Comments on “A Note on the Paper “Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors””

Journal of Optimization Theory and Applications - Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012)....     

SYNTHESIS OF SPIRO [1,3-BENZODIOXOLE-2,4′-(3′H) QUINAZOLINES]

Abstract

In the present investigation, the authors could obtain a new series of spiranes (1) through the reaction of the high potential quinone tetrachloro-o-benzoquinone with 2-aryl-3-phenyl-3H-quinazoline-4-thiones. Thus, 2,3-diphenyl- (2a), 2-p-tolyl-3-phenyl- (2b) and 2-p-anisyl-3-phenyl- (2c)-3H-quinazoline-4-thiones react readily with tetrachloro-o-benzoquinone, in boiling toluene, to give the corresponding spiro-1,3-benzodioxole-2,4′-(3′H)-quinazolines (1a-c), respectively.     

Adaptive Diagnosis for Fault Tolerant Data Fusion Based on α-Rényi Divergence Strategy for Vehicle Localization

When applying a diagnostic technique to complex systems, whose dynamics, constraints, and environment evolve over time, being able to re-evaluate the residuals that are capable of detecting defaults and proposing the most appropriate ones can quickly prove to make sense. For this purpose, the concept of adaptive diagnosis is introduced. In this work, the contributions of information theory are investigated in order to propose a Fault-Tolerant multi-sensor data fusion framework. This work is part of studies proposing an architecture combining a stochastic filter for state estimation with a diagnostic layer with the aim of proposing a safe and accurate state estimation from potentially inconsistent or erroneous sensors measurements. From the design of the residuals, using α-Rényi Divergence (α-RD), to the optimization of the decision threshold, through the establishment of a function that is dedicated to the choice of α at each moment, we detail each step of the proposed automated decision-support framework. We also dwell on: (1) the consequences of the degree of freedom provided by this α parameter and on (2) the application-dictated policy to design the α tuning function playing on the overall performance of the system (detection rate, false alarms, and missed detection rates). Finally, we present a real application case on which this framework has been tested. The problem of multi-sensor localization, integrating sensors whose operating range is variable according to the environment crossed, is a case study to illustrate the contributions of such an approach and show the performance.     

Lie algebras and separable morphisms in pro-affine algebraic groups

Let be an algebraically closed field of arbitrary characteristic, and let be a surjective morphism of connected pro-affine algebraic groups over . We show that if is bijective and separable, then is an isomorphism of pro-affine algebraic groups. Moreover, is separable if and only if (its differential) is surjective. Furthermore, if is separable, then .

     

Design,Synthesis, and Antimicrobial Activity of Certain New Indole-1,2,4 Triazole Conjugates

The increasing prevalence of microbial infections and the emergence of resistance to the currently available antimicrobial drugs urged the development of potent new chemical entities with eminent pharmacokinetic and/or pharmacodynamic profiles. Thus, a series of new indole-triazole conjugates 6a-u was designed and synthesized to be assessed as new antimicrobial candidates using the diameter of the inhibition zone and minimum inhibitory concentration assays against certain microbial strains. Their in vitro antibacterial evaluation revealed good to moderate activity against most of the tested Gram-negative strains with diameter of the inhibition zone (DIZ) values in the range of 11–15 mm and minimum inhibition concentration (MIC) values around 250 µg/mL. Meanwhile, their in vitro antifungal evaluation demonstrated a potent activity against Candida tropicalis with MIC value as low as 2 µg/mL for most of the tested compounds. Moreover, compound 6f is the most potent congener with an MIC value of 2 µg/mL against Candida albicans.     

Toeplitz operators on Bergman spaces

Let ? be an element in \(H^\infty (D) + C(\overline D )\) such that ?^* is locally sectorial. In this paper it is shown that the Toeplitz operator defined on the Bergman spaceA ² (D) is Fredholm. Also, it is proved that ifS is an operator onA ²(D) which commutes with the Toeplitz operatorT _? whose symbol ? is a finite Blaschke product, thenS H ^∞ (D) is contained inH ^∞ (D). Moreover, some spectral properties of Toeplitz operators are discussed, and it is shown that the spectrum of a class of Toeplitz operators defined on the Bergman spaceA ² (D), is not connected.     

Necessary optimality conditions for set-valued optimization problems via the extremal principle

The paper concerns first-order necessary optimality conditions for set-valued optimization problems. Based on the extremal principle developed by Mordukhovich [21], we derive fuzzy/approximate necessary optimality conditions. An example that illustrates the usefulness of our results is given.     

Free lateral vibration of beams of variable cross section

Zusammenfassung Es werden die freien Querschwingungen von Balken mit exponentiell veränderlichen Querschnitten und Trägheitsmomenten für verschiedene Randbedingungen untersucht. Die Frequenzengleichungen, Eigenfrequenzen und Schwingungsformen werden angegeben (wobei die Auswertung einfachheitshalber auf die beiden ersten Eigenschwingungen beschränkt bleibt).

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Notation x, y, z Rectangular coordinates - L span of beam - A(x) cross sectional area - I(x) moment of inertia of cross section - X normal function for beam - X _i thei-th normal function - T function of time - P _i circular frequency for thei-th mode     

Geometric Phases for Wave Packets of the Landau Problem

The Landau problem of a charged particle in a plane with a uniform perpendicular magnetic field is analysed in two oscillator modes. The coherent states for the problem have been found out using a general definition of displaced states. The time evolution and the associated nonadiabatic geometric phase for both initially displaced and non-displaced wave packets have been studied. The path integral is derived in a simple way through the calculation of Gaussian integrals via the concept of coherent state wavefunctions.