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This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).

Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 10³–10⁵. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (S_ψ and S_θ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Based on larger Nub¯, larger θ^ and optimal S_total values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum S_total) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.

This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of S_ψ (S_ψ,max), S_θ (S_θ,max) and magnitude of S_total vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (10³ ≤ Ra ≤ 10⁵) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

In 2009, the Third Circuit decided Hydrogen Peroxide, which announced a more rigorous standard under Federal Rule of Civil Procedure 23(b)(3) for assessing whether a putative class could establish antitrust injury. Earlier this year, the Supreme Court decided Comcast v. Behrend, a case that carries potentially broad implications for both antitrust cases and Rule 23(b)(3) class actions generally. A review of the case law starting with Hydrogen Peroxide and continuing through Comcast and its progeny reveals the new rigor in antitrust class action decisions and suggests what the future may hold, including the type of arguments that may provide defendants the most likely chance of defeating class certification. After Comcast, rigor under 23(b)(3) can no longer be avoided in assessing all class actions questions, and courts should now apply Daubert fully in the class setting concerning both impact and damages. Courts should also closely evaluate plaintiffs’ proposed methodologies for proving impact to determine if they apply to each class member. Finally, courts will inevitably have to determine how rigorously to scrutinize experts’ damages methodologies and whether Comcast requires or suggests more scrutiny in assessing common evidence for measuring damages.

This chapter offers the first full translation from Russian to English of the Balance of the National Economy of the USSR, 1924–26’s first chapter. Involving 12 authors and composed of 21 chapters, the Balance is a collective work published in June 1926 in Moscow by the Soviet Central Statistical Administration under the scientific supervision of its former director, Pavel Illich Popov (1872–1950). In this first chapter, titled ‘Studying the Balance of the National Economy: An Introduction’, Popov set the theoretical foundations of what might be considered as the first modern national accounting system and paved the way to multisector macroeconometric modelling.

The migration approach to credit risk measurement is based on historic rates of movements of individual loans among the classes of a lender’s risk‐rating or credit‐scoring system. This article applies the migration concept to farm‐level data from Illinois to estimate migration rates for a farmer’s credit score and other performance measures under different time‐averaging approaches. Empirical results suggest greater stability in rating migrations for longer time‐averaging periods (although less stable than bond migrations), and for the credit score criterion versus ROE and repayment capacity.

This study examines credit score migration rates of farm businesses, testing whether migration probabilities differ across business cycles. Results suggest that agricultural credit ratings are more likely to improve during expansions and deteriorate during recessions. The analysis also tests whether agricultural credit ratings depend on the previous period migration trends. The findings show that credit score ratings exhibit trend reversal where upgrades (downgrades) are more likely to be followed by downgrades (upgrades).

In multi-criteria decision-making with interval grey number information, decision makers usually take a risk to rank or choose some very similar alternatives. Additionally, when evaluating only one alternative, decision makers can only obtain a specific value using traditional decision-making methods and may find it hard to cluster the alternatives to the “correct class” because these methods lack predetermined reference points. To overcome this problem, this paper aims to propose a two-stage grey decision-making method.

First, a new type of clustering method for interval grey numbers is designed by proposing a new possibility function for grey numbers. Based on this clustering method, a new grey clustering evaluation model for interval grey numbers is proposed by which decision makers can obtain the grade rating information of each alternative. Then, according to the grey clustering evaluation model, a new two-stage decision-making method is introduced to solve the problem that some alternatives are very similar by designing a grey comprehensive decision coefficient of alternatives.

The authors propose a new grey clustering evaluation model to deal with interval grey numbers. They design a new model to obtain the membership degree for the interval grey numbers and then propose a new grey clustering evaluation model, which can evaluate only one alternative by predefined grey classes. Then, by the grey comprehensive decision coefficient, a two-stage grey evaluation decision-making method is put forward to solve the problem that some alternatives are very close and hard to be distinguished.

A new grey clustering evaluation model is proposed, which can evaluate only one alternative by predefined grey classes. A two-stage grey evaluation decision-making method is given to solve the problem that some alternatives are very close and hard to be distinguished.

During the past decades, journal impact data obtained from the Journal Citation Reports (JCR) have gained relevance in library management, research management and research evaluation. Hence, both information scientists and bibliometricians share the responsibility towards the users of the JCR to analyse the reliability and validity of its measures thoroughly, to indicate pitfalls and to suggest possible improvements. In this article, ageing patterns are examined in ‘formal’ use or impact of all scientific journals processed for the Science Citation Index (SCI) during 1981‐1995. A new classification system of journals in terms of their ageing characteristics is introduced. This system has been applied to as many as 3,098 journals covered by the Science Citation Index. Following an earlier suggestion by Glnzel and Schoepflin, a maturing and a decline phase are distinguished. From an analysis across all subfields it has been concluded that ageing characteristics are primarily specific to the individual journal rather than to the subfield, while the distribution of journals in terms of slowly or rapidly maturing or declining types is specific to the subfield. It is shown that the cited half life (CHL), printed in the JCR, is an inappropriate measure of decline of journal impact. Following earlier work by Line and others, a more adequate parameter of decline is calculated taking into account the size of annual volumes during a range of fifteen years. For 76 per cent of SCI journals the relative difference between this new parameter and the ISI CHL exceeds 5 per cent. The current JCR journal impact factor is proven to be biased towards journals revealing a rapid maturing and decline in impact. Therefore, a longer term impact factor is proposed, as well as a normalised impact statistic, taking into account citation characteristics of the research subfield covered by a journal and the type of documents published in it. When these new measures are combined with the proposed ageing classification system, they provide a significantly improved picture of a journal‘s impact to that obtained from the JCR.

This paper constructs real wage series for nineteenth-century Algeria and Tunisia, and compares them with existing Egyptian and Syrian series. Archival sources are used for price and nominal wage data. Following Allen (2001), nominal wages are deflated with a consumer price index. The series are tested for robustness. Real wages were initially dispersed, but converged to similar levels by the end of the period. There is no evidence of a broad-based improvement in living standards over the period, with real wage series declining in Algeria, and stagnating in Egypt, Tunisia and Syria. The findings paint a less optimistic picture of living standards compared to other measures like GDP per capita and compared to some of the historical literature. Data for the Maghreb are scarce, and more work will need to be done on finding more wage and price observations.