We consider L-functions \(L_1,\ldots ,L_k\) from the Selberg class which have polynomial Euler product and satisfy Selberg’s orthonormality condition. show that on every vertical line \(s=\sigma +it\) with \(\sigma \in (1/2,1)\), these simultaneously take large values of size \(\exp \left( c\frac{(\log t)^{1-\sigma }}{\log \log t}\right) \) inside a small neighborhood. Our method extends to =1\...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

The VC-dimension plays an important role for the algorithmic problem of guarding art galleries efficiently. We prove that inside a simple polygon at most 5 points can be shattered by L1-visibility polygons and give an example where 5 points are shattered. The VCdimension is exactly 5. The proof idea for the upper bound is different from previous approaches.

The reliability of quantum channels for transmitting information is profound importance from the perspective information. This naturally leads to question as how well a state preserved when subjected channel. We propose measure quantumness based on non-commutativity states that intuitive and easy compute. apply proposed some known noise channels, both Markovian non-Markovian find results are in...

While deep neural networks (DNNs) have proven to be efficient for numerous tasks, they come at a high memory and computation cost, thus making them impractical on resource-limited devices. However, these are known contain large number of parameters. Recent research has shown that their structure can more compact without compromising performance.In this paper, we present sparsity-inducing regula...