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The aim of this work is to introduce an extension forq-standard notations. Theq-Apostol type polynomials and study some of their properties. Besides, some relations between the mentioned polynomials and some other known polynomials are obtained.

Quantitative microwave imaging employing an ideal Veselago lens is demonstrated using synthetic 2D experiments. Reconstructions of the complex-valued dielectric constant of an arbitrary objectof-interest are obtained from noiseless data using a non-iterative technique. A closed-form Veselago lens Green's function is utilized in the formulation of the problem. The contrast sources corresponding to a single illumination of the object-of-interest is recovered using total-field measurements at several receiver points located in the lens' focusing region. Collecting the field in the presence of the ideal Veselago lens produces well-conditioned matrices for the discretized inverse source problem. The contrast is then directly obtained by first calculating the total-field within the object. Synthetic examples having features as small as λ/25 show that the resolution is only limited by the signal-to-noise ratio of data. Experiments with noisy data reveals that the inversion procedure directly mirrors the noise in the data. Two new filtering processes are introduced based on the truncated Singular Value Decomposition of the data operator and the domain operator involved in the inversion process. These successfully deal with noisy reconstructions. Results show that using the new filtering methods, even with a single illuminating source, outperforms the least-squares method with several illuminating sources.

The main purpose of this paper is to introduce and investigate a new class of generalized q-Bernoulli and q-Euler polynomials. The q-analogues of well-known formulas are derived. A generalization of the Srivastava-Pintér addition theorem is obtained.

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