Professor Ulrich Zwiener (1942-2004)-a tribute to ISP founding member

Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...

Constrained by limited energy and resources, organisms must compromise between offspring quantity and parental investment. This trade-off is represented by two primary reproductive strategies; K-strategists produce few offspring but provide substantial parental support, whereas r-strategists produce much progeny that receives little care. These strategies are related to an organism’s survival likelihood across its lifespan, which is represented by a survivorship curve. Three general types of...

In a galvanic cell, the electrical work is done by a redox system on its surroundings as electrons produced by the spontaneous redox reactions are transferred through an external circuit. Alternatively, an external circuit does work on a redox system by imposing a voltage sufficient to drive an otherwise nonspontaneous reaction in a process known as electrolysis. For instance, recharging a battery involves the use of an external power source to drive the spontaneous (discharge) cell reaction in...

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Electrochemistry is the science involved in the interconversion of electrical and chemical reactions. Such reactions are called reduction-oxidation, or redox reactions. These important reactions are defined by changes in oxidation states for one or more reactant elements and include a subset of reactions involving the transfer of electrons between reactant species. Electrochemistry as a field has evolved to yield sufficient insights on the fundamental principles of redox chemistry and multiple...

A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is subjected to a change in conditions that affects these reaction rates differently (a stress), then the rates are no longer equal and the system is not at equilibrium. The system will subsequently experience a net reaction in the direction of a greater rate (a shift) that will re-establish the equilibrium. This phenomenon is summarized by Le...