In this paper, we use polynomial splines of eleventh degree with three collocation
points to develop a method for computing approximations to the solution and its
derivatives up to ninth order for general linear and nonlinear ninth-order boundary-v
alue
problems (BVPs). The study shows that the spline method with three collocation points
when is applied to these problems is existent and unique. We prove that the proposed
method if applied to ninth-order BVPs is stable and consistent of order eleven, and it
possesses convergence rate greater than six.
Finally, some numerical experiments are presented for illustrating the theoretical
results and by comparing the results of our method with the other methods, we reveal that
the proposed method is better than others.
This research includes a set of mathematical models for simulating the financial
activities. Worked models are determined to approve the form of inflows to the bank and
outflows.
We tried to study different types of banks, and performed some condi
tions to make
sure that the bank is working in stabilized situation. Furthermore, we identified the factors
affecting the achievement of stability. These models allow more flexibility in the
discussion and analysis of banking operations, helping to discern periods approaching the
crisis and draw attention to the overall status of the bank. Analyzing these models gives
additional time to control withdrawal and take the necessary decision at the time.
Cephalometric superimpositions are the most commonly means used to assess
the orthodontic teeth movement – especially- in cases of extraction - with their attendant risks and
difficulty, therefore dental casts were an alternative way for serial ass
essment. So the aim was to evaluate
the stability of the medial end of the third palatal ruga as a landmark in maxilla in extraction cases, and
the possibility of using it in the mandible.
This study was conducted at the laboratories of Food Science Department,
Faculty of Agriculture, Damascus University to assess the indicators
determining the optimum time and final critical temperature required for
forming the meat emulsions.
In this paper, we focus on the importance of conducting the necessary tests either
field or laboratory in order to obtain realistic values for soil hydrodynamic parameters
allowing the best result to simulate the actual situation of any engineering
facility.
The importance of this research highlights in earth dams and dikes which have great
importance to economic, environmental and human. It is necessary to be complete
accuracy when creating a mathematical model to study stability of these structures. From
here comes the need to calculate these parameters rather than extracted from engineering
codes, that we will use them to simulate the effect of long rainfall on the distribution of
water content in the Hweez dam soil and hence its stability. We will build a mathematical
model for dam using PCSiWaPro® depending on transition flow chart. concerning that,
hydraulic conductivity and volumetric water content in the soil are functions of pore water
pressure. These equations with their functions give a smooth transition of the studied
model where the saturated state is considered as a special case of the used equations.
The present study describes a simple stability-indicating reversed-phase HPLC assay
for pentoxifylline in its pharmaceutical dosage forms. Separation of the drug and the
degradation products، under stress conditions was successfully achieved on a C
18 column
utilizing water: MeOH (60:40 v/v)، pumped at a flow rate of 1 ml min-1 with UV detection
at 272 nm. The retention time of pentoxifylline was about 14 min. The method was
satisfactorily validated with respect to linearity، precision، accuracy and selectivity. The
response was linear in the range of 0.6-3.5 μg/ml with R2 0.994. The method was accurate
(recovery 100.1%) and precise (RSD < 2%). Detection and quantification limit were 0.2
μg/ml and 0.4 μg/ml respectively. The suggested method was successfully applied for the
analysis of pentoxifylline in extended release tablets available in Syrian market.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
We present in this article a game of chance (Saint Petersburg Paradox) and
generalize it on a probability space as an example of a previsible (predictable) process,
from which we get a discrete stochastic integration (DSI). Then we define a marting
ale
and present it as a good integrator of a discrete stochastic integration ∫ , which is
called the martingale transform of by such that is a previsible process.
After that we present the most important properties of the DSI, which include that the
DSI is also a martingale , the theorem of stability for it, the definition of the covariation of
two given martingales and the proof that the DSI is centered with a specific given variance.
Finally, we define Doob-decomposition and the quadratic variation and present Itȏformula
as a certain sort of it.
