One-Pot Synthesis and Fungicidal Activity of Pyrimidinylidenamido- and Thiazolinylidenamidomonothiophosphoric Esters

A novel one-pot synthesis of four new classes of amidothiophosphoric esters and trisamidothiophosphoric esters is developed. (1-Alkyl-2-pyrimidinylidenamido)bis(diethylamido)thiophosphates, (1-alkyl-2-pyrimidinylidenamido)bis (O-2/4-methylphenyl)thiophosphates, (3-alkyl-2-thiazolinylidenamido)bis (diethylamido)thiophosphate and (3-alkyl-2-thiazolinylidenamido)bis(O-2/4-methylphenyl)thiophosphates are obtained from the nucleophilic substitution and oxidation of N-alkyl-2-cycloiminylidenaminodichlorophosphines generated in situ from the reaction of the corresponding N-alkyl-2-aminocycloiminium halide with phosphorus trichloride and triethylamine. The synthesized thiophosphoric esters have been investigated for fungicidal properties.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

Palladium(II)-catalyzed intramolecular aminoacetoxylation of sugar derived alkenyl tosylsulfonamide: Total synthesis of l-deoxyallonojirimycin

Palladium catalyzed intramolecular aminoacetoxylation of d-ribose derived alkenyl tosylsulfonamide to deliver l-deoxyallonojirimycin in an overall yield of 19%. The preliminary screening of l-deoxyallonojirimycin against carbohydrate processing enzymes showed moderate inhibitory activity against α-glucosidase (yeast) and α-mannosidases.     

Error estimates for integral constraint regularization of state-constrained elliptic control problems

The alternating direction method of multipliers (ADMM) is a benchmark for solving a two-block linearly constrained convex minimization model whose objective function is the sum of two functions without coupled variables. Meanwhile, it is known that the convergence is not guaranteed if the ADMM is directly extended to a multiple-block convex minimization model whose objective function has more than two functions. Recently, some authors have actively studied the strong convexity condition on the objective function to sufficiently ensure the convergence of the direct extension of ADMM or the resulting convergence when the original scheme is appropriately twisted. We focus on the three-block case of such a model whose objective function is the sum of three functions, and discuss the convergence of the direct extension of ADMM. We show that when one function in the objective is strongly convex, the penalty parameter and the operators in the linear equality constraint are appropriately restricted, it is sufficient to guarantee the convergence of the direct extension of ADMM. We further estimate the worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses, and derive the globally linear convergence in asymptotical sense under some additional conditions.     

Some equivalent problems in set optimization

Given a set-valued optimization problem (P), there is more than one way of defining the solutions associated with it. Depending on the decision maker’s preference, we consider the vector criterion or the set criterion. Both criteria of solution are considered together to solve problem (P) by reducing the feasible set.     

Inverse problems for multi-valued quasi variational inequalities and noncoercive variational inequalities with noisy data

ABSTRACT

We study the inverse problem of identifying a variable parameter in variational and quasi-variational inequalities. We consider a quasi-variational inequality involving a multi-valued monotone map and give a new existence result. We then formulate the inverse problem as an optimization problem and prove its solvability. We also conduct a thorough study of the inverse problem of parameter identification in noncoercive variational inequalities which appear commonly in applied models. We study the inverse problem by posing optimization problems using the output least-squares and the modified output least-squares. Using regularization, penalization, and smoothing, we obtain a single-valued parameter-to-selection map and study its differentiability. We consider optimization problems using the output least-squares and the modified output least-squares for the regularized, penalized and smoothened variational inequality. We give existence results, convergence analysis, and optimality conditions. We provide applications and numerical examples to justify the proposed framework.     

-contingent epiderivatives in reflexive spaces

In this paper we introduce a notion of the τ^w-contingent epiderivative of a set-valued map by considering the weak topology in the image space. We establish a chain rule formula for families of τ^w-contingent and contingent epiderivatives. When the image space is reflexive and the ordering cone a half-space, we give conditions for the existence of the family of τ^w-contingent epiderivatives of a stable set-valued map; moreover we obtain an interesting formula that connects this family with the contingent epiderivative of an associated scalar set-valued map. Finally we apply the previous results in order to establish optimality conditions for a set-valued optimization problem via epiderivatives with respect to half-spaces associated with the ordering cone. In particular we provide a scalarization method for computing these conditions in reflexive spaces.     

Stereoselective total synthesis of Jaspine B (Pachastrissamine) utilizing iodocyclization and an investigation of its cytotoxic activity

The stereoselective synthesis of Jaspine B has been achieved from easily available (S)-Garner’s aldehyde. The trisubstituted tetrahydrofuran core of Jaspine B was constructed by utilizing a diastereoselective iodocyclization as the key step. Deiodination and debenzylation were performed in a single step by using n-Bu₃SnH and ABCN as a conjugate catalyst system. The in vitro cytotoxicity of compounds 1 and 1a against 3 human cancer cell lines-A549 (lung), MCF7 (breast), and KB (oral); and a non-cancer cell line (NIH3T3) was determined by sulphorhodamine B based assay.     

A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location

The primary objective of this work is a detailed theoretical and computational study of the elasticity imaging inverse problem for tumor identification within the human body. Apart from this inverse problem's important and interesting application, it also poses noteworthy mathematical challenges since the underlying mathematical model is a system of elasticity involving incompressibility. This gives rise to the “locking” effect and special treatment is necessary for both the direct and inverse problems. To study the inverse problem in an optimization framework, we introduce a general computational scheme for handling parameter identification in saddle point problems along with the introduction and analysis of a new energy output least-squares objective functionals. We also present a treatment of the identification of discontinuous elasticity coefficients using the total variation regularization method. General formulas for the computation of the coefficient-to-solution map and a complete convergence analysis are given for the continuous problem as well as for its discrete analogue. Discrete formulas and implementation issues are discussed in detail and numerical examples for smooth and discontinuous coefficients are given.