Unique best response functions

Denote the best response function of the retailer by Rr Q) and the best response function of the wholesaler by Ryj A) both defined for zero initial inventory. At this point we have not demonstrated uniqueness or even existence of the equilibrium. It helps, however, to visualize the problem first. We begin by presenting the game graphically (see Figure 14.1, parameters are taken from the example in Section 6 with r = 8). The point A, is a Nash... 

Note that the objective function is concave, and hence the retailer s first-order condition characterizes the unique best response. For stationary policies, it is sufficient to consider the best response functions in the single-period game. The slope of the retailer s best-response function is found by implicit differentiation as follows ... 

Since the retailer s best response function is single-valued, the Stackelberg equilibrium exists. Further, we will show that the second derivative of the wholesaler s objective function is negative (i.e., the objective function is concave), and so the Stackelberg equilibrium is unique. The first derivative of the wholesaler s objective function is... 

Values for tte internal variabtes in thetmodynamic, internal equilibriwn are generally uniquely defined by the values for the external variables. For instance, in a simple, thermomechanical system (i.e. one that reacts mechanically solely volume-elastically) the equilibrium concentrations of the conformational isomers are uniquely described by temperature and pressure. In this case the conformational isomerism is not explicitly percqitible, but causes only overall effects, for example in the system s enthalpy or entropy. Elastic macroscopic effects may, however, occur when the relationship between internal and external variables is not single-valued. Then the response-functions of the system diverge or show discontinuities. The Systran undergoes a thermodynamic transformation. The best-known example of sudi a transformation based on conformational isomerism is the helix-coil transition displayed by sonte polymers in solution. An example in the scdid state is the crystal-to-condis crystal transition discussed in this paper. The conditions under which such transformations occur are dealt with in more detail in Sect 2.2. 

Then, the optimal payment scheme is characterized as the one that induces the second best production policy p (t) according to the differential piece rate and inventory penalty of Theorem 6. If the production cost function g p) is strictly convex, then p is the unique optimal production plan for the agent. If g p) is linear, then the second best policy p is an optimal response for the agent, but not the unique optimal response following standard practice in the economics literature, we assume that the agent will cooperate with the principal by selecting the second best policy. Structural properties of the second best production policy and optimal compensation scheme are discussed in Plam-beck and Zenios (2002). 

Bone tissue has a rather unique capability among human tissues in response to injury or other changes that alter its mechanical requirements it can continuously remodel itself to meet those mechanical needs best [51, 52], For example, when a bone fractures, the body creates new bone to connect the broken fragments together, and then remodels the new bone to optimize its mechanical function in the particular region of the skeleton that the fracture has occurred. Human skeletal tissue has several functions, but, when a bone is fractured by trauma, or removed surgically due to disease or tumor formation, we only seek solutions so that its mechanical function can be carried out [53, 54],... 

Because each enzyme sensor has its own unique response, it is necessary to construct the calibration curve for each sensor separately. In other words, there is no general theoretical response relationship, in the same sense as the Nernst equation is. As always, the best way to reduce interferences is to use two sensors and measure them differentially. Thus, it is possible to prepare two identical enzyme sensors and either omit or deactivate the enzyme in one of them. This sensor then acts as a reference. If the calibration curve is constructed by plotting the difference of the two outputs as the function of concentration of the substrate, the effects of variations in the composition of the sample as well as temperature and light variations can be substantially reduced. Examples of potentiometric enzyme electrodes are listed in Table 6.5. 

Serine proteases (SP) are a family of enzymes that use a uniquely activated serine residue in the substrate-binding pocket to catalytically hydrolyze peptide bonds [66], SP carry out a diverse array of physiological functions, of which the best known are digestion, blood clotting, fibrinolysis, fertilization, and complement activation during immune responses [67], They have also been shown to be abnormally expressed in many diseases including cancer, arthritis, and emphysema [42, 43, 67-70],... 

Within a period of perhaps 15 or 20 years, we have witnessed a profound maturation within the profession of pharmacy. The utterances of the profession, as projected in its hterature, have evolved from mostly self-centered and self-serving issues of trade protection to a composite of expressed professional interests that prominently include responsible explorations of scientiflc/technological questions and ethical issues that promote the best interests of the chentele served by the profession. With the pubhcation of Pharmacotherapy A Pathophysiologic Approach, pharmacy s utterances bespeak a matured practitioner who is able to caU upon unique knowledge and skills so as to function as an appropriately confident, independently competent pharmacotherapeutics expert. 

Material-tissue interactions are best described by the term biocompatibility. Generally defined, biocompatibihty is the ability of a material to perform with an appropriate host response in a specific application [96]. This implies that any material placed into a body will not be inert but will interact with the tissue. The biological response of a material is basically dependent on three factors the material properties, the host characteristics, and the functional demands on the material. Therefore, the biocompatibility of a material can only be assessed on the basis of its specific host function and has to be uniquely defined for each application. 

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