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The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain.

For positive and bounded initial data, the authors study the initial zero-boundary value problem.

The findings of this study showed the complete extinction of a continuous weak solution at a finite time.

The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.

The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

The singular perturbation character of the semiconductor device problem is well known by now. Various results on the structure of solutions (i.e. existence of spatial and temporal layers) have been obtained by means of singular perturbation theory. We use a rescaled form of the equations, which describes the evolution on the fast time scale, and discuss the asymptotic behavior of this system, i.e. its relationship to the initial layer problem, to the corresponding stationary problem and to the reduced problem. We show that the transient semiconductor problem fits in the framework of ‘fast reaction‐slow diffusion’ type equations, which are known from the analysis of chemical reacting systems. We use a multiple time scale expansion to give a new ‘dynamical’ derivation of the reduced problem.

The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip velocity condition.

Similarity transformation is used to reduce the system of partial differential equations into a system of nonlinear ordinary differential equations. The resulting equations are then solved numerically using “bvp4c” function in MATLAB software.

Dual solutions are found for a certain range of the unsteady, suction and stretching/shrinking parameters. Stability analysis is performed, and it is revealed that the first (upper branch) solution is stable and physically realizable, whereas the second (lower branch) solution is unstable.

The results obtained can be used to explain the characteristics and applications of the generalized slip in boundary layer flow. Such condition is applied for particulate fluids such as foams, emulsions, polymer solutions and suspensions. Furthermore, the phenomenon of stretching/shrinking sheet can be found on the manufacturing of polymer sheets, rising and shrinking balloon or moving and shrinking polymer film.

The present numerical results are original and new for the study of unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear Hadamard-type fractional differential equations.

The aim of this paper is to develop a numerical scheme for numerical solutions of Hadamard-type fractional differential equations. The classical Haar wavelets are modified to align them with Hadamard-type operators. Operational matrices are derived and used to convert differential equations to systems of algebraic equations.

The upper bound for error is estimated. With the help of quasilinearization, nonlinear problems are converted to sequences of linear problems and operational matrices for modified Haar wavelets are used to get their numerical solution. Several numerical examples are presented to demonstrate the applicability and validity of the proposed method.

The numerical method is purposed for solving Hadamard-type fractional differential equations.

The purpose of this paper is to discuss some fundamental aspects regarding the anomalies in the passive scalar field advected by forced homogenous and isotropic turbulence, by inspection of the analytical properties of the governing equations and with the aid of direct numerical simulation (DNS) data.

Results from a pseudo‐spectral DNS of a unitary‐Schmidt‐ number passive scalar advected by a low Reynolds number flow field, Re_λ=50 and 70 (based on the Taylor microscale λ) allow for a preliminary assessment of the developed numerical model.

Manipulation of the governing equations for the scalar field (which are monotonic) reveals that the unboundedness of the scalar gradient magnitude is not ruled out by the mathematical properties of the correspondent conservation equation. Classic intermittency effects in the passive scalar field have been reproduced, such as non‐Gaussian behavior of the passive scalar statistics, loss of local isotropy, and multi‐fractal scaling of scalar structure functions. Moreover, Taylor and Richardson theories are, surprisingly, not confirmed only in the dissipation range (small‐scales anomalies).

The authors suggest that the origin of intermittency (qualitatively pictured here as violent burst in spatial gradient quantities) should be sought in the loss of monotonicity of the evolution equation of the scalar gradient.

A collection of essays by a social economist seeking to balance economics as a science of means with the values deemed necessary to man′s finding the good life and society enduring as a civilized instrumentality. Looks for authority to great men of the past and to today′s moral philosopher: man is an ethical animal. The 13 essays are: 1. Evolutionary Economics: The End of It All? which challenges the view that Darwinism destroyed belief in a universe of purpose and design; 2. Schmoller′s Political Economy: Its Psychic, Moral and Legal Foundations, which centres on the belief that time‐honoured ethical values prevail in an economy formed by ties of common sentiment, ideas, customs and laws; 3. Adam Smith by Gustav von Schmoller – Schmoller rejects Smith′s natural law and sees him as simply spreading the message of Calvinism; 4. Pierre‐Joseph Proudhon, Socialist – Karl Marx, Communist: A Comparison; 5. Marxism and the Instauration of Man, which raises the question for Marx: is the flowering of the new man in Communist society the ultimate end to the dialectical movement of history?; 6. Ethical Progress and Economic Growth in Western Civilization; 7. Ethical Principles in American Society: An Appraisal; 8. The Ugent Need for a Consensus on Moral Values, which focuses on the real dangers inherent in there being no consensus on moral values; 9. Human Resources and the Good Society – man is not to be treated as an economic resource; man′s moral and material wellbeing is the goal; 10. The Social Economist on the Modern Dilemma: Ethical Dwarfs and Nuclear Giants, which argues that it is imperative to distinguish good from evil and to act accordingly: existentialism, situation ethics and evolutionary ethics savour of nihilism; 11. Ethical Principles: The Economist′s Quandary, which is the difficulty of balancing the claims of disinterested science and of the urge to better the human condition; 12. The Role of Government in the Advancement of Cultural Values, which discusses censorship and the funding of art against the background of the US Helms Amendment; 13. Man at the Crossroads draws earlier themes together; the author makes the case for rejecting determinism and the “operant conditioning” of the Skinner school in favour of the moral progress of autonomous man through adherence to traditional ethical values.

For decision‐makers, the cognitive limit is one of the most critical factors which determine the quality of decisions, when they do not have enough information about their decision environment, and when they must strike a balance between conflicting objectives within a time limit. In such a situation, their decision‐making is often characterized by satisficing behaviors with multiple objectives under uncertainty. This paper aims to formulate a multiple‐objective satisficing problem and to study its fundamental properties, such as (1) existence of collectively satisficing solutions, (2) relationship among collectively satisficing solutions, Pareto satisficing solutions, weak Pareto satisficing solutions and max‐min solutions, and (3) characterization of Pareto satisficing solutions and of weak Pareto satisficing solutions.

In this paper, the authors give a new version of the sub-super solution method and prove the existence of positive solution for a (p, q)-Laplacian system under weak assumptions than usually made in such systems. In particular, nonlinearities need not be monotone or positive.

The authors prove that the sub-super solution method can be proved by the Shcauder fixed-point theorem and use the method to prove the existence of a positive solution in elliptic systems, which appear in some problems of population dynamics.

The results complement and generalize some results already published for similar problems.

The result is completely new and does not appear elsewhere and will be a reference for this line of research.