The fundamental equation that describes limit cycles in nonlinear sampled-data systems was derived. The equivalence of limit cycles with finite pulsed systems having a periodically varying sampling-rate was observed, and the methods of analysis applied to the latter were extended to obtain these limit cycles with the aid of final value theorem. This fundamental equation is modified and simplified under certain assumptions as it can be applied to systems both with and without integrators. The limitation on the longest period of saturated and unsaturated oscillation is investigated and the critical gain for their existence is derived, starting from the modified fundamental equation. Also, the stability of limit cycles and the equilibrium point is considered, based on Neace's method. Various kinds of non-linearities, namely, pulse-width modulation, relay saturating amplifier with linear zone and quantized level amplifier are discussed. Self-excited oscillations are mainly examined, as well as the possible existence and stability of limit cycles, however, the method can be extended to forced oscillations.

Various techniques are available for the analysis of nonlinear sampled-data systems. Most of these methods use either the phase plane approach or the describing function technique. Since the performance of such a system is described, at sampling instants, by means of a difference equation, an approach based on the difference equation would seem to be both natural and direct. The principle of complex convolution for a transform is explained and its geometrical interpretation is given. It is shown how the application of the convolution transform is both direct and simple with respect to solving nonlinear difference equations when the equation is given in scalar form. Dependence of the convergence of the solution on the initial value and the degree of nonlinearity is pointed out. It is concluded that for difference equations of second order and higher, this method involves too much laborious computation to justify its use. A simple method is presented for examining free oscillations in a sampled-data system containing either relay or a saturating amplifier. In addition, a certain analytical technique, analogous to that for differential equations, is developed to investigate the stability of forced oscillations for certain types of nonlinear difference equations. (Author).

Despite what you might have been told, we’re not inherently selfish. The truth is we’re inherently kind.Scientific evidence has proven that kindness changes the brain, impacts the heart and immune system, is an antidote to depression and even slows the ageing process. We’re actually genetically wired to be kind. In The Five Side Effects of Kindness, David Hamilton shows that the effects of kindness are felt daily throughout our nervous system. When we’re kind we feel happier and our bodies are healthiest.In his down-to-earth and accessible style, David shares how: •Kindness makes us happier •Kindness is good for the heart •Kindness slows ageing •Kindness improves relationships •Kindness is contagious

Throughout history, alliances have taken many different forms and they have been difficult to understand in their totality. As we now experience an unprecedented pandemic, which highlights the need for both external alliances between states and internal alliances between governments and populations, understanding alliances is more than ever critical to apprehend an open and interactive world that knows no borders and in which challenges imposed on humans are global. The book “Living Alliances, Leaving Alliances” is an interdisciplinary approach to investigating past, present and future alliances on an interpersonal, subnational, international and transnational level. It is the result of a two-year project by AreaS, a research group in area studies located at the Østfold University College in Norway.

Metonymy and Language presents a new theory of language and communication in which the central focus is on the concept of metonymy, the recognition of partial matches and overlaps. Through the use of original data sets and rigorous primary research, Denroche characterizes metonymy as key to understanding why language is so ‘fit for purpose’ and how it achieves such great subtlety and flexibility. This study develops the notion of ‘metonymic competence’ and demonstrates that metonymic behavior is often pursued for its own sake in recreational activities, such as quizzes, puzzles and play, and shows the possible impact of the application of metonymic processing theory to professional fields, such as language teaching and translator training. Furthermore, it proposes a research approach with metonymy at its center, ‘metonymics,’ which Denroche suggests could provide a powerful framework for addressing issues in numerous fields of practice in the arts and sciences.

Scientific Perspectives of Tea Plant Horticulture and Productivity is a complete, step-by-step guide on how to maximize tea plant growth, yield and quality. Chapters focus on the methods of cultivation, soil and water management, plant physiology, plant protection and weed control, problems from pollution and climate change, and eco-friendly remedial actions. This is an essential read for plant biologists and tea horticulturalists as the tea industry is struggling due to high production costs, changing climates and diminishing plant yields, with countries in Asia declaring the industry at 'crisis point.' Horticulturalists need solutions to problems with plant productivity, quality, stress management and eco-friendly cultivation practices. There have been several technological advances in the field and horticulturalists need guidance on how best to implement new technologies, hence the importance of this new resource. - Written by a tea industry expert with almost 40 years' of experience - Provides a practical guide on all aspects of tea cultivation, with step-by-step protocols - Includes plantation troubleshooting and other remedial actions