A new collocation method for solution of mixed linear integro-differential-difference equations

Numerical solution of mixed linear integro-differential-difference equation is presented using Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms mixed linear integro-differential-difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple10.     

On the Bessel Heat Equation Related to the Bessel Diamond Operator

In this article, we study the equation

$\frac{\partial }{\partial t}u(x,t)=c^{2}\Diamond _{B}^{k}u(x,t)$

with the initial condition u(x,0)=f(x) for x∈? _n ⁺ . The operator ? _B ^k is named to be Bessel diamond operator iterated k-times and is defined by

$\Diamond _{B}^{k}=\bigl[(B_{x_{1}}+B_{x_{2}}+\cdots +B_{x_{p}})^{2}-(B_{x_{p+1}}+\cdots +B_{x_{p+q}})^{2}\bigr]^{k},$

where k is a positive integer, p+q=n, \(B_{x_{i}}=\frac{\partial ^{2}}{\partial x_{i}^{2}}+\frac{2v_{i}}{x_{i}}\frac{\partial }{\partial x_{i}},\) 2v _i =2α _i +1,\(\;\alpha _{i}>-\frac{1}{2}\), x _i >0, i=1,2,…,n, and n is the dimension of the ? _n ⁺ , u(x,t) is an unknown function of the form (x,t)=(x ₁,…,x _n ,t)∈? _n ⁺ ×(0,∞), f(x) is a given generalized function and c is a positive constant (see Levitan, Usp. Mat. 6(2(42)):102–143, 1951; Y?ld?r?m, Ph.D. Thesis, 1995; Y?ld?r?m and Sar?kaya, J. Inst. Math. Comput. Sci. 14(3):217–224, 2001; Y?ld?r?m, et al., Proc. Indian Acad. Sci. (Math. Sci.) 114(4):375–387, 2004; Sar?kaya, Ph.D. Thesis, 2007; Sar?kaya and Y?ld?r?m, Nonlinear Anal. 68:430–442, 2008, and Appl. Math. Comput. 189:910–917, 2007). We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel diamond heat kernel. Moreover, such Bessel diamond heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.

     

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing – both dynamic and static – is beneficial and assess the value of the dynamic policy.     

Spacelike helices in Minkowski 4-space $${E_1^4 }$$

In this paper, we give some characterizations for spacelike helices in Minkowski space–time E₁⁴{E_1^4}. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space–time E₁⁴{E_1^4}.     

A collocation method to solve higher order linear complex differential equations in rectangular domains

In this article, a collocation method is developed to find an approximate solution of higher order linear complex differential equations with variable coefficients in rectangular domains. This method is essentially based on the matrix representations of the truncated Taylor series of the expressions in equation and their derivates, which consist of collocation points defined in the given domain. Some numerical examples with initial and boundary conditions are given to show the properties of the method. All results were computed using a program written in scientific WorkPlace v5.5 and Maple v12. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

Experimental and theoretical FT‐IR and FT‐Raman spectroscopic analysis of N1‐methyl‐2‐chloroaniline

In this work, the experimental and theoretical vibrational spectra of N1‐methyl‐2‐chloroaniline (C₇H₈NCl) were studied. FT‐IR and FT‐Raman spectra of the title molecule in the liquid phase were recorded in the region 4000–400 cm^?1 and 3500–50 cm^?1, respectively. The structural and spectroscopic data of the molecule in the ground state were calculated by using density functional method (B3LYP) with the 6‐311++G(d,p) basis set. The vibrational frequencies were calculated and scaled values were compared with experimental FT‐IR and FT‐Raman spectra. The observed and calculated frequencies are found to be in good agreement. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. ¹³C and ¹H NMR chemical shifts results were compared with the experimental values. The optimized geometric parameters (bond lengths and bond angles) were given and are in agreement with the corresponding experimental values of aniline and p‐methyl aniline. Copyright © 2008 John Wiley & Sons, Ltd.     

The Effects of Different Doses of ROCK Inhibitor,Antifreeze Protein III,and Boron Added to Semen Extender on Semen Freezeability of Ankara Bucks

In the presented study, the effects of ROCK inhibitor Y-27632, antifreeze protein III, and boron at two different doses were investigated on the spermatological parameters of Ankara buck semen after freeze–thawing. Ejaculates were collected from bucks using an electroejaculator during the breeding season. The ejaculates that showed appropriate characteristics were pooled and used in the dilution and freezing of semen. The extender groups were formed by adding two different doses of three different additives (ROCK inhibitor Y-27632, 5 and 20 µM; antifreeze protein III, 1 and 4 µg/mL; boron, 0.25 and 1 mM) to the control extender. The semen was diluted with the different extenders at 35–37 °C and loaded into straws. Sperm samples frozen in liquid nitrogen vapors, following equilibration, were stored in liquid nitrogen. It was observed that extender supplementation improved post-thaw motility of Ankara buck semen after freeze–thawing. Differences were significant (p < 0.01) for 5 and 10 µM doses of ROCK inhibitor (71.82% and 74.04 % motility), as well as for 0.25 and 1 mM doses of boron (76.36% and 72.08% motility), compared to the control group (66.15% motility). With respect to the evaluation of acrosomal integrity and mitochondrial activity after freeze–thawing, although supplementation provided protection at all doses, the efficacy was not statistically significant (p > 0.05). It was observed that DNA damage was improved by antifreeze protein III at 1 µg/mL (1.23% ± 0.23%) and by boron at all doses (0.25 mM: 1.83% and 1 mM: 1.18%) compared to the control group (3.37%) (p < 0.01), following the thawing process. In the present study, it was determined that some additives added to the extender provided significant improvements in buck spermatozoa motility and DNA damage after thawing.     

Phloretin,as a Potent Anticancer Compound: From Chemistry to Cellular Interactions

Phloretin is a natural dihydrochalcone found in many fruits and vegetables, especially in apple tree leaves and the Manchurian apricots, exhibiting several therapeutic properties, such as antioxidant, antidiabetic, anti-inflammatory, and antitumor activities. In this review article, the diverse aspects of the anticancer potential of phloretin are addressed, presenting its antiproliferative, proapoptotic, antimetastatic, and antiangiogenic activities in many different preclinical cancer models. The fact that phloretin is a planar lipophilic polyphenol and, thus, a membrane-disrupting Pan-Assay Interference compound (PAIN) compromises the validity of the cell-based anticancer activities. Phloretin significantly reduces membrane dipole potential and, therefore, is expected to be able to activate a number of cellular signaling pathways in a non-specific way. In this way, the effects of this minor flavonoid on Bax and Bcl-2 proteins, caspases and MMPs, cytokines, and inflammatory enzymes are all analyzed in the current review. Moreover, besides the anticancer activities exerted by phloretin alone, its co-effects with conventional anticancer drugs are also under discussion. Therefore, this review presents a thorough overview of the preclinical anticancer potential of phloretin, allowing one to take the next steps in the development of novel drug candidates and move on to clinical trials.     

Tubular PAN/CNC thin film nanocomposite (TFN) pressure retarded osmosis (PRO) membrane: fabrication and preliminary evaluation in desalination process

Cellulose - The pressure retarded osmosis (PRO) process requires high performance, high flux, high rejection, and resistant membranes under harsh conditions. Since conventional phase-inversion...