Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

We consider the problem of optimizing the ratio of two convex functions over a closed and convex set in the space of matrices. This problem appears in several applications and can be classified as a double-convex fractional programming problem. In general, the objective function is nonconvex but, nevertheless, the problem has some special features. Taking advantage of these features, a conditional gradient method is proposed and analyzed, which is suitable for matrix problems. The proposed scheme is applied to two different specific problems, including the well-known trace ratio optimization problem which arises in many engineering and data processing applications. Preliminary numerical experiments are presented to illustrate the properties of the proposed scheme.     

Subfields of Nondegenerate Tame Semiramified Division Algebras

We show in this article that in many cases the subfields of a nondegenerate tame semiramified division algebra of prime power degree over a Henselian valued field are inertial field extensions of the center (Theorems 2.5, 2.12, and Proposition 2.16).     

An equilibrium model of how regulative and normative institutions influence micro-economic and organizational behavior

This paper investigates how pre-existing institutions foster economic development through trade. A non-cooperative game-theoretic model is proposed that combines three strands of social science: economics, political science, and sociology. Idealized market participants follow rational decision theory within a reward structure that embodies two types of institutions. Regulative institutions operate on threat of punishment, and normative institutions on perceptions of what is good and right. This composite model allows a more quantitative analysis of the question, raised by Douglas North, of how societies diverge from the efficient state predicted by classical micro-economics. The main finding is that value can be created by different types of institution even when they are imperfect, and the range of minimum–maximum effectiveness varies with the types of economic transactions that are technologically possible. It is hoped that further refinements of the model will yield greater understanding of how the success of societies and organizations can be predicted by a few simple rules.     

On Elliptic System Involving Critical Sobolev Exponent and Weights

This paper is devoted to the existence and nonexistence of positive solutions for a semilinear elliptic system involving critical Sobolev exponent and weights. We study the effect of the behavior of weights near their minima on the existence of solutions for the considered problem.     

Turbulent natural convection flow in a vertical channel with anti-symmetric heating

This paper presents the fluid flow characteristics of natural convection flow in an anti-symmetrically heated parallel-plate vertical channel using the Particle Image Velocimetry (PIV) system. The channel walls were subjected to uniform temperature conditions, with one wall heated above ambient and the opposing wall maintained below ambient temperature. Velocity measurements were conducted at three different sections on the horizontal plane to validate two-dimensionality of the flow and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate that the flow recirculation in the channel exhibits a similar character to that of a closed cavity and the induced flow rate is much lower than the one for a channel with both walls heated. A correlation for the dimensionless flow rate is developed.     

Volumetric,Compressibility and Viscometric Approach to Study the Interactional Behaviour of Sodium Cholate and Sodium Deoxycholate in Aqueous Glycyl Glycine

Viscosity, speed of sound (u), and density (ρ) have been measured in aqueous glycyl glycine solution over a temperature range from 293.15 to 313.15 K with a 5 K interlude to evaluate the volumetric and compressibility properties of bio-surfactants, namely sodium cholate (NaC; 1–20 mmol∙kg⁻¹) and sodium deoxycholate (NaDC; 1–10 mmol∙kg⁻¹). Density and viscosity findings provide information on both solute–solute and solute–solvent types of interactions. Many other metrics, such as apparent molar adiabatic compression (κS,φ), isentropic compressibility (κS), and apparent molar volume (Vφ), have been calculated from speed of sound and density measurements, utilising experimental data. The results show that the zwitterionic end group in the glycyl glycine strongly interacts with NaDC and NaC, promoting its micellization. Since the addition of glycyl glycine causes the bio-surfactant molecules to lose their hydrophobic hydration, the observed concentration-dependent changes in apparent molar volume and apparent molar adiabatic compression are likely attributable to changes in water–water interactions. Viscous relaxation time (τ) increases significantly with a rise in bio-surfactant concentration and decreases with increasing temperature, which may be because of structural relaxation processes resulting from molecular rearrangement. All of the estimated parameters have been analysed for their trends with regard to the different patterns of intermolecular interaction present in an aqueous glycyl glycine solution and bio-surfactant system.     

Etudes electrique et Raman des verres des systemes B2O3M2OM3PO4 (M=Li,Na)

New glasses with alkali carriers have been prepared in the system B₂O₃M₂OM₃PO₄ (M = Li, Na). The variation of the ionic conductivity has been discussed. Raman spectroscopy allows to characterize the behavior of the orthophosphate M₃PO₄ with respect to the boron-oxygen glass matrix.     

Localized Anisotropic Regularity Conditions for the Navier–Stokes Equations

We establish a sufficient regularity condition for local solutions of the Navier–Stokes equations. For a suitable weak solution (u, p) on a domain D we prove that if \(\partial _3 u\) belongs to the space \(L_t^{s_0}L_x^{r_0}(D)\) where \(2/s_0 + 3/r_0 \le 2 \) and \(9/4 \le r_0\le 5/2\), then the solution is Hölder continuous in D.