Abstract:
A theoretical model for blood flow in ramifying arteries was introduced and studied numerically (Quarteroni and Veneziani, 2003). A special experimental condition was considered on the artificial boundaries. In this paper, the aim is to analyze the well-posedness of this model, with the focus on the stilted boundary conditions. We use Brouwer’s fixed point theorem to show the existence of a solution to the stationary problem. For the evolutionary version, we use some energy estimates and Galerkin’s method to prove global existence, uniqueness, and stability of a weak solution. 1. Introduction Evolution systems with artificial boundaries are difficult to analyze as a result of the complex dynamics at the boundaries and very few papers have attempted to capture these processes from an analytical point of view. This paper explores this question regarding the flow of blood in a portion of a large artery and addresses the analysis of the Navier-Stokes problem, having provided boundary conditions which can be considered as a generalization of the mean pressure drop problem investigated in [1–3], as they arise in bioengineering applications. Our purpose is to consider both the stationary case and the nonstationary case. In this regard, we will prove the existence of a weak solution for the stationary case based on Brouwer’s fixed point theorem and afterwards, we will establish a well-posedness analysis for the nonstationary case based on a suitable energy estimate that we are going to derive as well as a well-known compactness argument. 1.1. Basic Notations In this subsection, we summarize some notations that will occur throughout the paper. Vectors and tensors are denoted by bold-face letters？ : location of fluid particle, ？ : velocity field of the flow, ？ : pressure, ？ : the pressure gradient, ？ : identity tensor, ？ : symmetric Cauchy stress tensor, ？ : dynamic viscosity, ？ : fluid mass density, ？ : the set of real numbers, ？ : the absolute value of and correspondingly, the norm of ,？ : a bounded domain in , ？ : the boundary of , ？ : the gradient of , ？ : the divergence of ,？ : the Laplacian of . The spaces , , , and and their vector-valued analogues , , , and are defined as usual, the superscript indicating continuous derivatives to a certain order and the subscript zero indicating functions with compact support. The space , the H？lder space , and the Sobolev space and their vector-valued analogues , , and are also defined as usual. In particular, . For functions depending on space and time, for a given space of space-dependent functions, we define (for

Abstract:
We use a double approximation technique to show existence result for a nonlocal and nonautonomous fragmentation dynamics occurring in a moving process. We consider the case where sizes of clusters are discrete and fragmentation rate is time, position, and size dependent. Our system involving transport and nonautonomous fragmentation processes, where in addition, new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of forward propagators associated with evolution semigroup theory and perturbation theory. The full generator is considered as a perturbation of the pure nonautonomous fragmentation operator. We can therefore make use of the truncation technique (McLaughlin et al., 1997), the resolvent approximation (Yosida, 1980), Duhamel formula (John, 1982), and Dyson-Phillips series (Phillips, 1953) to establish the existence of a solution for a discrete nonlocal and nonautonomous fragmentation process in a moving medium, hereby, bringing a contribution that may lead to the proof of uniqueness of strong solutions to this type of transport and nonautonomous fragmentation problem which remains unsolved. 1. Introduction and Useful Definitions Fragmentation models have attracted considerable attention lately as they can be found in many important areas of science and engineering. Examples range from the splitting of phytoplankton clusters, astrophysics, rock crushing, colloidal chemistry, and polymer science to depolymerization. The dynamical behavior of a nonautonomous system of phytoplankton clusters, for example, which are undergoing breakup to produce smaller particles in a moving medium can be derived by balancing loss and gain of clusters of size (with position ) over a short period of time and is given by the following differential equation as presented in [1]: where is the particle mass distribution function with respect to the mass at the position and time , ( is the mass distribution at some fixed time , is the distribution of particle masses and position , spawned by the fragmentation of a particle of mass at time , , and is the evolutionary time-dependent fragmentation rate, that is, the rate at which mass particles at position break up at a time . The velocity of the transport is supposed to be a known quantity, depending on the size of aggregates and their position . The combination of fragmentation equations and transport mechanisms have been successfully utilized to model a wide range of natural processes. Examples in chemical engineering include polymer breakup and solid drugs

Abstract:
We put side by side the methodology of two comparatively new analytical techniques to get to the bottom of the system of nonlinear fractional modified Kawahara equation. The technique is described and exemplified with a numerical example. The dependability of both methods and the lessening in computations give these methods a wider applicability. In addition, the computations implicated are very simple and undemanding. 1. Introduction Within the scope of fractional calculus in the recent decade several scholars have modeled physical and engineering problems. Respective scholar while dealing with real world problems found out that it is worth describing these phenomena with the idea of derivatives with fractional order. While searching the literature, we found out that, this concept of noninteger order derivative not only has been intensively used but also has played an essential role in assorted branches of sciences including but not limited to hydrology, chemistry, image processing, electronics and mechanics; the applicability of this philosophy can be found in [1–10]. In the foregone respective decennial, the research of travelling-wave solutions for nonlinear equations has played a crucial character in the examination of nonlinear physical phenomena. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction, and convection are very important in nonlinear wave equations. Concepts like solitons, peakons, kinks, breathers, cusps, and compactons have now been thoroughly investigated in the scientific literature [11–13]. Various powerful mathematical methods such as the inverse scattering method, bilinear transformation [14], the tanh-sech method [15, 16], extended tanh method [16], Exp-function method [17–19], sine-cosine method [20] Adomian decomposition method [21], Exp-function method [22], homotopy perturbation method [23] have been proposed for obtaining exact and approximate analytical solutions. The purpose of this paper is to examine the approximated solution of the nonlinear fractional modified Kawahara equation, using the relatively new analytical method, the Homotopy decomposition method (HDM), and the Sumudu transform method. The fractional partial differential equations under investigation here are given below as subject to the initial condition The outstanding of this paper is prearranged as follows. In Section 2 we present a succinct history of the fractional derivative order and their properties. We present the basic ideal of the HDM and the STM for solving high order nonlinear fractional partial differential equations. We

Abstract:
A discrete initial-value problem describing multiple fragmentation processes, where the fragmentation rate is size and position dependent and where new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of parameter-dependent operators together with the theory of substochastic semigroups with a parameter. The existence of semigroups is established for each parameter and “glued” together so as to obtain a semigroup to the full space. Under certain conditions on each fragmentation rate, we used Kato’s Theorem in to show the existence of the generator and we provide sufficient conditions for honesty. 1. Introduction The process of fragmentation of clusters occurs in numerous domains of pure and applied sciences, such as the depolymerization, the rock fractures, and break of droplets. The fragmentation rate can be size and position dependent, and new particles resulting from the fragmentation are spatially randomly distributed according to some probability density. When it is supposed that every group of size (one -group) in a system of particles clusters consists of identical fundamental units (monomers), then the mass of every group is simply a multiple positive integer of the mass of the monomer. We focus here on clusters that are discrete; that is, they consist of a finite number of elementary (unbreakable) particles which are assumed to be of unit mass. The state at a given time is the repartition at that time of all aggregates according to their size and their position . The evolution of such particle-mass-position distribution is given by an integrodifferential [1] equation as we will see in this paper. Before going farther let us review what have already been done. Various types of fragmentation equations have been comprehensively analyzed in numerous works (see, e.g., [2–9]). Conservative and nonconservative regimes for fragmentation equations have been thoroughly investigated, and, in particular, the breach of the mass conservation law (called shattering) has been attributed to a phase transition creating a dust of zero-size particles with nonzero mass, which are beyond the model resolution. Shattering can be interpreted from the probabilistic point of view as the explosion in the Markov process describing fragmentation [8, 10] and from an analytic point of view as dishonesty of the semigroup associated with the model [2, 7]. Kinetic-Type Models with Diffusion were investigated in [11] where the author showed that the diffusive part does not affect the breach of the conservation laws. But

Abstract:
The Economic Production Quantity (EPQ) model is commonly used by practitioners in the fields of production and inventory management to assist them in making decision on production lot size. The common assumptions in this model are that all units produced are perfect and shortages are not allowed. But, in real situation the defective items will be produced in each cycle of production and shortages and scrap are possible. These assumptions will underestimate the actual required quantity. Hence, the defective items can not be ignored in the production process. Rework process is necessary to convert those defective into finished goods. This study proposes EPQ model that incorporates both imperfect production quality and falsely not screening out a proportion of defects, thereby passing them on to customers, resulting in defect sales returns. To active this objective a suitable mathematical model is developed and the optimal production lot size which minimizes the total cost is derived. An illustrative example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

Abstract:
The study of Gynaecology over the years has been influenced by the culture and social attitudes of society to the body as a whole and to the genital organs in particular. Variations in these attitudes between different cultures and at different times have influenced the subsequent rate of progress in the study of the vulva and its diseases.

Abstract:
Object: To determine if vulvar melanosis progressed to melanoma over a period of 20 years or more. Methods: In 2010 the hospital records from the Royal Brisbane Hospital Vulvar Clinic between 1976 and 1988 were reviewed and cross checked with the state wide Queensland Centre for Gynaecological Cancer (QCGC) data base to determine if any patient had been lost to follow up and subsequently developed a vulvar melanoma. Data collected were stored and analysed using the computer software Statistical Package for the Social Sciences (SPSS) 11.0. Results: None of the 12 patients developed vulval melanoma in the years up to 2010. Conclusion: In this small group, followed for more than 20 years, melanosis was not a precursor of melanoma. One patient, who attended the Vulvar Clinic but was not included in this melanosis study, was found to have co-existing melanosis well away from her melanoma in situ and malignant melanoma at presentation. It was not possible to determine if these findings represented a progression of the benign to malignant. Biopsy of abnormal hyper pigmented vulvar skin is recommended. Current knowledge suggests that vulvar melanosis is a benign condition but to be on the safe side follow up of all hyper pigmented vulval lesions to detect early malignant change is recommended.

Abstract:
This article is aimed at providing information on variations in the clinical appearance of the vulva. The appearance of the vulva can be altered by reversible or permanent conditions both of which may result in minor or major changes. Reversible conditions include those associated with infections or acute trauma which results in distortion of the vulva. Some permanent changes are caused by life threatening conditions which are present at birth whereas others develop more slowly or as the result of a deliberate act either traditional female surgery or surgery performed by a registered medical practitioner. To the inexperienced practitioner changes from the normal vulvar appearance can be confusing. The aim of this article is to highlight and categorise changes that can affect the appearance of the vulva. Whatever the presentation the importance of obtaining a detailed history and performing an appropriate, sensitive and thorough examination can not be over emphasised.

Since IGY (International Geophysical Year),
through coordinated global observations, ionospheric research has been carried
out by many countries. This effort primarily helped in the design and operation
of HFradio wave communication
systems. The Indian region covers a highly
variable part of the equatorial electrojet and EIA (Equatorial Ionisation
Anomaly) phenomena making its predictability difficult. With the advent of
satellite communication and navigation, the need for accurate ionospheric TEC
(Total Electron Content) models at global and regional scales has been
stressed. The GAGAN (GPS Aided Geo Augmented Navigation) project jointly
undertaken by the Indian Space Research Organisation (ISRO) and the Airport Authority
of India (AAI) aims at effectively utilising the Global Navigational Satellite
System (GNSS) to determine position coordinates accurately for aircraft
precision landing applications. For this purpose the range errors are estimated
by using a ground network of TEC stations spread over Indian region. The near simultaneous data collected from these dual frequency GPS stations can be used to generate the geo-referenced TEC values
for various applications. The author has developed necessary algorithm and associated
computer programmes for a real-time vertical TEC (VTEC) model based on TEC data
collected from the GAGAN ground based network stations. The model has been
tested and sample results presented here show that it adequately provides for
the latitudinal resolution of 1° for the entire longitude span and also for two
longitude blocks (73 - 83 & 83-93°E)
separately. Cubic spline and bilinear interpolation techniques are used for
filling up temporal and spatial data gaps. The model provides tabulated output
of hourly average VTEC data with latitude for ready use, as well as graphical
displays of VTEC maps and contours for monitoring purpose. The real-time model
and its extensions are also being used for detailed scientific studies;
examples of these show small day to day variability of VTEC without any change
in solar activity and indication of the change in the shape of the VTEC diurnal
curve with season. The present model will be used for further studies to derive
the monthly average variation of the diurnal pattern and the relationship
between VTEC peak amplitudes with changes in solar activity. The

One commonly acknowledged challenge in polls or surveys is item non-response, i.e., a significant proportion of respondents conceal their preferences about particular questions. This paper applies the multiple imputation (MI) method to reconstruct the distribution of vote choice in the sample. Vote choice is one of most important dependent variables in political science studies. This paper shows how the MI procedure in general facilitates the work of reconstructing the distribution of a targeted variable. Particularly, it shows how MI can be applied to point-estimation in descriptive statistics. The three packages of R, AmeliaII, MICE, and mi, are employed for this project. The findings, based on a Taiwan Election and Democratization Study (TEDS) samples collected after the 2012 presidential election (N = 1826) suggest the following: First, there is little adjustment done given the MI methods; Second, the three tools based on two algorithms lead to similar results, while Amelia II and MICE perform better. Although the results are not striking, the implications of these findings are worthy of discussion.