Duality theorems for nondifferentiable semi-infinite interval-valued optimization problems with vanishing constraints

In this paper, we study the duality theorems of a nondifferentiable semi-infinite interval-valued optimization problem with vanishing constraints (IOPVC). By constructing the Wolfe and Mond–Weir type dual models, we give the weak duality, strong duality, converse duality, restricted converse duality, and strict converse duality theorems between IOPVC and its corresponding dual models under the assumptions of generalized convexity.

Unified Models for Coupled Inductors Applied to Multiphase PWM Converters

<div> <p>Circuit models for multiphase coupled inductors are summarized, compared, and unified. Multiwinding magnetic structures are classified into parallel-coupled structures and series-coupled structures. For parallel-coupled structures used for multiphase inductors, the relationships between a) inductance-matrix models, b) extended cantilever models, c) magnetic-circuit models, d) multiwinding transformer models, e) gyrator-capacitor models, and f) inductance-dual models are examined and discussed. These models represent identical physical relationships in the multiphase coupled inductors, but emphasize different physical aspects and offer distinct design insights. The circuit duality between the series-coupled structure and the parallel-coupled structure is explored. Design equations for interleaved multiphase buck converters based on these models are streamlined and summarized, and a simplified equation showing the relationships between current ripple with and without coupling is presented. The models and design equations are verified through theoretical derivation, SPICE simulation, and experimental measurements. <br></p></div>

On duality theory for multiobjective semi-infinite fractional optimization model using higher order convexity.

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond -Weir, Wolfe and Schaible are presented and then usual duality results are proved using higher-order [[EQUATION]] convexity assumptions. To show the existence of such generalized convex functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.

Confronting dual models of the strong interaction

Studies of the mathematical properties of Regge-pole and dual amplitudes are important both for their applications in high energy phenomenology and in their generalizations to strings, superstrings, branes, and other theoretical developments. In this paper, we investigate the similarities and differences between two classes of dual amplitudes: one with Mandelstam analyticity (DAMA) and another one with logarithmic trajectories (Dual-log). By using quantum (q-) deformations, new features of Dual-log amplitude are unveiled, in particular those concerning its asymptotic behavior and the spectrum of resonances. The two classes of dual amplitudes are compared in various kinematic regions: at fixed transferred momenta asymptotic, fixed angle asymptotic, and in the resonance region.

T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $$\alpha '$$ α ′ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to $$\alpha '$$ α ′ -corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $$A_2$$ A 2 , $$A_2 \oplus A_1$$ A 2 ⊕ A 1 and $$SL(2, \mathbb {R})$$ S L ( 2 , R ) . In this way, the PL self-duality of $$AdS_3 \times \mathbb {R}$$ A d S 3 × R space is discussed.

Nondifferentiable generalized minimax fractional programming under (Ф,ρ)-invexity

In this paper, a class of nonconvex nondifferentiable generalized minimax fractional programming problems is considered. Sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (?,?)-invexity. Further, two types of dual models are formulated and various duality theorems relating to the primal minimax fractional programming problem and dual problems are established. The results established in the paper generalize and extend several known results in the literature to a wider class of nondifferentiable minimax fractional programming problems. To the best of our knowledge, these results have not been established till now.

Unified Models for Multiphase Coupled Inductors

<div> <p>Circuit models for multiphase coupled inductors are summarized, compared, and unified. Multiwinding magnetic structures are classified into parallel-coupled structures and series-coupled structures. For parallel-coupled structures used for multiphase inductors, the relationships between a) inductance matrix models, b) extended cantilever models, c) magnetic circuit models, d) multiwinding transformer models, e) gyrator-capacitor models, and f) inductance dual models are examined and discussed. These models represent identical physical relationships in the multiphase coupled inductors, but emphasize different physical aspects and offer distinct design insights. The circuit duality between the series coupled structure and the parallel coupled structure is explored. Design equations arising from these models are streamlined and summarized, and a simplified equation showing the relationships between current ripple for interleaved multiphase buck converters with and without coupling is presented. The models and design equations are verified through theoretical derivation, SPICE simulation, and experimental measurements. <br></p></div>