Quantum calculus, which arises in the mathematical fields of combinatorics and special functions as well as in a number of areas, involving the study of fractals and multi−, fractal measures, and expressions for the entropy of chaotic dynamical systems, has attracted the attention of many researchers in recent years. In this paper, by virtue of some useful notations from q−, calculus, we define the q−, Fibonacci Dual bicomplex numbers and q−, Lucas Dual bicomplex numbers with a different perspective. Afterwards, we give the Binet formulas, binomial sums, exponential generating functions, Catalan identities, Cassini identities, d’, Ocagne identities and some algebraic properties for the q−, Fibonacci Dual bicomplex numbers and q−, Lucas Dual bicomplex numbers.

We define in a natural way the bicomplex analog of the frames (bc-frames) in the setting of  bicomplex infinite Hilbert spaces, and we characterize them in terms of their idempotent components. We also extend some classical results from frames theory to bc-frames and show that some of them do not remain valid for bc-frames in general. The construction of bc-frame operators and Weyl--Heisenberg bc-frames are also discussed.

In this paper, we introduced $m$-extension Dual complex Fibonacci $p$-numbers. We established the properties of $m$-extension Dual complex Fibonacci $p$-numbers. They are connected to complex Fibonacci numbers, complex Fibonacci $p$-numbers and Dual complex Fibonacci $p$-numbers.

In this paper, we first establish the bicomplex version of Rouche's theorem. Also, a new approach is given to prove the maximum modulus principle for bicomplex holomorphic functions. Our proof is based on the direct method and extends the result proved by Luna-Elizarraras et al. Finally, we generalize the Hurwitz's theorem to bicomplex space.

In this paper, we present the concept of D􀀀, topological Dual of a BC􀀀, module X with a D􀀀, norm k: kD, X and we , nd D􀀀, topological Duals of D􀀀, normed bicomplex BC􀀀, modules l| p (BC) for 1 ,p < 1: We also investigate some fundamental topological properties of bicomplex BC􀀀, modules l| p (BC) by de, ning some topological concepts such as solid space, monotone space, BK􀀀, space, symmetric space in the bicomplex setting by using the D􀀀, norm j: j|:

Introduction: Parkinson Disease (PD) is a degenerative and progressive disorder of the central nervous system. It results from degeneration of Substantia Nigra pars compacta (SNc) of the Basal Ganglia (BG). Gait disturbances in PD patients generally get worse over time. The underlying mechanism of gait disturbances in PD has not been elucidated yet. Methods: In this study, we tried to analyze changes in walking performance under both singleand Dual-task conditions in people with PD compared to healthy subjects. To this end, the participants’ trunk acceleration signals were recorded under Dual-task (counting the stride number while walking) and single-task (walking without performing any other secondary tasks) conditions. Results: The healthy subjects counted the number of their strides correctly; however, 85% of the patients made glaring errors in counting. Then variances of Stride Time Interval (STI) signals were calculated for each participant. STI signals of the patients had a higher variance than that of the healthy subjects in the Dual-task condition. Separating the two groups in a Dualtask condition is easier. Therefore, we think that the disease sate can be detected in early stages. It is thought that counting is performed independent of walking. Conclusion: PD affects the function of BG that leads to motor timing dysfunction. So, it seems that timing in motor tasks is disrupted while timing in cognitive tasks is not. Therefore, perhaps inconsistency between the two clocks (motor-tasks and cognitive-tasks clocks) is the main cause of Dual-task interference in patients’ gait.

This paper presents a modified nine switch inverter with two inputs and two Zsource networks. This inverter has two DC inputs and two AC outputs. Input DC voltages can be boosted to the required level. Amplitude, frequency and phase of AC output voltages can be controlled, independently. The proposed converter can be used in applications with two unregulated DC sources, which require feeding two independent loads. Compared to the conventional structure, the proposed converter requires reduced number of semiconductor switches hence improved converter reliability and less volume. While the authors have already presented a similar inverter (single z-source network Dual-input Dual-output inverter) with the above features, new inverter has some differences in the topology, control strategy and operation. In this paper, a new control strategy of space vector modulation for the new inverter is proposed. Also a new switching method utilizing carrier-based modulation concept is presented for both Dual (proposed) and single z-source network Dual-input Dual-output inverters. Performance of the proposed inverter is verified by simulation and experimental results.

This paper first improves Chen and Hsieh’ s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the -cutting sets or generalized -cutting sets, so that the generalized fuzzy numbers are integrated into a partial ordering set, a semi-ring and a complete non-separable metric space. Again, through two isomorphism theorem, the relationship between generalized fuzzy number space and fuzzy number space is established. Finally, as an application of generalized fuzzy numbers, the concept of continuous generalized fuzzy number-valued functions is introduced. And it is pointed out that many results of trapezoidal generalized fuzzy numbers can also be extended to generalized fuzzy numbers.