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THE DRAZIN INVERSES OF THE SUM OF TWO MATRICES AND BLOCK MATRIX
Shakoor, Abdul,Yang, Hu,Ali, Ilyas The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.3
In this paper, we give a formula of $(P+Q)^D$ under the conditions $P^2Q+QPQ=0$ and $P^3Q=0$. Then applying it to give some results of block matrix $M=(^A_C^B_D)$ (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.
The Drazin inverses of the sum of two matrices and block matrix
Abdul Shakoor,Hu Yang,Ilyas Ali 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.3
In this paper, we give a formula of (P +Q)D under the conditionsP2Q+QPQ = 0 and P3Q = 0. Then applying it to give some resultsof block matrix M =(A BC D)(A and D are square matrices) with generalizedSchur complement is zero under some conditions. Finally, numericalexamples are given to illustrate our results.
RETARDED NONLINEAR INTEGRAL INEQUALITIES OF GRONWALL-BELLMAN-PACHPATTE TYPE AND THEIR APPLICATIONS
Abdul Shakoor,Mahvish Samar,Samad Wali,Muzammil Saleem 호남수학회 2023 호남수학학술지 Vol.45 No.1
In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.
Synthesis and characterization of hexagonal ferrite Co2Sr2Fe12O22 with doped polypyrrole composites
Irshad Ali,Abdul Shakoor,M.U. Islam,Muhammad Saeed,Muhammad Naeem Ashiq,M.S. Awan 한국물리학회 2013 Current Applied Physics Vol.13 No.6
Y-type hexagonal ferrite Co2Sr2Fe12O22 was prepared by microemulsion route. A conducting polymer,polypyrrole was chemically synthesized and doped with dodecylbenzenesulphonic acid (PPy$DBSA). FTIR and magnetic properties of Co2Sr2Fe12O22 were investigated and compared with composite made by mixing the Co2Sr2Fe12O22 with this conducting polymer PPyeDBSA by 1:1 molar ratio. Phase analysis was performed by using X-ray diffraction (XRD). The microstructure was examined by scanning electron microscopy (SEM) showing heterogonous distribution of grains. The field dependent magnetic properties of the prepared samples were investigated at room temperature by using vibrating sample magnetometer (VSM). It has been observed that mixing of polymer in ferrite plays a crucial role in enhancing the coercivity, while saturation magnetization (Ms) and remanance were observed to decrease. Due to fine grain size, the density of grain boundaries increases where the domain wall pinning can take place,hence the coercivity of the composite samples increases. Appreciable improved value of coercivity guaranteed the use of these synthesized materials in the recording media, which is ¼1896(Oe) in the present samples. The suitable signal-to-noise ratio in the high density recording media can be achieved due to small particles size of this synthesized composite, which is expected in the present ferriteepolymer composite sample.
뉴캐슬대학, 농업대 식품 농촌개발학과 Muhammad Yousaf & Abdul Shakoor Chaudhtry 한국오리협회 2009 오리마을 Vol.67 No.-
따뜻한 날씨에서 추운 날씨로, 혹은 추운 날씨에서 따뜻한 날씨로 변하는 환절기에는 사람과 동물 모두 계절적인 변화를 견딜 수 있도록 적절한 대책과 배려를 필요로 하기 때문에 가축의 효과적인 유지 관리를 위해서는 각 계절에 따라 생산성의 효율을 증진시킬 수 있는 환경을 제공해야 한다.
Khan, Mohammad Mehedi Hasan,Chaudhry, Abdul Shakoor Asian Australasian Association of Animal Productio 2010 Animal Bioscience Vol.23 No.7
Spices can be used as novel supplements to enhance the utilization of low quality forages (LQF) and reduce nutrient wastage by ruminant animals. However, it is essential to characterize these spices alongside LQF before testing their potential use as supplements in ruminant diets. This study characterized four spices (cinnamon, cumin, clove and turmeric) alongside three forages (rice straw, wheat straw and hay) for their chemical components before evaluating their effect at four different doses (0, 10, 30 and 90 mg/g forage DM) on the in vitro rumen degradability of dry matter (DM) (IVD) and organic matter (OM) (IVOMD) of these forages at various incubation times. It appeared that some spices could provide complementary nutrients which could improve the utilization of LQF where hay had better chemical composition than the other two forages. Cumin contained more crude protein (CP), ether extract and mineral contents whereas turmeric contained more soluble sugars than the other spices. Cinnamon was least acceptable as a ruminant supplement due to its higher condensed tannin and saponin and lower CP and mineral contents. The IVD and IVOMD were highest for hay and lowest for wheat straw with all spices at all incubation times (p<0.001). Due to relatively better nutrient profiles, cumin and turmeric had greater effect on IVD and IVOMD of the forages. In contrast, cinnamon had negative effects on IVD and IVOMD. IVD and IVOMD were greater at 10 mg/g than at other levels of most spices suggesting that using certain amounts of spices can increase forage degradability. However, the choice of a spice will depend upon the forage type being offered to ruminants. Further studies will examine the effect of these spices on fermentation profile, methane production and nitrogenous loss by ruminants.