Optimal investment strategies with a reallocation constraint

We study a Merton type optimization problem under a reallocation constraint. Under this restriction, the stock holdings can not be liquidated faster than a certain rate. This is a common restriction in certain type of investment firms. Our main objective is to study the large time optimal growth rate of the expected value of the utility from wealth. We also consider a discounted infinite horizon problem as a step towards understanding the first problem. A numerical study is done by solving the dynamic programming equations. Under the assumption of a power utility function, an appropriate dimension reduction argument is used to reduce the original problem to a two dimensional one in a bounded domain with convenient boundary conditions. Computation of the optimal growth rate introduces additional numerical difficulties as the straightforward approach is unstable. In this direction, new analytical results characterizing the growth rate as the limit of a sequence of finite horizon problems with continuously derived utility are proved.     

Kasner Cosmological Models with Two-Fluid Source in General Relativity

In this paper we present Bianchi type-I metric of the Kasner form describing two-fluid source of the universe in general relativity. In Kasner cosmological models one fluid is a radiation field modeling the cosmic microwave background, while the other is a matter field, modeling material content of the universe. The radiation and matter content of the universe are in interactive phase. We have also presented anisotropic, homogeneous nature of Kasner cosmological models with two-fluid. The behavior of fluid parameters and kinematical parameters of the models are also discussed.     

On a Model of Associative Memory with Huge Storage Capacity

In Krotov et al. (in: Lee (eds) Advances in Neural Information Processing Systems, Curran Associates, Inc., Red Hook, 2016) Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the ”limit” as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.     

Pattern Hit-and-Run for sampling efficiently on polytopes

Pattern Hit-and-Run (PHR) is a Markov chain Monte Carlo sampler for a target distribution that was originally designed for general sets embedded in a box. A specific set of interest to many applications is a polytope intersected with discrete or mixed continuous/discrete lattices. PHR requires an acceptance/rejection mechanism along a bidirectional walk to guarantee feasibility. We remove this inefficiency by utilizing the linearity of the constraints defining the polytope, so each iteration of PHR can be efficiently implemented even though the variables are allowed to be integer valued. Moreover, PHR converges to a uniform distribution in polynomial time for a class of discrete polytopes.     

Stochastic control for a class of random evolution models

We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).     

Role of diet and trace elements in lithogenesis of renal calculi

Twenty eight stones were characterized for chemical composition and structure. The concentrations of trace elements were determined using INAA while EDXRF was used for determining the calcium contents of the stones. Twenty stones were found to be mainly composed of calcium, six were mixed type and the remaining two were of uric acid type. The concentrations of trace elements namely Zn, Sr, Fe and Cr were lower in uric acid stones as compared to calcium based stones. Diet analysis of 310 patients who were treated for renal stones showed a diet rich in calcium and oxalate and decreased water consumption.

     

Synthesis and antifungal evaluation of 1-aryl-2-dimethyl- aminomethyl-2-propen-1-one hydrochlorides

The development of resistance to current antifungal therapeutics drives the search for new effective agents. The fact that several acetophenone-derived Mannich bases had shown remarkable antifungal activities in our previous studies led us to design and synthesize some acetophenone-derived Mannich bases, 1-8 and 2-acetylthiophene-derived Mannich base 9, 1-aryl-2-dimethylaminomethyl-2-propen-1-one hydrochloride, to evaluate their antifungal activities. The designed chemical structures have α,β-unsaturated ketone moieties, which are responsible for the bioactivities of the Mannich bases. The aryl part was C?H?(1); 4-CH?C?H? (2); 4-CH?OC?H? (3); 4-ClC?H? (4); 4-FC?H? (5); 4-BrC?H? (6); 4-HOC?H? (7); 4-NO?C?H? (8); and C?H?S(2-yl) (9). In this study the designed compounds were synthesized by the conventional heating method and also by the microwave irradiation method to compare these methods in terms of reaction times and yields to find an optimum synthetic method, which can be applied for the synthesis of Mannich bases in further studies. Since there are limited number of studies reporting the synthesis of Mannich bases by microwave irradiation, this study may also contribute to the general literature on Mannich bases. Compound 7 was reported for the first time. Antifungal activities of all compounds and synthesis of the compounds by microwave irradiation were also reported for the first time by this study. Fungi (15 species) were used for antifungal activity test. Amphotericin B was tested as an antifungal reference compound. In conclusion, compounds 1-6, and 9, which had more potent (2-16 times) antifungal activity than the reference compound amphotericin B against some fungi, can be model compounds for further studies to develop new antifungal agents. In addition, microwave irradiation can be considered to reduce reaction period, while the conventional method can still be considered to obtain compounds with higher reaction yields in the synthesis of new Mannich bases.     

Reversibility of Rings with Respect to the Jacobson Radical

Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reversible if for any a, \(b \in R\), \(ab = 0\) implies \(ba \in J(R)\). In this paper, we give some properties of J-reversible rings. We prove that some results of reversible rings can be extended to J-reversible rings for this general setting. We show that J-quasipolar rings, local rings, semicommutative rings, central reversible rings and weakly reversible rings are J-reversible. As an application it is shown that every J-clean ring is directly finite.