Abstract: Calcium [Ca2+] dynamics is studied as a potential form
of neuron excitability that can control many irregular processes like
metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and
increases the synaptic strength and thus triggers the neurotransmitter
release. The modeling and analysis of calcium dynamics in neuron
cell becomes necessary for deeper understanding of the processes
involved. A mathematical model has been developed for cylindrical
shaped neuron cell by incorporating physiological parameters like
buffer, diffusion coefficient, and association rate. Appropriate initial
and boundary conditions have been framed. The closed form solution
has been developed in terms of modified Bessel function. A computer
program has been developed in MATLAB 7.11 for the whole
approach.
Abstract: In this paper, the effect of transmission codes on the
performance of coherent square M-ary quadrature amplitude
modulation (CSMQAM) under hybrid selection/maximal-ratio
combining (H-S/MRC) diversity is analysed. The fading channels are
modeled as frequency non-selective slow independent and identically
distributed Rayleigh fading channels corrupted by additive white
Gaussian noise (AWGN). The results for coded MQAM are
computed numerically for the case of (24,12) extended Golay code
and compared with uncoded MQAM under H-S/MRC diversity by
plotting error probabilities versus average signal to noise ratio (SNR)
for various values L and N in order to examine the improvement in
the performance of the digital communications system as the number
of selected diversity branches is increased. The results for no
diversity, conventional SC and Lth order MRC schemes are also
plotted for comparison. Closed form analytical results derived in this
paper are sufficiently simple and therefore can be computed
numerically without any approximations. The analytical results
presented in this paper are expected to provide useful information
needed for design and analysis of digital communication systems
over wireless fading channels.
Abstract: In a chirp spread spectrum (CSS) system, the overlap
technique is used for increasing bit rate. More overlaps can offer
higher data throughput; however, they may cause more intersymbol
interference (ISI) at the same time, resulting in serious bit error
rate (BER) performance degradation. In this paper, we perform the
BER analysis and derive a closed form BER expression for the
overlap-based CSS system. The derived BER expression includes
the number of overlaps as a parameter, and thus, would be very
useful in determining the number of overlaps for a specified BER.
The numerical results demonstrate that the BER derived in a closed
form closely agrees with the simulated BER.
Abstract: As we know, most differential equations concerning
physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be
so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e.,
We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this
reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be
necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.
Abstract: In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Abstract: Reliability assessment and risk analysis of rotating
machine rotors in various overload and malfunction situations
present challenge to engineers and operators. In this paper a new
analytical method for evaluation of rotor under large deformation is
addressed. Model is presented in general form to include also
composite rotors. Presented simulation procedure is based on
variational work method and has capability to account for geometric
nonlinearity, large displacement, nonlinear support effect and rotor
contacting other machine components. New shape functions are
presented which capable to predict accurate nonlinear profile of
rotor. The closed form solutions for various operating and
malfunction situations are expressed. Analytical simulation results
are discussed
Abstract: Relay based communication has gained considerable importance in the recent years. In this paper we find the end-toend statistics of a two hop non-regenerative relay branch, each hop being Nakagami-m faded. Closed form expressions for the probability density functions of the signal envelope at the output of a selection combiner and a maximal ratio combiner at the destination node are also derived and analytical formulations are verified through computer simulation. These density functions are useful in evaluating the system performance in terms of bit error rate and outage probability.
Abstract: This paper establishes some closed formulas for
Riemann- Liouville impulsive fractional integral calculus and also
for Riemann- Liouville and Caputo impulsive fractional
derivatives.
Abstract: In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.
Abstract: Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.
Abstract: The use of buffer thresholds, blocking and adequate
service strategies are well-known techniques for computer networks
traffic congestion control. This motivates the study of series queues
with blocking, feedback (service under Head of Line (HoL) priority
discipline) and finite capacity buffers with thresholds. In this paper,
the external traffic is modelled using the Poisson process and the
service times have been modelled using the exponential distribution.
We consider a three-station network with two finite buffers, for
which a set of thresholds (tm1 and tm2) is defined. This computer
network behaves as follows. A task, which finishes its service at
station B, gets sent back to station A for re-processing with
probability o. When the number of tasks in the second buffer exceeds
a threshold tm2 and the number of task in the first buffer is less than
tm1, the fed back task is served under HoL priority discipline. In
opposite case, for fed backed tasks, “no two priority services in
succession" procedure (preventing a possible overflow in the first
buffer) is applied. Using an open Markovian queuing schema with
blocking, priority feedback service and thresholds, a closed form
cost-effective analytical solution is obtained. The model of servers
linked in series is very accurate. It is derived directly from a twodimensional
state graph and a set of steady-state equations, followed
by calculations of main measures of effectiveness. Consequently,
efficient expressions of the low computational cost are determined.
Based on numerical experiments and collected results we conclude
that the proposed model with blocking, feedback and thresholds can
provide accurate performance estimates of linked in series networks.
Abstract: In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method.
Abstract: The performance of adaptive beamforming degrades
substantially in the presence of steering vector mismatches. This
degradation is especially severe in the near-field, for the
3-dimensional source location is more difficult to estimate than the
2-dimensional direction of arrival in far-field cases. As a solution, a
novel approach of near-field robust adaptive beamforming (RABF) is
proposed in this paper. It is a natural extension of the traditional
far-field RABF and belongs to the class of diagonal loading
approaches, with the loading level determined based on worst-case
performance optimization. However, different from the methods
solving the optimal loading by iteration, it suggests here a simple
closed-form solution after some approximations, and consequently,
the optimal weight vector can be expressed in a closed form. Besides
simplicity and low computational cost, the proposed approach reveals
how different factors affect the optimal loading as well as the weight
vector. Its excellent performance in the near-field is confirmed via a
number of numerical examples.
Abstract: In this paper, we consider a multi user multiple input
multiple output (MU-MIMO) based cooperative reporting system for
cognitive radio network. In the reporting network, the secondary
users forward the primary user data to the common fusion center
(FC). The FC is equipped with linear equalizers and an energy
detector to make the decision about the spectrum. The primary user
data are considered to be a digital video broadcasting - terrestrial
(DVB-T) signal. The sensing channel and the reporting channel are
assumed to be an additive white Gaussian noise and an independent
identically distributed Raleigh fading respectively. We analyzed the
detection probability of MU-MIMO system with linear equalizers and
arrived at the closed form expression for average detection
probability. Also the system performance is investigated under
various MIMO scenarios through Monte Carlo simulations.
Abstract: In this paper, the problem of estimating the optimal
radio capacity of a single-cell spread spectrum (SS) multiple-inputmultiple-
output (MIMO) system operating in a Rayleigh fading environment
is examined. The optimisation between the radio capacity
and the theoretically achievable average channel capacity (in the
sense of information theory) per user of a MIMO single-cell SS system
operating in a Rayleigh fading environment is presented. Then,
the spectral efficiency is estimated in terms of the achievable average
channel capacity per user, during the operation over a broadcast
time-varying link, and leads to a simple novel-closed form expression
for the optimal radio capacity value based on the maximization
of the achieved spectral efficiency. Numerical results are presented to
illustrate the proposed analysis.
Abstract: In this paper the vibration behaviors of a structure equipped with a tuned liquid column damper (TLCD) under a harmonic type of earthquake loading are studied. However, due to inherent nonlinear liquid damping, it is no doubt that a great deal of computational effort is required to search the optimum parameters of the TLCD, numerically. Therefore by linearization the equation of motion of the single degree of freedom structure equipped with the TLCD, the closed form solutions of the TLCD-structure system are derived. To find the reliability of the analytical method, the results have been compared with other researcher and have good agreement. Further, the effects of optimal design parameters such as length ratio and mass ratio on the performance of the TLCD for controlling the responses of a structure are investigated by using the harmonic type of earthquake excitation. Finally, the Citicorp Center which has a very flexible structure is used as an example to illustrate the design procedure for the TLCD under the earthquake excitation.
Abstract: We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.
Abstract: This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Abstract: The effect of streamwise conduction on the thermal
characteristics of forced convection for nanofluidic flow in
rectangular microchannel heat sinks under isothermal wall has been
investigated. By applying the fin approach, models with and without
streamwise conduction term in the energy equation were developed
for hydrodynamically and thermally fully-developed flow. These two
models were solved to obtain closed form analytical solutions for the
nanofluid and solid wall temperature distributions and the analysis
emphasized details of the variations induced by the streamwise
conduction on the nanofluid heat transport characteristics. The effects
of the Peclet number, nanoparticle volume fraction, thermal
conductivity ratio on the thermal characteristics of forced convection
in microchannel heat sinks are analyzed. Due to the anomalous
increase in the effective thermal conductivity of nanofluid compared
to its base fluid, the effect of streamwise conduction is expected to be
more significant. This study reveals the significance of the effect of
streamwise conduction under certain conditions of which the
streamwise conduction should not be neglected in the forced
convective heat transfer analysis of microchannel heat sinks.
Abstract: This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which
is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced
manipulator has a wide workspace and a high capability to reduce
the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by
a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step
arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.