In this note we prove several duality theorems in lattice theory. We also discuss the connection between spectral spaces and Priestley spaces, and interpret Priestley duality in terms of spectral spaces. The organization of this note is as follows. In the first section we collect appropriate definitions and basic results common to many of the various topics. The next four sections consider Birk...

In this paper first we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four significant conic problems in finite dimensional spaces, defined as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let φ be a homogeneous function of degree p > ...

We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.

TenderVoice/TenderNoise (TVTN) creates a platform to capture and communicate the complex dynamics of urban systems using acoustic data. It explores dualities in data sources, sensors, filters, audience and display, contrasting qualitative and personal attributes of the human voice with quantitative neighborhood decibel levels. TVTN also addresses the complementary relationship that exists betwe...

We study duality between input and output in the π-calculus. In dualisable versions of π, including πI and fusions, duality breaks with the addition of ordinary input/output types. We introduce π, intuitively the minimal symmetrical conservative extension of π with input/output types. We prove some duality properties for π and we study embeddings between π and π in both directions. As an exampl...

We investigate dual mechanisms for interacting particle systems. Generalizing an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we show that a simple linear transformation leads to a moment duality of suitably rescaled processes. More precisely, we show how dualities of interacting particle systems of the form H(A,B) = q|A∩B|, A,B ⊂ {0, 1} , q ∈ [−1, 1), are rescaled to ...

We give a complete picture of the interaction between Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras imposing the condition that standard filtrations of projective modules are...

Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for N = 2 quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric realization of quantum field theories together with a local application of mirror symmetry. This construction is not based on any duality...