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    Critical Business Environment Factors for SMEs in the UK Chemical Distribution Industry: A Qualitative Perspective

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    The UK chemical distribution industry is a significant and well-established, yet fragmented and subject to strong consolidation, part of the chemical industry and a major contributor to the UK economy and employment.  However, it remains largely unexplored, with limited research in the factors contributing to SMEs success. This paper, which is part of a larger-scale study, addresses a well-established gap in the UK chemical distribution industry and provides a qualitative perspective of the business environment factors critical to the success of small and medium-sized distributors. This research is based on the opinions of owners and very senior managers (Managing Directors, Directors, CEOs and CFO’s), an approach extensively used by other researchers. A total of 180 SMEs fulfilling the criteria of this study are identified with 118 owners/managers participating, generating a very satisfactory response rate of 65.5%. The paper informs key stakeholders and policy makers with a view to improve strategy formulation and decision-making process in supporting chemical distribution SMEs

    Fractional Power Series Method For Solving The time-fractional biological population model equation

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    In this paper, we present approximate analytical solution of the time-fractional biological population equation using the fractional power series method (FPSM). The fractional derivatives are described in the Caputo sense. Some examples are given and the results are compared with the exact solutions.The results reveal that FPSM is very effective simple and efficient technique to handle fractional differential equations

    Data Analysis and Modelling to assess the effectiveness of planned teaching programme on knowledge regarding depression among care givers of depressive patients

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    In this paper we assess the pre test and post test knowledge regarding depression among care givers of depressive patients in selected hospitals of city. Then we assess the effectiveness of planned teaching programme on depression among care givers of depressive patients. We find out the significant difference between pre test and post test knowledge score regarding depression among care givers of depressive patients.The pre-test the mean of the knowledge score obtained by the subjects was 8.00±3.08. The findings reveal that in pre test 63.33% of caregivers of depressive patients were having average knowledge, 23.33% had were having good, 10% poor and 3.33% had very good level of knowledge score. The minimum score in pre test was 2 and the maximum score was 19.In the post test mean of the knowledge score was 20.61±2.40. It reveals that in post test 25% of caregivers of depressive patients were having very good knowledge, 73.33% were having excellent and only 1.67% were having good level of knowledge score. The minimum score in post test was 14 and the maximum score was 25.The levels of knowledge during the pre test and post test are compared to prove the effectiveness of planned teaching programme. Significance of difference at 5% level  tested with  paired‘t’ test and tabulated ‘t’ value is compared with calculated ‘t’ value. Also the calculated ‘p’ values are compared with acceptable ‘p’ value i.e. 0.05.The care givers do not have knowledge regarding depression in pre test. There was a significant increase in the knowledge of subjects after the introduction of planned teaching. To find the effectiveness of planned teaching‘t’ test was applied and t value was calculated, post test score was significantly higher at 0.05 level than  pre test score. Thus it was concluded that planned teaching on depression was effective.

    Some Numerical Methods for Solving Linear Two-Dimensional Volterra Integral Equation

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    In this paper, the existence and uniqueness of solution of the linear twodimensional Volterra integral equation of the second kind(LT-DVIE) with Continuous Kernel are discussed and proved. Trapezoidal rule and Simpson's rule are used to solve this type of two dimensional Volterra integral equation of the second kind. Numerical examples are considered to illustrate the effectiveness of the proposed methods and the error is estimated

    QUASI-LINEAR EVOLUTION AND ELLIPTIC EQUATIONS

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    In this article we use a new type of nonlinear elliptic operators  that are associated with left side of elliptic equation and studied their properties. We draw up the form, that is associated with non-linear elliptic operator , studying the properties this operator by means of form. We proved some a priori estimates which are theorems about properties of solutions under certain conditions on the function that forming this equation. We proved the existence of solution of quasi-linear evolution equation with singular coefficients in  space by Galerkin method and showed that a given equationhas a solution in the Sobolev space

    Supplement-Duo Modules

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    In this note we consider a generalization of the notion of duo modules namely supplement duo modules. where an R module M is called a supplement duo module if every supplement submodule of M is a fully invariant. Many results about this concept are given. Also we study when the direct sum of supplement duo modules is supplement duo,and relationships between a supplement dou module and other modules

    Discrimination Methods For Solving Recovery and NonRecovery Oil Problems

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    Discriminant analysis is one of the most classical classification procedure used to discriminate and differentiate groups as possible by using one or more attributes. It also assigns observations to one of the pre-defined and separated groups. There are many parametric discriminant statistical methods such Fisher’s FDA, quadratic QDA, and logistic LoDA methods, and non-parametric operation researches methods such as maximize minimum of deviations MMD, and minimize sums of deviation MSD methods to discriminate the difference between groups and classify new observations to the suitable group. Operation researches methods are fixable and do not require any assumptions as statistical methods. This study introduces a comparison between three statistical methods and two linear programming models for solving recover and nonrecover oil problems. Section (1) includes an introduction of the study. Section (2) provides a suitable review of statistical and operation researches methods. Section (3) introduces an application of some discrimination methods for solving recovery and nonrecovery Oil data problems. Section (4) includes the analysis and recommendation of the study. Finally, at the end of the study, there is the references section in section (5)

    How to prove the Riemann Hypothesis

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    I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5 . I assume that any such zero is s =a+ bi .I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent , and verify that a = 0.5 .From equation (60) onward I view (a) as a parameter (a <0.5 ) and arrive at a contradiction. At the end of the proof (from equation (73)) and through the assumption that (a) is a parameter, I verify again that a = 0.

    Mathematical Proofs of the published mathematics cone at -1 Vedic Zero, and Prime numbers distributive calculus at Pythagoras 1:3

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    : This paper of proofs, proves by tables that the obvious calculus for distribution of prime numbers is based on +3 half-line, this a major discovery. These are also major proofs of Fundamentals of non- linear space. The published paper of 65 pages was very large and could not accommodate full formal proofs which were to be offered in a follow up paper .This is the full backup template of the mathematical proof presented in the extensive Paper published as above. The nodal points of the two prime number cords are clearly validated and indeed two prime number cords discovered by the author are the reality of mathematics. These proofs are a complete demonstration of the -1 cone and prime number placement at the half- line of + 3

    Physico-chemical Analysis of Ground Water Quality of Kalavad Taluka of Jamnagar District(Gujarat)

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    Physicochemical analysis of ground water samples were collected from different places of Kalavad taluka of Jamnagar district (India). These Fifteen samples of water samples from different places were analyzed for their physicochemical characteristics. All the samples were collected from the different places. People used water for drinking and irrigation purpose these water samples from fifteen different places of Kalavad, were analyzed for their physicochemical characteristics. Laboratory tests were performed for analysis as Temperature Calcium, Magnesium, hardness, pH; Chloride, Alkalinity, TDS, sulphate, phosphate and nitrate were studied. The usefulness of these parameters in predicting ground water quality characteristics were discussed. Thus an attempt has been made to find the quality of ground water in and around Kalavad suitable for drinking purposes after proper purification

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