Synthesis of 4-Benzidinyl Butyric Acid: A Key Intermediate for Antibodies Production Against Benzidin

a four-step synthesis of monoalkylated benzidin is reported for immunogen preparation against benzidin dye. Use of 10% H₂SO₄/ dioxan for N-Boc cleavage avoids the cyclisation of 4-benzidinyl butyric acid into the corresponding lactam observed with the classical TFA/ CH₂Cl₂ system.     

Missing boundary data recovery using Nash games: the Stokes system

We consider the Cauchy-Stokes problem. We use a new method based on Nash game theory to recover the missing velocity and normal stress on some inaccessible part of the boundary. This method is used with two different approaches. The first one is compared to a control type one. The numerical study attests that both approaches give accurate results. We compare these results with those of the energy-like minimization method.     

Entire large solutions of semilinear equations involving the fractional Laplacian

We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given.     

Potassium Fluoride on Alumina: Condensation of 1,4-Diacetylpiperazine-2,5-Dione with Aldehydes. Dry Condensation Under Microwave Irradiation. Synthesis of Albonursin and Analogues

1,4-Diacetylpiperazine-2,5-dione (1) was condensated with aldehydes (2) with KF on alumina without solvent under microwaves or in at room temperature in the presence of DMF. The reaction was stereoselective and some natural products (4a-c) like albonursin(4c) were synthesized.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.