The Role of Radical Bridges in Polynuclear Single-Molecule Magnets

Employing radical bridges between anisotropic metal ions has been a viable route to achieve high-performance single-molecule magnets (SMMs). While the bridges have been mainly considered for their ability to promote exchange interactions, the crystal-field effect arising from them has not been taken into account explicitly. This lack of consideration may distort the understanding and limit the development of the entire family. To shed light on this aspect, herein we report a theoretical investigation of a series of N -radical-bridged diterbium complexes. It is found that while promoting strong exchange coupling between the terbium ions, the N -radical induces a crystal field that interferes destructively with that of the outer ligands, and thus reduces the overall SMM behavior. Based on the theoretical results, we conclude that the SMM behavior in this series could be further maximized if the crystal field of the outer ligands is designed to be collinear with that of the radical bridge. This conclusion can be generalized to all exchange-coupled SMMs.     

Negatively Charged Metallacarborane Redox Couples with Both Members Stable to Air

The metallacarborane [3,3′‐Co(1,2‐closo‐C₂B₉H₁₁)₂]^? has been synthesized. This species allows the formation of redox couples in which both partners are negatively charged. The E_1/2 potential can be tuned by adjusting the nature and number of substituents on B and C. The octaiodinated species [3,3′‐Co(1,2‐closo‐C₂B₉H₇I₄)₂]^? is the most favorable, as it is isolatable and stable in air. A DFT study on stability and redox potentials of complexes has been performed.     

On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Algebraic decoding of (103, 52, 19) and (113, 57, 15) quadratic residue codes

In this paper, two algebraic decoders for the (103, 52, 19) and (113, 57, 15) quadratic residue codes, which have lengths greater than 100, are presented. The results have been verified by software simulation that programs in C++ language have been executed to check possible error patterns of both quadratic residue codes.     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Influence of exciton-exciton interaction with spin paired charge carriers and exciton-lattice interaction on the surface properties of crystalline solids

Applying tight-binding approximation and spin pairing of like charge carriers in a pair of excitons created in a lattice, the possibility of forming a bound exciton-exciton state is studied. It is found that, provided there exists strong exciton-lattice interaction, such a bound state may be formed and its energy may lie within the valence band deforming the material into a crystalline solid with no energy gap. Lowering of the energy is calculated in naphthalene and anthracene crystals where some experimental results are known. The excess energy released after the formation of such bound state can be adequate, depending on the material, to desorb neutral atoms or eject of electrons from surfaces.     

Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.     

On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Invex-convexlike functions and duality

We define a class of invex-convexlike functions, which contains all convex, pseudoconvex, invex, and convexlike functions, and prove that the Kuhn-Tucker sufficient optimality condition and the Wolfe duality hold for problems involving such functions. Applications in control theory are given.The author is grateful to Professor W. Stadler and the referees for many valuable remarks and suggestions, which have enabled him to improve considerably the paper.