A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

Owing to the dramatic change in the thermal conductivity of 4He when its temperature crosses the transition of superfluid (HeI) and normalfluid (HeII), a sealed-cell with a capillary is used to realize the lambda transition temperature, Tλ. A small heat flow is controlled through the capillary of the sealed-cell so as to realize the coexistence of HeI and HeII and maintain the stay of HeI/HeII interface in the capillary. A stable and flat lambda transition temperature "plateau" is obtained. Because there is a depression effect of Tλ caused by the heat flow through the capillary, a series of heat flows and several temperature plateaus are made and an extrapolation is applied to determine Tλ with zero heat flow. A rhodium-iron resistance thermometer with series number A34 (RIRT A34) has been used in 24 Tλ -realization experiments to derive Tλ with a standard deviation of 0.022mK, which proves the stability and reproducibility of Tλ.

A new notion of a realization of transfer matrix of (P;Q; V)-cone-system for discrete-time linear systems is proposed. Necessary and sufficient conditions for the existence of the realizations are established. A procedure is proposed for computation of a realization of a given proper transfer matrix T(z) of (P;Q; V)-cone-system. It is shown that there exists a realization of T(z) of (P;Q; V)-cone-system if and only if there exists a positive realization of T(z) = V T(z)Q!1, where V;Q and P are non-singular matrices generating the cones V;Q and P respectively.

A new class of positive fractional 2D hybrid linear systems is introduced. The solution of the hybrid system is derived. The classical Cayley-Hamilton theorem is extended for fractional 2D hybrid systems. Necessary and sufficient conditions for the positivity are established.

The study aims to examine the role of Self-Forgiveness in shaping the Human Flourishing of the adults. Two hundred fourteen participants (18 to 30 years) comprising 100 males (Mean Age = 22.15(1.61)) and 114 females (Mean Age = 22.00(1.95)) were chosen for the study. Self-forgiveness (Mudgal & Tiwari, 2017a) and Mental Health Continuum-Short Form (Keyes, 2005) were used as the tools. Self-forgiveness comprises Realization & Reparation, Guilt, Attribution and overall self-forgiveness (sum of the first three) while Human Flourishing consists of Hedonic and Eudaimonic (Social plus Psychological) Well-Being. The aggregate of Hedonic and Eudaimonic is overall Human Flourishing. The findings suggested no gender differences in Self-Forgiveness of the participants. Conversely, gender differences were observed in all the dimensions of Human Flourishing in favour of males. Irrespective of gender, Realization & Reparation was positively correlated with Hedonic, Social, Psychological and Eudaimonic Well-Being as well as Human Flourishing except for Guilt and Attribution that showed small positive or negative correlations. Irrespective of gender, Overall Self-Forgiveness correlated positively with all the dimensions of Flourishing. Gender and Realization & Reparation emerged as the significant predictors accounting for significant variance in all the dimensions of Flourishing while Guilt and Attribution did not. The findings suggested that remorse, easy acceptance of wrongdoing, repairing the relationship with self and others, ability to minimize negative emotions towards self, monitoring others’ positive behaviours and acknowledgements of valued and close relationships were the psychological mechanisms that may underlie the predictive strengths of self-forgiveness in regulating flourishing.

Bogusław Wolniewicz created an original formal system based on his considerations on the ontology and semantics embedded in Wittgenstein’s Tractatus. His system – called by Wolniewicz ‘ontology of situations’ – can be complemented by a philosophical interpretation. In this article I identify the implicit and intuitive underpinnings of the system, its formal content and its philosophical implications. I also indicate a few applications of the system to axiology and logical hermeneutics.

This work proposes an optimum design and implementation of fractional-order Butterworth filter of order (1 + α), with the help of analog reconfigurable field-programmable analog array (FPAA). The designed filter coefficients are obtained after dual constraint optimization to balance the tradeoffs between magnitude error and stability margin together. The resulting filter ensures better robustness with less sensitivity to parameter variation and minimum least square error (LSE) in magnitude responses, passband and stopband errors as well as a better –3 dB normalized frequency approximation at 1  rad/s and a stability margin. Finally, experimental results have shown both lowpass and highpass fractional step values. The FPAA-configured outputs represent the possibility to implement the real-time fractional filter behavior with close approximation to the theoretical design.

In this article, we propose the realization of XNOR logic function by using all-optical XOR and NOT logic gates. Initially, both XOR and NOT gates are designed, simulated and optimized for high contrast outputs. T-shaped waveguides are created on the photonic crystal platform to realize these logic gates. An extra input is used to perform the inversion operation in the NOT gate. Inputs in both the gates are applied with out of phase so as to have a destructive interference between them and produce negligible intensity for logic ‘0'. The XOR and NOT gates are simulated using Finite Difference Time Domain method which results with a high contrast ratio of 55.23 dB and 54.83 dB, respectively at a response time of 0.136 ps and 0.1256 ps. Later, both the gates are cascaded by superimposing the output branch of the waveguide of XOR gate with the input branch of the waveguide of NOT gate so that it can be resulted with compact size for XNOR logic function. The resultant structure of XNOR logic came out with the contrast ratio of 12.27 dB at a response time of 0.1588 ps. Finally, it can be concluded that the proposed structures with fair output performance can suitably be applied in the design of photonic integrated circuits for high speed computing and telecommunication systems.

The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown that there exists a positive (minimal) realization of an improper transfer function T(z) = n(z) / d(z) if the coefficients of polynomial n(z) are non-negative and of the polynomial d(z) are non-positive except the leading one, which should be positive. A procedure for computation of the positive (minimal) realization of the transfer function is proposed and illustrated by an example.

The chuch dedicated to The Holy Spirit, erected in Wrocław, in housing estate Huby, was created during the communist period, hence it was very difficult to design it, and to build. But it was also the period close to the collapse of this regime, so communist leaders were pressed to be more tolerant towards human rights than before, including the religious freedom and towards building new churches. The author of the church mentioned – a very active political oppositionist – when designing the strongly innovative church building, was simultaneously forced by fate to fight formal difficulties caused by oppressive rulers. Author makes the reader closer to those complicated double troubles: artistic, parallel to the political. Finally, the church building was happily completed, then became widely popular and accepted.

The presented article points to the issues of self-consciousness and the possibilities of its development. It defines in this context also concepts of self-evaluation, self-respect, self-appreciation, self-recognition, self-confidence and self-realization. In the text, it is emphasized that self-consciousness is related to the awareness of one´s own psychophysical and social identity - I myself and the world and my place in it. An important means for the development of the healthy self-consciousness is also praise. In the conclusion of the article, attention is paid to the psycho-hygiene as prevention of the failure.