New necessary and sufficient optimality conditions for strong bilevel programming problems

In this paper we are interested in a strong bilevel programming problem (S). For such a problem, we establish necessary and sufficient global optimality conditions. Our investigation is based on the use of a regularization of problem (S) and some well-known global optimization tools. These optimality conditions are new in the literature and are expressed in terms of \(\max \)–\(\min \) conditions with linked constraints.     

Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.     

Hinge peptide combinatorial libraries for inhilbitors of botulinum neurotoxins and saxitoxin: Deconvolution strategy

Combinatorial library screening offers a rapid process for identifying potential therapies to toxins. Hinge peptide libraries, which rely on conformational diversity rather than traditional molecular diversity, reduce the need for huge numbers of syntheses and screening steps and greatly expedite the discovery process of active molecules. Hinge peptide libraries having the structures: Acetyl-X₁–X₂–hinge–X₃–X₄–NH₂ (capped) and X₁–hinge–X₂–X₃ (uncapped), where X₁ through X₄ are near-equimolar mixtures of twelve L-amino acids and hinge = 4-aminobutyric acid, were screened for inhibitory activity in bioassays for botulinum neurotoxins A and B (BoNT/A, BoNT/B) and saxitoxin. The zinc protease activity of the reduced light chains of BoNT/A and /B was assayed by measuring the cleavage of synthetic substrates. Saxitoxin activity was measured by the restoration of the viability of neuroblastoma cells treated with ouabain and veratridine. Deconvolution of libraries was accomplished by fixing one position at a time beginning with the C-terminus. Primary library subsets in which position 4 was fixed showed moderate levels of inhibition for BoNT/A. Secondary library subsets showed stronger inhibition in the bioassays. In each of the bioassays, inhibitory potency was stronger when the second position to be fixed was on the opposite side of the hinge, rather than on the same side with respect to the C-terminus, suggesting that the hinge facilitates the interaction of side chains. Inhibitors for all three of the toxins studied were discovered within library subsets, although not necessarily in primary subsets. These studies demonstrate that (1) the best strategy for deconvoluting hinge peptide libraries is by fixing residues alternately on each side of the hinge moiety, and (2) it is essential to investigate secondary subsets even when primary subsets are inactive. The present findings support the concept that the increased flexibility imposed by the inclusion of a central hinge residue in small peptides increases the opportunity for side chain interactions, providing a distinct advantage for hinge peptide libraries over conventional peptide libraries. Hinge peptide libraries are a rich source of novel ligands for modulation of biomechanisms. The library subsets uncovered in this study may possess peptides that will lead to effective therapies to neurotoxin poisoning.     

C n -almost automorphic solutions for partial neutral functional differential equations

In this work, we study the existence of C ⁿ -almost periodic solutions and C ⁿ -almost automorphic solutions (n?≥?1), for partial neutral functional differential equations. We prove that the existence of a bounded integral solution on ?⁺ implies the existence of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions. When the exponential dichotomy holds for the homogeneous linear equation, we show the uniqueness of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions.     

AF-Domains and Their Generalizations

In this article, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A? _k B for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16 Wadsworth , A. R. ( 1979 ). The Krull dimension of tensor products of commutative algebras over a field . J. London Math. Soc. 19 : 391 – 401 .[Crossref], [Web of Science ®] , [Google Scholar]].     

A new method for solving Pareto eigenvalue complementarity problems

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNM_min and SNM_FB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201–213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125–137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.     

Interactions of gamma rays with undoped and Mn-doped sodium phosphate glasses

Ultraviolet and visible spectroscopic measurements were used to investigate prepared undoped and Mn-doped sodium phosphate glasses before and after successive gamma irradiation. The effects of both glass composition and MnO₂ content on the generation of radiation-induced defects were investigated. Undoped sodium phosphate glass shows strong UV absorption, which is attributed to the presence of trace iron impurities present in the raw materials. Mn-doped glasses reveal an additional visible broad band centered at about 500 nm due to Mn³⁺, which has recently been related to the ⁵E_g →⁵T_2g transition. The radiation-induced bands are correlated with the generation of liberated electron–hole pairs during the process of gamma irradiation and the possibility of photochemical reactions especially with trace iron impurities and manganese ions. The intensity and the position of the induced bands are observed to depend on the type and composition of glass, concentration of the dopant and also on the irradiation dose. Manganese ions when present in relatively higher content have been found to show a shielding behavior towards the effects of progressive gamma irradiation causing a retardation of the growth of the induced defects. Infrared and Raman spectra of the undoped and Mn-doped glasses were measured to investigate the structural phosphate groups present and the effect of MnO₂ on the network structure. An ESR investigation was carried out to confirm the state of manganese ions in the prepared sodium phosphate glasses.     

Semi-Analytical Simulation of Titanium-Indiffused Lithium Niobate–Integrated Optic Directional Couplers Consisting of Curved Waveguides

Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO ₃ curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.     

A general nonlocal nonlinear model for buckling of nanobeams

This study presents a unified model for the nonlocal response of nanobeams in buckling and postbuckling states. The formulation is suitable for the classical Euler–Bernoulli, first-order Timoshenko, and higher-order shear deformation beam theories. The small-scale effect is modeled according to the nonlocal elasticity theory of Eringen. The equations of equilibrium are obtained using the principle of virtual work. The stress resultants are developed taking into account the nonlocal effect. Analytical solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state are obtained. It is found out that as the nonlocal parameter increases, the critical buckling load reduces and the amplitude of buckling increases. Numerical results showing variation of the critical buckling load and the amplitude of buckling with the nonlocal parameter and the length-to-height ratio for simply supported and clamped–clamped nanobeams are presented.