead, if they have been studied more delicately, they include network structure. University is such a network in which different sections i.e. teaching, research, students and office work as a parallel structure. They consume some inputs of university commonly and some others individually. Then, they produce both dependent and independent outputs. These DMUs are called two-component DMUs
with network structure. In this paper, performance of the faculties of Zahedan branch is calculated by using relative efficiency model and also, a formula to compute relative efficiencies teaching and research components based on DEA are offered.