Stable and Holomorphic Implementation of Complex Functions Using a Unit Circle-Based Transform

A stable and holomorphic implementation of complex functions in ℂ plane making use of a unit circle-based transform is presented in this paper. In this method, any complex number or function can be represented as an infinite series sum of progressive products of a base complex unit and its conjugate only, where both are defined inside the unit circle. With each term in the infinite progression lying inside the unit circle, the sum ultimately converges to the complex function under consideration. Since infinitely large number of terms are present in the progression, the first element of which may be deemed as the base unit of the given complex number, it is addressed as complex baselet so that the complex number or function is termed as the complex baselet transform. Using this approach, various fundamental operations applied on the original complex number in ℂ are mapped to equivalent operations on the complex baselet inside the unit circle, and results are presented. This implementation has unique properties due to the fact that the constituent elements are all lying inside the unit circle. Out of numerous applications, two cases are presented: one of a stable implementation of an otherwise unstable system and the second case of functions not satisfying Cauchy–Riemann equations thereby not holomorphic in ℂ plane, which are made complex differentiable using the proposed transform-based implementation. Various lemmas and theorems related to this approach are also included with proofs.

CLAVATA3 mediated simultaneous control of transcriptional and post-translational processes provides robustness to the WUSCHEL gradient

Regulation of the homeodomain transcription factor WUSCHEL concentration is critical for stem cell homeostasis in Arabidopsis shoot apical meristems. WUSCHEL regulates the transcription of CLAVATA3 through a concentration-dependent activation-repression switch. CLAVATA3, a secreted peptide, activates receptor kinase signaling to repress WUSCHEL transcription. Considering the revised regulation, CLAVATA3 mediated repression of WUSCHEL transcription alone will lead to an unstable system. Here we show that CLAVATA3 signaling regulates nuclear-cytoplasmic partitioning of WUSCHEL to control nuclear levels and its diffusion into adjacent cells. Our work also reveals that WUSCHEL directly interacts with EXPORTINS via EAR-like domain which is also required for destabilizing WUSCHEL in the cytoplasm. We develop a combined experimental and computational modeling approach that integrates CLAVATA3-mediated transcriptional repression of WUSCHEL and post-translational control of nuclear levels with the WUSCHEL concentration-dependent regulation of CLAVATA3. We show that the dual control by the same signal forms a seamless connection between de novo WUSCHEL synthesis and sub-cellular partitioning in providing robustness to the WUSCHEL gradient.

Physical and Chemical Compatibility of Etomidate and Propofol Injectable Emulsions

<b><i>Introduction:</i></b> The mixture of etomidate and propofol is widely used in clinical practice to improve efficacy of general anesthesia and to minimize side effects. As a thermodynamically unstable system, emulsion is prone to destabilization through mechanisms including coalescence, flocculation, and creaming. Such unwanted phenomenon can induce fat embolism after intravenous administration. This study was aimed to investigate the physical and chemical stability of the mixture of etomidate and propofol in the dosage form of emulsion. <b><i>Methods:</i></b> This compatibility study focused on the critical quality attributes (CQAs) of drug-containing emulsions, such as appearance, pH, particle size and distribution, <i>zeta</i> potential, the observation under centrifugation, and drug content and impurity. <b><i>Results:</i></b> As the results, there were no significant changes in the CQAs of the mixed emulsions up to 24 h after mixing at refrigeration temperature (4°C), room temperature (25°C), and body temperature (37°C). <b><i>Conclusions:</i></b> These results demonstrate that etomidate emulsion is physically and chemically compatible with propofol emulsions up to 24 h at 4°C, 25°C, and 37°C, suggesting that etomidate and propofol can be administrated in mixture without adversely affecting product characteristics, at least in vitro.

Some special specifics of dimensioning of a hydraulic cylinder as an executive device of an electrohydraulic actuator system

The hydraulic cylinder is dimensioned based on a static or dynamic criterion, assuming the desired operating pressure. The paper further analyzes the dimensioning of cylinders according to different load categories. The sizing of the hydraulic cylinder affects the choice of control algorithm parameters but also the stability of the system. How the cylinder dimension and the gain of the distributor affect the choice of the integral constant in the control algorithm in the case when we have the PI control law is especially considered. Then we have by definition an unsTable system 1 / s2 to which we provide stability through feedback.

Overcoming ambiguity in assessing the financial sustainability of Crimean hospitality companies for anti-crisis management

The subject of the research is the system of methods of financial management of a company, in which a contradictory situation of conflict of goals of its development has developed, with the obligatory occurrence of systemic crises on the one hand, and the rule of constant preservation of a low risk of financial destabilization, on the other. The relevance of the study is due to the significant distance of system analysis in its categories from strategic financial analysis. Systemic destabilization of active investment outwardly looks the same as the end-of-life bankruptcy crisis, which significantly distorts the perception of potential investors in the industry in general. The scientific novelty lies in the substantiation of a method that makes it moving from a simple identification of the transitional (crisis) development stages of an unstable system (company) to the substantiation of the parameters of a strategic program, including within the framework of anti-crisis management. The aim of the research is to adapt analysis methods of the system’s crisis states to the provisions of the most system-oriented financial analysis techniques have being applied to disclose the unstable states of the “system-enterprise”. The system analysis has been chosen as the research method in various areas of its manifestation: from a general philosophical description of unstable system with characteristics of a company’s life cycle to a model for assessing the company’s financial stability for strategic purposes. The result of modeling the financial condition of such unstable companies taking into account provisions of the system analysis, was the formulation of a new category of strategic financial management — the Strategic zone for the financial stability transformation, which serves as the basis for a long-term program for the transformation of the financial condition. As a conclusion, it can be noted that applying of the financial analysis method for strategic purposes (“Fregat” model) in a single connection with the system analysis provides the possibility to identify the most dangerous crises from the standpoint of the identification complexity and consequences of the cochirid stage crises of the system development. Also, this allows to separate the investment (justified) destabilization from instability which could be the cause of wrong actions of the company’s management. All this makes it possible to objectively assess the macroeconomic indicators of the hospitality industry in general.